Grey-box Identification Research Articles

Evaluation Method of Comprehensive Ability of Students Majoring in Preschool Education Based on Computer Technology

In order to improve the comprehensive ability evaluation effect of students majoring in preschool education, this paper combines computer technology to evaluate the comprehensive ability of students majoring in preschool education. Through linearization, this paper deduces the state space model of data load of students’ comprehensive ability and the transfer function model of student’s comprehensive ability data load. Moreover, this paper establishes an analytical expression between the model coefficients of the transfer function of student’s comprehensive ability data load and the transfer parameters of student’s comprehensive ability data load. In addition, this paper analyzes and selects the identification method of the parameters of students’ comprehensive ability data load model. Since the parameters of the student comprehensive ability data load model have physical meanings, the parameter identification of the student comprehensive ability data load model is a gray box identification, and constraints are required when identifying the parameters of the student comprehensive ability data load model. The experimental study has verified that the comprehensive ability evaluation model of students majoring in preschool education based on computer technology can play an important role in the comprehensive ability evaluation of students majoring in preschool education. This article adopts the comprehensive load model in the Comprehensive Stability Calculation Program (PSASP) to eliminate the shortcomings of factor analysis in traditional teaching comprehensive evaluation, and has a certain reference value for the promotion of intelligent teaching in the future.

Multi-objective optimal input design for grey-box identification modelling of ship manoeuvring motion

ABSTRACT Grey-box modelling has been widely used to predict the ship manoeuvring motion. In order to design input signals for the grey-box model of ship manoeuvring motion, a multi-objective optimal input design (MOID) method is proposed in this paper. In the proposed method, the MOID is regarded as a multi-objective optimization problem (MOP), where both of D-optimality criterion and condition number are taken as two-objective functions to improve the accuracy and robustness of identifying the grey-box model. The correlation factor is also presented as a constraint for reducing the parameter drift. The MOP is solved by the non-dominated sorting genetic algorithm-II (NSGA-II) with a constraint handling technique. The technique for order preference by similarity to an ideal solution (TOPSIS) is also adopted to screen out an optimal solution from the Pareto solutions. The effectiveness of MOID signals is validated by Monte Carlo analysis and grey-box identification of the MMG model.

AI-Aristotle: A physics-informed framework for systems biology gray-box identification.

Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework-named AI-Aristotle-combines the eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility, and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. To test the performance of AI-Aristotle, we use sparse synthetic data perturbed by uniformly distributed noise. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.

Identification of the friction model of a single elastic robot actuator from video

Obtaining a highly accurate dynamic model from video data is a challenging task within system Identification. More specifically, in robotics, there is a constant need for precise models to optimize the performance and safety of these systems. With the developments in machine learning, algorithms such as convolutional neural networks (CNNs) have shown good performances in extracting features from images. Techniques like transfer learning (TL) can lower the computational cost and optimize the training task. This work aims to make the gray-box Identification of friction parameters of an actuator from video. The proposed approach is composed of three steps. Firstly, it compares the transfer learning performance of three pre-trained CNNs to estimate the pose of the motor and the link from video data. Secondly, a long-term short-term (LSTM) network is added to estimate the velocity and acceleration. Thirdly, the parameters of the two friction models are estimated using the estimated states and the dynamic equations of the system. Through these steps, a vision-based gray-box Identification is obtained. The approach is tested using an original elastomer-based series of elastic actuators (eSEA) benchmark. The results show that the VGG19 model combined with the LSTM layer is the optimal pre-trained CNN for the vision module, obtaining a coefficient of determination higher than 0.96 for all three states. From the state estimates, the parameters of the friction models are optimized. The best-performing friction model is the Coulomb-Stribeck, which decreases the mean absolute error (MAE) by 15.50% compared to the viscous linear model.

Multi-physical Modeling of Launcher Electromechanical Actuators Accounting for Production Variability and Thermal Effects

Abstract With the trend towards reusable launchers, there is a need to develop health monitoring systems for electromechanical actuators (EMAs) performing nozzle orientation. To tune such a health monitoring system (HMS), data sets reproducing EMA operation in healthy and faulty modes are needed. Besides, effect of production variability and thermal dependency should also be accounted for. In this paper, a systematic approach to determine an EMA model from which appropriate data sets can be generated is presented. The focus is on mechanical faults such as high friction level that may lead to jamming and excessive backlash. From available experimental data sets recorded on a fleet of EMA, grey box identification is used to estimate the friction parameters including their confidence level for the different EMAs. Production variability is then characterized by showing that each parameter estimate is represented by a Gaussian distribution at a given temperature. Next thermal effects are accounted for through a Gaussian Process characterizing parameter variability w.r.t. temperature. Validation of the model is finally performed with EMA healthy operation data.

Grey-box model and neural network disturbance predictor identification for economic MPC in building energy systems

This paper presents a novel model identification procedure to treat the occupancy induced unmeasured heat disturbance in the building model identification step for a model predictive control (MPC) implementation. First, we present a grey-box identification framework to estimate a dynamic building model that systematically accounts for the large unmeasured disturbance in the training data. Then, we discuss an approach to compute the confidence intervals (CIs) on the parameters estimated in the building model. Next, we develop a framework to identify a neural network (NN) using historical operational data to give the feedforward predictions of the heat disturbance in the MPC optimization problem. Further, we discuss the application of the composite building model and the NN disturbance predictor for energy cost optimization using an economic MPC formulation. We present case studies using a simple two time scale based building model, and demonstrate the effectiveness of the proposed grey-box model and the NN disturbance predictor identification procedures. We perform closed-loop simulations to highlight that additional energy cost savings of up to 4–5% are provided by including the feedforward NN disturbance predictions in the MPC controller. Finally, we also demonstrate the suitability of the proposed two-step model identification procedure to estimate accurate and reliable models using an industrial data set collected from a real office building.

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning.

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler-Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to "physics-informed" gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

Grey-box identification modeling of ship maneuvering motion based on LS-SVM

The establishment of a high precision ship motion model is helpful to predict the motion of ships in a short time, and improve the safety and stability of marine operations. Determining the parameters is the key to ensuring the accuracy of the model. In this paper, a 4-DOF grey-box model of ship maneuvering motion is established based on the MMG model. Combined with the training datasets obtained from the designed tests, the least square support vector machine (LS-SVM) method is used to identify the parameters in the grey-box model. It is verified that the model has good applicability in a clean system by comparing the results. Three different levels of noise are applied to the training datasets to simulate the system measurement errors, and the prediction accuracies of three ship test cases at different levels of disturbance are analyzed by calculating RMSE and MAPE. The results show that the model established by the grey-box identification modeling method has good validity and robustness under disturbance, and can provide a certain degree of reliable support for ship motion prediction.

Hybrid control of electrohydrodynamic 3D printer cone jet

In this article, the control of an electrohydrodynamic 3D printer is studied. The proposed controller has a hybrid piecewise linear feedback form which is designed based on a hybrid model of the printer. The hybrid model is obtained via a gray box identification process whose structure is proposed utilizing the results of the finite element simulation of the printer within the COMSOL Multiphysics software. The asymptotic stability of the hybrid control combined with a hybrid observer is proven using the Lyapunov theory. In addition, the obtained control is applied to the finite element model of the printer to check its performance which shows the success of the controlled system in tracking the reference height for the printer jet cone.

Modeling and Gray-Box Identification Applied to a Flow Rate Control Valve

Modeling and Gray-Box Identification Applied to a Flow Rate Control Valve

Parameter identification of ship motion mathematical model based on full-scale trial data

Using the full-scale trial data of vessel YUKUN, a parameter identification scheme, Support Vector Regression (SVR) combined with modified grey wolf optimizer (MGWO), is proposed for identifying ship motion model. This study establishes response mathematical model and 4 Degrees of Freedom (DOF) nonlinear whole-ship mathematical model of vessel YUKUN. The full-scale trial data of vessel YUKUN are processed and analyzed. In the study of grey box identification modeling, the rough parameters reference values of ship response mathematical model and nonlinear whole-ship mathematical model are obtained by SVR. Based on these rough reference values, the MGWO algorithm and Firefly Algorithm are used to further optimize them to obtain final parameter identification values. The final parameter identification values obtained by the three algorithms and recursive least squares with forgetting factor are substituted into the mathematical model to obtain the prediction results of ship motion state. The final prediction results of ship motion state show that the MGWO algorithm has strong search and optimization ability. In the case that the reference values obtained by SVR are not accurate, MGWO algorithm can be used to find accurate parameters of ship motion mathematical model in a given range. The proposed scheme provides a reference for the parameter identification of ship motion mathematical model.

Developing an operating instruction to attenuate pressure stress during fuel shortage events of a power boiler based on dynamic modelling

Stress control of boilers is a major concern in the aged power plants. The studied forced circulation boiler suffers from a malfunction of the combustion control system. In order to reduce cyclic stress on boiler equipment and prevent undesirable shutdowns of power unit during fuel shortage events, an operating instruction is proposed. In order to predict dynamic behavior of the boiler, a nonlinear state space model is developed using mathematical modelling approach. A gray box identification procedure is introduced using only steady state measurements of plant. The dynamic model is verified compared to actual plant data and accuracy of model parameters is evaluated by sigma-normalized sensitivity analysis. Considering aim of steam pressure regulation, a three-step optimization approach is proposed based on golden section search, parabolic interpolation and interior-point methods to optimize arbitrary parameters of the proposed manual control scheme. Simulation results for different loads and various fuel limitation scenarios show that proposed instruction improves the cyclic stress in superheater tubes at least 84.5%. In addition, Monte Carlo experiments illustrate despite a 10% operators’ error in implement of the instruction, the stress is still reduced by an average of 78.1% for a given case.

A gray-box harmonic resonance frequency identification method of multiple-inverter-fed power system oriented to system designers

This paper presents a gray-box harmonic resonance frequency identification method of multiple-inverter-fed power system, which enables modal analysis oriented to system designers based on only frequency response data provided by diverse vendors or measured by frequency scanning. First, admittance transfer functions of all grid-connected inverters (GCIs) are fitted using Matrix Pencil Method-Vector Fitting (MPM-VF) combined method. Then, node admittance matrix (NAM) is formed according to the topology of whole system. Finally, harmonic resonance frequency along with changes in number of GCIs are identified by NAM-based modal analysis (MA). The proposed gray-box identification method is implemented in a typical multiple-inverter-fed power system. The correctness of harmonic resonance frequency identification results and the effectiveness of the presented method are verified by simulation results obtained in Matlab/Simulink platform and OPAL-RT digital real-time simulation platform. Based on the identification results, a more stable and better power quality multiple-inverter-fed power system can be built by system designers though avoiding the appearance of harmonic sources with corresponding resonance frequency.

Grey-box model calibration and validation for a continuous horizontal fluidized bed dryer

Fully continuous drying can improve the production flexibility and throughput of tablets manufactured by wet granulation lines. A recently developed prototype incorporates a screw conveyor to a horizontal fluidized bed dryer for pharmaceutical particles. Research on advanced process control strategies led to the publication of a two-phase tanks-in-series framework to describe its dynamics. This paper calibrates the model to replicate the prototype behavior. A grey-box identification methodology estimates the empirical and uncertain parameters using experimental input-output data. The underlying assumptions are cross-validated with time-domain comparisons, output root mean square errors and confidence intervals. Results show that the model reproduces the observed trends in general and the discrepancies result from mechanical issues on the equipment.

Performance Assessment of an Electric Power Steering System for Driverless Formula Student Vehicles

In the context of automated driving, Electric Power Steering (EPS) systems represent an enabling technology. They introduce the ergonomic function of reducing the physical effort required by the driver during the steering maneuver. Furthermore, EPS gives the possibility of high precision control of the steering system, thus paving the way to autonomous driving capability. In this context, the present work presents a performance assessment of an EPS system designed for a full-electric all-wheel-drive electric prototype racing in Formula Student Driverless (FSD) competitions. Specifically, the system is based on the linear actuation of the steering rack by using a ball screw. The screw nut is rotated through a belt transmission driven by a brushless DC motor. Modeling and motion control techniques for this system are presented. Moreover, the numerical model is tuned through a grey-box identification approach. Finally, the performance of the proposed EPS system is tested experimentally on the vehicle through both sine-sweep profiles and co-simulated driverless sessions. The system performance is assessed in terms of reference tracking capability, thus showing favorable results for the proposed actuation solution.

From SIR to SEAIRD: A novel data-driven modeling approach based on the Grey-box System Theory to predict the dynamics of COVID-19.

Common compartmental modeling for COVID-19 is based on a priori knowledge and numerous assumptions. Additionally, they do not systematically incorporate asymptomatic cases. Our study aimed at providing a framework for data-driven approaches, by leveraging the strengths of the grey-box system theory or grey-box identification, known for its robustness in problem solving under partial, incomplete, or uncertain data. Empirical data on confirmed cases and deaths, extracted from an open source repository were used to develop the SEAIRD compartment model. Adjustments were made to fit current knowledge on the COVID-19 behavior. The model was implemented and solved using an Ordinary Differential Equation solver and an optimization tool. A cross-validation technique was applied, and the coefficient of determination R2 was computed in order to evaluate the goodness-of-fit of the model. Key epidemiological parameters were finally estimated and we provided the rationale for the construction of SEAIRD model. When applied to Brazil’s cases, SEAIRD produced an excellent agreement to the data, with an R2 ≥ 90%. The probability of COVID-19 transmission was generally high (≥ 95%). On the basis of a 20-day modeling data, the incidence rate of COVID-19 was as low as 3 infected cases per 100,000 exposed persons in Brazil and France. Within the same time frame, the fatality rate of COVID-19 was the highest in France (16.4%) followed by Brazil (6.9%), and the lowest in Russia (≤ 1%). SEAIRD represents an asset for modeling infectious diseases in their dynamical stable phase, especially for new viruses when pathophysiology knowledge is very limited.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10489-021-02379-2.

Identification, Uncertain Modelling, and Robust Control of Embedded Systems

This paper presents a methodology embodying identification procedures, uncertain modeling, and robust control design of embedded multivariable control systems. Concerning the identification, this methodology involved the determination of probabilistic uncertainty bounds for multivariable plants based on the black box or gray box identification. The bounds obtained were used in the derivation of an uncertain model in the form of upper Linear Fractional Transformation (LFT). This model was used in the robust control design implementing μ-synthesis. The problems arising on the different design stages were illustrated by an example presenting the embedded robust control of a two-input two-output analog model. The plant was identified by using black box and gray box identification methods that produced the necessary information to develop the corresponding uncertainty models. Two discrete-time robust controllers relevant to the two types of identification were designed and embedded in the physical system. Simulation results for the embedded closed-loop system and experimental results obtained by using the robust controllers were compared.

Simple Model and Predictive Control of a Pharmaceutical Batch Fluidized Bed Dryer

Abstract The fluidized bed theory can be complex, especially for heterogeneous flow descriptions with bypasses, generally resulting in large differential and algebraic systems of equations. Consequently, their applicability to model-based process control is limited. In this work, a simplified homogeneous model for pharmaceutical batch drying is derived from the two-phase fluidization theory using physical insights and simplifying assumptions, reducing more than a hundred equations to five. A nonlinear model predictive controller with an internal model structure is designed from these simple equations, showing the simplicity of tuning and implementation. Parameters of the model are calibrated through nonlinear grey-box identification using pilot scale experimental data. The validation demonstrates that the proposed simplifications do not impair the ability to replicate the process dynamics adequately with experimental conditions similar to the ones used for calibration. Closed-loop results in simulation attest the robustness of this control strategy.

Identification and nonlinearity compensation of hysteresis using NARX models

This paper deals with two problems: the identification and compensation of hysteresis nonlinearity in dynamical systems using nonlinear polynomial autoregressive models with exogenous inputs (NARX). First, based on gray-box identification techniques, some constraints on the structure and parameters of NARX models are proposed to ensure that the identified models display a key feature of hysteresis. In addition, a more general framework is developed to explain how hysteresis occurs in such models. Second, two strategies to design hysteresis compensators are presented. In one strategy, the compensation law is obtained through simple algebraic manipulations performed on the identified models. In the second strategy, the compensation law is directly identified from the data. Both numerical and experimental results are presented to illustrate the efficiency of the proposed procedures. Also, it has been found that the compensators based on gray-box models outperform the cases with models identified using black-box techniques.

Modeling, Identification and Control of Model Jet Engines for Jet Powered Robotics

The paper contributes towards the modeling, identification, and control of model jet engines. We propose a nonlinear, second order model in order to capture the model jet engines governing dynamics. The model structure is identified by applying sparse identification of nonlinear dynamics, and then the parameters of the model are found via gray-box identification procedures. Once the model has been identified, we approached the control of the model jet engine by designing two control laws. The first one is based on the classical Feedback Linearization technique while the second one on the Sliding Mode control. The overall methodology has been verified by modeling, identifying and controlling two model jet engines, i.e. P100-RX and P220-RXi developed by JetCat, which provide a maximum thrust of 100 N and 220 N, respectively.