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Highlights • Bayesian parameter learning for non-linear and non-Gaussian dynamical systems. • Impulsive noise, chaotic and numerically discretized systems are considered. • Applicable when sufficient statistics does not exist for such systems. • Overdispersion by introducing artificial parameter evolution is avoided. Abstract Dynamical systems elicited via state space models are systems that consist of two components: a state and a measurement equation model that evolve over time. This paper addresses Bayesian inference of unknown parameters, or parameter learning, of such systems. Particle-based parameter learning methods form a well-known class of procedures for obtaining inference in state space models where a collection of particles are used to represent the posterior distributions of parameters. However, particle-based learning procedures require the availability of sufficient statistics and tractable posterior distributions of parameters based on these statistics for sampling, which is not always the case in many situations. We address the problem of particle-based learning when sufficient statistics and tractable distributions for sampling are not available. An augmented sequential Markov Chain Monte Carlo (ASMCMC) algorithm is developed for obtaining the posterior distribution of unknown parameters. We provide three guiding examples of nonlinear dynamical systems for which sufficient statistics and tractable distributions for sampling are not available, and illustrate the proposed ASMCMC methodology on these examples based on simulated data. [ABSTRACT FROM AUTHOR]

Abstract Among other model-order reduction techniques, the proper generalized decomposition (PGD) has shown its efficiency to solve static and quasi-static problems in the time domain, in particular combined to the LATIN approach when dealing with nonlinearities. Until now, the PGD has been mostly used in the LATIN algorithm as a time-space decomposition. The first novelty of this paper is the introduction of the material parameters and loading conditions as extra-coordinates into the PGD decomposition in the context of the LATIN nonlinear solver, which has not been done before. The second novelty is the application of this strategy to 3D reinforced concrete structures whose nonlinear behavior is in particular driven by damage and for which a unilateral effect is taken into account. Highlights • The proper generalized decomposition (PGD) combined to the LATIN algorithm are used to solve parametrized nonlinear problems. • Material parameters and loading conditions are introduced into the PGD decomposition, a novelty in the LATIN framework. • The method is applied to the simulation of 3D concrete structures with a damage-driven nonlinear behavior with unilateral effect. • Some examples of virtuals charts are presented to exemplified the capabilities of the approach. [ABSTRACT FROM AUTHOR]

A hybrid invasive weed optimization (HIWO) algorithm based on the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is proposed for the problems on parameter inversion of the nonlinear models of sun shadow with integer variables in the study. Our presented algorithm can take full advantage of the local search ability of BFGS algorithm and the global search ability of invasive weed optimization (IWO) algorithm. The HIWO algorithm can not only reverse the date of sun shadow model successfully, but also conquer the weaknesses that the classic mathematical methods are hard to address integer nonlinear optimization problems by utilizing integers in some random variables from algorithms. The results of numerical experiments demonstrate that the HIWO algorithm has not only high computing accuracy, but also fast convergence speed. It can effectively improve the accuracy and efficiency of the techniques of sun shadow location, and afford an effective and efficient technique to handle the issues of integer parameter inversion in engineering applications. [ABSTRACT FROM AUTHOR]

Summary: A novel adaptive dynamic harmony search (ADHS) algorithm is proposed based on the dynamical parameters that are adjusted using the previous results of the harmony memory with a simple formulation. The accuracy and efficiency of ADHS algorithm are compared with the several improved versions of harmony search through mathematical benchmark examples. The optimum design database of tuned mass damper (TMD) parameters for a damped main system under white‐noise base excitation is extracted by the ADHS algorithm for applicable engineering problem. Four mathematical models are calibrated using the nonlinear training approach‐based ADHS for approximating the optimum tuning TMD parameters. By considering the root mean square error and confidence index, a best nonlinear model is selected among the proposed models using ADHS training scheme and several existing empirical models. A 10‐story benchmark structural example under earthquake excitation is considered for validation of the proposed nonlinear model. The simulation results demonstrate that the ADHS provides more accurate and efficient results than the improved harmony search algorithms for mathematical benchmark examples. The proposed nonlinear model also performs with the efficient computational burdens compared with the optimization algorithms for optimum tuning of TMD parameters of a 10‐story structure, more accurately. [ABSTRACT FROM AUTHOR]

This paper presents a numerical procedure based on a distribution approach for doing parameter estimation in nonlinear dynamical models. The originality of the paper is first, to present a complete study of the errors due to the method and due to the noise on the signal then, to apply it to a recent model describing the transmission of the chikungunya virus to the human population. The advantage of this numerical procedure is not to require any knowledge about the value of the parameters or about the statistics of measurement uncertainties. Furthermore, it attenuates a part of the noise improving consequently the results of the parameter estimation. The numerical results attest the relevance of this approach. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of parameters in estimating equation with nonignorably missing data is considered. Based on a logistic regression model for the response mechanism and an assumed parametric model for the distribution of respondents, we propose to use the sampling importance resampling (SIR) algorithm to calculate the conditional expectation for non-respondents. The proposed method can avoid the difficulty of high-dimensional kernel smoothing on calculating the conditional expectation under nonignorably missing data. Based on the SIR algorithm, we derive a modified estimating equation. To facilitate comparison, we apply the empirical likelihood method to derive the parameters estimator. Some numerical simulation results based on linear and nonlinear models show that the proposed method is robust and performs the best among the compared existing methods. So, we extend the estimation method of E [ g ( Y ) ] using SIR algorithm with nonignorably missing response to the estimation of parameters in generalized estimating equation, and obtain a new and more robust estimation method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a robust estimation procedure based on the exponential squared loss (ESL) function for the varying coefficient partially nonlinear model. Under some conditions, the asymptotic properties of proposed estimators are established. Furthermore, we develop a new minorization–maximization (MM) algorithm to calculate the estimates for both non-parametric and parametric parts, and introduce a data-driven procedure to select the tuning parameters. Simulation studies illustrate that the proposed method is more robust and efficient than the classical least squares technique when there are outliers in the dataset. Finally, we apply the proposed methodology to analyze a real dataset. The results reveal that the proposed has better the predictive ability. [ABSTRACT FROM AUTHOR]

Model-free reinforcement learning and nonlinear model predictive control are two different approaches for controlling a dynamic system in an optimal way according to a prescribed cost function. Reinforcement learning acquires a control policy through exploratory interaction with the system, while nonlinear model predictive control exploits an explicitly given mathematical model of the system. In this article, we provide a comprehensive comparison of the performance of reinforcement learning and nonlinear model predictive control for an ideal system as well as for a system with parametric and structural uncertainties. The comparison is based on two different criteria, namely the similarity of trajectories and the resulting rewards. The evaluation of both methods is performed on a standard benchmark problem: a cart–pendulum swing-up and balance task. We first find suitable mathematical formulations and discuss the effect of the differences in the problem formulations. Then, we investigate the robustness of reinforcement learning and nonlinear model predictive control against uncertainties. The results demonstrate that nonlinear model predictive control has advantages over reinforcement learning if uncertainties can be eliminated through identification of the system parameters. Otherwise, there exists a break-even point after which model-free reinforcement learning performs better than nonlinear model predictive control with an inaccurate model. These findings suggest that benefits can be obtained by combining these methods for real systems being subject to such uncertainties. In the future, we plan to develop a hybrid controller and evaluate its performance on a real seven-degree-of-freedom walking robot. [ABSTRACT FROM AUTHOR]

This paper proposes a nonlinear average model of three levels NPC inverter. This model takes into account the semiconductor non-linearity and static characteristics of these devices. The proposed technique uses experimental results to evaluate the different devices parameters. The developed nonlinear average model allows dissipated power and junction temperature evaluation. Unlike the circuit model (fine model), the proposed method has less computational burden. It can be applied to three levels Neutral-Point-Clamped inverter (NPC). [ABSTRACT FROM AUTHOR]

A one-parametric family of fourth-order iterative methods for solving nonlinear systems is presented, proving the fourth-order of convergence of all members in this family, except one of them whose order is five. The methods in our family are numerically compared with other known methods in terms of the classical efficiency index (order of convergence and number of functional evaluations) and in terms of the operational efficiency index, which also takes into account the total number of product-quotients per iteration. In order to analyze its stability and its dynamical properties, the parameter space for quadratic polynomials is shown. The stability of the strange fixed points is studied in this case. We note that even for this particular case, the family presents a very interesting dynamical behavior. The analysis of the parameter plane allows us to find values for the involved parameter with good stability properties as well as other values with bad numerical behavior. Finally, amongst the first ones, there is a special value of the parameter related to a fifth-order method in the family. [ABSTRACT FROM AUTHOR]

In this article, a new attributes double sampling plan for three-class products (ADSPTP) is presented, and the corresponding operating characteristic function is constructed based on the given procedure of performing ADSPTP. Average sample numbers (ASN) for complete inspection and curtailed inspection of the second sample are derived and the extreme point is discussed on the three-dimensional ASN surface. In addition, the differences arising from different parameters are studied. Sampling plans are designed by a nonlinear optimization model. Finally, numerical examples and discussions are given to illustrate the obtained results, and tables of the designed plans under various conditions are provided. [ABSTRACT FROM AUTHOR]

The brain activity is to a large extent determined by states of neural cortex microcircuits. Unfortunately, accuracy of results from neural circuits׳ mathematical models is often biased by the presence of uncertainties in underlying experimental data. Moreover, due to problems with uncertainties identification in a multidimensional parameters space, it is almost impossible to classify states of the neural cortex, which correspond to a particular set of the parameters. Here, we develop a complete methodology for determining uncertainties and the novel protocol for classifying all states in any neuroinformatic model. Further, we test this protocol on the mathematical, nonlinear model of such a microcircuit developed by Giugliano et al. (2008) and applied in the experimental data analysis of Huntington׳s disease. Up to now, the link between parameter domains in the mathematical model of Huntington׳s disease and the pathological states in cortical microcircuits has remained unclear. In this paper we precisely identify all the uncertainties, the most crucial input parameters and domains that drive the system into an unhealthy state. The scheme proposed here is general and can be easily applied to other mathematical models of biological phenomena. [ABSTRACT FROM AUTHOR]

We investigate here small sample properties of approximateF-tests about fixed effects parameters in nonlinear mixed models. For estimation of population fixed effects parameters as well as variance components, we apply the two-stage approach. This method is useful and popular when the number of observations per sampling unit is large enough. The approximateF-test is constructed based on large-sample approximation to the distribution of nonlinear least-squares estimates of subject-specific parameters. We recommend a modified test statistic that takes into consideration approximation to the large-sample Fisher information matrix (See [Volaufova J, Burton JH. Note on hypothesis testing in mixed models. Oral presentation at: LINSTAT 2012/21st IWMS; 2012; Bedlewo, Poland]). Our main focus is on comparing finite sample properties of broadly used approximate tests (Wald test and likelihood ratio test) and the modifiedF-test under the null hypothesis, especially accuracy ofp-values (See [Volaufova J, LaMotte L. Comparison of approximate tests of fixed effects in linear repeated measures design models with covariates. Tatra Mountains. 2008;39:17–25]). For that purpose two extensive simulation studies are conducted based on pharmacokinetic models (See [Hartford A, Davidian M. Consequences of misspecifying assumptions in nonlinear mixed effects models. Comput Stat and Data Anal. 2000;34:139–164; Pinheiro J, Bates D. Approximations to the log-likelihood function in the non-linear mixed-effects model. J Comput Graph Stat. 1995;4(1):12–35]). [ABSTRACT FROM AUTHOR]

The purpose of the optimum designs is to determine the optimal experimental conditions in terms of minimum variance of the estimated vector of parameters, so that statistical inferences can be generated as accurate as possible. This theory presupposes knowledge of the function relating the explanatory variables with the response variable. In this situation, usually get designs with support points as parameters in the model. Since p-point designs assume that the model function is known, these could not be optimal in some practical situations because they do not allow to test the goodness of fit of the assumed model. In this paper we present a generalization of the methodology proposed by to increase the number of support points in D-optimality criterion. An expression for the variance of the predicted response in terms of a constant δ will be provided, which allow to determine the points to be added to the D-optimal design. We propose a strategy for choosing δ. Finally we provide a pseudo-optimal design with (p + s) support points. [ABSTRACT FROM AUTHOR]

Abstract: Interest in soft robots is motivated by their enormous potential in applications with close contact to humans or unpredictable situations for which their soft structure and versatility is beneficial. New mathematical models and control strategies are required to optimize the geometry and performance of the soft components of these robots. The authors use a nonlinear rod model to describe a pneumatically actuated quadruped soft robot and to study the influences of different parameters on its performance. Although the model does not accommodate contact situations perfectly, it is suitable to study general interrelations. These resulting studies serve to enhance the development of soft robots. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]