Parameter Identification Methodology Research Articles

A methodology for direct parameter identification for experimental results using machine learning — Real world application to the highly non-linear deformation behavior of FRP

In this work, we demonstrate how Machine learning (ML) techniques can be employed to externalize the knowledge and time intensive process of material parameter identification. This is done on the example of a recent data driven material model for the non-linear shear behavior of glass fiber reinforced polypropylene (GF/PP) (Gerritzen, 2022). A convolutional neural network (CNN) based model architecture is trained to predict material modeling parameters based on the input of stress–strain-curves. The optimal model architecture and training setup are determined by hyperparameter optimization (HPO). Solely virtual data, generated using the target material model, is used throughout the training and HPO. The final CNN is capable of calculating model parameter combinations from experimental stress–strain-curves which lead to excellent agreement between experimental and associated model curve.

Non-linear modeling and parameter identification of a bolted joint using substructure synthesis theory

Engineering applications require accurate modeling and parameter identification to anticipate bolted joint behavior under different loading circumstances. Bolted joints are extensively used in civil and mechanical structures. In this research study, cubic stiffness non-linearity is examined and a comprehensive model, which can exhibit the non-linearity of joint behavior, is developed. This is achieved by modeling the bolted joint which is connected at one end of a cantilever beam. Mathematical model is established using concept of sub structure synthesis theory by considering non-linear translational stiffness and non-linear rotational stiffness as a boundary condition. Non-dimensional natural frequencies are estimated by assuming stiffness parameters and joint parameter estimation for translational spring having nonlinear stiffness is calculated using second order curve fitting technique. Furthermore, estimated and exact value of cubic stiffness coefficient are compared. The experimental results shows that the percentage error of estimation for all the modes are less than 8%. The experimentally determined natural frequencies are further contrasted with an analytical results to validate a precision of generated model. Present work contributes in improving the bolted joint analysis by providing a solid non-linear modeling and parameter identification methodology. This methodology enhances design practices and ensures the durability of engineering structures and mechanical systems by improving bolted joint comprehension.

Electrohydraulic and Electromechanical Buoyancy Change Device Unified Vertical Motion Model

Depth control is crucial for underwater vehicles, not only to perform certain tasks that require the vehicle to be still at a given depth but also because most propeller-driven vehicles waste a considerable amount of energy to counteract the passively tuned positive buoyancy. The use of a variable buoyancy system (VBS) can effectively address these items, increasing the energetic efficiency and thus mission length. Achieving accurate depth controllers is, however, a complex task, since experimental controller development in sea or even in test pools is unpractical and the use of simulation requires accurate vertical motion models whose parameters might be difficult to obtain or measure. The development of simple, yet comprehensive, dynamic models for devices incorporating VBS is therefore of upmost importance, as well as developing procedures that allow a simple determination of their parameters. This work contributes to this field by deriving a unified model for the vertical motion of a VBS actuated device, irrespective of the specific technological actuation solution employed, whether it be electromechanical or electrohydraulic. A concise analysis of the open-loop stability of the unified model is presented and a straightforward yet efficient procedure for identifying several of its parameters is introduced. This identification procedure is designed to be convenient and can be carried out in shallow waters, such as test pools, while its results are applicable to the deeper water model as well. To validate the procedure, experimental values obtained from an electromechanical VBS actuated device are used. Closed-loop control of the electromechanical VBS actuated device is conducted through simulation and experimental tests. The results confirm the effectiveness of the proposed unified model and the parameter identification methodology.

Inverse problem for parameters identification in a modified SIRD epidemic model using ensemble neural networks

In this paper, we propose a parameter identification methodology of the SIRD model, an extension of the classical SIR model, that considers the deceased as a separate category. In addition, our model includes one parameter which is the ratio between the real total number of infected and the number of infected that were documented in the official statistics. Due to many factors, like governmental decisions, several variants circulating, opening and closing of schools, the typical assumption that the parameters of the model stay constant for long periods of time is not realistic. Thus our objective is to create a method which works for short periods of time. In this scope, we approach the estimation relying on the previous 7 days of data and then use the identified parameters to make predictions. To perform the estimation of the parameters we propose the average of an ensemble of neural networks. Each neural network is constructed based on a database built by solving the SIRD for 7 days, with random parameters. In this way, the networks learn the parameters from the solution of the SIRD model. Lastly we use the ensemble to get estimates of the parameters from the real data of Covid19 in Romania and then we illustrate the predictions for different periods of time, from 10 up to 45 days, for the number of deaths. The main goal was to apply this approach on the analysis of COVID-19 evolution in Romania, but this was also exemplified on other countries like Hungary, Czech Republic and Poland with similar results. The results are backed by a theorem which guarantees that we can recover the parameters of the model from the reported data. We believe this methodology can be used as a general tool for dealing with short term predictions of infectious diseases or in other compartmental models.

Reinforcement learning and approximate Bayesian computation (RL-ABC) for model selection and parameter calibration of time-varying systems

This paper extends the recently developed methodology for model selection and parameter identification called RL-ABC (Ritto et al., 2022) (reinforced learning and approximate Bayesian computation) to time-varying systems. To tackle slowly-varying systems and detect abrupt changes, new features are proposed. (1) The probability of sampling the worst model has now a lower bound; because it cannot disappear, once it might be useful in the future as the system evolves. (2) A memory term (sliding window) is introduced such that past data can be forgotten whilst updating the reward; which might be useful depending on how fast the system changes. (3) The algorithm detects a change in the system by monitoring the models’ acceptance; a significant drop in acceptance indicates a change. If the system changes the algorithm is reset: new parameter ranges are computed and the rewards are restarted. To test the proposed strategy, new experimental data is obtained from a test rig with non-linear restoring force characteristics. The amplitude of the dynamical experiment is obtained with the control-based continuation strategy varying the excitation amplitude, and three Duffing-like models are used to represent the system. The results are consistent, and the strategy is able to detect changes and update parameter estimation and model predictions.

Parameter Identification of Bivariate Fractal Interpolation Surfaces by Using Convex Hulls

The scope of this article is to identify the parameters of bivariate fractal interpolation surfaces by using convex hulls as bounding volumes of appropriately chosen data points so that the resulting fractal (graph of) function provides a closer fit, with respect to some metric, to the original data points. In this way, when the parameters are appropriately chosen, one can approximate the shape of every rough surface. To achieve this, we first find the convex hull of each subset of data points in every subdomain of the original lattice, calculate the volume of each convex polyhedron and find the pairwise intersections between two convex polyhedra, i.e., the convex hull of the subdomain and the transformed one within this subdomain. Then, based on the proposed methodology for parameter identification, we minimise the symmetric difference between bounding volumes of an appropriately selected set of points. A methodology for constructing continuous fractal interpolation surfaces by using iterated function systems is also presented.

Rational Continuous Neural Network Identifier for Singular Perturbed Systems With Uncertain Dynamical Models.

This study aims at designing a robust nonparametric identifier for a class of singular perturbed systems (SPSs) with uncertain mathematical models. The identifier structure uses a novel identifier based on a differential neural network (DNN) with rational form, which can take into account the multirate nature of SPS. The identifier uses a mixed learning law including a rational formulation of neural networks which is useful to solve the identification of the fast dynamics in the SPS dynamics. The rational form of the design is proposed in such a way that no-singularities (denominator part of the rational form never touches the origin) are allowed in the identifier dynamics. A proposed control Lyapunov function and a nonlinear parameter identification methodology yield to design the learning laws for the class of novel rational DNN which appears as the main contribution of this study. A complementary matrix inequality-based optimization method allows to get the smallest attainable convergence invariant region. A detailed implementation methodology is also given in the study with the aim of clarifying how the proposed identifier can be used in diverse SPSs. A numerical example considering the dynamics of the enzymatic-substrate-inhibitor system with uncertain dynamics is showing how to apply the DNN identifier using the multirate nature of the proposed DNN identifier for SPSs. The proposed identifier is compared to a classical identifier which is not taking into account the multirate nature of SPS. The benefits of using the rational form for the identifier are highlighted in the numerical performance comparison based on the mean square error (MSE). This example justifies the ability of the suggested identifier to reconstruct both the fast and slow dynamics of the SPS.

Semi-online parameter identification methodology for maritime power lithium batteries

Due to the special working environment of power lithium battery (P-LiB) on all-electric ships, the high-efficiency battery management system (BMS) is required. In this study, a novel semi-online parameter identification methodology integrated with large-scale global optimization algorithm is developed, in order to ensure the high-quality performance of subsequent BMS functions like the equalization control and state-of-charge estimation. Firstly, the P-LiB parameter identification model is established based on the first-order Thevenin equivalent circuit. Then, the evolution strategy of identification model is developed for dynamically updating the model along with the entire charging/discharging process of P-LiB. Considering that the model complexity increases exponentially with dimensionality, the AMCCDE algorithm developed in our previous work is employed to optimize the dynamic model repeatedly. Moreover, the semi-online operation mechanism for AMCCDE is proposed, in which the multiple context vectors are used to exchange information and inherit the optimal solution between each two adjacent semi-online cycles, and the identification solutions can be dynamically corrected and output at the end of each cycle. Finally, the developed semi-online identification methodology is verified using the USTC-DST and USTC-UDDS datasets. Experimental results show that the developed methodology can well balance the identification accuracy and timeliness, and dynamically output the accurate identification solutions in real-time.

Using Numerical Models to Accelerate Electrolyte Transport Parameter Identification

A new electrolyte transport parameter identification methodology, based on the numerical solution of a symmetric Li–Li cell model, is presented. In contrast to available techniques in the literature, where small concentration perturbations are generated in testing setups and linearization is assumed to identify transport properties for the initial salt concentration, large currents are used here to excite nonlinear dynamics able to reveal concentration dependent transport properties. This approach allows a significant reduction in the experimental effort. The proposed methodology is applied to two synthetic experiments. Firstly, an ideal case (where all difficulties associated to stripping and plating dynamics on Li metal surface are neglected) is considered in order to show both the details of the proposed methodology and its performance (specially its robustness, including the effect of the noise level in the voltage measurements in the experiment). A second case considers the effect of complex stripping and plating dynamics to show that, provided (macroscopic) modelling/identification of this dynamics is carried out, the proposed methodology is still able to accurately identify electrolyte transport properties using a simple experimental test setup.

A novel methodology for modal parameter identification of arch dam based on multi-level information fusion

Operational modal analysis plays an important role in the structural health monitoring and safety diagnosis of arch dam. However, due to background noise, it is difficult to accurately extract the effective characteristics information of arch dam from the vibration responses whose amplitudes are too small under ambient vibration, and the deviation caused by traditional identification methods will directly affect the estimation accuracy for structural modal parameters. Therefore, a novel methodology for modal parameter identification of arch dam based on multi-level information fusion is proposed in this paper. The proposed method is based on multi-sensor data-level fusion to identify the structural natural frequency and damping ratio, which greatly preserves and extracts structural modal properties in the vibration responses. Meanwhile, structural mode shapes are identified based on dynamic feature-level fusion, which significantly improves the identification accuracy. The effectiveness and feasibility of the proposed method are verified by the modal results of digital signals and simulated signals in the 7-DOF system. Prototype engineering case shows that the closely spaced and high-frequency modes can be decomposed and identified by the proposed method, and this method has a higher identification accuracy, which can provide a new idea for modal parameter identification of arch dam.

Reinforcement learning and approximate Bayesian computation for model selection and parameter calibration applied to a nonlinear dynamical system

In the context of digital twins and integration of physics-based models with machine learning tools, this paper proposes a new methodology for model selection and parameter identification. It combines (i) reinforcement learning (RL) for model selection through a Thompson-like sampling with (ii) approximate Bayesian computation (ABC) for parameter identification and uncertainty quantification. These two methods are applied together to a nonlinear mechanical oscillator with periodic forcing. Experimental data are used in the analysis and two different nonlinear models are tested. The initial Beta distribution that represents the likelihood of the model is updated depending on how successful the model is at reproducing the reference data (reinforcement learning strategy). At the same time, the prior distribution of the model parameters is updated using a likelihood-free strategy (ABC). In the end, the rewards and the posterior distribution of the parameters of each model are obtained. The results show that the combined methodology (RL-ABC) is promising for model selection from bifurcation diagrams. Prior parameter distribution was successfully updated, correlations between parameters were found, probabilistic envelopes of the posterior model are consistent with the available data, the most rewarded model was selected, and the reinforcing strategy allows to speed up the selection process.

On the inverse identification methods for forming plasticity models using full-field measurements

The simulation of deep drawing processes and its quality is intrinsically dependent on the accuracy of the constitutive model in reproducing the mechanical behaviour of the sheet metal material. Today, the calibration of elastoplastic models – correspondent to the inverse identification of the material parameters – often uses full-field measurements, through Digital Image Correlation (DIC) techniques, to capture non-homogeneous strain fields and states, coupled with non-straightforward numerical inverse methodologies. In the last decade, new parameter identification methodologies, such as the Finite Element Model Updating (FEMU), the Constitutive Equation Gap (CEG) method, the Equilibrium Gap Method (EGM) and the Virtual Fields Method (VFM) have been developed and have proven to be effective for non-linear plasticity models. Nonetheless, the FEMU and the VFM have distinguished themselves from the others. More recently, supervised Machine Learning (ML) techniques have been also used as an inverse identification method. These artificial intelligence-based methods use large datasets of numerical tests to train an inverse model in which the input is the history of the strain field and loads during the test, and the output are directly the material parameters.The goal of this paper is to analyse, compare and discuss these inverse identification methods, with particular focus on the FEMU, VFM, and ML methodologies. A heterogeneous tensile-load test is considered to compare in detail the FEMU, VFM, and ML strategies.

Identification of control parameters of the permanent magnetic synchronous generator using least square method

This paper presents a new methodology for the identification of the control parameters of converters of Direct-drive Permanent Magnetic Synchronous Generator (DPMSG) using least square method. Firstly, the novel methodology for the control parameter identification was thoroughly introduced; after that, a complete model of DPMSG was built in DIgSILENT PowerFactory platform for generating testing signals; finally, the algorithm was tested through signals obtained using dynamic simulations of the complete model of DPMSG. The accurate estimation was obtained by this methodology, i.e. the maximum error of the identification results was less than 3.1%. This method was able to accurately identified the converter control parameters of DPMSG without setting initial values for the identification program.

Material Parameters Identification for Modelling of Carbon Rod Structures Delamination

The aim of the present work is to compare the interlaminar shear strength and fracture toughness of glued carbon fiber rods obtained using different experimental approaches and provide the effective way to characterise the interlaminar properties for reliable simulation of the delamination. Five different test methods (tension, single shear test, and double shear test, mode I and mode II delamination tests) were performed. Using the explicit LS-DYNA code the finite element model capable of simulating the damage process of bonded connection was developed. The interlaminar connection and delamination criteria were calibrated using the parameter identification methodology implemented in LS-OPT optimization tool.

Challenges in developing of 3D nonlinear viscoelastic models

Due to development of different material systems and structural elements, there is growing need for more complex material models, since linear elasticity or even more complicated linear viscoelasticity cannot capture the nuances of behaviour of these materials. This study describes the process and difficulties of development of 3D nonlinear viscoelastic model. Study proposes two models with different level of complexity and methodology for experimental parameter identification. The limitations of both of these models have been discussed.

Predicting cell behaviour parameters from glioblastoma on a chip images. A deep learning approach

The broad possibilities offered by microfluidic devices in relation to massive data monitoring and acquisition open the door to the use of deep learning technologies in a very promising field: cell culture monitoring. In this work, we develop a methodology for parameter identification in cell culture from fluorescence images using Convolutional Neural Networks (CNN). We apply this methodology to the in vitro study of glioblastoma (GBM), the most common, aggressive and lethal primary brain tumour. In particular, the aim is to predict the three parameters defining the go or grow GBM behaviour, which is determinant for the tumour prognosis and response to treatment. The data used to train the network are obtained from a mathematical model, previously validated with in vitro experimental results. The resulting CNN provides remarkably accurate predictions (Pearson's ρ > 0.99 for all the parameters). Besides, it proves to be sound, to filter noise and to generalise. After training and validation with synthetic data, we predict the parameters corresponding to a real image of a microfluidic experiment. The obtained results show good performance of the CNN. The proposed technique may set the first steps towards patient-specific tools, able to predict in real-time the tumour evolution for each particular patient, thanks to a combined in vitro-in silico approach.

On the Performance of Isotropic Hyperelastic Constitutive Models for Rubber-Like Materials: A State of the Art Review

Abstract Besides the well-known landmark models for the hyperelastic response of rubberlike materials, many new hyperelastic constitutive models have emerged over the last decade. Despite many reviews on constitutive modeling or elastomers, it is still a challenging endeavor for engineers to decide for a constitutive model for the specific rubber compound and application. In this work, we have reviewed 44 hyperelastic constitutive models for elastomers and assessed their strength and weaknesses under uniaxial, pure shear, and (equi)biaxial deformations. To this end, we first present a novel parameter identification methodology based on various multi-objective optimization strategies for the selection of the best constitutive models from a given set of uniaxial tension, pure shear, and (equi)biaxial tension experiments. We utilize a hybrid multi-objective optimization procedure using a genetic algorithm to generate multiple initial points for gradient-based search algorithm, Fmincon utility in matlab. The novelty of the approach is (i) simultaneous fitting with variable weight factors for uniaxial, equibiaxial, and pure shear data, and (ii) the sorting of the models based on objective normalized quality of fit metric. For the models incapable of simultaneously fitting the three distinct deformation data, the validity range is assessed through a threshold value for the quality of fit measure. Accordingly, 44 hyperelastic models are sorted with respect to their simultaneous fitting performance to the experimental dataset of Treloar and Kawabata. Based on the number of material parameters, and their fitting performance to experimental data, a detailed discussion is carried out.

Algorithms for Numerical Solution to the Problem of Diffusion in Nanoporous Media

Introduction. Mathematical modeling of mass transfer in heterogeneous media of microporous structure and construction of solutions to the corresponding problems of mass transfer was considered by many authors [1–9, etc.]. In [6, 7] authors proposed a methodology for modeling mass transfer systems and parameter identification in nanoporous particle media (diffusion, adsorption, competitive diffusion of gases, filtration consolidation), which are described by non-classical boundary and initial-boundary value problems taking into account the mutual influence of micro- and macro-transfer flows, heteroporosity, the structure of microporous particles, multicomponent and other factors. In [8, 9] for a mathematical model of nonstationary diffusion of a single substance in a nanoporous medium described in [2] in the form of a multi-scale differential mathematical problem, the classical problems in the weak formulation were obtained. In this paper, algorithms for solving the above mathematical problems are constructed by using the finite element method. The results of the numerical solution of the test problem are presented. The results confirm the efficiency of the developed algorithms. The purpose is to solve a problem of nonstationary diffusion of single substance in nanoporous medium by constructing discretization algorithms using FEM quadratic basis functions. Results. Algorithms for the numerical solution of the problem of nonstationary diffusion of single substance in a nanoporous medium are proposed. Peculiarities of discretization of the region and construction of the matrix of masses, stiffness, and vector of right-hand sides when solving the problem by using FEM are described. The efficiency of the developed algorithms is confirmed by the results of solving a model example. Keywords: mathematical modeling, numerical methods, nonstationary diffusion, nanoporous medium, finite element method.

Optimized parameter estimation of a PEMFC model based on improved Grass Fibrous Root Optimization Algorithm

This paper presents a new optimal methodology for parameter identification of a 50 kW polymer membrane fuel cell (PEMFC) based on the economical–functional model. The objective of the study is to optimal estimation of the system parameters such that the minimum total cost has been needed for the stack construction. The total cost here is the sum of the fuel cell stack cost and its auxiliaries by considering air and hydrogen stoichiometric coefficient, system pressure, the current density, and the system temperature. For solving the minimization problem, a newly modified model of the Grass Fibrous Root Optimization Algorithm (MGRA) has been presented. Final results are compared with some several well-known algorithms to indicate the system efficiency and the reliability of the system toward different parameters has been indicated by applying sensitivity analysis.

Exploiting dynamic modeling, parameter identification, and power electronics to implement a non-dissipative Li-ion battery hardware emulator

More and more applications encompass battery energy storage systems (BESSs) based on Li-ion batteries. However, when designing the power converter of a BESS or when studying the interaction between BESSs and other application components, relying on a real battery makes the process cumbersome, expensive, and time-consuming. Moreover, the battery could even suffer damages. The aim of the work is to show that it is possible to exploit suitable battery models and related parameter identification methodologies, as well as power converters and related control techniques, to develop a hardware device that emulates any given battery. In particular, this paper shows the design and the experimental prototype of a Li-ion battery emulator that is capable of both sourcing and sinking power at kilowatt scale. Unlike other similar devices available in the market or described in the technical literature, the proposed device is low-cost, it injects power into the grid during sink operation, and it can also reproduce battery dynamics. Design criteria are given in the manuscript. The proposed battery emulator has been tested and experimentally validated. The obtained device allows reducing the cost, time, and complexity of performing system tests in Li-ion BESS applications.