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Parametric identification is an important part of system theory since knowledge of the parameters allows the analysis and control of the system. The aim of this paper is to propose a novel robust (against measurement noise) parameter identification method for a class of nonlinear fractional-order systems. In order to solve the parametric identification we carry out this problem to a state estimation problem, we introduce a Fractional Algebraic Identifiability (FAI) property which allows to represent the system parameters as a function of the inputs and outputs of the system, this parameter identification method provides an on-line identification process (while the system is operating), we also propose a fractional-order differentiator which allows to reduce the effect of measurement noise as well as to provide the estimation of a fractional-order derivative of the system output. Moreover, we use the Mittag–Leffler boundedness to demonstrate the convergence of this method, a different approach for this stability analysis method is given in this paper. Finally, we illustrate the accuracy and robustness of our proposed method by means of the parametric identification of two nonlinear fractional-order systems: a time-varying nonlinear fractional-order system and a nonlinear fractional-order mathematical model of a simple pendulum.

This paper proposes an integrated geometric error prediction and compensation method to eliminate the positioning inaccuracy of tool ball for a double ball bar (DBB) caused by the translational axes’ geometric errors in a multi-axis machine tool (MAMT). Firstly, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, the positioning error model only considering the translational axes of a MAMT is established. Then, an integrated error parameter identification method (IEPIM) by using a laser interferometer is proposed. Meanwhile, the identification discrete results of geometric error parameters for the translational axes are obtained by identification experiments. According to the discrete values, the optimal polynomials of 18 position-dependent geometric errors (PDGEs) are founded. As a basis, an iterative compensation method is constructed to modify the NC codes generated with the ordinary compensation method in self-developed compensation software. Finally, simulation verification is conducted with these two compensation methods. Simulation results show the positioning errors for test path of tool ball calculated with the iterative compensation method that are limited within 0.001 mm, and its average accuracy and accuracy stability are improved by 79.5 and 52.2%, respectively. In order to further verify the feasibility of the presented method, a measuring experiment is carried out in XY plane of a five-axis machine tool by using DBB. The experiment results show that the maximum circularity error with the iterative compensation method is reduced about 40.4% than that with the ordinary compensation method. It is therefore reasonable to conclude that the proposed method in this paper can avoid the influence of the translational axes’ geometric errors on rotary ones during a DBB test.

In this manuscript, we systematically investigate projective difference synchronization between identical generalized Lotka–Volterra biological models of integer order using active control and parameter identification methods. We employ Lyapunov stability theory (LST) to construct the desired controllers, which ensures the global asymptotical convergence of a trajectory following synchronization errors. In addition, simulations were conducted in a MATLAB environment to illustrate the accuracy and efficiency of the proposed techniques. Exceptionally, both experimental and theoretical results are in excellent agreement. Comparative analysis between the considered strategy and previously published research findings is presented. Lastly, we describe an application of our considered combination difference synchronization in secure communication through numerical simulations.

Damping is a fundamental characteristic of bridge structures, reflecting their ability to dissipate energy during vibration. In the design and maintenance of bridges, the damping ratio has a direct impact on the safety and service life of the structure, thus affecting its sustainability. Currently, there is no suitable theoretical method for estimating structural damping at the design stage. Therefore, the modal damping ratio of a completed or under-construction bridge can only be obtained through field dynamic tests to ensure compliance with design specifications. To summarize the latest research findings on bridge structure damping models and identification methods, and to advance the development of damping identification techniques, this paper provides an in-depth review from several perspectives: Firstly, it offers a comprehensive analysis of the theoretical framework for structural damping. Secondly, it summarizes the damping models proposed by researchers from various countries. Thirdly, it reviews the research progress on identifying the modal damping ratio of bridge structures using time domain, frequency domain, and time-frequency domain methods based on environmental excitation. It also summarizes the methods and current status of identifying the modal damping ratio using artificial excitation. Finally, the future prospects and conclusions are discussed from three aspects: damping theory, test and identification method and data processing. This research and summary provide a solid theoretical foundation for advancing bridge structural damping theory and identification methods and offer valuable references for bridge operation and maintenance, as well as damage identification. From the perspective of modal parameter identification, it provides a theoretical basis for the sustainable development of bridges.

Since rail-to-ground insulation decreases, large-level direct currents (DCs) leak from railways and form metro stray currents, corroding the buried metal. To locate the rail-to-ground insulation deterioration area, a location method is proposed based on parameter identification methods and the monitored information including the station rail potentials, currents at the traction power substations (TPSs), and train traction currents and train positions. According to the monitoring information of two adjacent TPSs, the section location model of the metro line is proposed, in which the rail-to-ground conductances of the test section are equivalent to the lumped parameters. Using the rail resistivity and traction currents as the known information, the rail-to-ground conductances are calculated with the least square method (LSM). The rail-to-ground insulation deterioration sections are identified by comparing the calculated conductances with thresholds determined by the standard requirements and section lengths. Then, according to the section location results, a detailed location model of the degradation section is proposed, considering the location distance accuracy. Using the genetic algorithm (GA) to calculate the rail-to-ground conductances, degradation positions are located by comparing the threshold calculated with the standard requirements and location distance accuracy. The location method is verified by comparing the calculation results under different degradation conditions. Moreover, the applications of the proposed method to different degradation lengths and different numbers of degradation sections are analyzed. The results show that the proposed method can locate rail-to-ground insulation deterioration areas.

Rubber isolators are usually used to protect high-precision equipment of autonomous underwater vehicles (AUVs), avoiding damage from overlarge dynamic excitation. Considering the nonlinear properties of the rubber material, the nonlinear behavior of rubber isolators under shock exaltation is hard to be predict accurately without the available modal and accurate parameters. In view of this, the present study proposes a nonlinear model and parameter identification method of rubber isolators to present their transient responses under shock excitation. First, a nonlinear model of rubber isolators is introduced for simulating their amplitude and frequency-dependent deformation under shock excitation. A corresponding dynamic equation of the isolation system is proposed and analytically solved by the Newmark method and the Newton-arithmetic mean method. Secondly, a multilayer feed-forward neural network (MFFNN) is constructed with the current model to search the parameters, in which the differences between the estimated and tested responses are minimized. The sine-sweep and drop test are planned with MFFNN to build the parameter identification process of rubber isolators. Then, a T-shaped isolator composed of high-damping silicon rubber is selected as a sample, and its parameters were determined by the current identification process. The transient responses of the isolation system are reconstructed by the current mode with the identified parameter, which show good agreement with measured responses. The accuracy of the proposed model and parameter identification method is proved. Finally, the errors between the reconstructed responses and tested responses are analyzed, and the main mode of energy attenuation in the rubber isolator is discussed in order to provide an inside view of the current model.

To solve the problem of uncertain parameters in dynamic modelling of upper‐limb rehabilitation robots, a dynamic parameter identification method based on variable parameters particle swarm optimisation (PSO) is developed. Based on the dynamic model of the system, the algorithm changes the inertia parameter and learning law of the basic PSO algorithm from the fixed‐parameter to the function that changes with the number of iterations. It solves the problems of small search space in the early stage and slow convergence speed in the later stage of the basic PSO algorithm, which greatly improves its identification accuracy. Finally, through the comparison and analysis of the simulation results, compared with those of the least square (LS) and unmodified PSO identification algorithms, a great improvement in the identification accuracy of the algorithm is achieved. The control effect in the actual control system is also much better than those of the LS and PSO algorithms.

Battery modeling plays an important role in estimating battery states which include state of charge (SOC), state of health (SOH), state of energy (SOE), and state of power (SOP). This chapter provides a brief introduction of electrochemical models (EMs) and black box models, and explains equivalent circuit models (ECMs) as well as the methods to identify the parameters of ECMs in detail. Black box models can simulate a complex relationship between external parameters of batteries without knowing their internal electrochemical reaction process, such as the relationship of the SOC to battery terminal voltage and discharge current. Depending on the use of experiment data offline or online, parameter identification methods can be divided into the offline parameter identification method (OFFPIM) and online parameter identification method (ONPIM). The OFFPIM and the ONPIM are analyzed and evaluated by considering these uncertain factors, such as battery aging, battery type, and battery temperature.

A parameter identification method for generator speed governor system, which combines decoupling parameter identification and overall recognition with measured data, was proposed in the paper. The method bases on particle swarm optimization, and takes parameter identification as a parameters optimization problem under evaluation function. According to an intelligent optimization algorithms evolutionary strategy, the individual's status is continuously adjusted until the identification system and actual system output error is sufficiently small. Case studies show that the proposed method can be applied to the measured parameters and model validation work.

In this paper, based on log response in gas formation, effective identification curves for shallow gas reservoirs are preferred from casedhole compensated neutron log, neutron lifetime log and openhole logs, and 4 parameters and 5 overlap curves are developed for identification of shallow gas reservoirs in cased wells. A gas reservoir in cased wells is interpreted with proposed identification methods. The gas production testing results shows that the proposed methods can determine shallow gas reservoirs in cased wells accurately.