Data-driven discovery of the heat equation in an induction machine via sparse regression

Discovery of natural laws through input-output data analysis has been of considerable interest during the past decade. Various approach among which the increasingly growing body of sparsity-based algorithms have been recently proposed for the purpose of free-form system identification. There has however been limited discussion on the performance of these approaches when applied on experimental datasets. The aim of this paper is to study the capability of this technique for identifying the heat equation as the natural law of heat distribution from experimental data, obtained using a Totally-Enclosed-Fan-Cooled (TEFC) induction machine, with and without active cooling. The results confirm the usefulness of the algorithm as a method to identify the underlying natural law in a physical system in the form of a Partial Differential Equation (PDE)

Evolutionary-based sparse regression for the experimental identification of duffing oscillator

In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms as part of the ordinary differential equation of the system. Correct identification of this nonlinear system using sparse identification is hugely dependent on selecting the correct form of nonlinearity included in the function library. Consequently, in this work, the evolutionary-based sparse identification is replacing the need for user knowledge when constructing the library in sparse identification. Constructing the library based on the data-driven evolutionary approach is an effective way to extend the space of nonlinear functions, allowing for the sparse regression to be applied on an extensive space of functions. The results show that the method provides an effective algorithm for the purpose of unveiling the physical nature of the Duffing oscillator. In addition, the robustness of the identification algorithm is investigated for various levels of noise in simulation. The proposed method has possible applications to other nonlinear dynamic systems in mechatronics, robotics, and electronics

Sparse Identification of Nonlinear Duffing Oscillator From Measurement Data

In this paper we aim to apply an adaptation of the recently developed technique of sparse identification of nonlinear dynamical systems on a Duffing experimental setup with cubic feedback of the output. The Duffing oscillator described by nonlinear differential equation which demonstrates chaotic behavior and bifurcations, has received considerable attention in recent years as it arises in many real-world engineering applications. Therefore its identification is of interest for numerous practical problems. To adopt the existing identification method to this application, the optimization process which identifies the most important terms of the model has been modified. In addition, the impact of changing the amount of regularization parameter on the mean square error of the fit has been studied. Selection of the true model is done via balancing complexity and accuracy using Pareto front analysis. This study provides considerable insight into the employment of sparse identification method on the real-world setups and the results show that the developed algorithm is capable of finding the true nonlinear model of the considered application including a nonlinear friction term.Comment: 6 pages, 8 figures, conference pape

Data-driven symbolic models for mechatronic system identification and control

The primary goal of this doctoral thesis is to automate the process of finding ‘white-box' models that are interpretable and consist of symbolic equations with focus on mechatronic systems. To achieve this goal, we develop new algorithms for discovering mathematical models using symbolic regression. We focus on the application of symbolic regression towards mechatronic system identification, i.e. finding a symbolic expression for the governing input-output relationship of a complex mechatronic system; and control, i.e. discovering the control law from data. Our primary research goal is realized through three subgoals: (i) automated model building for system identification and control, (ii) automated model selection and (iii) realization of symbolic models and their application on mechatronic systems, namely mechanical Duffing oscillator, electric induction machine and weaving mill as examples of mechatronic systems. The developed algorithms and methods bring us many steps closer to the goal of realizing automated mathematical model extraction on physically dynamic systems in which the modeling cost is simplified and the user interaction can be limited or even eliminated.Het primair doel van dit doctoraal proefschrift is het automatiseren van het proces om `white-box' modellen op te bouwen die intepreteerbaar en extrapoleerbaar zijn en bestaan uit symbolische vergelijkingen. Dit met een specifieke focus op mechatronische systemen. Voor het verwezenlijken van dit doel ontwikkelen we nieuwe algoritmen voor het ontdekken van wiskundige modellen gebruik makende van symbolische regressie. We focussen op het toepassen van symbolische regressie voor (a) mechatronische systeemidentificatie, met name het vinden van symbolische vergelijkingen die het input-output gedrag van het complexe mechatronische systeem beschrijven. (b) mechatronische regeling, meer bepaald het ontdekken van regelwetten op basis van data. Het onderzoek bestaat uit volgende drie deeldoelen: (i) automatische modelvorming voor systeemidentificatie en controle, (ii) automatische modelselectie, (iii) realiseren van symbolische modellen en deze toepassen op mechatronische systemen, namelijk op een mechanische Duffing oscillator, elektrische inductiemachine, en een weefgetouw systeem die dienst doet als mechatronisch voorbeeld. De ontwikkelde algoritmen en methoden brengen ons heel wat stappen dichter bij het doel om wiskundige modellen voor fysische dynamische systemen te gaan extraheren waarbij de modelleringskost wordt vereenvoudigd en de gebruikersinteractie beperkt tot zelfs geëlimineerd kan worden

Sparse multi-sensor monitoring system design for vehicle application

In today's fast growing vehicle industry, the number of functionalities (comfort features, monitoring features, safety features, etc.) is steadily increasing. Each of these functionalities are developed independently from each other, hence the sensors are not shared among them. Although this design approach results into robust monitoring of these different functionalities, it requires a large number of sensors in different locations resulting in a complex hardware and software architecture (e.g. complex wires). This paper describes our approach where a multi sensor design method is used to optimally select locations of sensors that are shared by different functionalities. This results into a reduced number of sensors that monitor the same amount of functionalities. We demonstrate in this paper, an optimization algorithm based on Multi-Objective Integer Programming (MOIP) for optimal sensor placement for monitoring Motion Sickness Dose Value (MSDV) estimation and Speed Bump Detection (SBD) as part of a driver assistant system. The algorithm is further validated on a numerical data-set captured from an IPG CarMaker vehicle model. The methodology can be further extended to more functionalities with large number of applications in vehicle industry

A relaxed model selection method for Duffing oscillator identification

This study presents a relaxed model selection procedure based on the sparse regression system identification method for Duffing oscillator identification. A two-stage relaxation procedure is presented. In a first stage an elastic net optimizer underpins the sparse regression that enables to explore the possible models. The subsequent stage employs the Akaike information criteria that employs the one standard error rule (1-SE) to select the appropriate model. We study the effect of relaxation in both stages, i.e. providing more exploration capabilities in the regression and the selection, by applying the two-stage methodology on experimental data collected on a mechanical Duffing oscillator setup. Our analysis shows that relaxation is advantageous when dealing with noisy experimental data and allows to find model structures and associated parameter values in the mechatronic Duffing oscillator. Results show that relaxation is pivotal when dealing with noisy experimental data and that the methodology possesses the capability to find model structures and associated parameter values of a Duffing oscillator. The presented results can be of benefit when identifying the system behavior of other mechatronic systems that exhibit complex, chaotic behavior that is difficult to model starting from first principles