Doctoral Thesis in Materials Science and Engineering

Doctoral Thesis in Materials Science and Engineering

Applied Machine Learning in Steel Process Engineering

Using Supervised Machine Learning Models to Predict the Electrical Energy Consumption of Electric Arc Furnaces

LEO CARLSSON

Stockholm, Sweden 2021

of technology

Applied Machine Learning in Steel Process Engineering

Using Supervised Machine Learning Models to Predict the Electrical Energy Consumption of Electric Arc Furnaces

LEO CARLSSON

Doctoral Thesis in Materials Science and Engineering KTH Royal Institute of Technology

Stockholm, Sweden 2021

Academic Dissertation which, with due permission of the KTH Royal Institute of Technology, is submitted for public defence for the Degree of Doctor of Philosophy on Friday the 26th March 2021, at 2:00 p.m. in Digital and Green room, Osquars backe 41,

KTH Royal Institute of Technology, Stockholm.

ISBN 978-91-7873-777-2 TRITA-ITM-AVL 2021:7

Printed by: Universitetsservice US-AB, Sweden 2021

Leo S. Carlsson, leoc@kth.se

Materials Science and Engineering, Unit of Processes KTH Royal Institute of Technology

Places for Project

Stockholm, Sweden Avesta, Sweden Hofors, Sweden Oxelösund, Sweden

Examiner

Pär G. Jönsson

Materials Science and Engineering, Unit of Processes KTH Royal Institute of Technology

Supervisors

Pär G. Jönsson and Peter B. Samuelsson

Materials Science and Engineering, Unit of Processes KTH Royal Institute of Technology

Mikael Vejdemo-Johansson

CUNY College of Staten Island

CUNY Graduate Center

The steel industry is in constant need of improving its production processes. This is partly due to increasing competition and partly due to environmental concerns.

One commonly used method for improving these processes is through the act of

modeling. Models are representations of the reality that can be used to study and

test new processes and strategies without costly interventions. In recent years,

Machine Learning (ML) has emerged as a promising modeling approach for the

steel industry. This has partly been driven by the Industry 4.0 development, which

highlights ML as one of the key technologies for its realization. However, these

models are often difficult to interpret, which makes it impractical to validate if the

model accurately represents reality. This can lead to a lack of trust in ML models

by domain practitioners in the steel industry. Thus, the present work investigates

the practical usefulness of ML models in the context steel process engineering. The

chosen application to answer this research question is the prediction of the Electrical

Energy (EE) consumption of Electric Arc Furnaces (EAF). The EAF process was

chosen due to its widespread use in the steel industry and due to the difficulty

to accurately model the EE consumption using physical modeling. In the present

literature, the use of linear statistical models are commonly used even though

the EE consumption is non-linearly dependant on multiple important EAF process

variables. In addition, the literature does neither investigate the correlations between

input variables nor attempts to find the most optimal model with respect to model

complexity, predictive performance, stability, and generalizability. Furthermore, a

consistent reporting of predictive performance metrics and interpreting the non-

transparent models is lacking. These shortcomings motivated the development

of a Model Construction methodology and a Model Evaluation methodology that

eliminate these shortcomings by considering both the domain-specific (metallurgical)

aspects as well as the challenges imposed by ML modeling. By using the developed

methodologies, several important findings originated from the resulting ML models

predicting the EE consumption of two disparate EAF. A high model complexity,

governed by an elevated number of input variables and model coefficients, is not

necessary to achieve a state-of-the-art predictive performance on test data. This was

confirmed both by the extensive number of produced models and by the comparison

of the selected models with the models reported in the literature. To improve the

improvements. Experts in both process metallurgy and the specific process under study must be utilized when developing practically useful ML models. They support both in the selection of input variables and in the evaluation of the contribution of the input variables on the EE consumption prediction in relation to established physico- chemical laws and experiences with the specific EAF under study. In addition, a data cleaning strategy performed by an expert at one of the two EAF resulted in the best performing model. The scrap melting process in the EAF is complex and therefore challenging to accurately model using physico-chemical modeling. Using ML modeling, it was demonstrated that a scrap categorization based on the surface-area- to-volume ratio of scrap produced ML models with the highest predictive performance.

This agrees well with the physico-chemical phenomena that governs the melting of scrap; temperature gradients, alloying gradients, stirring velocity, and the freezing effect. Multiple different practical use cases of ML models were exemplified in the present work, since the model evaluation methodology demonstrated the possibility to reveal the true contributions by each input variable on the EE consumption. The most prominent example was the analysis of the contribution by various scrap categories on the EE consumption. Three of these scrap categories were confirmed by the steel plant engineers to be accurately interpreted by the model. However, to be able to draw specific conclusions, a higher model predictive performance is required. This can only be realized after significant data quality improvements. Lastly, the developed methodology is not limited to the case used in the present work. It can be used to develop supervised ML models for other processes in the steel industry. This is valuable for the steel industry moving forward in the Industry 4.0 development.

Keywords

Electric Arc Furnace; Electrical Energy Consumption; Statistical Modelling; Machine

Learning; Interpretable Machine Learning; Predictive Modelling; Industry 4.0

Stålindustrin är i ständigt behov av att förbättra sina produktionsprocesser. Detta beror dels på ökad konkurrens och dels på miljöhänsyn. En vanligt förekommande metod för att förbättra dessa processer är genom modellering. Modeller representerar verkligheten och kan därmed användas för att undersöka effekten av nya processer och strategier utan kostsamma interventioner. Under de senaste åren har maskininlärning (ML) framhävts som en lovande modelleringsmetod för stålindustrin. Detta har delvis drivits på av Industri 4.0, som lyfter fram ML som en av sina nyckelteknologier.

Dessa modeller är dock ofta svåra att tolka, vilket gör det opraktiskt att validera om modellen representerar verkligheten. Detta kan leda till brist på förtroende för ML-modeller som modelleringsverktyg inom stålindustrin. Målet med denna studie är att undersöka om ML modeller är praktiskt användbart inom stålprocessteknik.

För att besvara denna forskningsfråga har förbrukningen av elektrisk energi (EE) för

ljusbågsugnen valts som inriktning. Processen valdes på grund av dess omfattande

användning inom stålindustrin och på grund av svårigheten att exakt modellera

EE-förbrukningen med hjälp av metallurgi och termodynamik. I den aktuella

litteraturen används vanligtvis linjära statistiska modeller även om EE-konsumtionen

är icke-linjärt beroende av flera viktiga processvariabler. Dessutom undersöker inte

studierna i litteraturen korrelationerna mellan invariablerna eller försöker hitta den

mest optimala modellen med avseende på modellkomplexitet, prediktiv prestanda,

stabilitet och generaliserbarhet. Dessutom saknas en konsekvent rapportering av

prediktiva prestandamätvärden och tolkning av icke-transparenta modeller. Dessa

brister motiverade utvecklingen av en metodik för att skapa ML modeller och en

metodik för att utvärdera ML modeller. De båda metodikerna eliminerar dessa brister

genom att beakta både de processmetallurgiska aspekterna samt de utmaningar som

ML modelleringen medför. Genom användadet av de två metoderna kunde flera

viktiga slutsatser dras från de modeller som skapades baserat på data från två olika

ljusbågsugnar. I motsats till vad man tidigare trott är en hög modellkomplexitet, styrd

av ett förhöjt antal invariabler och modellkoefficienter, inte nödjvändigt för att uppnå

bäst prediktiv prestanda på testdata. Detta bekräftades både av det omfattande antalet

skapade modeller och av jämförelsen mellan de utvalda modellerna och de modeller

som rapporterats i litteraturen. För att förbättra modellernas prediktiva prestanda

bör fokus istället läggas på datakvalitetsförbättringar. Kompetens från experter inom

man utvecklar praktiskt användbara ML-modeller. Expertenas kompetens stödjer både valet av invariabler och tolkningen av effekterna invariablerna har på på EE- förbrukningen i förhållande till etablerade fysikaliska lagar och erfarenheter om den specifika ljusbågsugn som studerats. Dessutom resulterade en datarensning utförd av en expert på en av de två studerade ljusbågsugnarna i den bäst presterande modellen. Skrotsmältningsprocessen i ljusbågsugnen är komplicerad och därför utmanande att modellera med fysikalisk modellering. Med hjälp av ML-modellering visades det att en skrotkategorisering baserad på skrotets yta-till-volymsförhållande skapade ML-modeller med högst prediktiv prestanda. Detta stämmer väl med de fenomen som styr smältningen av skrot och som är proportionellt mot skrotets yta-till-volymsförhållande; temperaturgradienter, legeringsämnesgradienter, omrörningshastighet och frysningseffekten. Flera olika praktiska användningsfall har exemplifierats i denna avhandling eftersom modellutvärderingsmetoden påvisade de verkliga effekterna av varje invariabel på EE-förbrukningen. Det mest framträdande exemplet var effekten av olika skrotkategorier på EE-konsumtionen. Tre av dessa skrotkategorier tolkades korrekt av ML modellen enligt stålverkets processingenjörer.

För att kunna dra specifika slutsatser krävs dock en mycket högre prediktiv prestanda hos modellerna. Detta kan bara förverkligas efter betydande förbättringar av datakvaliteten. I sin tur kan detta endast genomföras av utvecklarna på det stålverk som ligger till grund för det data som användes för att skapa modellerna. Slutligen är den utvecklade metoden inte begränsad till den inriktning som används i detta arbete. Metoden kan användas för att utveckla ML-modeller för andra processer inom stålindustrin. Detta är värdefullt för stålindustrins utveckling av Industri 4.0.

Nyckelord

Ljusbågsugn; Elenergiförbrukning; Statistisk Modellering; Maskininlärning;

Tolkningsbar Maskininlärning; Prediktiv Modellering; Industri 4.0

The thesis would not have been possible to accomplish without the support from the scholarship fund ’Hugo Carlssons stipendiefond för vetenskaplig forskning’ and the Avesta and Hofors steel plants. For this I am most grateful. I want to thank process engineers Dr. Jesper Janis, Pär Ljungqvist, Patrik Undvall, and Jan Petterson for their assistance and data provisioning.

My heartfelt gratitude goes to my supervisors Dr. Peter Samuelsson, Prof. Pär Jönsson, and Assoc. Prof. Mikael Vejdemo-Johansson. In particular, Dr. Peter Samuelsson provided invaluable guidance and mentorship throughout the course of my PhD studies.

I also want to thank my family and my dear friends for their support during the toughest of times. You have all had an immense positive impact during the course of my PhD studies. I love you all.

Lastly, I want to thank my mentor, Andreas Pylarinos. You have had a major positive

influence in my life. In particular, as an advocate of patience and optimism throughout

this journey.

This doctoral thesis is a compendium of the following five Supplements:

Supplement 1: Predicting the Electrical Energy Consumption of Electric Arc Furnaces Using Statistical Modeling

Leo S. Carlsson, Peter B. Samuelsson and Pär G. Jönsson Metals, 2019, vol. 9, issue 9, No. 959.

Supplement 2: Using Statistical Modeling to Predict the Electrical Energy Consumption of an Electric Arc Furnace Producing Stainless Steel

Leo S. Carlsson, Peter B. Samuelsson and Pär G. Jönsson Metals, 2020, vol. 10, issue 1, No. 36.

Supplement 3: Interpretable Machine Learning—Tools to Interpret the Predictions of a Machine Learning Model Predicting the Electrical Energy Consumption of an Electric Arc Furnace

Leo S. Carlsson, Peter B. Samuelsson and Pär G. Jönsson

Steel Research International, 2020, vol. 91, issue 11, No. 2000053.

Supplement 4: Modeling the Effect of Scrap on the Electrical Energy Consumption of an Electric Arc Furnace

Leo S. Carlsson, Peter B. Samuelsson and Pär G. Jönsson Processes, 2020, vol. 8, issue 9, No. 1044.

Supplement 5: Fibers of Failure: Classifying Errors in Predictive Processes

Leo S. Carlsson, Mikael Vejdemo-Johansson, Gunnar Carlsson and Pär G.

Jönsson

Algorithms, 2020, vol. 13, issue 6, No. 150.

The Author’s Contribution to the Supplements:

Supplement 1: Structuring and categorization of the present literature, subsequent analysis, and major part of the writing.

Supplements 2-5: The experimental work and subsequent analyses, literature review,

and the major part of the writing of each manuscript.

CFD Computational Fluid Dynamics

EE Electrical Energy

TTT Tap-to-Tap Time

DRI Direct Reduced Iron HBI Hot Briquetted Iron

HM Heavy Melting scrap

EAF Electric Arc Furnace

LF Ladle Furnace

VTD Vacumm Tank Degassing

AOD Argon-Oxygen Decarburization CCM Continuous Casting Machine MLR Multivariate Linear Regression ANN Artificial Neural Network

DNN Deep Neural Network

RNN Recurrent Neural Network

RF Random Forest

DT Decision Tree

SVM Support Vector Machine

MSE Mean Squared Error

RMSE Root Mean Squared Error PLS Partial Least Squares

FI Permutation Feature Importance SHAP Shapley Additive Explanations

KS Kolmogorov–Smirnov

CDF Cumulative Distribution Function dCor Distance Correlation

IQR Interquartile Range KPI Key Performance Indicator

VB Variable Batch

AI Artificial Intelligence

ML Machine Learning

TDA Topological Data Analysis FiFa Fibers of Failure

PCA Principal Component Analysis V&V Verification and Validation

NAFEMS National Agency for Finite Element Methods and Standards NRC National Research Council

QOI Quantities of Interest

IT Information Technology

1 Introduction 1

1.1 Objectives . . . . 2

1.2 Structure of the thesis . . . . 3

2 Background 5 2.1 Machine learning modeling . . . . 5

2.1.1 Machine learning as a new modeling regimen? . . . . 5

2.1.2 Machine learning in the present work . . . . 6

2.1.3 Training statistical models . . . . 8

2.1.4 Model construction considerations . . . . 8

2.1.5 Model evaluation considerations . . . . 13

2.2 The electric arc furnace (EAF) process . . . . 15

2.2.1 An idealized description of the EAF process . . . . 15

2.2.2 Energy sources and energy sinks . . . . 15

2.2.3 Non-linearity . . . . 16

2.3 Modeling the electrical energy consumption of the EAF . . . . 19

2.3.1 Reasons for modeling . . . . 19

2.3.2 The physico-chemical perspective . . . . 20

2.3.3 The statistical perspective . . . . 24

2.4 Model verification and validation . . . . 27

2.4.1 Validation of machine learning models . . . . 28

2.4.2 Verification of machine learning models . . . . 30

3 Materials and methods 33 3.1 Electric arc furnaces in the experiments . . . . 33

3.1.1 Specifications . . . . 33

3.1.2 Process strategies . . . . 33

3.1.3 Data retrieval . . . . 34

3.2 Statistical modeling frameworks . . . . 35

3.2.1 Modeling frameworks . . . . 35

3.2.2 Grid search . . . . 39

3.3 Statistical tools . . . . 40

3.3.1 Data normalization . . . . 40

3.3.2 Tukey’s fences . . . . 41

3.3.3 Correlation metrics . . . . 41

3.3.4 Kolmogorov-Smirnov test . . . . 43

3.3.5 Predictive performance metrics . . . . 45

3.3.6 Permutation feature importance . . . . 47

3.3.7 Shapley additive explanations . . . . 48

3.4 Topological data analysis . . . . 52

3.4.1 Mapper . . . . 53

3.4.2 Fibers of failure . . . . 55

3.5 Software . . . . 56

4 Review of reported statistical models 57 4.1 Introduction . . . . 57

4.2 Results and discussion . . . . 57

4.2.1 Model construction . . . . 57

4.2.2 Model evaluation . . . . 76

4.3 Summary . . . . 83

5 Model construction 85 5.1 Introduction . . . . 85

5.2 Results and discussion . . . . 86

5.2.1 Developed model construction methodology . . . . 86

5.2.2 Electrical energy consumption models . . . 106

5.2.3 Grid search metadata . . . 113

5.3 Summary . . . 114

6 Model evaluation 117 6.1 Introduction . . . 117

6.2 Results and discussion . . . 118

6.2.1 Predictive performance analysis . . . 118

6.2.2 Predictive performance drift analysis . . . 124

6.2.3 Contributions by input variables on EE consumption . . . 133

6.2.4 Fibers of failure qualitative analysis . . . 142

6.3 Summary . . . 145

7 Conclusions 148 7.1 Concluding discussion . . . 148

7.2 Main conclusions . . . 150

8 Future outlook 152 8.1 Further work . . . 152

8.2 Sustainability . . . 154

References 155

1 Introduction

The steel industry is in constant need of improving its production processes which is partly due to increasing competition and partly due to environmental concerns. One commonly used method for improving these processes is through the act of modeling.

Models are representations of the reality which means that models can be used for studying and testing new process designs and strategies without the need for process intervention. Process intervention often requires that the process is temporarily halted, which is costly for the steel plant. A commonly used modeling framework within steel process engineering is Computational Fluid Dynamics (CFD) modeling, which uses equations governed by physico-chemical laws on finite elements [1].

Another commonly used modeling framework is the use of linear or non-linear programming to solve physico-chemical equations at each time-step of the process [2–

20]. These equations are typically mass-balance and energy-balance equations.

Recent years have seen a surge of interest in machine learning (ML) as a tool to model various processes within the steel industry. One main driver is the Industry 4.0 development, which highlights ML as one of the key technologies for its realization [21].

Focal to this development has also been the seemingly overused term ’Big Data’, which has been one of the more influential buzzwords encompassing much of the overall hype around the, presumably high, potential of ML. However, these models often look good on paper but convey a lack of trustworthiness in the eyes of domain practitioners.

Hence, one of the main issues at hand is if the utilization of ’Big Data’, through the use ML algorithms, requires a ’Big’ or a ’Small’ effort in order to construct models that are both trustworthy in the eyes of domain practitioners and satisfactory with respect to the accuracy and precision demands on the model. This effort is partly governed by the methodological approach used to construct the model and partly governed by two evaluation concepts that applies to any model that is used in practice. These two concepts are model Verification and Validation (V&V), which evaluates the behaviour of the model and its representativeness to the real world. The usefulness of any model is, by and large, dependent on its ability to accurately represent the real world.

Methods for the V&V of ML models are underdeveloped as opposed to methods for the V&V of more established modeling frameworks such as CFD modeling. However, some prominent developments have recently been provided by the field of interpretable machine learning [22], which can potentially facilitate an improved practice in V&V of ML models used in the context of steel processes.

The present work investigates the practical usefulness of ML models in the context of

steel process engineering. Predicting the Electrical Energy (EE) consumption of the

Electric Arc Furnace (EAF) will be the chosen application. A thorough review over the

statistical modeling of the EE consumption of the EAF is presented in Supplement 1 of the present work. There are three reasons why this prediction problem was chosen. First, the EAF process accounted for some 28% of the total world production of steel, on average, between 2008 and 2017 [23]. Hence, the improvements made throughout the course of the present work have the potential to be of value for the overall steel industry. Second, the EE consumption of the EAF process is difficult to accurately predict using models based solely on physico-chemical equations. Using a modeling framework based on statistics could prove to be an approach that produces more accurate models predicting the EE consumption of the EAF. Third, the EE consumption is well-defined in the EAF transformer system and is therefore prone to negligible error. This simplifies the evaluation effort of the resulting ML model.

1.1 Objectives

The aim of this thesis is to investigate if supervised ML models can be practically useful when applied in the context of steel processes. The use of supervised ML models to predict the EE consumption of the EAF acts as the application of interest to answer the aforementioned main research question. Furthermore, the research is demarcated to the first two parts of the ML model life-cycle; Model Construction and Model Evaluation. The last two parts of the machine ML life-cycle, Model Deployment and Model Maintenance, consider the challenges imposed by the implementation and continuous maintenance of the ML model when it is used in the steel plant as a process control tool. This means that the present work only focuses on the practical usefulness of ML models when they are used offline. Two universal examples of offline usage of ML models are explained below:

1. Draw domain-specific conclusions based on the representativeness of the model to the real world.

2. Investigate the predictive performance on a data set separate from the data used to adapt the coefficients of the model.

The aforementioned aim and demarcations of the present work lead to objectives which are formulated in Table 1.1.1.

The study governing Supplement 5 was performed at the onset of the research work

reported in this thesis. Hence, some of the methods developed in Supplements 1-4

are not used in Supplement 5. However, the author decided to include Supplement

5 as it illuminates a ML model evaluation method which did not materialize as

expected.

Table 1.1.1: An overview of the objectives of each supplement accompanying this thesis.

# Supplement Title Objectives

1 Predicting the Electrical Energy Consumption of Electric Arc Furnaces Using Statistical Modeling

• Structure and bring clarity to the available statistical models predicting the EE consumption of the EAF in light of challenges and considerations that are imposed by statistical modeling and process metallurgy.

• Identify shortcomings found in the available research with respect to Model Construction and Model Evaluation.

2 Using Statistical Modeling to Predict the Electrical Energy Consumption of an Electric Arc Furnace Producing Stainless Steel

• Provide a Model Construction methodology addressing the shortcomings identified in Supplement 1.

• Analyze and explain the reasons behind the predictive performance changes of the model between the training and test data by using statistical tools and process metallurgical reasoning.

3 Interpretable Machine Learning – Tools to Interpret the Predictions of a Machine Learning Model Predicting the Electrical Energy Consumption of an Electric Arc Furnace

• Introduce Shapley Additive Explanations (SHAP) as a Model Evaluation tool to study the specific contributions by each input variable on the EE consumption predictions.

• Evaluate one of the models created in Supplement 2 with respect to physico-chemical relations and process metallurgical experience.

4 Modeling the Effect of Scrap on the Electrical Energy Consumption of an Electric Arc Furnace

• Compare different cleaning strategies and their effect on the generalizability and predictive performance of the resulting model.

• Find the most optimal scrap representation with respect to the predictive performance of the resulting model.

• Analyze the contribution of each scrap category on the EE consumption predictions of a selected ML model.

5 Fibers of Failure: Classifying Errors in Predictive Processes

• Evaluate the Mapper algorithm from Topological Data Analysis (TDA) as a means to analyze subgroups of predictions with high negative error or high positive error.

• Investigate the connection between the input variables, which distinguish these groups from the rest of the data, and process metallurgy.

1.2 Structure of the thesis

The contents of this thesis are based on five supplements which are related and categorized as shown in Figure 1.2.1. The categories Literature Review, Model Construction, and Model Evaluation, illustrates the central thread of this thesis. The contents of the following chapters are detailed below:

Chapter 2 explains the theoretical background of the main objective as well as the practical challenges and considerations that are imposed by statistical modeling in the context of predicting the EE consumption of EAF producing steel.

Chapter 3 explains the various statistical methods and tools used in the experiments

Literature Review

Model

construction Model evaluation

Supplement 1

Supplement 2

Supplement 3

Supplement 4

Supplement 5

Model

deployment Model maintenance Thesis

Figure 1.2.1: Thesis work overview in relation to the Machine Learning (ML) model life-cycle.

governing this thesis. It also provides specifications of the two EAF that governs the data that will be used to create the ML models.

Chapter 4 is based on the work conducted in Supplement 1, which is a review of previous research that creates or uses statistical models that predicts the EE consumption of the EAF. It is written from the perspective of the practical challenges and considerations governing statistical models in the context of EAF process engineering. The chapter is overall divided into Model Construction and Model Evaluation.

Chapter 5 presents the Model Construction methodology developed in Supplements 2 and 4 as well as the results, discussion, and conclusions related to the Model Construction considerations presented in the two supplements.

Chapter 6 focuses on the four Model Evaluation methods used in Supplements 2- 5. The results, discussion, and conclusions based on these evaluation methods are presented as well as the categorization of each method into either verification or validation of ML models.

Chapter 7 provides the concluding discussion with respect to the aim of this thesis and the main conclusions.

Chapter 8 presents recommendations for future work based on the findings in

Chapters 4-7 as well as on the later parts of the ML model life-cycle; Model Deployment

and Model Maintenance.

2 Background

2.1 Machine learning modeling

2.1.1 Machine learning as a new modeling regimen?

In a seminal paper published by Breiman in year 2001 [24], two cultures comprising the field of statistical modeling were described. The first culture uses data modeling, which consists of statistical models which can be easily evaluated using algorithms that stem from solid mathematical theory and proofs. By using data modeling, one assumes that the data is generated by a stochastic process, which has a mathematical form pre-determined by the modeler. One common data modeling framework is linear regression, which produces models that can be expressed as an analytical equation. However, these types of statistical models is limited in its ability to model complex relationships in data. According to Breiman, most of the academic community concerning statistics focuses on data modeling. The second culture uses algorithmic modeling, which produces models that have the ability to successfully model complex relationships in data. In essence, an algorithm is created that closely resembles the unknown process which generates outputs, y, based on the inputs, X. While these models can achieve very high accuracy on complex problems, they are very difficult to interpret due to their lack of transparency in the prediction process. Consequently, these types of models are prominent within industries where an understanding of the model is less relevant and where the risks caused by faulty predictions are low. An illustration of the two statistical modeling cultures in relation to an arbitrary process of interest is shown in Figure 2.1.1.

In essence, all ML models originate from algorithmic modeling algorithms. Thus, ML is not a new technology, rather it is yet another approach to statistical modeling.

Further supporting this claim is the contemporary developments in ML, which have

primarily been governed by the emerging low-cost computing power and storage

solutions and not by novel modeling concepts. For example, Artificial Neural Networks

(ANN), which is a commonly used ML model framework and the forerunner to all

neural network model frameworks such as Convolutional Neural Networks (CNN)

and Recurrent Neural Networks (RNN), dates back to year 1958 [25]. Random

Forests (RF), which is another commonly used ML model framework, is a later

development but uses decision trees as one of the main concepts when constructing

the model [26]. The use of decision trees in statistics dates back to at least as early as

year 1959 [27].

X y

Data Modeling

Algorithmic Modeling (Machine Learning)

X y

X y

linear regression logistic regression

Unknown

algorithm Process

? Process of Interest

Figure 2.1.1: The data modeling and algorithmic modeling approaches to model an arbitrary process of interest. The data modeling culture assumes that the process can be expressed as a function of a specific form while the algorithmic modeling culture attempts to find an algorithm that as closely as possible resembles the predictive performance of the unknown process. The question-mark highlights the lack of transparency of the resulting model.

2.1.2 Machine learning in the present work

Statistical modeling is a sub-field of Artificial Intelligence (AI), which is a field that comprises of many different technologies and approaches that can be used to construct systems that think and act rationally as well as systems that think and act like humans [28]. Within statistical modeling, there exists data modeling and algorithmic modeling approaches, as explained in the previous section. ML comprises of a set of approaches and frameworks that can be used to predict outcomes based on a set of inputs. Figure 2.1.2 illustrates how the fields of ML and AI relates to one another. The ML modeling approach that will be used in the present work is supervised learning, which means that each instance of input data that is used to either train or test the ML model has only one corresponding instance of output data. This output data, in the training and test phases, are known. The predictive performance is gauged on the true values of the output data, i.e. the ML model is ’supervised’.

Machine Learning (ML) modeling frameworks represents the various algorithms that

can be used to construct a model that as closely as possible represents the process

of interest. The frameworks that will be used are described in Section 3.2. Many

ML model frameworks have the ability to model both on classification and regression

problems. The former concerns categorical values while the latter concerns continuous

values. The present work only utilizes regression, since the Electrical Energy (EE)

consumption of the Electric Arc Furnace (EAF) process is represented by continuous

values. For supervised statistical models, the input variables of the data used to train

Artificial Intelligence (AI)

Statistical modeling

Other techniques Data modeling

Algorithmic modeling (Machine Learning)

Machine Learning (ML) Approaches

Supervised learning Unsupervised learning Semi-supervised learning

Reinforcement learning . . .

Frameworks Artificial Neural Networks (ANN)

Random Forest (RF) Convolutional Neural Networks (CNN)

Recurrent Neural Networks (RNN) . . .

Figure 2.1.2: The relation between Machine Learning (ML) and Artificial Intelligence (AI), both of which have been highlighted as central technologies in the Industry 4.0 development [21].

and test the model always have corresponding values for the output variable. These output values are to the model considered the true values and are therefore the values that the model tries to fit as closely as possible. Since the goal of the models in the experiments is to predict the EE consumption as good as possible, supervised statistical models are hereby motivated.

Some clarifications have to be done with regards to the terms used throughout the present work. ML modeling will refer to algorithmic modeling as defined in the seminal paper by Breiman [24]. ML model refers to a model created by a ML modeling framework. Statistical modeling refers to either data model or algorithmic modeling. Statistical model refers to statistical models created by either data modeling or algorithmic modeling. The terms statistical modeling and statistical models will be used when the topic under focus is concerning both data modeling and algorithmic modeling or their resulting models. ML modeling or ML models will be used when the topic under focus is only relevant for ML models. In addition, linear statistical models refer to statistical models that can only learn linear relationships between variables. Non-linear statistical models refer to statistical models that can learn both linear and non-linear relationships between variables. Almost all ML models are non- linear statistical models.

Since statistical models will be contrasted with phyico-chemical models in some parts

of the present work, the following categorization is also made. Statistical modeling and

physico-chemical modeling are two different modeling principles. For example, CFD is a modeling framework within physico-chemical modeling and ANN is a modeling framework within ML modeling, which is a subcategory of statistical modeling.

2.1.3 Training statistical models

For the general case of supervised statistical models of regression type, the following components are needed to train (adapt) and test the model. An input data matrix, X, of dimension n × m where n is the number of data points (observations) and m is the number of variables (features). The input data matrix has a corresponding output vector, ¯ y, of dimension 1 ×m. A model that has not been adapted to the data, f model (Θ), where Θ is the model coefficients yet to be fit by data. In the scope of the present work, the terms ’adapt’ and ’train’ both refer to the training of a statistical model.

The general supervised regression case proceeds in the following steps:

1. The input data, X, with corresponding output data, ¯ y, is split into a training data set and a test data set; (X _train , ¯ y _train ) and (X _test , ¯ y _test ), such that n _train + n _test = n 2. Using the training data set, (X train , ¯ y train ), the f model (Θ) is adapted such that

f _model ( ˆ Θ, X _train ) ≈ ¯y train , where ˆ Θ is the model coefficients after the training phase is completed. The adaption of the model to the training data is conducted using a loss function, L(f model ( ˆ Θ, X train ), ¯ y train ), which aims to minimize the overall error of the model. The loss function could be, for example, the Mean Squared Error (MSE): M SE = ¹ _n ∑ n

i=1 (y _train ⁱ − f model ( ˆ Θ, X ⁱ _train )) ² 3. The model is tested on the test data set, f _model ( ˆ Θ, X _test ).

4. Depending on the magnitude of the error, M SE = _n ¹ ∑ n

i=1 (y _test ⁱ − f _model ( ˆ Θ, X ⁱ _test )) ² , the model is either considered to be practically useful or discarded.

The modifications to the general case gives rise to the numerous different modeling frameworks. Specific frameworks will be presented in Section 3.2.

2.1.4 Model construction considerations

Data quality

Data with high quality is an essential part of a successful statistical analysis or modeling onset. Data with poor quality impacts all aspects of the resulting ML model;

predictive performance, relevance, and subsequent model evaluation attempts. There

are numerous different sources that can give rise to poor data quality. The sources

can be at the boundaries between the various Information Technology (IT) systems,

which generates or uses the data, or be the result of insufficient metadata or hardware limitations. A thorough review over all possible sources that impacts the data quality negatively is beyond the scope of the present work. Figure 2.1.3 illustrates a flow- chart that illuminates a hypothetical path that a logged measurement can take and the various interfaces and systems that the value passes before arriving at the database.

The term system in the figure is used to describe the various sources that impose errors on the data. These are, for example, human operators, measurement devices, value transformations, and production systems using the data which results in new data.

Data source System 1

System 2

System 3

Database

Error propagation

Users Models Analyses

Figure 2.1.3: The path of data generated from an arbitrary data source. The ’error propagation’-arrow illustrates the increasing error from the original data source as it travels through the different systems.

The database is where all data is collected and is often the only interface where the users can select and make use of the data for analysis and modeling development. Thus, any effect that impacts the data quality before arriving at the database is often unknown.

It is therefore important to both correctly define the logged data with respect to what the data represent and to be aware of the limitations of the data. By being aware of the definition and the limitation of the logged data, it is possible to make a qualified assessment if it is sensible to create a ML model that can be used in practice.

The consistency of the data quality, or lack thereof, is also relevant for the ML model.

A systematic error source present in the data used to both adapt and test the ML model will be less harmful than a sudden change in data quality imposed by a stochastic error source. However, this does not validate the use of data that contains systematic error if it is possible to mitigate or remove these errors.

Data variability

The variations in the data are what a statistical model learns from and then uses

to make predictions on new data. Hence, near constant variables barely add any

new information to a statistical model. Statistical models require variations in

the data to function properly. In the eyes of a practitioner in physico-chemical

modeling, the importance of data variability is perhaps one of the most counter-

intuitive traits of statistical models, since a constant term in a physico-chemical model is important.

Correlation

Correlation is a statistical method that is used to measure the relation between variables. There are numerous correlation metrics, some of which will be explained further in Section 3.3.3. A high correlation value indicates that the variables are strongly related while a low correlation value indicates that the variables are weakly related. Several examples of causal relationships between variables will be explained with accompanying illustrations in Figure 2.1.4.

I) Variable B is causally related with variable A. They have a causal and correlated relationship. II) Variable A affects variable C indirectly by affecting variable B.

Variable C is causally related with variable A and B. III) Variable A affects variables B and C, which means that B and C is causally related with A. Thus, B and C may be correlated but they are not causally related. IV) Variables B and C affects variable A, which means that A is causally related with B and C. There could exist correlation between B and C, but not in a causal way. V) An illustration of a more complicated variable relationship structure where variable A is causally related with variables B- F.

A C B

E F D

A B

A B C

A

B C

A

B C

I)

II)

III)

IV)

V)

Figure 2.1.4: Five illustrations of causal relationships as described in the adjacent text.

Strongly correlated variables are redundant variables since they scarcely add new

information that increases the predictive performance of the ML model. Weakly

correlated variables, on the other hand, may be redundant. The degree of redundancy

for weakly correlated variables is closely related to the intra-correlation between the

variable and other variables. In the present work, the term, intra-correlation, will be

used to refer to the mutual information that exists between input variables. The term,

inter-correlation, on the other hand, will be used to refer to the mutual information

between input variables and the output variable.

It is important to interpret the correlation values using domain knowledge, since correlation metrics do not provide any information regarding the causal relation between the variables. This is one occasion where domain expertise plays a role in determining the choice of input variables in the model predicting an outcome of interest. However, correlation can point to areas where causality may be present.

Likewise, ML algorithms do not possess the ability to automatically distinguish causal variables from variables that are not causal. Any relationship between the variables, which is either causal or non-causal, may be learnt by the ML model. Hence, it is up to the modeler to select a reasonable number of relevant variables and find out which combination is the most optimal with respect to the intended use of the model.

Curse of dimensionality

There exists numerous manifestations of the phenomena known as the curse of dimensionality. However, the commonality among these manifestations is that they arise due to the increase in the number of dimensions of the input space. An intuitive example is the number of data points required to evenly cover the complete input space [29]. Figure 2.1.5 illustrates this example.

x x

y

z

y

x

a) b) c)

Figure 2.1.5: An illustration of the ’Curse of dimensionality’, which arises due to the exponential growth in the data space. a) 1-dimensional space contains 4 (4

) sub-spaces. b) 2-dimensional space contains 16 (4

) sub-spaces. c) 3-dimensional space contains 64 (4

) sub-spaces.

To cover the complete input space with the same density of data points, an exponential

number of data points must be used. If 30 data points is required to cover an 1-

dimensional input space, 900 data points will be needed to cover the 2-dimensional

input space. For a 3-dimensional and 4-dimensional input space, the number of data

points required are 27,000 and 810,000, respectively! Covering the complete input

space is thus challenging from a practical standpoint. This is especially the case in

application areas where the number of data points is sparse in relation to the number

of relevant input variables.

Principle of parsimony

The principle of parsimony states that any explanation or solution should not use more factors than necessary. This principle has been referenced by many scholars throughout history. One of these is William of Occam, which exhorted that ”plurality must never be posited without necessity” and that ”it is futile to do with more what can be done with less” [30]. Hence, Occam’s Razor is another term for the principle of parsimony which may be more familiar to some readers.

In ML modeling, there exists a trade-off mechanism between the goodness-of-fit and the parsimony of any given model [30]. A commonly used goodness-of-fit metric is R-square (R ² ). A complex model (low parsimony) has the ability to learn complex relationships between data in such a manner that it achieves an excellent fit to the data (high goodness-of-fit). The main risk here is if the model learns the noise in the data, which is the non-reproducible part of the data. Most data consists of a non-reproducible part (noise) and a reproducible part (signal). In this case, the model will not be able to predict well on data that has not been used to fit the coefficients of the model during the training phase. On the contrary, too simplistic models will fail to capture the relevant signals in the data that will enable the model to predict well on previously unseen data. Model complexity is partly governed by the number of input variables used and partly by the parameters specific to the selected ML modeling framework. Both of these contributions to model complexity must be carefully considered during the Model Construction step in order to adhere to the principle of parsimony.

The principle of parsimony in tandem with goodness-of-fit metrics allows for the discovery of supervised ML models that strike the optimal balance between model complexity and goodness-of-fit.

Rashomon effect

The Rashomon Effect is a term first coined by Breiman to describe the possible

availability of multiple models that have very similar error rates on a given data

set [24]. This is also known as the multiplicity of good models. Breiman illustrated

the Rashomon effect using three Multivariate Linear Regression (MLR) models, each

trained on 5 variables that were not used in any of the other two models but had

an residual sum-of-squares within 1% of the other two models. This outcome is not

surprising since the intra-correlations between input variables make them in part

interchangeable when used in a ML model. However, input variables that more

closely resembles quantities that are recognizable from a domain-perspective should

be prioritized above other types of input variables.

2.1.5 Model evaluation considerations

Stability

Stability, in the context of the present work, is the ability for a specific ML model type to have similar predictive performance on the training or test data independent of model instance. A model type is defined as a specific model framework with a specific setup of parameters. A model instance is one trained instance of a model type. Using a model type that is stable is important for two reasons. First, the calculated predictive performance values must be as consistent as possible and not be to a large extent dependent on a random outcome of the ML model algorithm. Second, the evaluation of the model type will mostly be based on one model instance. Consequently, the behavior of the model understood through the model evaluation process cannot be dominated by effects produced by a random outcome of the ML model algorithm.

In order to investigate the stability of a model type, multiple instances of the same model type can be trained and tested using the same set of training and test data. The stability of the model type can then be investigated by analyzing the distributions of the predictive performance values. However, the criterion what is considered a stable model has to be pre-specified by the modeler, since a universally applicable criterion for ML model stability does not yet exist.

Predictive performance

The predictive performance of a statistical model is its ability to as closely as possible predict the true output value given a set of input values. A commonly used predictive performance metric for regression models is the error expressed as the difference between the true output value and the predicted output value. The various predictive performance metrics used in the present work will be further exemplified in Section 3.3.5. Predictive performance on the training data is dependent on the information inherent within the input variables that aids the prediction. Correlation metric values between the input variables and the correlation metrics values between the input variables and the output variables can be used as an indicator which input variables may be the most aiding in the prediction. The predictive performance on the training data is also dependent on the selected parameters of the model framework, i.e. if the parameters combined provide a model type that can adapt to the important relationships inherent within the variables.

From a model evaluation perspective, the predictive performance of the model

measures the accuracy and the precision of the model without taking into consideration

any domain-specific demands such as the actual effect by each input variable on the

output variable. Using the information from the values on the predictive performance metrics, it is possible to only partly judge whether or not the model is good enough for the intended uses of the model. In the present work, the term ’predictive performance’ refers to any of the predictive performance metrics used if not otherwise specified.

Generalizability

Generalizability is the ability for any given model to predict on test data with a similar predictive performance as on the data that is used to train the model. Thus, a common measurement of model generalizability is the difference in predictive performance between the training and test data. A large difference means that the model does not predict well on new data, i.e. the model has low generalizability. While the predictive performance on the test data precedes the predictive performance on training data, the difference between the two highlights that the model has either overfitted on the training data or that the change in variable distributions between the training and test data is large. The latter is bound to happen within any data set. However, the difference is not expected to be large if the test data is either a random sample of the complete data set or is in adjacent chronological order with respect to the training data. It is up to the modeler to find out which of these two reasons is the most predominant one.

Interpretability

While ML is not a new technology, it imposes several challenges due to the nature of its approach to adapt the model coefficients to the underlying data. The main challenge is the lack of transparency in the model predictions, which impedes the interpretability of the model. Consequently, the users will not be able to understand the model.

Understanding a model is critical for determining its trustworthiness when used in a practical context.

The lexical definition of interpret is ”to explain or tell the meaning of” or ”present in understandable terms” [31]. Hence, interpretability is the ability of the model to reveal the reasons behind its predictions in understandable terms. Molnar uses the following description of interpretability [22]:

”A model is better interpretable than another model if its decisions are easier for a human to comprehend than decisions from the other model.”

Recent developments in the field of interpretable ML have provided the ML community

with algorithms that enable the interpretation of ML models [22]. Thus, it is now

possible to investigate how well a ML model adheres to the rules set out by the

domain in which the model is applied. As with any type of modelling, domain-

specific knowledge and experience should be the guiding light during the construction and evaluation of statistical models. Otherwise, the modeling effort risks becoming a haphazard process that ultimately results in disappointment for the involved stakeholders.

2.2 The electric arc furnace (EAF) process

2.2.1 An idealized description of the EAF process

The EAF process begins with a charging step where a basket of raw materials is charged into the furnace. Depending on the target composition of the steel, the raw materials can be, for example, steel scrap, Direct Reduced Iron (DRI), and various alloys. At the end of the charging step, the graphite electrodes are bored down and the power is turned on. During the first melting step, the goal is to melt enough scrap to make room for the second basket of scrap. Burners are used to remove cold spots present in the vicinity of the edges of the triangular ”shape” formed by the three electrodes. The cold spots hampers an even melting behaviour. The second charging step is conducted in a similar fashion as the first charging step. The goal of the second melting step is to get the steel melt into a flat-bath state during which most of the steel is liquid.

When the steel achieves flat-bath, the refining stage is started where occasionally additional alloys are added to reach the target composition and to generate heat from exothermic chemical reactions. Additional burner injection may be conducted to get the steel to the wanted temperature. When the steel has the correct pre-determined composition and temperature, the tapping step starts. The steel is poured into a ladle for further processing in downstream process steps. Lastly, any necessary preparations are made to the furnace before the next heat starts. This can be, for example, fettling of the refractory walls or stacking of new graphite electrodes. A process scheme of the idealized EAF process can be seen in Figure 2.2.1.

2.2.2 Energy sources and energy sinks

Table 2.2.1 presents estimates of the energy sources and energy sinks governing the

EAF process. The values act as an additional guidance for input variable selection

when creating ML models predicting the EAF EE consumption. Each value has been

synthesized based on values reported in studies that have analyzed the energy balance

of various EAF [10, 32–35]. The percentage range of each energy factor is because

the compiled data comes from 20 different EAF, some of which uses up to 90% DRI

as opposed to 100% scrap as raw materials. To facilitate a foaming slag, additional

slag-formers must be used during the process for the EAF types that utilize a large

P,B

t Burner (B)

Power (P)

M C

C M R T

C - Charging M - Melting R - Refining T - Tapping P - Preparations

P

Figure 2.2.1: A scheme of the described idealized EAF process for one full Tap-to-Tap Time (TTT) cycle.

percentage of DRI as raw materials. This addition of materials naturally adds to the energy consumption. Furthermore, the amount of injected oxygen ranged from 5 m ³ /t to 40 m ³ /t, which explains the large difference in heat generated by the oxidation of alloying elements [10].

Table 2.2.1: Percentage ranges for energy sources and energy sinks based on a synthesis of values reported in [10, 32–35].

Energy Factor % of Total Energy Sources or Energy Sinks

In Electric 40–66%

Oxidation of alloying elements 20–50%

Burner fuel 2–11%

Out Liquid steel 45–60%

Slag and dust 4–10%

Off-gas 11–35%

Cooling 8–29%

Radiation and electrical losses 2–6%

2.2.3 Non-linearity

The EAF process is far from idealized when taking into consideration the vast number of non-linearities imposed by various sources. These sources can be either governed by physico-chemical (metallurgical) relations or governed by relations specific to the EAF under study. Several important sources of non-linearity can be identified.

Heat loss: During the earlier stages of the EAF process, when most of the steel is

in solid form, the heat loss to the surroundings are low compared to the latter stages

when the steel is melted. The heat loss is a combination of conductive, convective,

and radiative heat transfer, of which the latter is proportional to T ⁴ , where T is the temperature of the steel. Thus, the amount of time in each respective step also contributes to the non-linearity.

Delays: Unarguably, industrial processes are susceptible to various events that gives rise to delays. This extends the total time needed to finish the heat, usually measured by the Tap-to-Tap Time (TTT). One can divide the measurement of delays into two categories. First, a pre-defined nominal time is compared to the actual time for an expected event. An example is the charging of the furnace whose nominal time could be set to 4.5 minutes. If the charging step takes longer than 4.5 minutes, the subsequent delay will be added to the total delay. This expected delay in each step can be expressed as:

t ^exp _step = t ^actual _step − t ^nom step (2.1)

where t ^nom _step is the nominal time for the step and t ^actual _step is the actual time taken for the step to complete. The condition t ^nom _step ≤ t ^actual step represents delays while t ^nom _step ≥ t ^actual step

represents the case when the step finishes faster than nominal.

Second, any unplanned event such as those imposed by equipment failure straightforwardly increases the total delay of the process. These unexpected delays in each step can be explained by a sum of gamma distributions where each gamma distribution gives the time contribution for one unique delay source.

t ^unexp _step ∼

∑ n i=1

Gamma(t i , k i , θ i ) =

∑ n i=1

1

(k i − 1)! t ^k _i

⁻¹ e ^−t

^/θ

(2.2) where n is the total number of unique sources of delays. The main idea is not to specify the correct analytical expression for the delays imposed on the EAF process but rather to illustrate the contribution to the non-linearity of the process. Consequently, the total delay in each step can be expressed as:

t ^delay _step = t ^exp _step + t ^unexp _step (2.3)

Henceforth, the total time of each sub-process explained in Section 2.2.1 can be expressed as follows:

t ^tot _step = t ^nom _step + t ^delay _step (2.4)

Using this definition, the TTT of the EAF process can be expressed as:

t _{T T T} = ∑

step

(t ^nom _step + t ^delay _step ) (2.5)

where step ∈ {Charging, Melting, Refining, T apping, P reparation}.

Depending on when the delay occurs during the process, it will have varying impact on the heat loss. A delay in the earlier stages of the process has a smaller contribution to heat loss compared to a delay that occurs when all of the steel has melted. Again, the radiative heat transfer is proportional to T ⁴ , where T is the temperature of the steel.

Scrap types and charging strategies:

The total time in the melting step is not only governed by the amount of total raw materials charged in the EAF, it is also impacted by the scrap types and charging strategies used.

A comprehensive review in the field of steel scrap melting was compiled in 1984 by Friedrichs [36]. Later developments have been summarized in a recent review [37].

Four melting mechanisms can be identified from the latter work; heat transfer and alloying element transfer between the solid scrap and the steel melt, stirring intensity of the steel bath, and the freezing effect [37]. For the EAF, the stirring intensity is expected to not drastically influence the melting rate. This is contrary to the scrap melting rate in the basic oxygen furnace. The shape of scrap has a large impact on the melting rate because the effect of the mechanisms is proportional to the exposed surface-area to the steel melt. In addition, the mass of a scrap piece, which is proportional the the volume, is also an important factor. The mass of a scrap piece decreases the melting rate, since more mass of alloying elements has to be transported between scrap-melt interface and more mass has to be heated by the steel melt.

Consequently, the surface-area-to-volume ratio of the scrap pieces is a dominant factor determining the melting time of the scrap. This ratio can be expressed as:

R SV = A

V = A · ρ s

m (2.6)

where A is the surface-area, V is the volume, m is the mass, and ρ s is the density of the scrap metal.

For simple shapes, the surface-to-volume-ratio is proportional to the thickness, l, since

A

V = _A·l ^A = ¹ _l . To facilitate shorter melting times, the EAF should be charged with as

much thin-walled scrap as possible. However, aspects other than wall thickness are

determining the mix of scrap types used in the charge mix for any given heat. This adds to the non-linearity of the EAF process, since the operators have to combine disparate types of scrap, all of which uniquely contributes to the total time in the melting step of the process. Hence, an indirect effect on the EE consumption of the EAF process is the available scrap types. The available scrap types are governed both by scrap generated from the specific steel plant and by scrap purchased from the global scrap market.

Steel types: The range of steel types produced at any given steel plant non-linearly affects the EAF process times. For example, high performance steel and stainless steel grades require multiple downstream processes before the steel is cast compared to carbon steel grades. These include the Ladle Furnace (LF) and Argon-Oxygen Decarburization (AOD) processes. Multiple downstream processes lead to a more complicated supply chain system within the steel plant. This leads to additional indirect causes of delays to the EAF process.

Varying market demand for the steel grades will also lead to changes in the production planning system of the steel plant. This will both indirectly and directly impact the EAF process, both of which is additional sources of non-linearity. For example, producing steel grades that require longer refining times will increase the EE consumption compared to steel grades that require shorter refining times.

The non-linearity of the EAF process also has direct implications on which statistical modeling frameworks are suitable to use when constructing a model that is both accurate and relevant in practice.

2.3 Modeling the electrical energy consumption of the EAF

2.3.1 Reasons for modeling

In abstraction, models are representations of reality and the predictive performance

of any model is closely related to its practical usefulness. The main motivation of

using models in steel process engineering is because models reduce the resources

needed to study the effects of new operational practices and strategies. By studying a

representation of reality, i.e. a model, the effects of a change can be observed without

intervening in the production flow, investing in new equipment, or conducting full-

scale process experiments. All of these examples are more or less costly for the steel

plant. Three stakeholder-defined examples are given. First, the result from modeling

can enable process engineers to evaluate the performance of current process strategies