Grey-box Model Research Articles

An approach to characterize Lorentz force transfer function for superconducting cavities

Superconducting radio-frequency (SRF) cavities are preferred in many modern accelerator facilities to reduce the operation cost of the RF power systems. SC cavities are usually sensitive to small mechanical perturbations because of their narrow bandwidth. These perturbations such as microphonics and Lorentz force detuning (LFD) can significantly detune the SRF cavity and therefore not only deteriorate the cavity field stabilities but also increase the RF power requirements. Piezo-electric actuators are widely adopted to suppress the cavity detuning caused by LFD and microphonics. Many advanced detuning compensation strategies were proposed to suppress the microphonics and LFD in recent years. The dynamic models of the LFD and piezo actuator are essential in these activities. Generally, the models of LFD can be identified by modulating the cavity field with sinusoidal signals and then measuring the corresponding steady-state amplitude and phase response of the cavity. However, for some SRF cavities, the cavity field may becomes unstable because of the presence of the ponderomotive effects, leading to a unacceptable measurement result. We present a new approach to identify the dominant modes of the LFD model based on a grey-box models estimation method. The validity of the approach was demonstrated by comparing the model output and measurement results on SRF cavities of real accelerator facilities.

A data-driven approach to simultaneous fault detection and diagnosis in data centers

The failure of cooling systems in data centers (DCs) leads to higher indoor temperatures, causing crucial electronic devices to fail, and produces a significant economic loss. To circumvent this issue, fault detection and diagnosis (FDD) algorithms and associated control strategies can be applied to detect, diagnose, and isolate faults. Existing methods that apply FDD to DC cooling systems are designed to successfully overcome individually occurring faults but have difficulty in handling simultaneous faults. These methods either require expensive measurements or those made over a wide range of conditions to develop training models, which can be time-consuming and costly. We develop a rapid and accurate, single and multiple FDD strategy for a DC with a row-based cooling system using data-driven fault classifiers informed by a gray-box temperature prediction model. The gray-box model provides thermal maps of the DC airspace for single as well as a few simultaneous failure conditions, which are used as inputs for two different data-driven classifiers, CNN and RNN, to rapidly predict multiple simultaneous failures. The model is validated with testing data from an experimental DC. Also, the effect of adding Gaussian white noise to training data is discussed and observed that even with low noisy environment, the FDD strategy can diagnose multiple faults with accuracy as high as 100% while requiring relatively few simultaneous fault training data samples. Finally, the different classifiers are compared in terms of accuracy, confusion matrix, precision, recall and F1-score.

Derivation and validation of gray-box models to estimate noninvasive in-vivo percentage glycated hemoglobin using digital volume pulse waveform

Glycated hemoglobin and blood oxygenation are the two most important factors for monitoring a patient’s average blood glucose and blood oxygen levels. Digital volume pulse acquisition is a convenient method, even for a person with no previous training or experience, can be utilized to estimate the two abovementioned physiological parameters. The physiological basis assumptions are utilized to develop two-finger models for estimating the percent glycated hemoglobin and blood oxygenation levels. The first model consists of a blood-vessel-only hypothesis, whereas the second model is based on a whole-finger model system. The two gray-box systems were validated on diabetic and nondiabetic patients. The mean absolute errors for the percent glycated hemoglobin (%HbA1c) and percent oxygen saturation (%SpO2) were 0.375 and 1.676 for the blood-vessel model and 0.271 and 1.395 for the whole-finger model, respectively. The repeatability analysis indicated that these models resulted in a mean percent coefficient of variation (%CV) of 2.08% and 1.74% for %HbA1c and 0.54% and 0.49% for %SpO2 in the respective models. Herein, both models exhibited similar performances (HbA1c estimation Pearson’s R values were 0.92 and 0.96, respectively), despite the model assumptions differing greatly. The bias values in the Bland–Altman analysis for both models were – 0.03 ± 0.458 and – 0.063 ± 0.326 for HbA1c estimation, and 0.178 ± 2.002 and – 0.246 ± 1.69 for SpO2 estimation, respectively. Both models have a very high potential for use in real-world scenarios. The whole-finger model with a lower standard deviation in bias and higher Pearson’s R value performs better in terms of higher precision and accuracy than the blood-vessel model.

Feature assessment frameworks to evaluate reduced-order grey-box building energy models

With a drive towards achieving an integrated energy system, there is a need for holistic and scalable building modelling approaches for the commercial building stock. Existing grey-box modelling approaches often fail to produce a generalised network structure, which limits the suitability of models for different applications. Furthermore, existing feature assessment frameworks provide limited opportunities to quantify the potential of model characteristics in terms of flexibility, scalability and interoperability. Considering the diversity of the possible characterisation approaches, this study aims to define and assess a set of basic and derived features for reduced-order grey-box models through a generalisable framework that would act as a decision support tool for the identification of appropriate model characteristics. This research proposes an integrated methodology to test and evaluate model features, namely, scalability, flexibility, and interoperability for reduced-order grey-box models and formulates test-cases with the available commercial reference buildings published by the Department of Energy of the United States. The model scalability errors lie between 3.42% and 4.35% that indicates the suitability of implementing a zone level model for model predictions at the whole building level. The model flexibility error decreased from 5.73% to 4.78% when considering a trade-off between accuracy and complexity. These frameworks produce scalable and flexible models that facilitate urban energy modelling of building stocks and subsequent evaluation of retrofit strategies. Furthermore, the devised models aid the implementation of heat demand reduction scenarios in a building cluster to achieve an integrated energy system.

A novel structural safety assessment method of large liquid tank based on the belief rule base and finite element method

The structural safety assessment of large liquid tanks (LLT) has attracted an extensive attention. As a typical gray box model, the belief rule base (BRB) model can handle qualitative information and quantitative data simultaneously, which is a suitable modeling tool for structural safety assessment. However, it is difficult to establish and train the BRB model when there is a lack of expert experience and fault samples of LLT. Therefore, a novel safety assessment model for LLT based on BRB and finite element method (FEM-BRB) is proposed in this paper. The FEM is introduced to construct the BRB model by combining expert knowledge and industry standards for the first time, which can effectively compensate for the lack of expert experience. The fault samples are generated in the mechanism simulation model under different working conditions. Based on the fault samples generated by the FEM and historical samples, the projection covariance matrix adaption evolution strategy (P-CMA-ES) optimization algorithm is then used to train the model, which further improves the structural safety assessment accuracy when lacking fault samples. A case study of three actual oil tanks in a coastal port is conducted to illustrate the effectiveness and advantage of the developed structural safety assessment method.

Mechanistic Grey-Box Modeling of a Packed-Bed Regenerator for Industrial Applications

Thermal energy storage is essential to compensate for energy peaks and troughs of renewable energy sources. However, to implement this storage in new or existing industries, robust and accurate component models are required. This work examines the development of a mechanistic grey-box model for a sensible thermal energy storage, a packed-bed regenerator. The mechanistic grey-box model consists of physical relations/equations and uses experimental data to optimize specific parameters of these equations. Using this approach, a basic model and two models with extensions I and II, which vary in their number from Equations (3) to (5) and parameters (3 to 6) to be fitted, are proposed. The three models’ results are analyzed and compared to existing models of the regenerator, a data-driven and a purely physical model. The results show that all developed grey-box models can extrapolate and approximate the physical behavior of the regenerator well. In particular, the extended model II shows excellent performance. While the existing data-driven model lacks robustness and the purely physical model lacks accuracy, the hybrid grey-box models do not show significant disadvantages. Compared to the data-driven and physical model, the grey-box models especially stands out due to their high accuracy, low computational effort, and high robustness.

Simulation and optimal control of heating and cooling systems: A case study of a commercial building

This paper proposes a novel energy conservation measure that optimizes the planning of heating and cooling systems for tertiary sector buildings. It consists of a model-based predictive control approach that employs a grey-box model built from the building and weather data that predicts the building heat load and indoor temperature. Different from classical optimization approaches where the discretized differential algebraic equations are integrated into the optimization formulation, our model is calibrated using black-box multiobjective optimization, which allows for decoupling the predictive model from the optimization problem, thus having more flexibility and reducing the total computational time. Moreover, rather than requiring the angle of solar radiation, solar orientation and solar masks to calculate the radiation data, our approach requires only a simple model of the solar irradiance. The calibrated model is then used by heating and cooling optimization strategies that aim at reducing the energy consumption of the building in the next day while satisfying the indoor thermal constraints. The proposed approach was applied in a case study of a commercial building during heating and cooling seasons and the results show that it was able to yield up to 12% of energy savings while having a mean power forecast error of 8%.

Sum-of-delay models for pressure control in Water Distribution Networks

Service pressure control is a powerful tool to reduce leakage and risk of pipe bursts in Water Distribution Networks (WDNs). However, to obtain good control performances, it is essential to rely on a good model of the plant. A typical approach consists of the identification of a linear, local model of the system around the desired working point. Previous works relied on black-box, high order models to demonstrate that WDNs are characterised by a very complex dynamic behaviour, which should be properly modelled to avoid stability issues resulting from poor regulator design. This work aims at providing a physical justification for such complex dynamic behaviour, by means of a particular grey-box model structure, with pure delays as its fundamental blocks. Moreover, this works demonstrates that the new model structure can be very effective and efficient in modelling the WDN dynamics. Finally, to proper exploit the new model, this work proposes a bi-objective optimisation based procedure for the regulator design. The potentialities of both model identification and regulator design phases are assessed by means of simulated experiments performed on a detailed unsteady flow model of three different WDNs.

Exergic Analysis of an ISCC System for Power Generation and Refrigeration

Exergic analysis has become an effective method of thermodynamic behavior evaluation for power systems. The current study focuses on an integrated solar–gas combined cycle (ISCC) system for electric power generation and refrigeration. Exergic analysis of the ISCC system is conducted by using the gray-box model as well as the Ebsilon software. The results show that under the rated working condition, the total exergy loss and overall exergy efficiency of the ISCC system are 119.078 MW and 44.63 %. The two largest exergy losses exist in the combustion chamber and solar DSG system, which are 56.45 MW and 28.52 MW, respectively. The LiBr–H2O absorption chiller system, HRSG, steam turbine and condenser have the same grade exergy losses. When the solar intensity augments, though the solar DSG system has an increase in the exergy efficiency, its exergy loss also increases, leading to the increase in the total exergy loss as well as the decrease in the overall exergy efficiency of the ISCC system. Therefore, further optimizations of the ISCC system should focus on the improvements of the solar DSG system and combustion chamber. The economic and ecological evaluations demonstrate that the ISCC system is economically feasible and ecologically friendly.

Experimental and numerical validation of a proportional solenoid valve based on the data-driven model

Solenoid valves are widely used in mechatronics, robotic systems and industrial occasions. An accurate model is very important for the design and control of a solenoid valve. The dynamical model of the solenoid valve is difficult to obtain due to the complexity of the structure and the interaction of multiple physical fields. This paper proposes two kinds of model of solenoid valve: grey box model and black box model, on the basis of experimental data. ARX model is selected as the basic structure of the grey box model. After clustering the data with the fuzzy c-means algorithm, the overall experimental data is divided into several local linear sub-models, and the model coefficients of the local linear model are obtained by partial least square regression. The overall expression of the model is obtained by combining the local sub-models with membership degree. For the black box model, support vector regression algorithm is used to identify. On the basis of selecting the appropriate parameters, we obtain the black box model of solenoid valve based on data. For the above two models, we carry out experimental verification and error analysis, and compare with the traditional modelling method. According to the results, it can be seen that on the basis of the experimental data, using the data-driven method to construct the model has many advantages, avoiding complex physical analysis, and has high accuracy. The model with high precision will be used in the accurate control and observing estimation of the solenoid valve.

Grid Resilience Enhancement by Reference Shaping based on Gray-Box Model

Grid Resilience Enhancement by Reference Shaping based on Gray-Box Model

Analysis of gray Box Modelling of Transformers,

Calculation of power system transients involving transformers require models that incorporate capacitive behavior. The paper outlines how classical low-frequency transformer models can be extended with capacitances and how to fit the parameters based on typical values, test report and frequency response measurements. Justified tuning factors are proposed. The responses of the models are compared to measurements in frequency domain, and with detailed black-box models in studies of transient recovery voltage and lightning. The models show reasonable agreement including the first resonance point, but with too low damping without proper adjustments.

Enhancing energy efficiency and comfort in buildings through model predictive control for dynamic façades with electrochromic glazing

Reducing building energy consumption while ensuring indoor comfort conditions is driving the building envelope transition from static to responsive . In this context, electrochromic windows represent a promising solution to manage optical and thermal requirements in response to changing boundary conditions or user requirements, and control strategies play a central role in the exploitation of this technology. The present paper proposes a Hybrid Model Predictive Control strategy for the online operation optimization of an electrochromic-based active façade . The controller was implemented and tested on a simulated case study. This was achieved by co-simulating the optimal controller which used reduced data-driven grey-box model, with a high accuracy white-box physical model. This setup enabled to close the control loop and to perform an accurate performance benchmarking. Results showed that the proposed Hybrid Model Predictive Control strategy outperformed two baseline Rule Based Controllers, reducing simultaneously energy consumption, peak power and percentage of discomfort hours by up to 82%, 71% and 51% respectively. In comparison with the two baseline controllers and considering all the scenarios, the overall energy consumption could be reduced by approximately 40%–60% on average. In addition the work demonstrates how tuning the Hybrid Model Predictive Control weights adds flexibility to the controller, significantly changing its behaviour to meet the requirements of the designer. • A test cell equipped with a switchable electrochromic window was modelled. • A grey-box model of the zone and window was developed and calibrated. • A Hybrid Model Predictive Control strategy was formulated for the window control. • A comprehensive controller performance benchmarking was performed.

Machine Learning Driven Prediction of Residual Stresses for the Shot Peening Process Using a Finite Element Based Grey-Box Model Approach

The shot peening process is a common procedure to enhance fatigue strength on load-bearing components in the metal processing environment. The determination of optimal process parameters is often carried out by costly practical experiments. An efficient method to predict the resulting residual stress profile using different parameters is finite element analysis. However, it is not possible to include all influencing factors of the materials’ physical behavior and the process conditions in a reasonable simulation. Therefore, data-driven models in combination with experimental data tend to generate a significant advantage for the accuracy of the resulting process model. For this reason, this paper describes the development of a grey-box model, using a two-dimensional geometry finite element modeling approach. Based on this model, a Python framework was developed, which is capable of predicting residual stresses for common shot peening scenarios. This white-box-based model serves as an initial state for the machine learning technique introduced in this work. The resulting algorithm is able to add input data from practical residual stress experiments by adapting the initial model, resulting in a steady increase of accuracy. To demonstrate the practical usage, a corresponding Graphical User Interface capable of recommending shot peening parameters based on user-required residual stresses was developed.

Quantification of deviations between grey-box and constant efficiency modeling and optimization of trigeneration systems using a data-driven RMSD indicator

Optimization of energy systems witnessed the use of simple (constant efficiency) equipment models. Alternatively, grey-box (variable efficiency with part load) models were used to simulate a more real behavior of such systems. However, limited attention was given to deviations due to part load effect in planning, sizing, scheduling and sensitivity analyses. This paper provides a quantified methodology to reflect such deviations and to show to what extent simple model is valid. A detailed comparison between both models is developed by optimizing a trigeneration system to find its configuration, rated capacities, operating schedule and sensitivity to prices. A data-driven comparative criterion -root mean square deviation- is developed to compare models. It depends on deviations in combined efficiency that is based on four key performance energy, economy, environment and exergy indicators in addition to economic parameters being the decision attributes. Results show that the deviations in the combined efficiency; net present value; payback period; and internal rate of return are 40.45%; −71.26%; 30.37%; and −24.30% respectively, leading to an overall root mean square deviation of 45.35%. Simple model approach is valid to be used in the planning phase only. However, the grey-box model is the way forward for optimization of polygeneration systems.

A data driven method for optimal sensor placement in multi-zone buildings

In this paper, we propose a data-driven methodology to identify the optimal placement of sensors in a multi-zone building. The proposed methodology is based on statistical tests that study the (in) dependence of measurements from various available sensors. The tests advice on a set of most dissimilar sensors to be retained, as they would convey the maximum information. The method starts with an initial setup that can provide measurements of every building zone to carry out this study; any of these sensors can be removed eventually to decrease costs in normal operation. The method has the advantages of being purely data driven and computationally efficient, as against several methods proposed in the scientific literature, that operate under the premise that detailed building models are available, to evaluate the number/position of the required sensors. This property makes the method scale to different buildings, in an expert free manner. The methodology can help towards better characterization of a building for optimal control and monitoring applications. It is validated against a widely used method – Kalman filtering with Grey-box models, using two different case studies. In both cases, the proposed approach agrees with the results using grey box models, suggesting that the method is reliable, while being quick and efficient.

Grey-box models for wave loading prediction

The quantification of wave loading on offshore structures and components is a crucial element in the assessment of their useful remaining life. In many applications the well-known Morison’s equation is employed to estimate the forcing from waves with assumed particle velocities and accelerations. This paper develops a grey-box modelling approach to improve the predictions of the force on structural members. A grey-box model intends to exploit the enhanced predictive capabilities of data-based modelling whilst retaining physical insight into the behaviour of the system; in the context of the work carried out here, this can be considered as physics-informed machine learning. There are a number of possible approaches to establish a grey-box model. This paper demonstrates two means of combining physics (white box) and data-based (black box) components; one where the model is a simple summation of the two components, the second where the white-box prediction is fed into the black box as an additional input. Here Morison’s equation is used as the physics-based component in combination with a data-based Gaussian process NARX – a dynamic variant of the more well-known Gaussian process regression. Two key challenges with employing the GP-NARX formulation that are addressed here are the selection of appropriate lag terms and the proper treatment of uncertainty propagation within the dynamic GP. The best performing grey-box model, the residual modelling GP-NARX, was able to achieve a 29.13% and 5.48% relative reduction in NMSE over Morison’s Equation and a black-box GP-NARX respectively, alongside significant benefits in extrapolative capabilities of the model, in circumstances of low dataset coverage.

Synchronized Motion Profiles for Inverse-Dynamics-Based Online Control of Three Inextensible Segments of Trunk-Type Robot Actuators

This study proposes a novel method for the positioning and spatial orientation control of three inextensible segments of trunk-type robots. The suggested algorithm imposes a soft constraint assumption for the end-effector’s endpoint and a mandatory constraint on its direction. Simultaneously, the algorithm by-design enforces nonholonomic features on the robot segments in the form of arcs. An approximate robot spine curve is the key to the final robot state configuration based on the given conditions. The numeric simulation showed acceptable (less than 1 s) performance for single-core processing tasks. The parametric method finds the best proximate robot state solution and represents the gray box model in addition to existing learning or black-box inverse dynamics approaches. This study also shows that a multiple inverse kinematics answer constructs a single inverse dynamics solution that defines the robot actuators’ motion profiles, synchronized in time. Finally, this text presents rotational expressions and their outlines for controlling the manipulator’s tendons.

A Vision for Leveraging the Concept of Digital Twins to Support the Provision of Personalized Cancer Care

Exploring the opportunity for applying digital twins in the healthcare context is an emerging research area that has the potential to support more personalized care. A recognized aspect in cancer care is the need for more personalized treatment planning to complement the recent advances in precision medicine. In this article, we present a classification of digital twins into Grey Box, Surrogate, and Black Box models using systems and mathematical modeling theory. We then explore one possible approach, namely a Black Box classification for incorporating the use of digital twins in the context of personalized uterine cancer care. This article presents one of the first attempts to use digital twins in this capacity and represents an amalgamation of three key domains: clinical, digital health, and computer science, respectively.

Virtual metering of heat supplied by zone-level perimeter heaters: An investigation with three inverse modelling approaches

Virtual metering at the equipment level provides a non-intrusive tool to understand energy flows in commercial buildings and monitor building energy performance. The accuracy of virtual meters depends on the modelling approach and its ability to capture the underlying physical processes. This paper presents a novel comparison and provides guidance for the selection of inverse modelling approaches used to create virtual meters to estimate the heat supplied by zone-level hydronic perimeter heaters. The approaches investigated are: steady-state inverse greybox modelling, transient inverse greybox modelling, and water-side load disaggregation. Models that represent these three approaches are trained using data from a highly instrumented academic building in Ottawa, Canada. Model parameters are identified using the genetic algorithm and used in creating virtual meters that can estimate the heat added by perimeter heaters into building variable air volume zones. The accuracy of these virtual meters is assessed by comparing them to physical meters installed in these zones. The results indicate that the three modelling approaches can estimate the daily heating energy supplied by perimeter heaters at a normalized root-mean-square error between 16% and 18%. However, the accuracy of the virtual meters declines as the number of zones increases. The performance of the three modelling approaches is evaluated through illustrative examples that compare modelling assumptions, data requirements, data processing, and model prediction accuracy.