Convergence Of Parameter Estimates Research Articles

Advanced parameter estimation for lithium-ion battery model using the information sharing group teaching optimization algorithm

Accurate battery modeling is crucial for optimizing the performance and safety of Lithium-ion batteries (LiBs), particularly in applications such as electric vehicles and smart grids. This paper introduces the Information Sharing Group Teaching Optimization Algorithm (ISGTOA), a novel human-based metaheuristic algorithm designed to estimate the 21 parameters of third-order Equivalent Circuit Model (ECM) for LiBs. Unlike existing methods, ISGTOA effectively manages the increased complexity of a model through advanced group teaching strategies and sophisticated information-sharing mechanisms inspired by classroom dynamics. We validated the effectiveness of ISGTOA using two distinct datasets—High Dynamic Profile (HDP) and Urban Dynamometer Driving Schedule (UDDS)—across various LiB chemistries (NCA and NMC) and temperature conditions (−5 °C, 25 °C and 45 °C). The results demonstrate that ISGTOA achieves superior parameter estimation accuracy and convergence speed compared to established and recent optimization methods such as TLBO, TLSBO, AISA, MTBO, and DTBO. Specifically, ISGTOA attained a minimum RMSE of 8.357 mV with rapid convergence and high stability in the HDP dataset and minimized RMSE to 10 mV within ten iterations at both 25 °C and 45 °C in the UDDS dataset. Additionally, ISGTOA exhibited high efficiency (up to 97.75 %) under varying thermal environments. This work not only introduces a novel algorithm for complex battery modeling but also sets the stage for future advancements in real-time battery management systems, emphasizing the importance of robust, versatile, and efficient parameter estimation techniques.

Adaptive control of bilateral teleoperators with convergent parameter estimation and guaranteed compliance

Although adaptive control has been studied for teleoperation systems in the past decades, the convergence of parameter estimation is generally difficult to claim in the existing methods, and thus only specific scenarios (e.g., free motion) and partial operation performance (e.g., synchronization) have been addressed. In this paper, we found that the convergence of parameter estimation is crucial for bilateral teleoperation systems to retain the guaranteed operation performances, including compliance in the tracking motion and transparency in the contact motion. Accordingly, this paper suggests an alternative adaptive control for bilateral teleoperation systems, where a new adaptive law with the estimation errors as leakage terms is developed to obtain finite-time convergence of the parameter estimation. This convergent property allows to compensate for the undesired dynamics (e.g., gravity) in the closed-loop system so as to achieve ideal compliance and transparency. The control system’s stability and performances under constant time delays are analyzed for three scenarios: free motion, tracking motion, and contact motion. The quantitative relationship between the joint velocities and the human torques in the tracking motion is also studied, and the transparency is addressed in the contact motion. Simulations and experiments on a Baxter robot all showcase the effectiveness and superiority of the developed approach.

Parameter identification of linear systems with heat sensors subject to unknown space-varying parameters

We extend existing works on control of (finite-dimensional) linear systems with (infinite-dimensional) heat sensors [6]. The extension lies on the one hand, in the fact that all system poles and zeros are unknown and, on the other, in the fact that sensor equations include unknown spatially-varying parameters. These uncertainties make the problem of parameter identification quite challenging. The existing adaptive observers for this type of systems prove not to be applicable in the presence of these uncertainties. Presently, we develop an identification method that involves multi-sine exciting input signals. Doing so, the inaccessible signal at the junction point, between the system and the sensor, can be given an affine parameterized form. It turns out that the identification problem of the sensor is decoupled from that of the system. Then, a parameter estimator involving K-filters is designed to get estimates of the sensor parameters as well as those of the inaccessible signal at the junction point. A new persistent excitation concept is introduced that ensures exponential convergence of the sensor parameter estimates and the estimated junction signal. The latter is then used to identify the parameters of the system dynamics.

Shrinking Small Sample Problems in Multilevel Structural Equation Modeling via Regularization of the Sample Covariance Matrix

Small sample sizes pose a severe threat to convergence and accuracy of between-group level parameter estimates in multilevel structural equation modeling (SEM). However, in certain situations, such as pilot studies or when populations are inherently small, increasing samples sizes is not feasible. As a remedy, we propose a two-stage regularized estimation approach designed for scenarios with both a small number of groups and small group sizes, and a low ICC. The method employs the wide format approach to multilevel SEM, where, at first, the sample covariance matrix is replaced by a shrinkage estimate, and then, this estimate is used to fit the SEM. By means of a simulation study, we evaluated the effectiveness of our two-stage approach. Our findings demonstrate that this method consistently ensures model convergence, provides more accurate between-level estimates, and even improves accuracy of within-level estimates in cases of very small group sizes.

Implications of stop-and-go traffic on training learning-based car-following control

Learning-based car-following control (LCC) of connected and autonomous vehicles (CAVs) is gaining significant attention with the advancement of computing power and data accessibility. While the flexibility and large model capacity of model-free architecture enable LCC to potentially outperform the model-based car-following (CF) model in improving traffic efficiency and mitigating congestion, the generalizability of LCC for traffic conditions different from the training environment/dataset is not well-understood. This study seeks to explore the impact of stop-and-go traffic in the training dataset on the generalizability of LCC. It uses the characteristics of lead vehicle trajectories to describe stop-and-go traffic, and links the theory of identifiability (i.e., obtaining a unique parameter estimation result using sensor measurements) to the generalizability of behavior cloning (BC) and policy-based deep reinforcement learning (DRL). Correspondingly, the study shows theoretically that: (i) stop-and-go traffic can enable the property of identifiability and enhance the control performance of BC-based LCC in different traffic conditions; (ii) stop-and-go traffic is not necessary for DRL-based LCC to generalize to different traffic conditions; (iii) DRL-based LCC trained with only constant-speed lead vehicle trajectories (not sufficient to ensure identifiability) can be generalized to different traffic conditions; and (iv) stop-and-go traffic increases variance in the training dataset, which improves the convergence of parameter estimation while negatively impacting the convergence of DRL to the optimal control policy. Numerical experiments validate the above findings, illustrating that BC-based LCC entails comprehensive training datasets for generalizing to different traffic conditions, while DRL-based LCC can achieve generalization with simple free-flow traffic training environments. This further suggests DRL as a more promising and cost-effective LCC approach to reduce operational costs, mitigate traffic congestion, and enhance safety and mobility, which can accelerate the deployment and acceptance of CAVs.

Optimizing statistical evaluation of multiclass classification in diagnostic radiology: a study of the two-parameter multidimensional nominal response model.

This study aimed to enhance the multidimensional nominal response model (MDNRM) for multiclass classification in diagnostic radiology. This retrospective study involved the extension of the conventional nominal response model (NRM) to create the two-parameter MDNRM (2PL-MDNRM). Seven models of MDNRM, including the original MDNRM and subtypes of 2PL-MDNRM, were employed to estimate test-takers' abilities and test item complexity. These models were applied to a clinical diagnostic radiology dataset. Rhat values were calculated to evaluate model convergence. Additionally, values of the widely applicable information criterion (wAIC) and Pareto-smoothed importance sampling leave-one-out cross-validation (LOO) were calculated to evaluate the goodness of fit of the seven models. The best-performing model was selected based on the values of wAIC and LOO. Probability of direction (PD) was used to evaluate whether one estimated parameter significantly differed. All estimated parameters across the seven models demonstrated Rhat values below 1.10, indicating stable convergence. The best wAIC and LOO values (988 and 1,121, respectively) were achieved with 2PL-MDNRM r using the truncated normal distribution and 2PL-MDNRM a using the truncated normal distribution. Notably, one test-taker (radiologist) exhibited significantly superior ability compared to another based on PD results from the best models, while no significant difference was observed in nonoptimal models. 2PL-MDNRM successfully achieved parameter estimation convergence, and its superiority over the original MDNRM was demonstrated through wAIC and LOO values.

Research on Financial Default Model with Stochastic Intensity Using Filtered Likelihood Method

This paper investigates the financial default model with stochastic intensity by incomplete data. On the strength of the process-designated point process, the likelihood function of the model in the parameter estimation can be decomposed into the factor likelihood term and event likelihood term. The event likelihood term can be successfully estimated by the filtered likelihood method, and the factor likelihood term can be calculated in a standardized manner. The empirical study reveals that, under the filtered likelihood method, the first model outperforms the other in terms of parameter estimation efficiency, convergence speed, and estimation accuracy, and has a better prediction effect on the default data in China’s financial market, which can also be extended to other countries, which is of great significance in the default risk control of financial institutions.

Two-timescale stochastic gradient descent in continuous time with applications to joint online parameter estimation and optimal sensor placement

In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known results in discrete time. We analyse algorithms with additive noise and those with non-additive noise. In the non-additive case, our analysis is carried out under the assumption that the noise is a continuous-time Markov process, controlled by the algorithm states. The algorithms we consider can be applied to a broad class of bilevel optimisation problems. We study one such problem in detail, namely, the problem of joint online parameter estimation and optimal sensor placement for a partially observed diffusion process. We demonstrate how this can be formulated as a bilevel optimisation problem, and propose a solution in the form of a continuous-time, two-timescale, stochastic gradient descent algorithm. Furthermore, under suitable conditions on the latent signal, the filter, and the filter derivatives, we establish almost sure convergence of the online parameter estimates and optimal sensor placements to the stationary points of the asymptotic log-likelihood and asymptotic filter covariance, respectively. We also provide numerical examples, illustrating the application of the proposed methodology to a partially observed Beneš equation, and a partially observed stochastic advection-diffusion equation.

Method for identification of sinusoidal signal parameters with variable unknown amplitude

A new method proposed for identifying the parameters of sinusoidal signal with unknown variable amplitude. The problem of estimating the parameters of sinusoidal signals is relevant in the problems of dynamic positioning and disturbance compensation, for the synthesis of control laws that take into account external disturbances. In the proposed method, the restriction on the signal amplitude is removed. In contrast to known approaches, where the amplitude must be fixed, in the proposed method the signal amplitude can be variable. To implement the proposed identification algorithm, the Jordan matrix form and delay operators are used. During parameterization, a regression model is formed containing unknown stationary parameters. To search for unknown parameters, the method of dynamic expansion of the regressor and mixing is used. The results of computer simulation demonstrate the efficiency of the proposed algorithm. The simulation results confirmed the convergence of parameter estimation to the true values. The proposed approach can be applied to a wide class of applied problems related to disturbance compensation in vibration protection systems, monitoring systems in determining the parameters of high-rise or large-span building structures, and in robotic object control systems.

RELEVANT MOMENT SELECTION UNDER MIXED IDENTIFICATION STRENGTH

This paper proposes a robust moment selection method aiming to pick the best model even if this is a moment condition model with mixed identification strength, that is, moment conditions including moment functions that are local to zero uniformly over the parameter set. We show that the relevant moment selection procedure of Hall et al. (2007, Journal of Econometrics 138, 488–512) is inconsistent in this setting as it does not explicitly account for the rate of convergence of parameter estimation of the candidate models which may vary. We introduce a new moment selection procedure based on a criterion that automatically accounts for both the convergence rate of the candidate model’s parameter estimate and the entropy of the estimator’s asymptotic distribution. The benchmark estimator that we consider is the two-step efficient generalized method of moments estimator, which is known to be efficient in this framework as well. A family of penalization functions is introduced that guarantees the consistency of the selection procedure. The finite-sample performance of the proposed method is assessed through Monte Carlo simulations.

From Nonlinear Dominant System to Linear Dominant System: Virtual Equivalent System Approach for Multiple Variable Self-Tuning Control System Analysis

The stability and convergence analysis of a multivariable stochastic self-tuning system (STC) is very difficult because of its highly nonlinear structure. In this paper, based on the virtual equivalent system method, the structural nonlinear or nonlinear dominated multivariable self-tuning system is transformed into a structural linear or linear dominated system, thus simplifying the stability and convergence analysis of multivariable STC systems. For the control process of a multivariable stochastic STC system, parameter estimation is required, and there may be three cases of parameter estimation convergence, convergence to the actual value and divergence. For these three cases, this paper provides four theorems and two corollaries. Given the theorems and corollaries, it can be directly concluded that the convergence of parameter estimation is a sufficient condition for the stability and convergence of stochastic STC systems but not a necessary condition, and the four theorems and two corollaries proposed in this paper are independent of specific controller design strategies and specific parameter estimation algorithms. The virtual equivalent system theory proposed in this paper does not need specific control strategies, parameters and estimation algorithms but only needs the nature of the system itself, which can judge the stability and convergence of the self-tuning system and relax the dependence of the system stability convergence criterion on the system structure information. The virtual equivalent system method proposed in this paper is proved to be effective when the parameter estimation may have convergence, convergence to the actual value and divergence.

Adaptive robust predictive control with sample-based persistent excitation

We propose a robust adaptive Model Predictive Control strategy with online set-based estimation for constrained linear systems with unknown parameters and bounded disturbances. A sample-based test applied to predicted trajectories is used to ensure convergence of parameter estimates by enforcing a persistence of excitation condition on the closed loop system. The control law robustly satisfies constraints and has guarantees of feasibility and input-to-state stability. Convergence of parameter set estimates to the actual system parameter vector is guaranteed under conditions on reachability and tightness of disturbance bounds.

Adaptive Observation-Based Efficient Reinforcement Learning for Uncertain Systems.

This article develops an adaptive observation-based efficient reinforcement learning (RL) approach for systems with uncertain drift dynamics. A novel concurrent learning adaptive extended observer (CL-AEO) is first designed to jointly estimate the system state and parameter. This observer has a two-time-scale structure and does not require any additional numerical techniques to calculate the state derivative information. The idea of concurrent learning (CL) is leveraged to use the recorded data, which leads to a relaxed verifiable excitation condition for the convergence of parameter estimation. Based on the estimated state and parameter provided by the CL-AEO, a simulation of experience-based RL scheme is developed to online approximate the optimal control policy. Rigorous theoretical analysis is given to show that the practical convergence of the system state to the origin and the developed policy to the ideal optimal policy can be achieved without the persistence of excitation (PE) condition. Finally, the effectiveness and superiority of the developed methodology are demonstrated via comparative simulations.

A Novel Adaptive Model Predictive Control Strategy of Solid Oxide Fuel Cell in DC Microgrids

Solid oxide fuel cell (SOFC) becomes increasingly popular in dc microgrid applications. Controlling SOFC is challenging because the dynamics of SOFC are difficult to maintain under complex internal reactions and changing operating conditions. To solve these problems, this article proposes a novel adaptive model predictive control (AMPC) algorithm, which adopts a parameter estimator to update the system parameters online. The robustness of the proposed AMPC is investigated under different microgrid scenarios, including the overload, underload, short-circuit, and significant dc bus voltage drop situations. The proposed AMPC algorithm produces superior SOFC control performance over the conventional model predictive control (MPC), Wiener MPC, and PI and fuzzy PI controllers. Furthermore, it significantly reduces the system model dependence that is shared by nearly all the model-based SOFC control methods. The convergence of parameter estimation in the proposed AMPC is rigorously proved. The effectiveness of the proposed algorithm is validated through hardware-in-the-loop experiments under various operating conditions and system parameter variations.

Finite-time composite learning control for trajectory tracking of dynamic positioning vessels

This paper studies the trajectory tracking control method for dynamic positioning vessels with state constraints and parameter uncertainties. A composite learning method is introduced to identify unknown parameters online. Regressor filtering together with dynamic regressor extension and mixing procedure are combined not only to relax the dependence of parameter estimation convergence process on the persistent excitation condition, but also to ensure the independence and flexibility of each parameter. Subsequently, a finite-time composite learning controller is designed based on asymmetric integral barrier Lyapunov functions, which guarantees the asymmetric constraints on vessel states. Furthermore, Lyapunov stability shows that the parameter identification and tracking errors can converge to zero in finite-time. Finally, tracking control task for dynamic positioning systems is carried out to illustrate the merits of the proposed method.

Novel Adaptive Extended State Observer for Dynamic Parameter Identification with Asymptotic Convergence

In this paper, a novel method of parameter identification of linear in parameter dynamic systems is presented. The proposed scheme employs an Extended State Observer to online estimate a state of the plant and momentary value of total disturbance present in the system. A notion is made that for properly redefined dynamics of the system, this estimate can be interpreted as a measure of modeling error caused by the parameter uncertainty. Under this notion, a disturbance estimate is used as a basis for classic gradient identification. A global convergence of both state and parameter estimates to their true values is proved using the Lyapunov approach under an assumption of a persistent excitation. Finally, results of simulation and experiments are presented to support the theoretical analysis. The experiments were conducted using a compliant manipulator joint and obtained results show the usefulness of the proposed method in drive control systems and robotics.

A Novel Adaptive Model Predictive Control for Proton Exchange Membrane Fuel Cell in DC Microgrids

In this paper, a novel adaptive model predictive control (AMPC) algorithm is proposed for proton exchange membrane fuel cells (PEMFCs) to improve its output power tracking performance in DC microgrids. The proposed AMPC algorithm is capable of producing superior PEMFC control performance over the conventional MPC and PI controllers. Compared with PI control, AMPC is able to handle physical constraints, which ensures the safe operation of PEMFC under different conditions. Furthermore, it overcomes the common problem of system model dependence that is shared by nearly all the model-based control methods. The convergence of parameter estimation in the proposed AMPC is rigorously proved. The effectiveness of the proposed algorithm under various operating conditions and system parameter variations are verified by simulation results.

Kinetics of the Direct DME Synthesis: State of the Art and Comprehensive Comparison of Semi-Mechanistic, Data-Based and Hybrid Modeling Approaches

Hybrid kinetic models represent a promising alternative to describe and evaluate the effect of multiple variables in the performance of complex chemical processes, since they combine system knowledge and extrapolability of the (semi-)mechanistic models in a wide range of reaction conditions with the adaptability and fast convergence of data-based approaches (e.g., artificial neural networks—ANNs). For the first time, a hybrid kinetic model for the direct DME synthesis was developed consisting of a reactor model, i.e., balance equations, and an ANN for the reaction kinetics. The accuracy, computational time, interpolation and extrapolation ability of the new hybrid model were compared to those of a lumped and a data-based model with the same validity range, using both simulations and experiments. The convergence of parameter estimation and simulations with the hybrid model is much faster than with the lumped model, and the predictions show a greater degree of accuracy within the models’ validity range. A satisfactory dimension and range extrapolation was reached when the extrapolated variable was included in the knowledge module of the model. This feature is particularly dependent on the network architecture and phenomena covered by the underlying model, and less on the experimental conditions evaluated during model development.

Switched Adaptive Concurrent Learning Control using a Stance Foot Model for Gait Rehabilitation using a Hybrid Exoskeleton

Lower-limb hybrid exoskeletons integrate powered mechanisms and functional electrical stimulation (FES) to provide assistive forces and activate muscles for restoring gait function after a neurological injury. Particularly, improving the load-bearing ability is a primary rehabilitation goal. Hence, the control of the exoskeleton and FES is critical within the stance phase of walking to ensure smooth weight transfer between limbs, and achieve a sound loading response and leg propulsion. This paper develops a concurrent learning adaptive control technique to provide torque assistance about the hip and knee joints using a cable-driven exoskeleton, and activate the quadriceps and hamstrings muscle groups via FES for treadmill walking. The human-exoskeleton dynamics are modeled with phase-dependent switching dynamics to strategically update the concurrent learning controller at early stance (heel strike), late stance (toe-off), and the swing phases of walking. Thus, the adaptive switching controller compensates for the dynamic changes within the stance phase and its transition to swing, while achieving joint kinematic tracking and estimating a subset of the leg's uncertain parameters. A multiple Lyapunov function analysis is developed to demonstrate stability of the overall phase-dependent switched system requiring a dwell-time condition that guarantees exponential tracking and parameter estimation convergence.

The (in)stability of Bayesian model selection criteria in disease mapping

Several model comparison techniques exist to select the best fitting model from a set of candidate models. This study explores the performance of model comparison tools that are commonly used in Bayesian spatial disease mapping and that are available among several Bayesian software packages: the deviance information criterion (DIC), the Watanabe–Akaike information criterion (WAIC) and the log marginal predictive likelihood (LMPL). We compare R packages CARBayes and NIMBLE, and R interfaces to OpenBUGS (R2OpenBUGS) and Stan (RStan), by fitting Poisson models to disease incidence outcomes with intrinsic conditional autoregressive, convolution conditional autoregressive and log-normal error terms. From three data analyses that differ in the number of areal units and background incidence/prevalence of the outcome of interest, we learn that the estimates of model comparison statistics coming from different software packages can lead to disagreements regarding model preference. Furthermore, we show that the distributional convergence of parameter estimates does not necessarily imply numerical convergence of the model comparison tool. We warn users to be careful when doing model comparison when using different software packages, and to make use of one specific method for the calculation of the model selection criteria.