MASTER’S THESIS
Machine Learning for NCC’s
Concrete Pile Production
Konrad Pohl
Department of Mathematical Statistics
CHALMERS UNIVERSITY OF TECHNOLOGY
UNIVERSITY OF GOTHENBURG
Gothenburg, Sweden 2021

Thesis for the degree of Master of Science
Machine Learning for NCC’s
Concrete Pile Production
Konrad Pohl
Supervisors: Holger Rootzen, University of Gothenburg
Rasmus Rempling, NCC
Jonas Magnusson, NCC
Collaborator: Deco Josephson, Karlstad University
Department of Mathematical Statistics
CHALMERS UNIVERSITY OF TECHNOLOGY
UNIVERSITY OF GOTHENBURG
Gothenburg, Sweden 2021

Abstract
In this thesis, the usefulness of machine learning (ML) is evaluated for the
processes of NCC’s subsidiary company Hercules. It is evaluated with regard
to ML’s ability to assist reduction of CO2 footprint and costs. The work
comprises analysis of Hercules’ processes and analysis of data from these
processes as well as a search for an appropriate ML model for predicting
compressive strength of concrete. Results show that gradient boosted trees
through the CatBoost library is a suitable ML model. However, additional
data is needed to develop any such an ML model that is fit for use. A
general example of how the CatBoost library can be used to predict strength
of concrete is given. This example can be used as a starting point for
future work on predicting compressive strength of concrete and for other
ML problems at NCC. It was also found that Hercules’ logistical system
would benefit from further investigation. Short order times stresses the
organisation and there may be a case for ML to improve the logistical system.
v

Acknowledgements
I wish to express my deepest gratitude for all support recieved during this
project.
Thank you Holger Rootzen for your insightful and compassionate super-
vision. Thank you Rasmus Rempling and Jonas Magnusson for having this
interesting project and for your support. Thank you Deco Josephson for our
collaboration and times together. Thank you Umberto Picchini for examin-
ing me. Thank you Peter Elmgren, Iad Saleh and workers on the shop floor
for taking time to answer questions about the pile production. Thank you
Louise Westin Elger for your continuous and untiring support during this
project. Finally, thanks to all friends and family that have supported me
with questions about the proceedings of the project.
I also wish to commemorate this work to loved friends and family that
have passed or have been close to pass away.
vii

Notations and Abbreviations
Mathematical notations
j - index of predictive variable
i - row index, specifies an observation
iˆ - estimated improvement
R - Region
P - Set of all predictive variables
p - Size of P
2P - Power set of P
S - Subset of P
s - size of S
v - value function in a coalition game
x - observed values of predictive vari-
able
y - observed values of outcome vari-
able
yˆ - estimated values of outcome
y¯ - mean of y
∅ - The empty set
∑
- sum operator, sums all variables
which fulfills a logical condition as
specified in its indices.
Mathematical abbreviations
ANN - Artificial Neural Network, al-
gorithm
CART - Classification AND Regres-
sion Tree
DNN - Deep Neural Network
GA-ANFIS - Generic Algorithm-
Adaptive Neuro Fuzzy Inference Sys-
tem
kNN - k Nearest Neighbours
MAPE - Mean Absolute Percentage
Error
MARS - Multivariate Adaptive Re-
gression Splines
MLP - Multilayer Perceptron
MLR - Multiple Linear Regression
Resnet - Residual Neural Network
RF - Random Forest
RMSE - Root Mean Square Error
R2 - Coefficient of determination
SHAP - SHapley Additive exPlana-
tions
SVM - Support Vector Machine
Further notations
fc - Compressive strength of concrete
fck - Characteristic strength of con-
crete
f¯ct - Mean value of strength test from
the last t days
Fillers - Small size particles in con-
crete. Rock dust is a type of filler
that is usually unwanted while fly
ash and blast furnace slag are added
intentionally.
Hercules - NCC’s subsidiary com-
pany specialized in building founda-
tions.
Internal rate - Expected return on
invested money in the company.
Metodia - Software used by Hercules
to estimate compressive strength de-
velopment based on temperature de-
velopment in the concrete.
Tied up capital - Expenses of a com-
pany that are yet to be realized as
revenue. Tied up capital is regarded
as expenses through the company’s
internal rate and the time the capital
is tied up.
Ucklum - Production site of concrete
piles.
Further abbreviations
CA - Coarse Aggregates
FA - Fine Aggregates
ML - Machine Learning
TQM - Total Quality Management
W/C - Water Cement ratio
W/P - Water Particle ratio
ix
Contents
Abstract v
Acknowledgements vii
Notations and Abbreviations ix
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Financial reference points . . . . . . . . . . . . . . . . 1
1.1.2 Concrete piles . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Outline of the concrete pile production . . . . . . . . . 3
1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Specified purpose . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Method 6
2.1 Methods for the specified purpose . . . . . . . . . . . . . . . . 6
2.2 Work procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Theory 8
3.1 Mathematical framework of ML . . . . . . . . . . . . . . . . . 8
3.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.1 Pearson’s correlation coefficient . . . . . . . . . . . . . 11
3.3 Decision Trees - CART . . . . . . . . . . . . . . . . . . . . . . 12
3.3.1 Decision stumps . . . . . . . . . . . . . . . . . . . . . 12
3.3.2 Decision trees . . . . . . . . . . . . . . . . . . . . . . . 13
3.3.3 Regression trees and squared loss . . . . . . . . . . . . 13
3.4 Boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 Gradient Boosting . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6 SHAP values . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.7 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.7.1 Certifications . . . . . . . . . . . . . . . . . . . . . . . 17
3.7.2 Components of concrete mixtures . . . . . . . . . . . . 18
3.8 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.8.1 Machine learning for quality . . . . . . . . . . . . . . . 19
3.8.2 Variation in processes . . . . . . . . . . . . . . . . . . 20
4 Results 21
4.1 Interviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.1 First round of interviews: Requirements for an ML
model . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.2 Later interviews with stakeholders . . . . . . . . . . . 21
x
4.1.3 Interviews in Hercules plant in Ucklum . . . . . . . . 22
4.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2.1 Mapping of data collection . . . . . . . . . . . . . . . 22
4.2.2 Reliability of concrete cube measurements . . . . . . . 23
4.3 Literature studies . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3.1 Other works with ML for concrete strength . . . . . . 24
4.3.2 ”Off-the-shelf” ML algorithms . . . . . . . . . . . . . 26
4.3.3 Programming libraries . . . . . . . . . . . . . . . . . . 27
4.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.1 First round of data: Compressive strength, W/C and
Dates . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4.2 Second round of data: Temperature, Weight and Hu-
midity . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.4.3 Compressive strength - unaccessible data . . . . . . . 31
4.4.4 I-Cheng Yeh’s data . . . . . . . . . . . . . . . . . . . . 35
4.4.5 Reinforcement data . . . . . . . . . . . . . . . . . . . 36
4.4.6 Production data . . . . . . . . . . . . . . . . . . . . . 37
4.5 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.5.1 First round of data . . . . . . . . . . . . . . . . . . . . 38
4.5.2 Second round of data . . . . . . . . . . . . . . . . . . 42
4.5.3 Compressive strength - unaccessible data . . . . . . . 45
4.5.4 I-Cheng Yeh’s data . . . . . . . . . . . . . . . . . . . . 45
4.5.5 Reinforcement data . . . . . . . . . . . . . . . . . . . 46
4.5.6 Production data . . . . . . . . . . . . . . . . . . . . . 49
5 Discussion 51
5.1 Discussion of the specfied purpose . . . . . . . . . . . . . . . 51
5.2 Proposed further work . . . . . . . . . . . . . . . . . . . . . . 57
6 Conclusions 58
7 Appendix i
7.1 Enlarged figures 10, 18, 45 . . . . . . . . . . . . . . . . . . . . i
xi
1 Introduction
As concrete has a large climate footprint and today’s technologies provide
means for sophisticated data analysis, this project has investigated these
two subjects at one of the largest producers of concrete in Sweden.
1.1 Background
NCC’s subsidiary company Hercules is the leading concrete pile producer in
Sweden. They have production lines in two plants, one in Ucklum and one
in Va¨ster˚as. The production of the piles is to a large extent automated and
thereby data is automatically gathered from the processes. Controlling the
relationship between the production’s in-parameters and quality measures of
the piles is of importance for development of the production line of tomorrow.
Enabling prediction of quality measures would help create better quality at
a lower cost.
NCC was also interested in examining the possibilities of predicting qual-
ity measures of piles of theoretical material compositions for possible future
use. Such predictions would give means to reduce the proportion of cement
in the concrete piles. Cement is an expensive material, both with regards to
climate footprint and costs. Cement comprises up to 90% of CO2-emissions
of concrete [6] and the cement industry is liable for 7% of the global CO2-
emissions [4]. However, the carbon footprint of cement can be lowered by
partially substituting cement with waste products from other industries such
as fly ash and blast furnace slag. Cement also comprises 2/3 of the material
costs in the concrete mixed in Hercules Ucklum. However, the principal
motivation for the project was the climate aspect as “reducing the climate
footprint is essential for NCC’s survival” 1.
1.1.1 Financial reference points
Hercules’ production plant in Ucklum was studied in this report. They had
the following financial highlights 2020:
• Carbon footprint of cement: 3 700 tonnes CO2-eq.2
• Total carbon footprint of piles: 6 700 tonnes CO2-eq 3
• Material costs of cement: 5 Msek
• Net billing: 55 Msek
1Rasmus Rempling, coordinator of the project
2Carbon footprint of cement = 0.581 CO2-eq/tonne [10]. Mass of cement obtained
from Mixomemory in Ucklum.
3Carbon footprint of piles = (24.7+33.9)/2 CO2-eq/m [21].
1
For reference, Sweden’s total carbon footprint of 2020 has preliminary been
estimated to 47,4 Mtonnes CO2-eq [22]. Hercules Ucklum’s carbon foot-
prints then makes up 0.008% and 0.014% of Sweden’s carbon footprint, for
cement only and total emissions from produced piles.
1.1.2 Concrete piles
Concrete piles are typically between 5-14 m long, and 235-350 mm wide,
steel reinforced elements used to stabilize building foundations. The piles
are hammered down the ground to transfer the load of a building deep into
the earth, preferably all the way to the bedrock. Piles may be joined together
to reach depths of up to 70 m. Figure 1 and figure 2 show concrete piles,
ready for delivery and at installation.
Figure 1: Concrete piles in storage [1].
2
Figure 2: Concrete piles at installation [1].
Concrete piles are generally the most cost efficient type of piles for deep
foundation. Raw materials are inexpensive and the procedure of forming
concrete is advantageous compared to other materials with similar load bear-
ing properties. Concrete mixtures contain water, cement and aggregates and
solidify in about 24 hours. For specific physical properties of the concrete,
admixtures can be added. Admixtures are chemical compounds which can
be used to control the rate of strength development and air content of con-
crete. See [12] for further reference.
1.1.3 Outline of the concrete pile production
The pile production revolves around two major activities, mixing concrete
and steel assembly. An overview of the processes and material flow of the
concrete pile production is presented in fig. 3
3
Figure 3: Overview of the processes and material flow of the concrete pile
production.
1.2 Purpose
The purpose of this project is for NCC and Hercules to gain knowledge of
parameters from the production of concrete piles that influence the quality
of the piles. This is to enable control of the piles’ carbon footprint and costs.
Influential parameters were expected to originate from the following areas;
material composition, manufacturing environment, manufacturing processes
and the installment process of the concrete piles. Knowledge about these
parameters can act as a basis for making data driven, or fact-based decisions
and contribute to improved quality and lower CO2-emissions and lower costs
of the concrete piles.
1.3 Aims
The aim of the project was to:
1. Find a machine learning (ML)-model that predicts quality measures
related to the production of concrete piles.
2. Enable virtual testing of possible new material compositions, with fo-
cus on compositions where fly ash partly substitutes cement.
1.4 Specified purpose
The purpose is specified by the following questions:
1. What measures are relevant for concrete pile quality?
2. What is the present state of data collection in Hercules’ processes?
4
3. Which ML-algorithms are appropriate to predict relevant quality mea-
sures in Hercules plant in Ucklum?
4. Does the present state of data collection in Hercules’ processes allow
for ML?
5
2 Method
The whole project was composed as a proposal and demonstration of using
machine learning for quality control of NCC’s processes.
2.1 Methods for the specified purpose
Work methods used are literature studies, unstructured interviews and ob-
servations in the plant in Ucklum. The following list relates the work meth-
ods used to answer the questions in the specified purpose.
1. What measures are relevant for concrete pile quality?
-Literature studies, unstructured interviews, observations in the plant
in Ucklum
2. What properties of an ML-model would benefit NCC and Hercules?
-Unstructured interviews
3. What is the present-day state of data collection in Hercules’ processes
today?
-Unstructured interviews, observations in the plant in Ucklum
(a) What relations are viable in this data?
-Unstructured interviews, observations in the plant in Ucklum
(b) What effects the reliability of this data?
-Literature studies, unstructured interviews, observations in the
plant in Ucklum.
4. Which ML-algorithms are appropriate to predict relevant quality mea-
sures?
-Literature studies
2.2 Work procedure
Projects of this type, with many interacting uncertainties are most suit-
able to agile project management. Therefore, an iterative cycle of methods
was used: Unstructured interviews enabled data acquisition, which in turn
enabled data analysis, which in turn enabled development of ML-models.
Completed ML-models were then evaluated and the performance of ML-
models provided ground for further interviews. Literature studies were car-
ried out in parallel to interviews, data analysis, ML-model development and
ML-model evaluation. This cycle is visualized in fig 5.
6
Figure 4: Iterative cycle of work methods for the project.
2.3 Participants
The project was organized as a joint master’s thesis project, with one stu-
dent from mathematical statistics and one from engineering mechanics. The
following people participated in the project:
• Student from engineering mechanics. [12] refers to his work. (Karlstad
University)
• Coordinator of ML-development (NCC)
• Senior Technical Specialists in concrete structures (NCC)
• Plant manager from Ucklum (Hercules)
7
3 Theory
This chapter contains the theoretical background for machine learning, a
summary of the theory of concrete mixtures and an introduction to the sub-
ject of quality. The chapter begins with a framework for ML, and describes
four important aspects to consider when dealing with ML; data types, ex-
trapolation, overfitting and learning speed. Then, the mathematical theory
behind two simple ML models, linear models and classification and regres-
sion trees (CART) are described. These models are part of base learners,
simple ML models which may be refined through further algorithms. Boost-
ing is such an algorithm, and section 3.4 accounts for how a CART model
can be drastically improved through the gradient boosted trees algorithm.
At the end of the chapter, section 3.7 describes how concrete piles are cer-
tified through the concrete’s compressive strength. Lastly, section 3.8 gives
an introduction to the theory of quality and lean production, a widespread
production philosophy which NCC adopts.
3.1 Mathematical framework of ML
With some data, one wants to find a relation between some features, or
predictive variables/predictors X = (X1, X2, ...) and one output variable Y
as this could increase understanding of a real-world phenomenon. One has
a set of observed values (x, y) for the predictive variables and the output
variable 4. So each data point can be described as a vector of observations
of a set of variables (x, y). The objective of ML is to describe the relation
between predictor and output through some function5 g:
y = g(x) (1)
But, two important aspects must be considered. Firstly, the model needs to
be useful. Just any mathematical function may not be a suitable represen-
tation of real-world phenomena. Secondly, the predictive data may not be
reliable. One cannot expect to find a model which perfectly represents the
real world. Both these aspects are dealt with by introducing an error term,
:
y = g(x) +  (2)
Then, separate the relevant relation g from the errors  by acknowledging
that we estimate y from x. Estimates of y are denoted yˆ and are described
by:
yˆ = gˆ(x) = y − ˆ ⇐⇒ ˆ = y − yˆ (3)
4The setting with access to observed output values is called supervised ML and ML is
not necessary constrained to settings where observed output values are available.
5Refer to g as ”General ML model”
8
The facts that there is a variety of models out of which no one describes
reality perfectly and that perfect data does not exist is commonly depicted
by the following quote:
”All models are wrong, but some are useful”-George Box
Note now that the error term  allows for evaluation of the usefulness of
a model. By some quantifying function q(), the impact of the errors can be
investigated and model usefulness can be assessed.
Notations used further down are:
• x denotes observed values of the predictive variable(s) X, in other
words realizations of the random variable or vector X. In the same
way, y are regarded realizations of Y .
• Xj , p = 1, 2, ..., p denotes the j:th subscript of X if X is a vector.
Similarly for xj .
• (xi, yi), i = 1, 2, ..., N denotes the i:th pair of observations (x, y).
• x denotes a N × p matrix of N observations and p features.
• ”hat-values”, e.g. yˆ denote a parameter or function approximated from
data.
• m denotes indices of various models g.
Concepts to consider when working with ML are:
• Data types. Measurements may be qualitative or quantitative. Con-
sider two variables X1 and X2. X1 describes a material type and takes
values on {steel, plastic}, whereas X2 describes temperature in an en-
vironment and may take values on [10, 40]. Then, X1 holds qualitative
information and X2 holds quantitative information. The two types of
data create two main types of problems in machine learning, classifica-
tion problems and regression problems. In classification problems, the
output variable is of qualitative data type and in regression problems,
the output variable is quantitative.
• Training and test data. In order to improve on the model’s ability to
describe reality, the data is partitioned into training and testing sets:
Data = {xtrain, ytrain,xtest, ytest}. Then, a set {gˆm} of models are cre-
ated by {xtrain, ytrain}. Thereafter, models are tested by calculating
{gˆm(xtest)} = {yˆtest m}. This makes it possible to obtain approxima-
tions of the models’ {gˆm} ability to predict on ”real-world-data”, since
ˆtest = ytest − yˆtest. It is also easy to calculate ˆtrain = ytrain − yˆtrain,
and by comparing ˆtrain to ˆtest, one can see if a model is overfitted,
9
i.e. the complexity of a model is unjustified, which leads to decreased
training errors but increased test errors in comparison to a less com-
plex model.
• Extrapolation is when a model is used on new data which does not lie in
the interval of the training data, gˆ(xnew) and xnew 6∈ [min(xtrain),max(xtrain)].
This can be dangerous as this model may not be useful in the region
of xnew.
• Learning speed denotes how much data is needed for a model to per-
form optimally. There is usually a trade-off in model selection between
how much data the model requires for finding its optimal fit and how
well the model may perform with an abundance of data. In cases
where data is expensive, it is desired to have a model which performs
well with a small training data set.
3.2 Linear regression
Linear regression is a well-established starting point for working with ML.
Due to its mathematical simplicity, it is easy to work with and easy to
interpret [11]. Simple linear regression is fitting a straight line
yˆ = βˆ0 + βˆ1x = g(x) (4)
to a data set, so that the distance between the line and the data points
are minimized. The following notions can be derived from this concept:
• RSS =
∑
i(yˆi − yi)
2 = q(). The smaller the residual sum of squares,
the squared distance between observed and predicted values, the bet-
ter the model fits the data. The distance between one observed and
predicted value, |yˆ − y|, is called a residual.
• Finding the set of parameters (βˆ0, βˆ1) that minimizes the RSS is
done by differentiating RSS and setting the derivative equal to zero,
RSS′(β0) = 0, RSS′(β1) = 0.
• One can see that observations far away from the center of the xi-s
will have greater influence on the estimated parameters (βˆ0, βˆ1) than
observations closer to the center.
General linear regression, can be viewed as an extension of the concept
of simple linear regression. This extension may take three directions.
Firstly, multiple linear regression can be done using multiple predictive
variables. With n predictive variables, this creates expressions for yˆ as:
yˆ = βˆ0 + βˆ1x1 + ...+ βˆnxn (5)
10
so, yˆ is approximated by a n-dimensional hyperplane instead of a line.
Secondly, linear regression allows for transformations of either the pre-
dictive or the response variables, or both. For example, in the case of an
exponential model where
log(y) = β0 + β1x (6)
is assumed, yˆ may be estimated as
yˆ = eβˆ0+βˆ1x (7)
Thirdly, multiple linear regression may be used to do polynomial regres-
sion. Thereby, model complexity may be increased by increasing the degree
of the polynomial. For a polynomial of degree p, this gives the expression:
yˆ = βˆ0 + βˆ1x+ βˆ1x
2 + ...+ βˆpx
p (8)
Note that equations 5 and 8 both describes multiple linear regression.
In conclusion, as all these three directions of increased complexity may be
combined, linear regression is not limited to two dimensions nor to straight
lines or straight hyperplanes. Any regression where the underlying model is
linear in the parameters, is a linear regression.
3.2.1 Pearson’s correlation coefficient
Prior to starting with any ML problem, it is useful to visualize a summary
of the data one intends to work with. One such visualization is to plot the
estimated correlation between variables. Pearson’s correlation coefficient
ρX1,X2 is commonly used. It is defined as:
ρX1,X2 =
cov(X1, X2)
σX1, σX2
(9)
for two random variables X1 and X2. Here, cov(X1, X2) refers to the co-
variance defined as:
cov(X1, X2) = E[(X1−E[X1])(X2−E[X2])] = E[X1X2]−E[X1]E[X2] (10)
So ρX1,X2 is the covariance normalized with regard to the standard de-
viations of X1 and X2. ρX1,X2 takes values on [−1, 1] and can be estimated
from an existing data set. ρˆX1,X2 = −1 or ρˆX1,X2 = 1 implies that all data
points lie perfectly on a line, a simple linear regression model describes the
relation between X1 and X1 perfectly. ρˆX1,X1 = 0 implies that a simple
linear model does not explain the relation between X1 and X1 at all. Low
correlation is generally desired between predictive variables. Highly corre-
lated variables usually contain the same underlying information and may
cause problems in ML algorithms. Hence, adding an predictive variable
which correlates with another predictive variable is undesirable.
11
3.3 Decision Trees - CART
Classification and Regression Trees (CART) or decision trees is another type
of simple ML method. CART is also considered an ideal base for Boosting
algorithms. ML problems may constitute a classification or regression prob-
lem based on qualitative or quantitative input data. One advantage of CART
models are that they can be used on all such problems and that it easily
transitions between them. [11]. Let A be a logical statement and I be the
indicator function:
I(A) = 1 If A is a true statement, I(Afalse) = 0 f A is false. (11)
further, let {Rm} be a set of disjoint rectangular regions and {cm} be
a set of constants for some index set m. Then CART can conceptually be
described by the following estimation of the response variable:
Yˆ =
∑
m
cmI(X ∈ Rm) (12)
This translates to: ”If the predictive variable X is in the rectangular
region Rm, set Yˆ = cm”.
However, the regions Rm and the constants cm must be obtained accord-
ing to some optimization of a performance measure before a CART model
constitutes meaningful ML. This section describes how decision trees are
created by first describing them in their simplest forms, decision stumps,
and then how the stumps can be joined into decision trees.
3.3.1 Decision stumps
In their simplest forms, decision trees only split the feature space into two
regions: R1 and R2, i.e m = 2, through one single split in the feature space.
Such decision trees are called decision stumps. The method for determining
the optimal regions R1 and R2 is to :
1. Split the feature space into two regions R1 and R2:
R1(j, s) = {X|Xj ≤ s} and R2(j, s) = {X|Xj > s} (13)
for a splitting variable j and a split point s.
2. Evaluate the regions according to some performance measure, typically
the squared loss for regression trees, see section 3.3.3 further down. See
e.g. Gini index in [11] for classification trees.
3. Select the regions R1 and R2 with the best performance measure.
12
3.3.2 Decision trees
Knowing how to make a decision stump, or split, it is possible to create
many splits and hence to create decision trees. Decision trees grow in com-
plexity with increased amount of splits, but also with the amount of input
parameters and the amount of data points, as these lead to more regions to
evaluate and more calculations to make. However, the procedure is in princi-
ple a repetitive process of creating decision stumps. The amount of splits in
the tree is usually determined by some stopping criteria for the algorithm,
this could be a predetermined amount of splits or a minimum amount of
data in created regions or something else. The following pseudo-algorithm
describes how to build a decision tree top-down:
1. Initiate a counting variable: a = 1
2. Consider the the space of the input variables as a set of regions as at
step q: {Rma}. ma is the index set of the regions at step a.
3. While(stopping criteria is not reached)
(a) set a = a+ 1
(b) Let the set of input regions {Rma} be the set of regions created
by making decision stumps in each of the regions in {Rma−1}.
Note that by this algorithm, the splits created are dependent on splits
made in previous iterations. This implies that the algorithm is not guar-
anteed to find the set of regions {Rm} with the best global fit to the data,
but that it is proceeding according to the best local fit in each iteration. To
improve the tree further, techniques for removing redundant splits can be
applied. Such techniques are referred to as pruning.
3.3.3 Regression trees and squared loss
In regression, the constants cm in equation 12 are set as the mean value of
y in region Rm:
yˆm = cm =
1
Nm
∑
yi∈Rm
yi (14)
Further, the regions Rm are selected to minimize the selected loss function.
The squared loss function, which is commonly used, is:
L(y, yˆ) =
∑
yi∈Rm
(yi − yˆi)
2 (15)
which is the same as the RSS seen in linear regression.
13
3.4 Boosting
The main idea that makes up boosting is developing ”a set of weak learners
that create a single strong learner” and that each recursion in the algorithm
should learn from previous steps. This section aims to give an idea of how
this works through describing the gradient boosted trees algorithm.
3.5 Gradient Boosting
Gradient Boosting builds on the idea that parameters of a regression or
classification model can be generated by moving iteratively in the direction
in which errors are decreasing in the fastest pace.
Consider a variable γ, a regression tree denoted g(x) as a base learner,
with J − 1 allowed splits in the tree and a loss function L(yi, g(xi)) =
1
2(yi − g(xi))
2. The negative derivative of the loss function is then equal to
residuals −∂L(yi, g(xi))/∂g(xi) = ri = yi − g(xi). Let M be the number of
iterations for the algorithm and N the amount of observations. Gradient
boosted trees for regression are then constructed as follows:
1. Initialize g0(x) = arg minγ
∑N
i=1 L(yi, γ)
2. For m = 1 to M :
(a) For i = 1 to N , compute residuals:
rim = −[∂L(yi, gm−1(xi))/∂gm−1(xi)] = yi − gm−1(xi)
(b) Fit a regression tree to the residuals rim, giving terminal regions
Rjm, j = 1 to J
(c) For j = 1 to J , compute
γjm = arg minγ
N∑
xi∈Rjm
L(yi, gm−1(xi) + γ)
(d) Update gm(x) = gm−1(x) +
∑J
j=1 γjmI(xi ∈ Rjm)
3. Output g(x) = gM (x)
Note that by this algorithm, g(x) gets constructed through sums of dif-
ferent γ-values, and the γ-values are just the means of the residuals in the
regions they minimize the loss in, Rjm. The algorithm starts with the first
tree predicting the output equal to the mean of all the observed output
values and then continues to add different γ-values to different regions.
Note also that this description of the Gradient boosting algorithm is
simplified by
14
• Stating J as constant. However, J is usually defined as the maximum
allowed number of splits in the tree and may therefore vary. J is
commonly in the interval 4 ≤ J ≤ 8 and variations of J are then
caused by early stopping of the tree building.
• Not accounting for general types of loss functions. Although L(yi, g(xi)) =
L(yi, g(xi)) = 12(yi − g(xi))
2 is commonly used, the algorithm al-
lows for other loss functions too. Residuals then gets exchanged to
”pseudo residuals”, still fulfilling the same purpose and still calculated
as ri = −[∂L(yi, g(xi))/∂g(xi)].
• Not accounting for shrinkage. The test error of gradient boosting
models gets improved by slowing down the rate by which the algorithm
gets fitted to the training data. This is carried out by scaling the step
size in line 2 (d) by a factor ν ∈ [0, 1]:
gm(x) = gm−1(x) + ν
J∑
j=1
γjI(xi ∈ Rjm) (16)
Where ν < 0.1 is common in practise. However, M and ν are not
independent. The smaller ν, the more iterations of the algorithm are
needed.
[11]
Relative variable importance One tool for interpreting models is through
calculations of relative variable importance. This measure describes how
much each of the predictive variables contributes to model output. For a
predictive variable X` in a tree T , the variable importance is calculated as:
I2` (T ) =
J−1∑
t=1
iˆ2t I(v(t) = `) (17)
Here, J is the number of splits in the tree. iˆ2t is the improvement in
performance measure, squared error loss, from split t in the tree. v(t) is a
function which outputs the index of the predictive variable that gives the
best improvement iˆ2t . Then for boosted trees, the variable importance of
variable ` is calculated as:
I2` =
1
M
M∑
m=1
I2` (T )m (18)
[11] A visualization of outputted relative variable importance is given
in fig. 30. Such plots describes how much each type of input data has
contributed to creating the model. When inferring about the importance
15
of used input variables, note that a relative variable importance plot sums
up to 1, or 100%. A variable with high reported variable importance may
not be important if the model’s predictive ability is low. Note also that a
relative variable importance plot depends on the distribution of the data
provided to the model. A narrow distribution will cause a lower relative
variable importance, resulting in potentially undeserved low variable impor-
tance values. Or vice versa for variables with wide distributions in the input
data.
3.6 SHAP values
A recently developed tool for model interpretation are SHapley Additive
exPlanation values (SHAP)[15]. This section aims to introduce this concept.
SHAP values are, just as the relative variable importance, a measure of each
of the predictive variable’s contribution to the model’s output. However,
they make deeper understanding of the model possible by describing how
much each observation xi contributes to the models output yˆi in the native
unit of the output y. SHAP values can be based on Shapley values alone,
but may require combinations of Shapley values and other methods due to
issues with computational complexity. Shapley values are derived from game
theory and are constructed as follows:
φj(g, x) =
∑
S⊆P\j
s!(p− s− 1)!
p!
[gx(S ∪ j)− gx(S)] (19)
This looks a bit difficult, but the following list will break down the
expression into parts and then describe it with an intuitive interpretation:
• φi(g, x) is the Shapley values of the j:th feature, in learning model g
with observations of the predictive variables x.
• P is the set of all input features, |P |= p.
• S is the set of non-zero feature indices (the features that are being
observed and not unknown), |S|= s.
• Recall s! and p! as the total amounts of possible permutations without
repetitions. So,
s!(p− s− 1)!
p!
is the total amount of permutations of size s, averaged over the total
amount of permutations p!.
• gx(S) is the output of the model, with the subset of predictive variables
xj : j ∈ S.
16
Shapley values for feature j are constructed by creating the learning
model on all possible subsets of features which does not include j, and then
adding j and creating all those models as well. The contribution of feature j
is then the average of the difference in model output between each set with
and without j.
A SHAP plot depicts predictive variables in a descending order according
to variable importance on separate SHAP-axes, this shows each observation’s
xijs contribution to model output in relation to the mean of observed outputs
y¯. The distribution of each variable is represented with a color heat scale.
A SHAP plot is shown in fig. 32.
3.7 Concrete
This section summarizes theory of concrete strength.
3.7.1 Certifications
Industries in Europe are highly regulated by a system of certifications. Al-
most any product produced and sold on an industrial scale must achieve a
set of standards determined either by the Swedish or European institute for
standards. In the case of concrete piles, the most important requirements
of these standards are related to the compressive strength of concrete.
Compressive strength of concrete is certified through the following quan-
tities:
• fc - Compressive strength of a single measurement
• fck - Characteristic strength of concrete. Denotes a certain strength
class, a threshold which the strength measurements should surpass.
fck = 60 MPa in this project, see further down.
• f¯ct - Mean value of strength test from the last t days.
• σˆf¯ct - Estimated standard deviation of f¯ct.
The class of concrete is denoted by two numbers. The concrete in this
project, ”C50/60”, means that the concrete are supposed to measure a com-
pressive strength fc > 50 MPa if tested on cylinders and a compressive
strength fc > 60 MPa if tested on cubes. [12]. However, for continuous
production of concrete, the certification requirements [20] are redefined to:
f¯c ≥ fck − 4 (N/mm
2) (20)
f¯ct ≥ fck + 1, 48σˆfct (N/mm
2) (21)
Moreover, Two additional conditions are made for the concrete piles;
fc >= 25 MPa at the time of removal of piles from the formwork, fc > 50
17
MPa at the time of delivery of piles to customer. Formwork removal and
delivery to customer are currently set to one and seven days after casting.
3.7.2 Components of concrete mixtures
The development of compressive strength of concrete is affected by a many
factors and the following parameters of a concrete recipe influences the qual-
ity and compressive strength of concrete and must be considered for an ML
model:
• Age of concrete
• Cement: Type and amount
• Water: Amount
• Water/cement ratio
• Aggregates: Grain size, grain shapes and amount
• Fillers: Type and amount
• Admixtures: Type and amount
• Temperature in curing environment
• Humidity in curing environment
For further reference of concrete theory, see[12].
3.8 Quality
Quality is, much like probability a complex subject. Almost anyone has an
intuition of what quality and probability is, but when studied as scientific
subjects they have both required vast efforts of the academic community to
define. [5] Introduces quality through 9 established definitions and continues
to create their own definition:
Quality of a product is its ability to satisfy and preferably surpass the
customers’ requirements and expectations
It should be noted that further reasoning in [5] sees every stakeholder to the
producer as a customer. So, quality is a complex subject, and seeing quality
as a main attraction for buyers, it is useful to identify ML’s possible role in
quality improvement. The subject of quality is far more extensive than what
is possible to cover in this report and is mainly been described by an intro-
duction of Total Quality Management (TQM) in section 3.8.1. Moreover,
section 3.8.2 describes variation in production processes as problematic.
18
3.8.1 Machine learning for quality
TQM is a strategy for proactively working with all aspects of quality in an
enterprise. A comprehensive strategy for quality management is necessary
as quality lays the foundation for a customer’s long term attraction to a
business. A quick summary of the keystones in TQM is to [5]:
1. Have customers in the centre of the enterprise’s focus. Customers are
defined as the group the enterprise aims to create value for, not only
the consumers of products.
2. Work with processes. Processes being the activities which are repeated
by the enterprise.
3. Work with continuous improvements.
4. Enable participation.
5. Make fact-based decisions.
6. Have a management committed to strengthen the above-mentioned
values in the organisation.
The fifth principle, to make fact-based decisions, is in TQM taught to be
achieved by using a set of 14 analytical tools. 7 of these analytical tools are
based on numerical and statistical analysis. [5].
With ML regarded as advanced data analysis, it should be regarded as a
development of the tools for making fact-based decisions. Even though TQM
promotes the simplicity of its tools for numerical analysis as an advantage,
ML’s position in TQM must remain unchanged with regard to the above-
stated principles. ML should be regarded as a tool which enables mainly
one of the six important principles for achieving quality. At the same time,
the basis for making fact-based decisions exists in symbiosis with the other
principles. As work with ML demands complex computations, it requires
software development. Software development is a subject found to benefit
especially from the principle of working with processes. The Software En-
gineering Institute has produced a model for evaluation of an enterprise’s
process of software development, the Capability Maturity Model (CMM) [5].
CMM identifies five distinct levels of organisational maturity, with the two
extremes: ”The enterprise does not view software development as a process”
and ”The enterprise continuously works with improving the process of soft-
ware development from all aspects of TQM”. At each of these five levels,
CMM provides a set of questions that are aimed at aiding the organisation
to reach the next level. Here, it is only beneficial to work with the set of
questions corresponding to the actual level of the company, as questions
corresponding to other levels are not expected to benefit the enterprise.
19
3.8.2 Variation in processes
Recall processes as the activities which are repeated by an enterprise. Vari-
ation in production processes is regarded as problematic in many, if not all
schools of production management, which aim to achieve improved quality.
Lean production is a management strategy which aims to improve an enter-
prise by identifying and eliminating all factors in an enterprise which do not
create value. Such factors are described in lean production’s origin, Toyota
production system (TPS) to be:
• Over-straining the enterprise
• Inconsistent processes
• Unnecessary activities or wastes
and are developed in [13] to a set of 14 principles to eliminate redundant
factors, in which principle 4 promotes the importance of a level workload,
and principle 6 to have standardized processes. In conclusion, variation in
processes is undesired in a lean production system as inconsistent processes
are difficult to control and may over-strain the enterprise. It should be noted
that a successful implementation of lean production requires a comprehen-
sive implementation of all principles of lean production. Many attempts to
work according to lean production fails or halt due to an unbalanced focus
on the principles.
20
4 Results
This chapter describes the findings from interviews, observations and liter-
ature studies and also from data acquisition and data analysis.
4.1 Interviews
This section contains the main results of the interviews conducted during
the project.
4.1.1 First round of interviews: Requirements for an ML model
The main requirements on the ML model expressed by NCC were that it:
• Contributes to reduction of the concrete pile’s climate footprint, as
measured in CO2.
• Enables financial analysis, so that costs can be reduced.
• Is easy to use and implement, and can be implemented in Microsoft
Azure.
• Can act as a showcase that demonstrates the usefulness of data and
ML for both NCC and Hercules.
4.1.2 Later interviews with stakeholders
The area within concrete pile production where machine learning is the
most feasible is in the relation between concrete-production processes and
the quality of concrete. This area produces most of the data and includes
the least uncontrolled variables. Other possible areas are failure frequency
of piles during installation and performance of the steel parts of the piles.
The constraints created by standards and processes described in section
3.7.1 are not completely fixed. fck as the characteristic strength is fixed,
but the time tresholds may be possible to vary. If sufficient compressive
strength requires more time than 1, 7 or 28 days when removing piles from
forms after 1 day, delivering to customers after 7 days or even after the main
certification test after 28 days, it can be of interest to allow for more time
in order to obtain a lower climate footprint.
NCC means to adopt and implement lean production. The implemen-
tation may not have come as far in Hercules, but they mean to adopt lean
production as well.
A possible reason for variability in compressive strength may be varying
quality of cement, which supposedly decrease during summer.
The plant in Va¨ster˚as was able to reduce their cement use by 12 % by
switching the source of aggregates, i.e. gravel mine.
21
4.1.3 Interviews in Hercules plant in Ucklum
One of the biggest problem in the plant is related to the logistics. Customers
of Hercules occasionally ask for deliveries within the next day, whereas the
concrete needs to cure for seven days. This phenomenon is most common
during the summer, when demand is high in general, but occurs occasionally
throughout the year. At the same time, the permitted size of the stockpile is
limited since storing concrete piles in heaps higher than 2 meters is consid-
ered a safety hazard. Hercules also produces many variations of pile dimen-
sions, so maximizing stockpile costs a substantial amount through tied up
capital. Tied up capital is expenses of a company that are yet to be realized
as revenue. Tied up capital is regarded as expenses through the company’s
internal rate and the time the capital is tied up. This problem is empha-
sized by the plant manager and also pointed out by a worker in the plant.
Two workers were, independently of the manager, asked: ”Where would you
consider an ML model to contribute the most in the production?”. To which
they replied ”the logistics situation” and ”I do not know”.
A possible reason for decreased compressive strength during the sum-
mer was proposed during interviews with the workers. The summer heat
increases the amount of filler in the aggregate. Fillers are small size par-
ticles, here rock dust but may refer to other small size particles as well.
This causes several problems. Fillers reduce the compressive strength of the
concrete according to the experience of workers, interviews with technical
specialists at NCC and literature studies[12]. Fillers also increases the vis-
cosity of the concrete mixture, tricking workers to believe that more water is
needed. When high viscosity is caused by fillers, it is, however, not helpful
to add more water to the mixture. Instead, some addmixtures are needed.
It was also stated that no data exists on faulty concrete mixtures, as
such mixtures do not occur.
With regard to the reinforcement data, it was said that there is data
showing a problem with differing strength measurements, but the cause of
this problem is hard to persuade.
4.2 Observations
This section accounts for observations made in the production plant.
4.2.1 Mapping of data collection
A visualization of where various data sets are collected in Hercules’ processes
is presented in fig. 5, which is an expended version of fig. 39
22
Figure 5: Overview of where in Hercules’ processes the data sets found
during this project are collected. Data sets are marked by blue sharp-edged
rectangles. See section 4.4 for further description of the data.
4.2.2 Reliability of concrete cube measurements
The creation and measurement processes of concrete cubes was inspected
and the following was found:
The size of the cube sides are not supposed to vary more than 150 ±0, 75
mm and are continuously reported as 150 mm. However, produced cubes
were inspected until one faulty cube was found, and a cube of 146×150 mm
was found at the fourth draw, see fig. 6. This variation is likely due to two
reasons. Firstly, operators follow different procedures in packing concrete
into the cube form. Some pack the form in three layers, some fill the form
in one movement. Secondly, the form gets vibrated after being filled up, the
precision in the vibration machine is very rough. Overvibrating is therefore
likely, which leads to shrunken volume and possibly also segregation in the
concrete cube. This affects the reliability of compressive strength measure-
ments as these are carried out through testing the load at which a cube
cracks. The load is then divided by a constant area of 150×150 mm but this
area is actually a variable.
23
Figure 6: The sizes of the concrete cubes vary. This affects the compressive
strength measurements which depend on the surface area.
4.3 Literature studies
4.3.1 Other works with ML for concrete strength
This section summarizes the findings of literature studies regarding predict-
ing of compressive strength of concrete using machine learning. The main
findings are that tree-based methods and neural networks are commonly
used and that large data sets are scarce.
Yeh’s data
Three papers works with a data set on compressive strength provided by
Yeh[24], ( for further data description, see section 4.4.4):
Feng et al. [9] evaluates AdaBoost on Yeh’s data set and presents perfor-
mance measures after cross-validation: R2 = 0.982, RMSE (MPa) = 2.20,
MAPE = 6.78 %, MAE (MPa) = 1.64. This performance is from CART
based AdaBoost and is reported to be superior to Artificial Neural Net-
works (ANN), Support Vector Machines (SVM), Classification and Regres-
sion Trees (CART), Linear Regression (LR), stacking with CART+SVM+LR
and Gradient boosted ANN.
Farooq et al. [8] compares other methods to Feng et al.’s work with
AdaBoost and finds Random Forest (RF) and Decision Trees with bagging
to be the best methods.
24
Nguyen et al. [16] find XGBoost and Gradient Boosted Regressor (GBR)
to be appropriate for Yeh’s data set. Both methods reports R2 = 0.97 after
cross-validation. These methods are superior to SVM and Multilayer Per-
ceptron (MLP), according to [16].
Other findings
Sevim et al. [19] reports that Generic Algorithm-Adaptive Neuro Fuzzy
Inference System (GA-ANFIS) is more appropriate than ANN’s and Mul-
tiple Linear Regression (MLR) to predict compressive strength of concrete
based on fly ash content. This investigation is mainly focused on investi-
gating the potential for substituting cement with fly ash. This is based on
their own data where fly ash substitutes cement with 10-40%. R2 = 0.946
for GA-ANFIS on the test data set.
Ouyang et al. [18] evaluate the learning curves of polynomial regression
(PR), ANN and RF and find all three methods to be useful but points
especially to the trade-off between learning quickly, with few data points,
and achieving high accuracy.
Nguyen et al. [17] reports that the ANN’s Residual Neural Network
(Resnet) and Deep Neural Network (DNN) are appropriate for predicting
compressive strength of green fly ash based geopolymers, which is not con-
crete but similar to concrete. They gather their own data base through
experiments and use the chemical composition of the fly ash as covariates.
Findings without predictive performance measure
Reference [3] contains another data set with 2400 observations of 16
features out of which 12 are relevant for this project.
Chopra [7] finds the the optimal polynomial model to be a multivariate
power equation, based on [14]:
fc28 = A0
( w
cm
)A1
(
FA
cm
)A2 (CA1
cm
)A3 (CA2
cm
)A4
(22)
This yields R2 = 0.9905 and MSE = 0.0236 on concrete with medium
workability and unknown size of the data. However, it is not mentioned
whether performance is measured on a training or test set. Parameters are
water (w), cement content (cm), fine aggregates (FA) size < 10 mm, coarse
aggregates > 20 (CA1) and coarse aggregates > 10 (CA2). Measurements
are distributed over 15 cubes from each of 30 different mixtures.
Ziolkowski and Niedostatkiewicz [25] evaluate a 4-5-1 ANN with the
input variables: weight of {cement, water, fine aggregates, coarse aggre-
gates}. No general performance measure of the ANN is presented, but the
25
authors claim ANN to be a reliable method. The utilized data set contains
741 measurements.
4.3.2 ”Off-the-shelf” ML algorithms
This section summarizes the findings of literature studies regarding appro-
priate ML algorithms from a general perspective.
ML problems usually contains some characteristic challenges.
Firstly, data for ML problems are generally messy; containing both quan-
titative and qualitative data. Distributions of variables are often long-tailed,
skewed and data points might be missing. Secondly, it is often unknown
which variables are relevant for predictions of the outcome. Thirdly, some
ML algorithms performs well, but are hard to interpret. Many times it is
desirable to understand the relationship between input and output variables.
Finally, it is desirable for the algorithm to be suited to the amount of data.
When the data is expensive, a quick learning speed can reduce the cost
of data collection. With large amounts of data, complex algorithms may
require an unfeasible amount of computations.
Decision trees have been compared [11] to neural networks, support vec-
tor machines (SVM), multivariate adaptive regression splines (MARS), k-
nearest neighbours (kNN) and performs well with regards to:
• Mixed data types
• Missing values
• Outliers in input space
• Monotone transformations of data
• Large data sets
• Irrelevant input variables
None of the other algorithms, Neural networks, SVM, MARS, kNN, per-
forms well in all the areas listed above. However, decision trees fall short in
regard to:
• Ability to extract linear combination of features
• Interpretability of model
• Predicitve ability
26
However, boosted trees often have a dramatically better predictive ability
than ordinary trees. This comes however with the sacrifice of learning speed
and interpretability. As boosted trees generally require more calculations
which requires more time to train the model. Hence, boosted trees are
deemed the best ”off-the-shelf” ML algorithm.
4.3.3 Programming libraries
”CatBoost is a high-performance open source library for gradient boost-
ing on decision trees” built by Yandex, initially released in 2017 and fully
released in 2020. The CatBoost-website reports superior performance mea-
sures compared to its competitors LightGBM, XGBoost and H2O on a set of
data sets from old ML-competitions. Such a representation is of course bi-
ased, but indicates none the less that CatBoost is a well-functioning library.
CatBoost also claims to be easy to use, as desired according to interviews.
CatBoost is supposed to be implementable without considering usual prob-
lems in ML, specifically CatBoost claims [23] to:
• Not demand parameter tuning, although parameter tuning can lead
to small improvements in performance.
• Handle both categorical and numerical data automatically.
• Deal with overfitting automatically.
• Have a fast learning speed, requiring little time to render gradient
boosted trees.
Other packages used in this project were:
• The SHAP-package, to generate SHAP plots. (Python)
• The gbm-package, to use gradient boosted trees. (R)
4.4 Data
This section describes the data sets obtained during the project. Each data
set is presented by descriptive statistics, its relation to the production system
of concrete piles, its format and the process which generated the data.
4.4.1 First round of data: Compressive strength, W/C and Dates
The primary data set, which initiated this project, contains information on
the compressive strength, fc, of the concrete, the water-cement ratio, W/C,
and the dates, Date, of casting the concrete. For the year of 2020, this
comprised a 214×3 matrix.
27
The main parameter of interest is fc by which the quality of the concrete
piles is determined and certified. A cube of 15×15 cm is taken, stored in
an environment of controlled temperature and humidity, and thereafter its
ultimate loading capacity is tested after 28 days. A histogram of fc is shown
in 7 [12].
W/C is supposed to be the most influential parameter on fc, and there-
fore it must be controlled and measured daily in order to certify the quality
of the piles [12]. The W/C is measured in the concrete mixer through a
moisture metre with precision of two decimals.
Date in itself is not meant to be a parameter with direct influence on
compressive strength. Yet, dates are essential information in case customers
would report insufficient strength in the piles. Date could also correlate
with other influential parameters, such as temperature, humidity, or others.
Figure 7: Histogram of compressive strength, fc, measurements of 2020.
The black line marks the mean value.
4.4.2 Second round of data: Temperature, Weight and Humidity
Some additional data related to the concrete cubes was found to be collected.
This data was also required for the quality certification of the concrete piles.
The parameters of this data was: Concrete temperature at the moment of
pouring it into the mold, Tconcrete, weight of the cubes, Weight, relative
humidity in the lab at day 0 for the cube, Humidity. In addition, tempera-
ture data for Even˚as, a village some kilometers away from Hercules Ucklum,
was available at [2]. Hence, a final feature, TEven˚as, was included in the
data, resulting in a total of 6 predictors to work with. Furthermore, data
28
on fc, W/C, Date was obtained for the period 2015-2020 and for the ad-
ditional parameters, only for 2020. This rendered matrices of sizes 1225×3
and 214×7.
Tconcrete is of interest as temperature and temperature development in
the concrete influences fc in several ways. See [12] for further reference
and note that Tconcrete only provides a point measure and says little about
temperature development during the time frame during which temperature
affects the strength development. TEven˚as was obtained as an attempt to
obtain more information on the temperature processes in the concrete.
Weight could hold information on density of the concrete, and primarily
indicates air content, which is expected to influence fc [12]. The relation be-
tween density of the concrete would also be affected by the ratios of concrete
ingredients in each specific concrete mixture, complicating the usefulness of
Weight as a predictor for air content. Humidity is supposed to have a
negative relation to fc [12]. The full data from 2020 is visualized in fig. 10
and 11.
Figure 8: Compressive strength over time for the period 2015 to 2020. Recall
that fc was seen to drop during the summer in 2020 as in fig. 22, dashed
lines marks the same summer period in previous years. The drop during
summer is reoccurring.
29
Figure 9: Histogram of W/C values from 2015-2020. Again, a large majority
are distributed over a short interval. One notable outlier is present at 0.25.
Figure 10: Pairsplot of the full 2020 data. An enlarged version of this figure
is found in appendix 7.1.
30
Figure 11: Correlation plot, a vizualization of the correlation matrix of the
of the full 2020 data. Red scale colors represent a negative correlation and
blue scale colors represent a positive correlation. Pie sizes shows the absolute
value of the Pearson correlation coefficient.
4.4.3 Compressive strength - unaccessible data
This section describes the types of data that was found to be collected with
consistency, but hard to utilize due to issues with the way it is collected.
Sieve curves are reported for each batch of aggregates. The propor-
tions of different sizes of aggregates influence the compressive strength of
concrete. However, the amount of information in these curves is hard to
evaluate further than with visual inspection of the curves, as only 20 curves
were obtained for 2020. Furthermore, no reasonable way to relate curves
to concrete cubes was found except to visually inspect if curves from the
summer differ from the rest of the year. The curves are also reported in pdf
files, which complicates the process of obtaining numerical values.
31
Figure 12: An example of a sieve curve. Although the type of information
in the curve is expected to be informative, the data is hard to use.
Mixing reports are created for each batch of mixed concrete, containing
information on:
• Amount of total concrete (kg and m3)
• W/C with 3 decimals
• W/P with 3 decimals, the ratio between water W and small particles
P
• Amount of fine aggregates, size 0-8 mm (kg)
• Amount of coarse aggregates, size 8-16 mm (kg)
• Amount of large aggregates, size 30-40 mm (kg)
• Amount of cement (kg)
• Amount of water (kg)
• Time stamps for the actions that the mixer carries out (hh:mm:ss)
• A batch id
• General information about what concrete is being mixed
• A curve for the ampere of the mixer while mixing the concrete
The mixing reports are accessible as pdf files, but the software which gen-
erates them does not allow to export multiple files at a time.
32
Figure 13: An example of page 1 of a mixing report.
Figure 14: An example of page 2 of a mixing report.
Concrete logs During the first 7 days, core and ambient temperature are
measured in the concrete piles. This data is collected by a software named
33
Metodia and written in .mxl files where these temperature curves acts as a
basis for estimating the compressive strength of the concrete. This way of
working is allowed by certifying authorities. Although, the .mxl files look a
lot like excel files, it was not possible to extract their data except for one
file at a time. As this was a time consuming process, only 12 data sets from
August and from November-December was obtained. This data is plotted
in fig. 15 and 16.
Figure 15: 24 samples of development of compressive strength of piles over
the first 7 days as estimated based on temperature development, by the
metodia software. Black show curves from August, Red from November-
December.
34
Figure 16: The same 24 curves as in fig 15. Dotted lines connect each sample
to its related cube’s compressive strength.
4.4.4 I-Cheng Yeh’s data
This data set was used to evaluate the appropriateness of the CatBoost
library for a general ML application whose primary aim is to enable CO2
reduction of a concrete recipe. The data does not relate to Hercules’ produc-
tion and analysis of this data is an unsuitable basis for changing Hercules’
concrete composition. The data contains 1030 measurements on compressive
strength and the 8 quantitative input parameters:
• Cement (kg in a m3 mixture)
• Blast Furnace Slag (kg in a m3 mixture)
• Fly Ash (kg in a m3 mixture)
• Water (kg in a m3 mixture)
• Superplasticizer (kg in a m3 mixture)
• Coarse Aggregae (kg in a m3 mixture)
• Fine Aggregate (kg in a m3 mixture)
• Age (Days)
Note that this data is from Taiwan, 1998. A pairsplot and correlation plot
is shown in fig. 18
35
Figure 17: Pairsplot of I-Cheng Yeh’s data. fc is represented at the bottom
right. An enlarged version of this figure is found in appendix 7.1.
Figure 18: Correlation plot of I-Cheng Yeh’s data.
4.4.5 Reinforcement data
Two types of data exists which relate to steel reinforcement, one accessible
and one unaccessible. The accessible data describes measurements of yield
strength (Re) and ultimate tensile strength (Rm) of the reinforcement steel.
36
The suppliers measurements and the measurements ordered by Hercules to
be carried out by a certifying authority in Sweden vary more than what
should be expected when accounting for strain hardening, see fig. 19.
Figure 19: Difference between the supplier’s and Hercules’ measurements of
tensile strength of Reinforcement steel. Colors represent different dimensions
of the steel. Due to the processes at Hercules, the tensile strength can be
expected to drop with up to 20 MPa. The dotted lines show this region.
The unaccessible data consists of hundreds of pdf files containing infor-
mation on the chemical composition of a batch of reinforcement steel. One
line of such data is presented in table 1.
C Mn Si P S N Ceq Re(MPa) Rm(MPa) ...
0,17 1,10 0,19 0,022 0,028 0,009 0,41 552 639 ...
Table 1: An example data point of the chemical compositions that are avail-
able in pdf files for each batch of reinforcement steel.
4.4.6 Production data
The obtained data relating to production was from 2016-2020 and comprised
monthly information on:
• Worked hours (h)
• Sick leave (%)
• Delivered meters (m)
37
• Produced meters (m)
• Billing (sek)
• Delivered meters within Hercules’ organisation (m)
• Billing within Hercules’ organisation (sek)
• Delivered meters to external customers (m)
4.5 Data analysis
This section describes the findings from analysis of the data sets described
in section 4.4.
4.5.1 First round of data
The relation between fc and W/C was examined with a simple linear re-
gression, see fig. 20. R2 = 0.022 and visual inspection of the plotted data
indicates that this relation is not useful in itself. The low variation of W/C
data from 2020 is concluded to be the cause of the low R2 value, see fig. 21.
80% of the W/C data is distributed in {0.39, 0.40}.
Figure 20: Linear regression between fc and W/C.
38
Figure 21: Histogram of W/C values from 2020, the supposedly most influ-
ential parameter on fc. Note that 80% of the data points are distributed on
0.39 and 0.40.
Compressive strength over time during 2020 is presented in fig 22. There
is a noteworthy drop in compressive strength during the summer.
39
Figure 22: Compressive strength over time for 2020. Note the drop during
the summer.
This relation was examined with three approaches: Fitting a sinusoidal
model to the data, evaluating the data with mean values for two periods;
when water for concrete mixtures is heated or not heated, evaluating the
same two periods with a quadratic model when the water is not heated and
the mean when water is heated. The R2-values of 0.27-0.38 could suggest a
useful relation, but the residuals do not seem evenly distributed for any of
the models, see Figures 23, 24 and 25.
40
Figure 23: Sinusoidal model fitted to compressive strength over time for
2020.
Figure 24: Model of means of two periods fitted to compressive strength
over time for 2020.
41
Figure 25: Model as mean of compressive strength when water is heated
and a quadratic model when water is not heated. Fitted to data from 2020.
4.5.2 Second round of data
Simple linear regression models were fitted to the variables TEven˚as, Tconcrete,
Weight, Humidity, W/C, see figures 26 27, 28 and 29. The models were
concluded by visual inspection to be fit enough to disregard the usefulness
of the variables based on their low R2-values.
A multilinear model was fitted on all available parameters, and gave
R2 = 0.21.
42
Figure 26
Figure 27
43
Figure 28
Figure 29
To get a final sense of the predictive ability of the full 2020 data set, a gra-
dient boosted tree was fitted to the complete data set with fc as output and
TEven˚as, Tconcrete,Weight,Humidity,W/C,Days as input variables. Table
2 shows R2-values and cross-validated R2cv-values over 4 folds, and for shrink-
age ν = 0.1, 0.05, 0.01, 0.001. Fig. 30 shows the relative influence of the in-
put variables for the model with best predictive performance, which is when
ν = 0.05. This model was fitted with the gbm-package in R.
44
ν R2 R2cv
0.1 0.65 0.33
0.05 0.60 0.35
0.01 0.56 0.31
0.001 0.58 0.31
Table 2: R2-values and cross-validated R2cv-values for a gradient boosted
tree over 4 folds and for shrinkage values ν = (0.1, 0.05, 0.01, 0.001).
Figure 30: Relative variable importance of input parameters on a gradient
boosted tree trained on the full 2020 data set with shrinkage tuned to ν =
0.05.
4.5.3 Compressive strength - unaccessible data
No further analysis than what is presented in section 4.4.3 has been made.
4.5.4 I-Cheng Yeh’s data
Table 3 compares the results of an untuned CatBoost model to the results
of [16] where XGBoost is tuned to predict compressive strength of concrete
based on the same data set.
45
Boosting Library R2 R2 basis
CatBoostuntuned 0.93 test set
XGBoosttuned 0.97 cross-validation
Table 3: Comparison of an untuned CatBoost machine with a tuned XG-
Boost [16] machine.
Variable importance and SHAP plots are shown in figures 31 and 32.
These plots are used to interpret the model, they visualize how much the
different input parameters contribute to the created ML model.
Figure 31: Feature importance of a CatBoost model created with the appli-
cation.
Figure 32: SHAP values and distributions of features of a CatBoost model
created with the application. The data point for which Age contributes most
is found at the top right. The Age-value of this data point contributes with
a prediction which is 15 MPa higher than the mean of compressive strength.
The Age-value of this data point is close to the mean as its color is purple.
4.5.5 Reinforcement data
Differences in strength measurements are shown in figures 33-38.
Some data points origin from the same batch of steel. The subsets of data
46
for each dimension correspond to 20 unique batches for dimension 12b, 14
unique batches for dimension 16b and 30 unique batches for dimension 16c.
Figure 33: Histogram of suppliers’ measurements (blue) and certifying mea-
surements (white) of yield strength for steel with dimension 12b.
Figure 34: Plot of suppliers’ measurements (blue) and certifying measure-
ments (white) of yield strength for steel with dimension 12b.
47
Figure 35: Histogram of suppliers’ measurements (blue) and certifying mea-
surements (white) of yield strength for steel with dimension 16b.
Figure 36: Plot of suppliers’ measurements (blue) and certifying measure-
ments (white) of yield strength for steel with dimension 16b.
Figure 37: Histogram of suppliers’ measurements (blue) and certifying mea-
surements (white) of yield strength for steel with dimension 16c.
48
Figure 38: Plot of suppliers’ measurements (blue) and certifying measure-
ments (white) of yield strength for steel with dimension 16c.
Unaccessible data of reinforcement steel is yet to be analyzed. It would
be interesting to examine the relation between chemical compounds and
strength measures with the gradient boosted trees algorithm.
4.5.6 Production data
The production data reveals that pile meters per month, for delivery, pro-
duction and storage, during the years 2016-2020, vary between 7 600-34
000, 10 600-27 800 and 8200-28 600. Here, storage values are based on the
assumption that starting storage as of January 2016 is 20 000 pile meters.
Fig. 39 shows these measures developed in time and reveals a seasonal trend
in demand. Demand is high during the summer except for 2018 when the
lowest demand during the whole 6-year period occurs during the summer.
An increase in demand can be seen in the beginning of each year as well, a
trend that is consistent throughout the 6-year period.
49
Figure 39: Monthly meters of production (green), delivery (blue) and simu-
lated storage (red) of concrete piles, 2016-2020. Storage values are calculated
on the assumption that starting storage is equal to 20 000 pile meters.
50
5 Discussion
This chapter begins by discussing the results in their relation to the specified
purpose and continues to propose how further work towards the purpose can
be carried out.
5.1 Discussion of the specfied purpose
The following section discusses theory and results in relation to the specified
purpose of section 1.4.
What measures are relevant for concrete pile quality?
Concrete pile quality is mainly determined through the compressive strength,
fc, of the concrete. Concrete strength of concrete piles produced at Hercules
Ucklum needs to meet 3 conditions ; fc > 25 MPa at the time of removal
of piles from the formwork, fc > 50 MPa at the time of delivery of piles to
customer, fc > 56 MPa and the mean of the 35 latest strength tests must
fulfill f¯c35 > fc + 1, 48σˆfc35 at 28 days after casting the concrete. Formwork
removal and delivery to customer are currently set to one and seven days
after casting. Although there is a possibility to extend the three points of
time by restructuring production and certification processes, 25, 50 and 56
and 60 + 1, 48σˆfc35 MPa must be achieved to allow for formwork removal,
delivery to customer and final certification of the piles respectively.
Table 4 reports measures required for well-founded predictions of fc and
the type of information each measure constitutes. Information containing
time and chemical properties have been emphasized with their own columns
as these types of information stand out. Time series can result in challenges
when using ML models and needs to be considered with extra care. Chemical
properties of concrete ingredients has been used as predictive variables in
other works considering compressive strength of concrete as the outcome,
however these may not need to be considered.
The general purpose was to enable control of the piles’ carbon footprint
and costs. Therefore, proportional CO2 footprint and the cost of each of
the ingredients in a concrete mixture needs to be assessed as these would
enable evaluation of reduction of carbon footprint and cost. See [12] for a
more comprehensive account of the theory of concrete ingredients.
Concrete piles also need to be certified through the yield strength of
reinforcement steel. Measures for basis of predicting steel strength needs
further investigation.
What is the present state of data collection in Hercules’ processes?
In the current state of Hercules’ processes, most data is collected for the re-
quirements of various certification processes. See section 4.4 for a complete
51
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52
description of data found during the project and fig. 5 for an overview of
where the various data is produced in relation to the Hercules’ production
system. Column 6 in table 4 accounts for the relevant measures of compres-
sive strength of concrete in relation to Hercules’ collection of information.
Some interesting data is unavailable for analysis due to software issues. The
mixing reports, which hold information from multiple parameters in con-
crete mixtures, are produced in a local computer with a software that does
not allow a compilation of multiple mixing reports. One mixing report may
be rendered at a time, so to analyze the data in the mixing reports two
challenges occur: Generating the mixing report which describes the con-
crete mixture from which the concrete cube is produced, and translating
the mixing report-file into a database suitable for analysis in statistical soft-
ware.
The reliability of the data is affected mainly by the fact that concrete
cubes are produced with different procedures, see [12]. Cubes may vary in
both number of layers of packed concrete and in size. Otherwise most data
is collected automatically. The reliability of automatically collected data
has not been considered.
Which ML-algorithms are appropriate to predict relevant quality measures
in Hercules plant in Ucklum?
According to literature studies, efforts with similar aims to this project con-
clude that compressive strength is best predicted through the use of Boosted
trees and Neural networks. Gradient boosted trees, especially through the
CatBoost library, best meets the requirement of easy implementation. Cat-
boost does not demand parameter tuning, although parameter tuning is
likely to improve predictive performance to some extent. CatBoost auto-
matically deals with categorical and numerical data as well as with overfit-
ting. CatBoost also has a fast learning rate, which is advantageous as the
data required for prediciting compressive strength is expensive.
A CatBoost model was tested on Yeh’s data [24] and gave an R2 of 0.93
for an untuned model evaluated on a test data set which indicates that the
CatBoost is suitable for easy access ML on compressive strength of concrete.
How does the present state of data collection in Hercules’ processes allow
for ML?
This question has been approached by trying to predict compressive
strength of concrete with variables collected prior to the strength tests.
Studied ML models have been linear models and gradient boosted trees.
Through this data analysis, the date when a concrete is mixed stands out as
the most useful variable for ML. However, no R2 value of any model indicate
that the model would be useful to base decisions on. The date of concrete
53
mixing stands out with higher R2-values, but this parameter in itself is not
a physical parameter supposed to influence the compressive strength of con-
crete. Data on other relevant physical quantities produced too low R2 values
with linear models to evaluate the models further. When analysing the data
through gradient boosted trees, the conclusion was made again that no mea-
sured physical quantity supposed to influence the compressive strength of
concrete could predict the compressive strength of concrete. However, the
notable drop in compressive strength during the summer should be noted
and investigated further and gives means to improve the production of the
cubes [12]. In addition, access to the mixing reports could add important
data which would present a better case for ML in Hercules’ processes.
Fig. 40 gives an illustration of the conclusions about collected data sets
allowance for ML.
Figure 40: Overview of where in Hercules’ processes the data sets found
during this project are collected. Green represents data that helped achieve
the aims of this project. Yellow represents data that was available for ML
application but served no use during this project. Red represents data that
was generated in Hercules’ processes but not in an accessible format. An
enlarged version of this figure is found in appendix 7.1.
In hindsight, the poor case for ML could have been anticipated. There
is already a system for controlling the compressive strength of the cubes
through the certification requirements. The available data is collected only
to monitor that the most important parameters are within certain ranges
which aims to ensure that compressive strength is controlled. This lies in
contrast to collect data with the aim to explain an output variable. The
project was started with the assumption that some data is collected in Her-
54
cules’ processes which could enable a reduction of CO2-emissions through
reduced cement usage in the recipe. However, Hercules’ has produced the
same mixture of concrete for the all years represented in the data, 2015-
2020. None of the parameters that are supposed to affect the compressive
strength of concrete have purposely been made to vary and are tightly con-
trolled through the certification system. It has emerged during the project
that changes to the recipe, even minor, are too risky since a batch of concrete
costs too much. Furthermore, Hercules manages their processes well enough
to never need to scrap mixed concrete. In essence, there are no major errors
in the production, which ML may learn from or attempt to prevent and the
information from just one recipe is not sufficient to propose a new recipe. In
this context, one recipe is just one data point and any deviation from this
recipe would involve extrapolation. However, both the work summarized in
section 4.3 and the untuned CatBoost machines performance on Yeh’s data
set [24] suggests that ML is a viable tool for estimating compressive strength
of theoretical concrete mixtures.
The situation with the reinforcement steel data demands further atten-
tion. Data shows that there are troublesome deviances between the sup-
plier’s and the certifying organ’s measurements. If these deviances are due
to problems in Hercules’ processes or shortfalls in any measuring process is
unclear. But the reliability of these measurements needs to be understood.
As a final comment, the data analysis has revealed some potential for re-
duction of compressive strength of the cubes. Maybe this can translate to a
reduction of CO2-emissions and costs. The data on compressive strength re-
veals that Hercules’ measurements from the last 6 years overperforms with 4
MPa on average compared to the recommended mean compressive strength
of 67 MPa, see fig. 42. This overperformance gives room for some reduction
of cement in the concrete mixtures through an increase in W/C ratio. Such
an increase requires consideration of the technical properties of concrete, but
it appears feasible to increase the W/C ratio with about 0.04 on average, see
[12] for a technical motivation. An increase of 0.04 in the average W/C ratio
in the concrete recipe used in Hercules Ucklum implies a 0.1% decrease of
cement useage. However, a 0.1% decrease in cement usage, which approxi-
mates to a decrease in CO2-emissions of 0.07% and 6000 sek per year. It can
be concluded that efforts to decrease the CO2-emissions or costs should not
aim at increasing the W/C ratio or other small alterations of the proportion
of cement in the recipe.
55
Figure 41: The current mean value of fc = 71 MPa is overperforming.
Recommended mean is 67 MPa, certification allows for 65 MPa with retained
standard deviation. All values must fulfill fc > 56 MPa.
Figure 42: The analysis from fig. 41 on data from 2015-2020. The conclusion
is almost the same, but note that a few data points touch the limit fc > 56
MPa and that standard deviation is increased for this data.
56
5.2 Proposed further work
Further work with regard to quality improvements is suggested to take on
two subjects depending on what the purpose is for any continued research.
Three major subjects have been in focus in the communication with NCC;
firstly, reduce CO2 footprint. Secondly, reduce costs. Thirdly, comprise an
example which demonstrates the benefit of efficient data collection through
the use of ML.
Reducing CO2 is recommended to aim for by investigating how fly ash
or other ingredients with smaller carbon footprint can substitute cement.
Future work should then comprise careful planning of how data outlined
in table 4 should be collected in order to produce trustworthy predictions
of concrete strength through a CatBoost model. If such data is acquired,
SHAP and variable importance plots can provide insights of how the model
interprets the data. Range of data in all input parameters must be con-
sidered, but also the precision with which ingredients can be distributed in
Hercules’ processes. If a recipe is implemented which works well in precise
laboratory mixtures, it might be costly to implement in Hercules. If a batch
of concrete contains more fillers in reality than what has been planned in
theory, concrete compressive strength might fall below the certifying limit.
Reducing costs and demonstrating the use of data collection, is recom-
mended to aim for with an investigation of the logistical data system. It was
mentioned by two independent respondents that Hercules would benefit from
developing the logistical system. It was also revealed that order times are
shorter than production times on a regular basis, which causes stress within
the organisation. Produced pile meter per month varies greatly, which is
not in line with lean production. Aiming to improve this situation is likely
to improve Hercules’ economy and well being of workers as well as make
time available in Hercules for engaging in other quality work activities. In
addition, ML models can be usable in this setting since forecasting usually
builds around non-complex ML models.
A good start to attending the logistical situation would be to provide a
financial incentive for making early orders. I propose to increase the price
on late orders or decrease the price on early orders by a reasonable amount.
A suggestion for NCC is also to implement a standard requiring that
any data collecting system should reach or surpass a baseline level. Such a
baseline level should be that data collection results in Excel files available
through the cloud, or equivalently.
57
6 Conclusions
The main conclusions of this project are:
• This project has found that data available in Hercules Ucklum’s pro-
cesses provides no basis for reduction of CO2.
• The CatBoost library provides easy access to ML through the gradient
boosted trees algorithm. The SHAP package can be used to interpret
created models.
• For further work, two pathways are proposed. A reduction of CO2-
emissions can be achieved by obtaining data on a variety of concrete
recipes and find an optimized recipe with a CatBoost model.
• Reducing costs and demonstrating the value of data analysis is rec-
ommended to aim for via an investigation of the logistical situation in
Hercules Ucklum.
• Two suggestions for facilitating Hercules’ and NCC’s activities are
made: Quantify the cost of short-timed orders and introduce a lower
limit standard for data collection systems, preferably that all data is
available in Excel files.
58
References
[1] Hercules.se. Accessed: 2021-06-01.
[2] temperatur.nu/evenas.html. accessed: 2021-03-01.
[3] Amged O. Abdelatif, Amir M.Y. Shaddad, Mohammed B. Fathallah,
Mohammed S. Ibrahim, and Mohammed H. Twfeeq. Concrete mix
design and aggregate tests data between 2009 and 2017 in sudan. Data
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7 Appendix
7.1 Enlarged figures 10, 18, 45
i
Figure 43: Enlarged pairsplot of the full 2020 data.
ii
Figure 44: Enlarged pairsplot of I-Cheng Yeh’s data.
iii
Figure 45: Enlarged overview of where in Hercules’ processes the data sets
found during this project are collected. Green represents data that helped
achieve the aims of this project. Yellow represents data that was available for
ML application but served no use during this project. Red represents data
that was generated in Hercules’ processes but not in an accessible format.
iv