Grey-box Model Research Articles

Vulnerability Assessment Method for Electronic Devices Excited by Transient Electromagnetic Disturbances

Vulnerability assessment of electronic devices excited by various transient electromagnetic disturbances (TEDs) has been a key issue in electromagnetic susceptibility research. This paper proposes a generalized vulnerability assessment method that includes acquiring data and building assessment model. The data is normally acquired by carrying out experiments, while the assessment model is mainly determined by prior information. As different devices under test (DUTs) could offer a different amount of prior information, a generalized assessment model consisting of a white-box model, a grey-box model, and a black-box model is built to deal with situations of sufficient prior information, partial prior information, and no prior information, respectively.

EEGG: An Analytic Brain-Computer Interface Algorithm.

Modeling the brain as a white box is vital for investigating the brain. However, the physical properties of the human brain are unclear. Therefore, BCI algorithms using EEG signals are generally a data-driven approach and generate a black- or gray-box model. This paper presents the first EEG-based BCI algorithm (EEG-BCI using Gang neurons, EEGG) decomposing the brain into some simple components with physical meaning and integrating recognition and analysis of brain activity. Independent and interactive components of neurons or brain regions can fully describe the brain. This paper constructed a relation frame based on the independent and interactive compositions for intention recognition and analysis using a novel dendrite module of Gang neurons. A total of 4,906 EEG data of left- and right-hand motor imagery (MI) from 26 subjects were obtained from GigaDB. Firstly, this paper explored EEGG's classification performance by cross-subject accuracy. Secondly, this paper transformed the trained EEGG model into a relation spectrum expressing independent and interactive components of brain regions. Then, the relation spectrum was verified using the known ERD/ERS phenomenon. Finally, this paper explored the previously unreachable further BCI-based analysis of the brain. (1) EEGG was more robust than typical "CSP+" algorithms for the low-quality data. (2) The relation spectrum showed the known ERD/ERS phenomenon. (3) Interestingly, EEGG showed that interactive components between brain regions suppressed ERD/ERS effects on classification. This means that generating fine hand intention needs more centralized activation in the brain. EEGG decomposed the biological EEG-intention system of this paper into the relation spectrum inheriting the Taylor series (in analogy with the data-driven but human-readable Fourier transform and frequency spectrum), which offers a novel frame for analysis of the brain.

Reliable nonlinear dynamic gray-box modeling by regularized training data estimation and sensitivity analysis

Dynamic process models are a key requirement for advanced process control and the application of process optimization techniques. The derivation of these models is time consuming and error-prone in cases where a lack of physico-chemical understanding is present. Machine learning (ML) methods can be employed in these cases to extract models or model elements from data. To reduce the amount of necessary data and to increase the extrapolation capabilities, gray-box models can be used that combine mechanistic equations with ML models. For embedded ML-models, the selection of a suitable model structure is challenging. Therefore, we propose a methodology to approach this problem in several steps by firstly estimating what values the ML-models should predict to accurately describe the experimental data. Subsequently, the ML-submodels can be trained using any ML-toolbox. Finally, a full parameter estimation is performed using a dynamic simulation in the cost function. We investigate different algorithmic options and show promising results for a case study of the fermentation of a sporulating bacterium.

Model Predictive Control Prototyping and Validation for a Large Central Cooling System

In this paper we present an application of Model Predictive Control (MPC) to a commercial building cooling system. The MPC models are a combination of white, grey and black box models derived from the experimental dataset and ensure energy and mass conservation is the system. Individual equipment models are validated against the actual measurements to ensure they accurately represent the physical system. A comparison of MPC performance to that of a business-as-usual operation scenario indicates up to 25% savings in operating costs with MPC.

Cost-aware Resource Recommendation for DAG-based Big Data Workflows: An Apache Spark Case Study

The era of personal resources being sufficient for enterprise big data computations has passed. As computations are executed in the cloud, small policy changes of cloud operators may cause considerable changes in operational costs. Carefully choosing the amount of resources for a given application is thus of great importance. This, however, requires a priori knowledge of the application's performance under different configurations. Creating a performance prediction model needs to account for the heterogeneity of resources and the diversity in application workflows. Previous approaches for heterogeneous environments consider a black-box representation of the application which results in single-purpose models. This paper addresses the problem with two gray-box prediction models using linear programming (LP) and mixed-integer linear programming (MILP). Given a set of available resources, the models consider Apache Spark applications and their Directed Acyclic Graph (DAG) of workflow running on top of a Hadoop-YARN cluster. We then propose a configuration recommendation algorithm to optimize the cost-performance trade-offs when renting machine instances. The accuracy of the proposed models is evaluated with real-world executions of several representative applications on the Wikipedia dataset and the TPC-DS benchmark. The average error of only 3.28% for the proposed prediction models demonstrates the practicality of the proposed approach in handling cost-performance trade-offs.

Glucose-insulin dynamics: a grey-box analogy

Regulating plasma glucose levels for both type I and type II diabetic patients is a challenging task. Understanding the effects of meals taken, the physical exercises and stress levels will contribute significantly to the overall management of the plasma glucose levels. This paper provides an extension of the Bergman minimal model to represent 12-compartmental models associated with meals taken, physical exercises and stress levels interactions within a semi-closed loop system using stochastic differential equations (SDE). The mathematical modelling is constructed following the grey-box model analogy as applied on an identifiable patient. Obtained results from the study demonstrate the predictive capability of the model to be good and its sensitivity is enhanced with increased dataset.

Equivalent Broadband Electrical Circuit of Synchronous Machine Winding for Frequency Response Analysis Based on Gray Box Model

Frequency response analysis (FRA) is a popular tool to detect transformer winding deformation faults. It has been recently used to diagnose the winding inter-turn short circuit fault of the electric machine. The application of FRA is based on the fact that the winding can be equivalent to an electrical circuit consisting of resistance, inductance, and capacitance. Therefore, to obtain an accurate broadband equivalent circuit model of synchronous machine and perform the fault analysis and diagnosis, this paper introduces the gray box model technique based on the state space and genetic algorithm. The electrical circuit of a form-wound coil of a 4 kW machine with known electrical parameters is used to verify the proposed method primarily. Besides, the equivalent circuit modeling is carried out and experimentally verified on an actual 5 kW synchronous machine. Finally, the fault simulation analyses of winding inter-turn short circuits are performed based on the proposed equivalent electrical circuit. The verification result shows that the circuit parameters identified by the proposed method are accurate. Moreover, the fault simulation results indicate that the inter-turn short circuit faults can cause apparent variations in the frequency response curves. It is feasible to detect the winding fault of the synchronous machine by the FRA method.

Big Data Analytics and Machine Learning of Harbour Craft Vessels to Achieve Fuel Efficiency: A Review

The global greenhouse gas emitted from shipping activities is one of the factors contributing to global warming; thus, there is an urgent need to mitigate the adverse effect of climate change. One of the key strategies is to build a vibrant maritime industry with the use of innovation and digital technologies as well as intelligent systems. The digitization of the shipping industry not only provides a competitive edge to the shipping business model but also enhances ship operational and energy efficiency. This review paper focuses on the big data analytics and machine learning applied to harbour craft vessels with the aim to achieve fuel efficiency. The paper reviews the telemetry system requires for the digitalization of harbour craft vessels, its challenges in installation, the vessel monitoring and data transmission system. The commonly used methods for data cleaning are also presented. Last but not least, the paper considers two types of the machine learning systems, i.e., supervised and unsupervised machine learning systems. The multi-linear regression and hidden Markov model for supervised machine learning system and the artificial neural network, grey box model and long short-term memory model for unsupervised machine learning are discussed, and their pros and cons are presented.

Hybrid Machine Learning Approaches and a Systematic Model Selection Process for Predicting Soot Emissions in Compression Ignition Engines

The standards for emissions from diesel engines are becoming more stringent and accurate emission modeling is crucial in order to control the engine to meet these standards. Soot emissions are formed through a complex process and are challenging to model. A comprehensive analysis of diesel engine soot emissions modeling for control applications is presented in this paper. Physical, black-box, and gray-box models are developed for soot emissions prediction. Additionally, different feature sets based on the least absolute shrinkage and selection operator (LASSO) feature selection method and physical knowledge are examined to develop computationally efficient soot models with good precision. The physical model is a virtual engine modeled in GT-Power software that is parameterized using a portion of experimental data. Different machine learning methods, including Regression Tree (RT), Ensemble of Regression Trees (ERT), Support Vector Machines (SVM), Gaussian Process Regression (GPR), Artificial Neural Network (ANN), and Bayesian Neural Network (BNN) are used to develop the black-box models. The gray-box models include a combination of the physical and black-box models. A total of five feature sets and eight different machine learning methods are tested. An analysis of the accuracy, training time and test time of the models is performed using the K-means clustering algorithm. It provides a systematic way for categorizing the feature sets and methods based on their performance and selecting the best method for a specific application. According to the analysis, the black-box model consisting of GPR and feature selection by LASSO shows the best performance with test R2 of 0.96. The best gray-box model consists of SVM-based method with physical insight feature set along with LASSO for feature selection with test R2 of 0.97.

Hybrid Process Modeling of an Industrial Process

AbstractThe current revival and intensified research on machine learning take place while an intensified focus of companies on digitalization developed. The willingness and acceptance to apply innovative methods in industry has grown. Gray box or hybrid process modeling represents the combination of rigorous (white box) process modeling with machine learning (black box) models. In recent applications, the presented method has been utilized for process models at Evonik. This article describes the workflow for developing hybrid process models and is meant to share the experiences made during the process.

On gray-box modeling for virtual flow metering

A virtual flow meter (VFM) enables continuous prediction of flow rates in petroleum production systems. The predicted flow rates may aid the daily control and optimization of a petroleum asset. Gray-box modeling is an approach that combines mechanistic and data-driven modeling. The objective is to create a computationally feasible VFM for use in real-time applications, with high prediction accuracy and scientifically consistent behavior. This article investigates five different gray-box model types in an industrial case study using real, historical production data from 10 petroleum wells, spanning at most four years of production. The results are diverse with an oil flow rate prediction error in the range of 1.8%–40.6%. Further, the study casts light upon the nontrivial task of balancing learning from both physics and data. Therefore, providing general recommendations towards the suitability of different hybrid models is challenging. Nevertheless, the results are promising and indicate that gray-box VFMs can reduce the prediction error of a mechanistic VFM while remaining scientifically consistent. The findings motivate further experimentation with gray-box VFM models and suggest several future research directions to improve upon the performance and scientific consistency.

Interpretable Mamdani neuro-fuzzy model through context awareness and linguistic adaptation

Interpretable machine learning is trending as it aims to build a human-understandable decision process. There are two main types of machine learning systems: white-box and black-box models. White-box models are inherently interpretable but commonly suffer from under-fitting phenomena; on the other hand, black-box models perform quite well in a wide range of application domain problems, but their reasoning behind a decision is hard or even impossible to understand. In the soft-computing area, fuzzy inference systems are rule-based systems that use fuzzy reasoning, bringing human perception modeling and computing with word capability. These rule-based systems are designed either manually or automatically but are commonly optimized to fit better some phenomena’ data (in a supervised learning task). After the optimization process, the initial semantic meaning of fuzzy sets is modified (slightly, in the best cases), creating a gray-box model. The principal objective of the proposed methodology in this paper is to extract a high-quality rule in terms of comprehensibility, accuracy and fidelity. This is accomplished by using a fuzzy linguistic interpretable model from an optimized neuro-fuzzy model, considering the initial knowledge context with which it was built. A grammar-guided genetic algorithm is used as the optimization process to find the interpretable description of the model. A collection of 16 datasets for classification tasks were used to evaluate our proposal, obtaining an f1-score of 0.814 with 0.026 standard deviation in the optimized model; the obtained fidelity, in terms of similarity from the interpretable model to the optimized one, was 0.93 of mean with 0.018 standard deviation. Obtained results show that neuro-fuzzy systems could play an important role in interpretable machine learning, providing natural language explanations from previous knowledge.

Comparing statistical modeling techniques for heat loss coefficient estimation using in-situ data

The combination of in-situ collected data and statistical modelling techniques proved to be a promising approach in actual building energy performance assessments, such as heat loss coefficient (HLC) evaluation. In this study, based on datasets of co-heating and pseudo-random binary sequence heating tests on a portable site office, the performance of three types of statistical models (i.e. multiple linear regression (MLR), autoregressive with exogenous terms (ARX), and grey-box models) on HLC-determination are examined. It is revealed that a similar HLC estimation outcome (about 115 W/K) is offered by the aforesaid three types of statistical models, but with different confidence intervals (CIs), where the 95% CIs of MLR (±3.1%) and ARX (±2.4%) are relatively narrow and the ones of grey box models are somewhat wider (around ± 9%). Moreover, for the current case study building, with evenly orientation-wise distributed glazed envelope, integrating B-splines into the grey-box model, to characterize the solar aperture (gA) and solar gain dynamics more precisely, imposed insignificant effects on the HLC estimation and corresponding 95% CIs, compared to the grey-box model with a constant gA assumption.

Self-adjusting model predictive control for modular subsystems in HVAC systems

In order to reduce the energy consumption and CO2 emissions in the building sector, an efficient control strategy, such as model predictive control (MPC) is required. However, MPC is rarely applied in buildings since the implementation and modeling is complex, time consuming and costly. To bring MPC into practice, controllers and models are needed, that automatically adapt their behavior to the controlled system. In this work, such a self-adjusting MPC applicable to heating, ventilation and air-conditioning (HVAC) systems is developed. The MPC is based on a simple grey-box model that is able to cover the general dynamics of the considered subsystem. The controller adapts the model parameters online according to the past measurements of the controlled system using a moving horizon estimation. The developed self-adjusting MPC is applied to three heating coils in a simulation. Compared with a PID controller, the self-adjusting MPC is able to increase the control quality up to 10%, while no manual tuning is needed. Additionally, the model predictive approach is able to reduce the power consumption of the pump by 80%.

Metamodels’ Development for High Pressure Die Casting of Aluminum Alloy

Simulation is a very useful tool in the design of the part and process conditions of high-pressure die casting (HPDC), due to the intrinsic complexity of this manufacturing process. Usually, physics-based models solved by finite element or finite volume methods are used, but their main drawback is the long calculation time. In order to apply optimization strategies in the design process or to implement online predictive systems, faster models are required. One solution is the use of surrogate models, also called metamodels or grey-box models. The novelty of the work presented here lies in the development of several metamodels for the HPDC process. These metamodels are based on a gradient boosting regressor technique and derived from a physics-based finite element model. The results show that the developed metamodels are able to predict with high accuracy the secondary dendrite arm spacing (SDAS) of the cast parts and, with good accuracy, the misrun risk and the shrinkage level. Results obtained in the predictions of microporosity and macroporosity, eutectic percentage, and grain density were less accurate. The metamodels were very fast (less than 1 s); therefore, they can be used for optimization activities or be integrated into online prediction systems for the HPDC industry. The case study corresponds to several parts of aluminum cast alloys, used in the automotive industry, manufactured by high-pressure die casting in a multicavity mold.

Detailed Thermodynamic Modeling of Multi-Zone Buildings with Resistive-Capacitive Method

Increased use of energy in buildings and HVAC systems requires advanced control schemes like model-based control to improve energy efficiency, which in turn requires accurate thermodynamic models of buildings. The Resistive-Capacitive (RC) method is a popular and versatile approach for thermal modeling of buildings. Despite this, it is not easy to find practical solutions of implementation of the RC method. It is the goal of this paper to clarify the RC method and demonstrate simple implementation of this method, especially for multi-zone buildings, which have more potential for energy savings from use of model-based control. This paper provides two contributions. First is a detailed explanation of the RC method, focusing on its use for developing a structure of a model and first-principles approach for estimation of parameters of a model. Second is a demonstration of an algorithm that enables automatic development of the structure of a model from basic information about a building (layout, construction elements) and its combination with data-based parameter estimation. Use of the algorithm is presented with a case-study on industrial multi-zone building, for which such a grey-box model is developed and analyzed. The resulting model is rapidly developed and used in a simulation with the measured data. The outputs of the model are compared with the measured temperatures and they show good fit.

Vibration based pavement roughness monitoring system using vehicle dynamics and smartphone with estimated vehicle parameters

Due to the high cost associated with pavement roughness monitoring, researches are going on to develop new techniques of pavement monitoring which are cost effective, frequent and easily implementable. Conventionally, pavement monitoring is performed using road profilers consisting of laser and inertial sensors. Though these profilers provide measurements of high accuracy, the high operating cost of these devices makes it difficult to ensure regular pavement monitoring. With the development of technology, new researches are being performed for the development of low-cost pavement monitoring systems using ordinary vehicle and smartphones. However, in most of the studies, the effect of vehicle suspension system on pavement monitoring was not considered and also direct reconstruction of pavement profile was not performed to compute the International Roughness Index (IRI), widely used for pavement roughness monitoring system. Instead, some correlation based procedures have been followed for measurement of pavement roughness. In this paper, a vibration based method for monitoring of pavement condition is introduced using ordinary vehicle and smartphone as vibration sensors which includes calibration for vehicle suspension system. The whole process can be divided into two stages. The unknown dynamic parameters of the ordinary vehicle are identified first. The vehicle is driven over a speed bump of known dimension and vehicle vertical acceleration is recorded. State-space representation of the vehicle model with unknown parameters is performed and the parameters are estimated using Grey-Box model system identification technique. Secondly, a new pavement profile reconstruction technique is proposed based on inverse formulation of vehicle dynamics. The vertical acceleration of the vehicle with known parameters are collected by driving it over the pavement, the condition of which needs to be monitored. A new mathematical formulation of vehicle dynamics is developed and using the collected acceleration data, pavement profile is reconstructed. Further, International Roughness Index of the reconstructed pavement is calculated. Numerical simulations and field testing of the proposed method are performed for various pavement roughness conditions and vehicle speeds performed for determining its viability for pavement condition monitoring.

Artificial neural network grey-box model for design and optimization of 50 MWe-scale combined supercritical CO2 Brayton cycle-ORC coal-fired power plant

Supercritical CO2 (sCO2) Brayton cycle is a promising technology for coal-fired power generation with high efficiency and compact equipment size. However, its sophisticated construct and high-temperature waste heat rejection require a systematic design to maximize its performance. Herein, we develop a combined sCO2 Brayton cycle-organic Rankine cycle (ORC) design for coal-fired power plant. A novel glass-box model that considers the specific designs of sCO2 boiler, recuperators, coolers, and turbomachinery is formulated to optimize the power plant. A high-accuracy artificial neural network model is also developed to estimate the system’s pressure drop to reduce model complexity. As a result, the glass-box model is reformulated into a grey-box model. The model is applied to three different combined cycles’ design problem to evaluate their performance. Result shows that the grey-box model saves more than 50% of CPU time. With the turbine inlet at 620 °C/25 MPa and the main compressor inlet at 35 °C/7.38 MPa, the proposed combined cycle reaches a thermal efficiency of 45.73%, thereby achieving a 2.75 percentage point improvement compared with the standalone design. Sensitivity analysis is also carried out to evaluate the effects of ORC working fluid, flue gas temperature at the cooling wall outlet, main compressor inlet pressure, and evaporating temperature of ORC, on the system’s performance.

Grey-box modeling and hypothesis testing of functional near-infrared spectroscopy-based cerebrovascular reactivity to anodal high-definition tDCS in healthy humans

Transcranial direct current stimulation (tDCS) has been shown to evoke hemodynamics response; however, the mechanisms have not been investigated systematically using systems biology approaches. Our study presents a grey-box linear model that was developed from a physiologically detailed multi-compartmental neurovascular unit model consisting of the vascular smooth muscle, perivascular space, synaptic space, and astrocyte glial cell. Then, model linearization was performed on the physiologically detailed nonlinear model to find appropriate complexity (Akaike information criterion) to fit functional near-infrared spectroscopy (fNIRS) based measure of blood volume changes, called cerebrovascular reactivity (CVR), to high-definition (HD) tDCS. The grey-box linear model was applied on the fNIRS-based CVR during the first 150 seconds of anodal HD-tDCS in eleven healthy humans. The grey-box linear models for each of the four nested pathways starting from tDCS scalp current density that perturbed synaptic potassium released from active neurons for Pathway 1, astrocytic transmembrane current for Pathway 2, perivascular potassium concentration for Pathway 3, and voltage-gated ion channel current on the smooth muscle cell for Pathway 4 were fitted to the total hemoglobin concentration (tHb) changes from optodes in the vicinity of 4x1 HD-tDCS electrodes as well as on the contralateral sensorimotor cortex. We found that the tDCS perturbation Pathway 3 presented the least mean square error (MSE, median <2.5%) and the lowest Akaike information criterion (AIC, median -1.726) from the individual grey-box linear model fitting at the targeted-region. Then, minimal realization transfer function with reduced-order approximations of the grey-box model pathways was fitted to the ensemble average tHb time series. Again, Pathway 3 with nine poles and two zeros (all free parameters), provided the best Goodness of Fit of 0.0078 for Chi-Square difference test of nested pathways. Therefore, our study provided a systems biology approach to investigate the initial transient hemodynamic response to tDCS based on fNIRS tHb data. Future studies need to investigate the steady-state responses, including steady-state oscillations found to be driven by calcium dynamics, where transcranial alternating current stimulation may provide frequency-dependent physiological entrainment for system identification. We postulate that such a mechanistic understanding from system identification of the hemodynamics response to transcranial electrical stimulation can facilitate adequate delivery of the current density to the neurovascular tissue under simultaneous portable imaging in various cerebrovascular diseases.

Machine learning based digital twin for stochastic nonlinear multi-degree of freedom dynamical system

The potential of digital twin technology is immense, specifically in the infrastructure, aerospace, and automotive sector. However, practical implementation of this technology is not at an expected speed, specifically because of lack of application-specific details. In this paper, we propose a novel digital twin framework for stochastic nonlinear multi-degree of freedom (MDOF) dynamical systems. The proposed digital twin has four modules — (a) a physics-based nominal model, (b) a data collection module, (c) algorithm for real-time update of the digital twin and (d) module for predicting future state. The modules for real-time update and prediction are based on the so-called gray-box modeling approach, and utilizes both physics based and data driven frameworks; this enables the proposed digital twin to generalize and predict future responses. The gray box modeling framework used within the digital twin is developed by coupling Bayesian filtering and machine learning algorithm. Although, the proposed digital twin can be used with any machine learning regression algorithm, we have used Gaussian process in this study. Performance of the proposed approach is illustrated using two examples. Results obtained indicate the applicability and excellent performance of the proposed digital twin framework.