Minimum Prediction Error Research Articles

Transmissibility Enhanced Inverse Chatter Stability Solution

Abstract The structural dynamics of a machine tool at the tool center point characterizes its vibration response and machining stability which affects productivity. The dynamics are mostly dominated by the spindle-holder-tool assembly whose main vibration mode can change during machining due to centrifugal forces, thermal expansion, and gyroscopic moments generated at high spindle speeds. This paper proposes the identification of the spindle's in-process modal parameters: natural frequency, damping ratio and modal constant, by using a limited number of vibration transmissibility and critical chatter stability measurements. The classical inverse stability solution, which tunes the modal parameters to minimize prediction errors in chatter stability limits, is augmented with vibration transmissibility under two methods: (1) transmissibility-enhanced inverse stability solution: the modal parameters are updated to minimize prediction errors in chatter stability, and vibration transmissibility; (2) artificial neural network (ANN)-integrated inverse stability solution: the ANN uses vibration transmissibility to estimate the natural frequency and damping ratio, such that the inverse stability solution only needs to identify the modal constant. While both methods are experimentally validated, it is shown that the transmissibility-enhanced inverse stability solution is a more effective approach than the time-consuming ANN alternative for the estimation of in-process spindle dynamics.

Markov Chain Monte Carlo Parameter Estimation for Nonzero Slip Models of Wheeled Mobile Robots: A Skid-Steer Case Study

Abstract An accurate modeling, simulation, and estimation of the wheel-terrain interaction and its effects on a robot movement plays a key role in control and navigation tasks, specially in constantly changing environments. We study the calibration of wheel slip models using Particle Markov Chain Monte Carlo methods to approximate the posterior distributions of their parameters. In contrast to classic identification approaches, considering the parameters as random variables allows to obtain a probability measure of the parameter estimations and subsequently propagate their uncertainty to wheel slip-related variables. Extensive simulation and experimental results showed that the proposed methodology can effectively get reliable posterior approximations from noisy sensor measurements in changing terrains. Validation tests also include the applicability assessment of the proposed methodology by comparing it with the integrated prediction error minimization methodology. Field results presented up to 66% of improvement in the robot motion prediction with the proposed calibration approach.

Learning with reinforcement prediction errors in a model of the Drosophila mushroom body

Effective decision making in a changing environment demands that accurate predictions are learned about decision outcomes. In Drosophila, such learning is orchestrated in part by the mushroom body, where dopamine neurons signal reinforcing stimuli to modulate plasticity presynaptic to mushroom body output neurons. Building on previous mushroom body models, in which dopamine neurons signal absolute reinforcement, we propose instead that dopamine neurons signal reinforcement prediction errors by utilising feedback reinforcement predictions from output neurons. We formulate plasticity rules that minimise prediction errors, verify that output neurons learn accurate reinforcement predictions in simulations, and postulate connectivity that explains more physiological observations than an experimentally constrained model. The constrained and augmented models reproduce a broad range of conditioning and blocking experiments, and we demonstrate that the absence of blocking does not imply the absence of prediction error dependent learning. Our results provide five predictions that can be tested using established experimental methods.

Predicting temperature of Erbil City applying deep learning and neural network

<span>One of the most significant and daunting activities in today's world is temperature prediction. The meteorologists traditionally predict temperature via some statistical models aimed to forecast the fluctuations that might have happened to atmospheric parameters such as temperature, humidity, etc. The main objective of this paper is to build an intelligent temperature prediction model of Erbil city in KRG/ Iraq based on a historical dataset from 1992 to 2016 in each year there are twelve months’ average temperature readings from (January to December). Hence to resolve this prediction problem an up-to-date deep learning neural network has been used, the network model is based on <span id="docs-internal-guid-850bd062-7fff-c6c8-9146-ba6427eb24e0" style="font-size: 9pt; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: 400; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">long short-term memory</span> (LSTM) as an artificial recurrent neural network (RNN) architecture which employed to estimate the future average temperature. The implementing model uses the dataset from real-time 30 weather stations deployed in the area of the city. The prediction performance of the proposed recurrent neural network model has been compared with some state of art algorithms like Adeline neural network, Autoregressive neural network (NAR), and <span id="docs-internal-guid-14d37b98-7fff-0f76-848f-ad9f89224f77" style="font-size: 9pt; font-family: 'Times New Roman'; color: #000000; background-color: transparent; font-weight: 400; font-style: normal; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> generalized regression neural network</span> (GRNN). The results show that the proposed model based on deep learning gives minimum prediction error.</span>

Predictive Processing in Cognitive Robotics: A Review.

Predictive processing has become an influential framework in cognitive sciences. This framework turns the traditional view of perception upside down, claiming that the main flow of information processing is realized in a top-down, hierarchical manner. Furthermore, it aims at unifying perception, cognition, and action as a single inferential process. However, in the related literature, the predictive processing framework and its associated schemes, such as predictive coding, active inference, perceptual inference, and free-energy principle, tend to be used interchangeably. In the field of cognitive robotics, there is no clear-cut distinction on which schemes have been implemented and under which assumptions. In this letter, working definitions are set with the main aim of analyzing the state of the art in cognitive robotics research working under the predictive processing framework as well as some related nonrobotic models. The analysis suggests that, first, research in both cognitive robotics implementations and nonrobotic models needs to be extended to the study of how multiple exteroceptive modalities can be integrated into prediction error minimization schemes. Second, a relevant distinction found here is that cognitive robotics implementations tend to emphasize the learning of a generative model, while in nonrobotics models, it is almost absent. Third, despite the relevance for active inference, few cognitive robotics implementations examine the issues around control and whether it should result from the substitution of inverse models with proprioceptive predictions. Finally, limited attention has been placed on precision weighting and the tracking of prediction error dynamics. These mechanisms should help to explore more complex behaviors and tasks in cognitive robotics research under the predictive processing framework.

A Novel Approach Investigating the Remaining Useful Life Predication of Retired Power Lithium-Ion Batteries Using Genetic Programming Method

Abstract Electric vehicles (EVs) have been widely cherished by consumers in recent years. However, as the number of EVs continues to increase, the number of retired power batteries will also increase, especially retired power lithium-ion batteries (LIBs), which will cause serious energy waste. To reuse sufficiently retired power LIBs, we studied the remaining useful life (RUL) of the power LIBs after retirement, so that the battery can be used in different usage scenarios, such as electric bicycles, grid energy storage, and communication base stations. The study first considers the inconsistency of the internal resistance and capacity of the LIBs pack and uses the battery available energy to predict the RUL of the retired power LIBs. Then, we further use the genetic programming (GP) method to predict the RUL of retired power LIBs. The case study shows the prediction accuracy of GP is better than response surface methodology (RSM), Kriging, and radial basis function (RBF) surrogate model. When the LIBs cycles are 100, 110, 120, and 130, the GP model prediction is relatively accurate and the minimum prediction error is only 5.26%.

Model-Based Monitoring of Patient Response to Staged Thyroidectomy

The goal of this study is to develop a model-based control chart for monitoring patient behavior in a staged thyroidectomy considering risk factors and clinical prescription. prospectively collected data are gathered from thyroid surgery unit of a hospital located in Tehran, Iran for 80 staged thyroidectomy patients discharged from 2009 to 2013. A risk adjusted state space model is developed based on the staged thyroidectomy. Variables to be included in the model are determined as a part of the model building process. Performance criteria, clinical prescription and patient risk factors are three variable components for the model. The appropriate risk factors are directly involved in the model and no scoring system is used for the model construction. Model identification is performed in two steps; model order selection and parameter estimation. In the first step, Hankel singular value decomposition (HSVD) is used for detecting the model order and in the second step, unknown parameters are estimated by the prediction error minimization (PEM) method. For monitoring patient responses, a group individual (GI) control chart is introduced and applied to a real-world problem. Results indicate that the suggested control chart can monitor the staged thyroidectomy patient’s behavior with an acceptable accuracy. Also, computer aided diagnosis (CAD) systems can be developed based on the proposed identification and monitoring method.

Smart “Predict, then Optimize”

Many real-world analytics problems involve two significant challenges: prediction and optimization. Because of the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in the downstream optimization problem. In contrast, we propose a new and very general framework, called Smart “Predict, then Optimize” (SPO), which directly leverages the optimization problem structure—that is, its objective and constraints—for designing better prediction models. A key component of our framework is the SPO loss function, which measures the decision error induced by a prediction. Training a prediction model with respect to the SPO loss is computationally challenging, and, thus, we derive, using duality theory, a convex surrogate loss function, which we call the SPO+ loss. Most importantly, we prove that the SPO+ loss is statistically consistent with respect to the SPO loss under mild conditions. Our SPO+ loss function can tractably handle any polyhedral, convex, or even mixed-integer optimization problem with a linear objective. Numerical experiments on shortest-path and portfolio-optimization problems show that the SPO framework can lead to significant improvement under the predict-then-optimize paradigm, in particular, when the prediction model being trained is misspecified. We find that linear models trained using SPO+ loss tend to dominate random-forest algorithms, even when the ground truth is highly nonlinear. This paper was accepted by Yinyu Ye, optimization. Supplemental Material: Data and the online appendix are available at https://doi.org/10.1287/mnsc.2020.3922

Artificial intelligence in forecasting central pressure drop and maximum sustained wind speed of cyclonic systems over Arabian Sea: skill comparison with conventional models

An attempt is made in this study to forecast the central pressure drop (PD) and maximum sustained wind speed (MSWS) associated with cyclonic systems at the stage of the highest intensity over Arabian Sea using artificial neural network models. The cyclonic systems include the phases from deep depression to extreme severe cyclones. The sea surface temperature, mid-tropospheric relative humidity, surface to middle tropospheric equivalent potential temperature gradient, inverse of wind shear and vertical wind velocity at 200 hPa level are evaluated as the most suitable predictors through principal component analysis. Various neural network models with different architectures have been trained with the data from 1990 to 2012 to select the best forecast model. The prediction skill of the intelligent models is evaluated by different accuracy measures. The results show that the multi-layer perceptron (MLP) model with five input layers, one hidden layer with four nodes and one output layer is the best model for forecasting PD with minimum prediction error of 0.14 at 36 h lead time, whereas the MLP model with five input layers, one hidden layer with five nodes and one output layer is found to be the best model for forecasting MSWS with minimum prediction error of 0.19 at 48 h (h) lead time. The results are well validated with the observations from 2013 to 2018. The forecast skill of MLP model is compared with multiple linear regression model and existing operational and numerical weather prediction models.

Endpoint-based optimal fractal interpolation for predicting BDS-3 system time offsets

In order to improve the interoperability within the Global Navigation Satellite System (GNSS), the International Committee on Global Navigation Satellite Systems published a joint statement in December 2019 that stated that all GNSS providers agree to monitor and broadcast the time offsets between each system timescale and the Universal Time Coordinated (UTC) or the rapid realization of UTC (UTCr). This commitment requires the study of precise prediction models for system time offsets. The prediction model of system time offsets is different from that of the atomic clock because of the control of the system timescale. The offsets between the system time of the Beidou Satellite Navigation System-3 (BDS-3) and the National Time Service Center (NTSC), called [UTC(NTSC)-BDT], have two main periods of 12 h and 24 h, according to the Fast Fourier Transform analysis. The rescaled range (R/S) analysis demonstrates that it has long memory, making it a fractal time series with a memory period of about 10.4 h. While using the fractal interpolation method to predict the [UTC(NTSC)-BDT] series, we found that the prediction error reaches its minimum value if adding disturbance on the estimated endpoint of the forecasted interval. After verifying the correlation between the estimated endpoints with the minimal interpolation error and minimal prediction error and proving the existence and uniqueness of the estimated endpoint with the minimal interpolation error, we established the endpoint-based optimal fractal interpolation prediction method. The experimental results indicate that the average prediction accuracy of the proposed prediction model is improved by 57.90% and 39.26% compared to that of a quadratic model and standard fractal prediction model, respectively. The accuracy analysis results of numerical tests indicate that the proposed prediction model can restrain the divergence of prediction error. Finally, we transform the [UTC(NTSC)-BDT] into [UTCr -BDT] using the [UTCr-UTC(NTSC)] published by the Bureau International des Poids et Mesures (BIPM) to meet the requirement of GNSS interoperability. The prediction accuracies of daily [UTCr-BDT] using the proposed prediction model are no more than 1.5 ns with uncertainty about 6 ns.

Neural network-based photovoltaic generation capacity prediction system with benefit-oriented modification

Photovoltaic (PV) generation prediction is a critical technology for integrating solar energy in power systems and markets. Accuracy is the target for most PV prediction models, which represents the minimisation of the average error. However, minimisation of prediction error is to obtain a minimum cost from impact of prediction inaccuracy. The lowest average error may not always relate to the minimum cost. Thus, this paper proposes an integrated PV prediction structure that targets minimum industrial cost from prediction error other than using pure accuracy. The object of machine learning model is modified into the further industrial cost of prediction error, which is the cost of backup generation participation in power dispatch for power grid energy balancing. A feed-forward neural network is selected as typical machine learning model for integration. Additionally, to solve the nesting optimisation problem in network training, an equivalent model is constructed to remove the sub-optimisation and make gradient-based training optimisation feasible. A numerical study shows that the integrated structure leads to prediction results with a lower cost than those of an accuracy-based structure.

Toward an Embodied, Embedded Predictive Processing Account.

In this paper, I argue for an embodied, embedded approach to predictive processing and thus align the framework with situated cognition. The recent popularity of theories conceiving of the brain as a predictive organ has given rise to two broad camps in the literature that I call free energy enactivism and cognitivist predictive processing. The two approaches vary in scope and methodology. The scope of cognitivist predictive processing is narrow and restricts cognition to brain processes and structures; it does not consider the body-beyond-brain and the environment as constituents of cognitive processes. Free energy enactivism, on the other hand, includes all self-organizing systems that minimize free energy (including non-living systems) and thus does not offer any unique explanations for more complex cognitive phenomena that are unique to human cognition. Furthermore, because of its strong commitment to the mind-life continuity thesis, it does not provide an explanation of what distinguishes more sophisticated cognitive systems from simple systems. The account that I develop in this paper rejects both of these radical extremes. Instead, I propose a compromise that highlights the necessary components of predictive processing by making use of a mechanistic methodology of explanation. The starting point of the argument in this paper is that despite the interchangeable use of the terms, prediction error minimization and the free energy principle are not identical. But this distinction does not need to disrupt the status quo of the literature if we consider an alternative approach: Embodied, Embedded Predictive Processing (EEPP). EEPP accommodates the free energy principle, as argued for by free energy enactivism, but it also allows for mental representations in its explanation of cognition. Furthermore, EEPP explains how prediction error minimization is realized but, unlike cognitivist PP, it allocates a constitutive role to the body in cognition. Despite highlighting concerns regarding cognitivist PP, I do not wish to discredit the role of the neural domain or representations as free energy enactivism does. Neural structures and processes undeniably contribute to the minimization of prediction error but the role of the body is equally important. On my account, prediction error minimization and free energy minimization are deeply dependent on the body of an agent, such that the body-beyond-brain plays a constitutive role in cognitive processing. I suggest that the body plays three constitutive roles in prediction error minimization: The body regulates cognitive activity, ensuring that cognition and action are intricately linked. The body acts as distributor in the sense that it carries some of the cognitive load by fulfilling the function of minimizing prediction error. Finally, the body serves to constrain the information that is processed by an agent. In fulfilling these three roles, the agent and environment enter into a bidirectional relation through influencing and modeling the structure of the other. This connects EEPP to the free energy principle because the whole embodied agent minimizes free energy in virtue of being a model of its econiche. This grants the body a constitutive role as part of the collection of mechanisms that minimize prediction error and free energy. The body can only fulfill its role when embedded in an environment, of which it is a model. In this sense, EEPP offers the most promising alternative to cognitivist predictive processing and free energy enactivism.

Regularizing axis-aligned ensembles via data rotations that favor simpler learners

To overcome the inherent limitations of axis-aligned base learners in ensemble learning, several methods of rotating the feature space have been discussed in the literature. In particular, smoother decision boundaries can often be obtained from axis-aligned ensembles by rotating the feature space. In the present paper, we introduce a low-cost regularization technique that favors rotations which produce compact base learners. The restated problem adds a shrinkage term to the loss function that explicitly accounts for the complexity of the base learners. For example, for tree-based ensembles, we apply a penalty based on the median number of nodes and the median depth of the trees in the forest. Rather than jointly minimizing prediction error and model complexity, which is computationally infeasible, we first generate a prioritized weighting of the available feature rotations that promotes lower model complexity and subsequently minimize prediction errors on each of the selected rotations. We show that the resulting ensembles tend to be significantly more dense, faster to evaluate, and competitive at generalizing in out-of-sample predictions.

IDENTIFICATION OF MATHEMATICAL MODEL OF TURBINE GENERATOR UNIT IN PRESENCE OF UNCERTAINTY

An identification procedure of mathematical model of turbine generator unit in the presence of uncertainty is studied for using in the interconnected robust control automated system. The procedure is based on “worst-case” identification approach. The controlled object is modelled by the matrix transfer function with additive uncertainty. The identification consists of two stages: first is to identify transfer function with nominal parameters with the use of prediction error minimization algorithm, second – to determine weight function in additive uncertainty model using finding the worst-case log-magnitude curve of uncertainties. Identification is performed in active way, determining datasets for each control channel from individual experiments. A linear frequency-modulated signal is selected as the input test disturbance. A simulation model of the controlled object is constructed and the numerical experiment is conducted using the identification procedure. References 11, figures 7.

Online State of Charge Prediction in Next Generation Vehicle Batteries Using Deep Recurrent Neural Networks and Continuous Model Size Control

This investigation presents a data-driven Long-short Term Memory battery model for predicting State of Charge for lithium-ion batteries LiFePO4 for next-generation vehicle operations. Our modified algorithm builds and updates a model using multivariate inputs that include physical properties, voltage, current, and ambient temperature during operations. The primary research goal is to improve prediction performance on future values from multiple training examples using an online learning scheme. Initial results demonstrate excellent predictions that outperform results from literature and other neural network algorithms. Due to computing constraints in on-board vehicle systems, the authors develop online training with autonomous control of lag (window width). The control algorithm embeds in the model with rules that govern and adjust lag during training. This method ensures the minimization of computational cost and prediction errors with the use of standard computing equipment during driving conditions.

Rapid Detection of Pomelo Fruit Quality Using Near-Infrared Hyperspectral Imaging Combined With Chemometric Methods.

Pomelo is an important agricultural product in southern China. Near-infrared hyperspectral imaging (NIRHI) technology is applied to the rapid detection of pomelo fruit quality. Advanced chemometric methods have been investigated for the optimization of the NIRHI spectral calibration model. The partial least squares (PLS) method is improved for non-linear regression by combining it with the kernel Gaussian radial basis function (RBF). In this study, the core parameters of the PLS latent variables and the RBF kernel width were designed for grid search selection to observe the minimum prediction error and a relatively high correlation coefficient. A deep learning architecture was proposed for the parametric scaling optimization of the RBF-PLS modeling process for NIRHI data in the spectral dimension. The RBF-PLS models were established for the quantitative prediction of the sugar (SU), vitamin C (VC), and organic acid (OA) contents in pomelo samples. Experimental results showed that the proposed RBF-PLS method performed well in the parameter deep search progress for the prediction of the target contents. The predictive errors for model training were 1.076% for SU, 41.381 mg/kg for VC, and 1.136 g/kg for OA, which were under 15% of their reference chemical measurements. The corresponding model testing results were acceptably good. Therefore, the NIRHI technology combined with the study of chemometric methods is applicable for the rapid quantitative detection of pomelo fruit quality, and the proposed algorithmic framework may be promoted for the detection of other agricultural products.

Research on residual life prediction method of lithium ion battery for pure electric vehicle

To overcome the complexity of the lithium-ion battery inside the chemical reaction resulting in a low battery life remaining prediction accuracy, the paper proposes a new electric vehicle lithium ion battery remaining life prediction method based on a correlation vector machine. According to the operating characteristics of lithium-ion batteries in electric vehicles, this method selects health factors that affect battery life, and selects related factors. According to the marginal likelihood function, the factor weights are integrated to obtain the health factor sequence target. Relevance vector machine is used to optimise and evaluate the characteristics of health factors, and complete the prediction of electric vehicle lithium-ion battery capacity and remaining battery life. Comparative experiments show that the prediction effect and stability of the method in this paper are better, and the minimum prediction error is only 0.013.

The Role of the Medial Prefontal Cortex in Self-Agency in Schizophrenia.

Schizophrenia is a disorder of the self. In particular, patients show cardinal deficits in self-agency (i.e., the experience and awareness of being the agent of one’s own thoughts and actions) that directly contribute to positive psychotic symptoms of hallucinations and delusions and distort reality monitoring (defined as distinguishing self-generated information from externally-derived information). Predictive coding models suggest that the experience of self-agency results from a minimal prediction error between the predicted sensory consequence of a self-generated action and the actual outcome. In other words, the experience of self-agency is thought to be driven by making reliable predictions about the expected outcomes of one’s own actions. Most of the agency literature has focused on the motor system; here we present a novel viewpoint that examines agency from a different lens using distinct tasks of reality monitoring and speech monitoring. The self-prediction mechanism that leads to self-agency is necessary for reality monitoring in that self-predictions represent a critical precursor for the successful encoding and memory retrieval of one’s own thoughts and actions during reality monitoring to enable accurate self-agency judgments (i.e., accurate identification of self-generated information). This self-prediction mechanism is also critical for speech monitoring where we continually compare auditory feedback (i.e., what we hear ourselves say) with what we expect to hear. Prior research has shown that the medial prefrontal cortex (mPFC) may represent one potential neural substrate of this self-prediction mechanism. Unfortunately, patients with schizophrenia (SZ) show mPFC hypoactivity associated with self-agency impairments on reality and speech monitoring tasks, as well as aberrant mPFC functional connectivity during intrinsic measures of agency during resting states that predicted worsening psychotic symptoms. Causal neurostimulation and neurofeedback techniques can move the frontiers of schizophrenia research into a new era where we implement techniques to manipulate excitability in key neural regions, such as the mPFC, to modulate patients’ reliance on self-prediction mechanisms on distinct tasks of reality and speech monitoring. We hypothesize these findings will show that mPFC provides a unitary basis for self-agency, driven by reliance on self-prediction mechanisms, which will facilitate the development of new targeted treatments in patients with schizophrenia.

ARX Model Identification using Generalized Spectral Decomposition

This article is concerned with the identification of autoregressive models with exogenous inputs (ARX). Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized to estimate ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input-output orders and delay. In this paper, we propose a novel automated spectral decomposition framework that recovers orders, delay, output noise distribution, along with parameter estimates. The proposed algorithm systematically estimates all the parameters in two steps. The first step estimates the order by examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the proposed method’s efficacy and are observed to deliver consistent estimates even at low signal-to-noise ratio (SNR).

Прогнозирование электропотребления промышленных предприятий с помощью модели авторегрессии проинтегрированного скользящего среднего

The problems concerned with forecasting the amount of electricity consumed by industrial enterprises are of utmost importance. An effective way of resolving conflicts between an industrial enterprise and a power supply company and preventing the occurrence of additional costs is to perform maximally accurate prediction of electricity consumption parameters, which can be achieved by reducing them for a contractual settlement period. Electricity consumption forecasting is of importance both from the technological and economical points of view, and its completeness has a direct effect on improving the competitiveness of manufactured products. This, in turn, is determined by a significant fraction of electricity expenditures in the enterprise output net cost. In determining the forecasted indicators of electricity consumption by industrial enterprises, it is advisable to use modern high-precision forecasting methods that ensure the minimum prediction error. The article addresses matters concerned with forecasting the electricity consumption by industrial enterprises with applying the autoregressive integrated moving average (ARIMA) method and using the Python 3.9 programming language (with involvement of the following software packages: statsmodels, numpy, pandas, pmdarima, and matplotlib) taking a metallurgical enterprise in the Republic of Uzbekistan as an example. An outline flowchart of electricity consumption prediction algorithm using the autoregressive integrated moving average method has been developed. The electricity consumption value predicted using the developed model is compared with the actual electricity consumption data. The adequacy of the developed models is validated by low absolute and relative errors between the actual and predicted data. An analysis of prediction error values has shown that the low prediction error in percentage terms is due to adequately developed mathematical models of electricity consumption parameters, due to which these can be applied to forecast the electricity consumption parameters at ferrous metallurgy enterprises.