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Predictive models are used in many different fields of science and engineering and are always prone to make faulty predictions. These faulty predictions can be more or less malignant depending on the model application. We describe fibers of failure (FiFa), a method to classify failure modes of predictive processes. Our method uses Mapper, an algorithm from topological data analysis (TDA), to build a graphical model of input data stratified by prediction errors. We demonstrate two ways to use the failure mode groupings: either to produce a correction layer that adjusts predictions by similarity to the failure modes; or to inspect members of the failure modes to illustrate and investigate what characterizes each failure mode. We demonstrate FiFa on two scenarios: a convolutional neural network (CNN) predicting MNIST images with added noise, and an artificial neural network (ANN) predicting the electrical energy consumption of an electric arc furnace (EAF). The correction layer on the CNN model improved its prediction accuracy significantly while the inspection of failure modes for the EAF model provided guiding insights into the domain-specific reasons behind several high-error regions.

The non-linearity of the Electric Arc Furnace (EAF) process and the correlative behavior between the process variables impose challenges that have to be considered if one aims to create a statistical model that is relevant and useful in practice. In this regard, both the statistical modeling framework and the statistical tools used in the modeling pipeline must be selected with the aim of handling these challenges. To achieve this, a non-linear statistical modeling framework known as Artificial Neural Networks (ANN) has been used to predict the Electrical Energy (EE) consumption of an EAF producing stainless steel. The statistical tools Feature Importance (FI), Distance Correlation (dCor) and Kolmogorov−Smirnov (KS) tests are applied to investigate the most influencing input variables as well as reasons behind model performance differences when predicting the EE consumption on future heats. The performance, measured as kWh per heat, of the best model was comparable to the performance of the best model reported in the literature while requiring substantially fewer input variables.

Statistical modeling, also known as machine learning, has gained increased attention in part due to the Industry 4.0 development. However, a review of the statistical models within the scope of steel processes has not previously been conducted. This paper reviews available statistical models in the literature predicting the Electrical Energy (EE) consumption of the Electric Arc Furnace (EAF). The aim was to structure published data and to bring clarity to the subject in light of challenges and considerations that are imposed by statistical models. These include data complexity and data treatment, model validation and error reporting, choice of input variables, and model transparency with respect to process metallurgy. A majority of the models are never tested on future heats, which essentially renders the models useless in a practical industrial setting. In addition, nonlinear models outperform linear models but lack transparency with regards to which input variables are influencing the EE consumption prediction. Some input variables that heavily influence the EE consumption are rarely used in the models. The scrap composition and additive materials are two such examples. These observed shortcomings have to be correctly addressed in future research applying statistical modeling on steel processes. Lastly, the paper provides three key recommendations for future research applying statistical modeling on steel processes.