Model Parameters Identification and Backstepping Control of Lower Limb Exoskeleton Based on Enhanced Whale Algorithm

Exoskeletons generally require accurate dynamic models to design the model-based controller conveniently under the human-robot interaction condition.However,due to unknown model parameters such as the mass,moment of inertia and mechanical size,the dynamic model of exoskeletons is difficult to construct.Hence,an enhanced whale optimization algorithm(EWOA)is proposed to identify the exoskeleton model parameters.Meanwhile,the periodic excitation trajectories are designed by finite Fourier series to input the desired position demand of exoskeletons with mechanical physical constraints.Then a backstepping controller based on the identified model is adopted to improve the human-robot wearable comfortable performance under cooperative motion.Finally,the proposed Model parameters identification and control are verified by a two-DOF exoskeletons platform.The knee joint motion achieves a steady-state response after 0.5 s.Meanwhile,the position error of hip joint response is less than 0.03 rad after 0.9 s.In addition,the steady-state human-robot interaction torque of the two joints is constrained within 15 N·m.This research proposes a whale optimization algorithm to optimize the excitation trajectory and identify model parameters.Furthermore,an enhanced mutation strategy is adopted to avoid whale evolution’s unsatisfactory local optimal value.

Quaternion-Based Adaptive Trajectory Tracking Control of a Rotor-Missile with Unknown Parameters Identification

This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties.First,considering the uncertainty of structural and aerodynamic parameters,the six-degree-of-freedom(6Do F) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established,respectively,in the inertial and body-fixed reference frames.Next,a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6Do F dynamics.Then,a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix.As long as the finitely excited condition is satisfied,the precise identification of unknown parameters can be achieved.Finally,the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.

Flight Flutter Modal Parameters Identification with Atmospheric Turbulence Excitation Based on Wavelet Transformation

In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters is presented. This approach firstly uses random decrement technique to gain free decays corresponding to the acceleration response of the structure to some non-zero initial conditions. Then the continuous Morlet wavelet transformation of the free decays is performed; and the Parseval formula and residue theorem are used to simplify the transformation. The maximal wavelet transformation coefficients in different scales are searched out by means of band-filtering characteristic of Morlet wavelet, and then the modal parameters are identified according to the relationships with maximal modulus and angle of the wavelet transform. In addition, the condition of modal uncoupling is discussed according to variation trend of flight flutter modal parameters in the flight flutter state. The analysis results of simulation and flight flutter test data show that this approach is not only simple, effective and feasible, but also having good noise immunity.

Synchronization and Parameters Identification of Chaotic Systems via Adaptive Control

Based on Lyapunov stability theory, a novel adaptive controller is designed for a class of chaotic systems .The parameters identification and synchronization of chaotic systems can be carried out simultaneously. The controller and the updating law of parameters identification are directly constructed by analytic formula. Simulation results with Chen’s system and R?ssler system show the effectiveness of the proposed controller.

PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.

THEORY AND METHOD OF OPTIMAL CONTROL SOLUTION TODYNAMIC SYSTEM PARAMETERS IDENTIFICATION (Ⅰ)──FUNDAMENTAL CONCEPT AND DETERMINISTIC SYSTEM PARAMETERS IDENTIFICATION

Based on the concept of optimal control solution to dynamic system parameters identification and the optimal control theory of deterministic system,dyna-mics system parameters identfication problem is brought into correspondence with optimal control problem. Then the theory and algorithm of optimal control are introduced into the study of dynamic system parameters identification. According to the theory of Hamilton-Jacobi-Bellman (HJB) equations solution, the existence and uniqueness of optimal control solution to dynamic system parameters identification are resolved in this paper. At last, the parameters identification algorithm of determi-nistic dynamic system is presented also based on above mentioned theory and concept.

THEORY AND ALGORITHM OF OPTIMAL CONTROL SOLUTION TO DYNAMIC SYSTEM PARAMETERS IDENTIFICATION(Ⅱ)──STOCHASTIC SYSTEM PARAMETERS IDENTIFICATION AND APPLICATION EXAMPLE

Based on the contents Of part (Ⅰ) and stochastic optimal control theory, the concept of optimal control solution to parameters identification of stochastic dynamic system is discussed at first. For the completeness of the theory developed in this paper and part (Ⅰ), then the procedure of establishing HamiltonJacobi-Bellman (HJB) equations of parameters identification problem is presented.And then, parameters identification algorithm of stochastic dynamic system is introduced. At last, an application example-local nonlinear parameters identification of dynamic system is presented.

Electrical model parameters identification of radiofrequency discharge in argon through 1D3V/PIC-MC model

This work represents a contribution to the modeling of a radiofrequency（RF） discharge in argon at low pressure（from 25 to 200 mTorr）.It is started by the validation of the collision cross sections used in the particle model through a comparison between the transport coefficients calculated by these data and the measurements of the transport coefficients already exist in the literature,the particle model is also validated by a comparison between the calculated plasma density and that measured in the literature.The electrical model proposed in this work consists of replacing the RF discharge by a passive circuit（resistance in series with a capacitor）,where the resistance represents the plasma medium and the obstruction of the passage of the electronic current,and the capacitor represents the sheaths and the appearance of the displacement current in these regions.The parameters of the electrical model are obtained through particle modeling.The electrical model presented accurately reproduces the current of the discharge,but without considering the phenomenon of distortion.The total harmonic distortion rate follows the variation of the plasma density;its maximum value is 5.75% at 100 mTorr.

THE APPLICATION OF ACOUSTIC LOGGING METHOD IN THE MODEL AND PARAMETERS IDENTIFICATION OF ROCK MASS

This paper describes the new method that is introduced into prediction of subsidence using system engineering method with acoustic logging and density logging. According to the result of acoustic logging, the real and complex rock beds are divided into a set of different bed groups and the equivalent mechanical model is to be built. Based on the modern control theory,according to the input data (convergence or settlement of the roof) and the output data (surface movement and deformation) of the system, the static parameters of equivalent rock beds can be derived from back calculation using the optimum method. Then the reqression relationship between the dynamic and static parameters can be built. So the prediction of rock and ground movements for other areas in the same district can be done, when using this relationship with the acoustic logging data and density logging data in situ.

Numerical-experimental method for elastic parameters identification of a composite panel

A hybrid numerical-experimental approach to identify elastic modulus of a textile composite panel using vibration test data is proposed and investi- gated. Homogenization method is adopted to predict the initial values of elastic parameters of the composite, and parameter identification is transformed to an optimization problem in which the objective function is the minimization of the discrepancies between the experimental and numerical modal data. Case study is conducted employing a woven fabric reinforced composite panel. Three parameters （Ell, E22, G12） with higher sensitivities are selected to be identified. It is shown that the elastic parameters can be accurately identified from experimental modal data.

Parameters Identification of Tunnel Jointed Surrounding Rock Based on Gaussian Process Regression Optimized by Difference Evolution Algorithm

Due to the geological body uncertainty,the identification of the surrounding rock parameters in the tunnel construction process is of great significance to the calculation of tunnel stability.The ubiquitous-joint model and three-dimensional numerical simulation have advantages in the parameter identification of surrounding rock with weak planes,but conventional methods have certain problems,such as a large number of parameters and large time consumption.To solve the problems,this study combines the orthogonal design,Gaussian process(GP)regression,and difference evolution(DE)optimization,and it constructs the parameters identification method of the jointed surrounding rock.The calculation process of parameters identification of a tunnel jointed surrounding rock based on the GP optimized by the DE includes the following steps.First,a three-dimensional numerical simulation based on the ubiquitous-joint model is conducted according to the orthogonal and uniform design parameters combing schemes,where the model input consists of jointed rock parameters and model output is the information on the surrounding rock displacement and stress.Then,the GP regress model optimized by DE is trained by the data samples.Finally,the GP model is integrated into the DE algorithm,and the absolute differences in the displacement and stress between calculated and monitored values are used as the objective function,while the parameters of the jointed surrounding rock are used as variables and identified.The proposed method is verified by the experiments with a joint rock surface in the Dadongshan tunnel,which is located in Dalian,China.The obtained calculation and analysis results are as follows:CR=0.9,F=0.6,NP=100,and the difference strategy DE/Best/1 is recommended.The results of the back analysis are compared with the field monitored values,and the relative error is 4.58%,which is satisfactory.The algorithm influencing factors are also discussed,and it is found that the local correlation coefficientσf and noise standard deviationσn affected the prediction accuracy of the GP model.The results show that the proposed method is feasible and can achieve high identification precision.The study provides an effective reference for parameter identification of jointed surrounding rock in a tunnel.

STPGTN-AMulti-Branch Parameters Identification Method Considering Spatial Constraints and Transient Measurement Data

Transmission line(TL)Parameter Identification(PI)method plays an essential role in the transmission system.The existing PI methods usually have two limitations:(1)These methods only model for single TL,and can not consider the topology connection of multiple branches for simultaneous identification.(2)Transient bad data is ignored by methods,and the random selection of terminal section data may cause the distortion of PI and have serious consequences.Therefore,a multi-task PI model considering multiple TLs’spatial constraints and massive electrical section data is proposed in this paper.The Graph Attention Network module is used to draw a single TL into a node and calculate its influence coefficient in the transmission network.Multi-Task strategy of Hard Parameter Sharing is used to identify the conductance ofmultiple branches simultaneously.Experiments show that themethod has good accuracy and robustness.Due to the consideration of spatial constraints,the method can also obtain more accurate conductance values under different training and testing conditions.

TIME DOMAIN PARAMETERS IDENTIFICATION OF FOUNDATION-STRUCTURE INTERACTION SYSTEM

The time domain parameter laenuncauon memoa oi me iounuauon-structure interaction system is presented. On the basis of building the computation mode and the motion equation of the foundation-structure interaction system, the system parameter identification method was established by using the extended Kalman filter （EKF） technique and taking the unknown parameters in the system as the augment state variables. And the time parameter identification process of the foundation-structure interaction system was implemented by using the data of the layer foundation-storehouse interaction system model test on the large vibration platform. The computation result shows that the established parameter identification method can induce good parameter estimation.

Parameters identification of the compound cage rotor induction machine based on linearized Kalman filtering

A mathematical model has been built up for compound cage rotor induction machine with the rotor resistance and leakage inductance in the model identified through Kalman filtering method. Using the identified parameters, simulation studies are performed, and simulation results are compared with testing results.

Parameters Identification for Extended Debye Model of XLPE Cables Based on Sparsity-Promoting Dynamic Mode Decomposition Method

To identify the parameters of the extended Debye model of XLPE cables,and therefore evaluate the insulation performance of the samples,the sparsity-promoting dynamicmode decomposition(SPDMD)methodwas introduced,aswell the basics and processes of its applicationwere explained.The amplitude vector based on polarization current was first calculated.Based on the non-zero elements of the vector,the number of branches and parameters including the coefficients and time constants of each branch of the extended Debye model were derived.Further research on parameter identification of XLPE cables at different aging stages based on the SPDMD method was carried out to verify the practicability of the method.Compared with the traditional differential method,the simulation and experiment indicated that the SPDMD method can effectively avoid problems such as the relaxation peak being unobvious,and possessing more accuracy during the parameter identification.And due to the polarization current being less affected by the measurement noise than the depolarization current,the SPDMD identification results based on the polarization current spectral line proved to be better at reflecting the response characteristics of the dielectric.In addition,the time domain polarization current test results can be converted into the frequency domain,and then used to obtain the dielectric loss factor spectrum of the insulation.The integral of the dielectric loss factor on a frequency domain can effectively evaluate the insulation condition of the XLPE cable.

An innovative inertial parameters identification method for non-cooperative space targets based on electrostatic interaction

Inertial characteristics of non-cooperative targets are crucial for space capture and sub-sequent on-orbit servicing.Previous methods for identifying inertial parameters involve proximity operations,which are associated with the risk of collision with non-cooperative targets.This paper introduces a long-range,contactless method for identifying the inertial parameters of a non-cooperative target during the pre-capture phase.Specifically,electrostatic interaction is used as an external excitation to alter the target's motion.A force estimation algorithm that uses measure-ments from visual and potential sensors is proposed to estimate the electrostatic interaction and eliminate the need for force sensors.Furthermore,a recursive estimation-identification framework is presented to concurrently estimate the coupled motion state,weak electrostatic interaction,and inertial parameters of the target.The simulation results show that the proposed method extends the identification distance to 170 times that of the previous method while maintaining high identifica-tion precision forall parameters.

Online battery model parameters identification approach based on bias-compensated forgetting factor recursive least squares

Accuracy of a lithium-ion battery model is pivotal in faithfully representing actual state of battery,thereby influencing safety of entire electric vehicles.Precise estimation of battery model parameters using key measured signals is essential.However,measured signals inevitably carry random noise due to complex real-world operating environments and sensor errors,potentially diminishing model estimation accuracy.Addressing the challenge of accuracy reduction caused by noise,this paper introduces a Bias-Compensated Forgetting Factor Recursive Least Squares(BCFFRLS)method.Initially,a variational error model is crafted to estimate the average weighted variance of random noise.Subsequently,an augmentation matrix is devised to calculate the bias term using augmented and extended parameter vectors,compensating for bias in the parameter estimates.To assess the proposed method's effectiveness in improving parameter identification accuracy,lithium-ion battery experiments were conducted in three test conditions—Urban Dynamometer Driving Schedule(UDDS),Dynamic Stress Test(DST),and Hybrid Pulse Power Characterization(HPPC).The proposed method,alongside two contrasting methods—the offline identification method and Forgetting Factor Recursive Least Squares(FFRLS)—was employed for battery model parameter identification.Comparative analysis reveals substantial improvements,with the mean absolute error reduced by 25%,28%,and 15%,and the root mean square error reduced by 25.1%,42.7%,and 15.9%in UDDS,HPPC,and DST operating conditions,respectively,when compared to the FFRLS method.

State of charge estimation by finite difference extended Kalman filter with HPPC parameters identification

State of charge(SOC) is a key parameter of lithium-ion battery. In this paper, a finite difference extended Kalman filter(FDEKF)with Hybrid Pulse Power Characterization(HPPC) parameters identification is proposed to estimate the SOC. The finite difference(FD) algorithm is benefit to compute the partial derivative of nonlinear function, which can reduce the linearization error generated by the extended Kalman filter(EKF). The FDEKF algorithm can reduce the computational load of controller in engineering practice without solving the Jacobian matrix. It is simple of dynamic model of lithium-ion battery to adopt a secondorder resistor-capacitor(2 RC) network, the parameters of which are identified by the HPPC. Two conditions, both constant current discharge(CCD) and urban dynamometer driving schedule(UDDS), are utilized to validate the FDEKF algorithm.Comparing convergence rate and accuracy between the FDEKF and the EKF algorithm, it can be seen that the former is a better candidate to estimate the SOC.

A comparative study of different online model parameters identification methods for lithium-ion battery

Precise states estimation for the lithium-ion battery is one of the fundamental tasks in the battery management system(BMS),where building an accurate battery model is the first step in model-based estimation algorithms.To date,although the comparative studies on different battery models have been performed intensively,little attention is paid to the comparison among different online parameters identification methods regarding model accuracy,robustness ability,adaptability to the different battery operating conditions and computation cost.In this paper,based on the Thevenin model,the three most widely used online parameters identification methods,including extended Kalman filter(EKF),particle swarm optimization(PSO),and recursive least square(RLS),are evaluated comprehensively under static and dynamic tests.It is worth noting that,although the built model’s terminal voltage may well follow a measured curve,these identified model parameters may significantly out of reasonable range,which means that the error between measured and predicted terminal voltage cannot be seen as a gist to determine which model is the most accurate.To evaluate model accuracy more rigorously,battery state-of-charge(SOC)is further estimated based on identified model parameters under static and dynamic tests.The SOC prediction results show that EKF and RLS algorithms are more suitable to be used for online model parameters identification under static and dynamic tests,respectively.Moreover,the random offset is added into originally measured data to verify the robustness ability of different methods,whose results indicate EKF and RLS have more satisfactory ability against imprecisely sampled data under static and dynamic tests,respectively.Considering model accuracy,robustness ability,adaptability to the different battery operating conditions and computation cost simultaneously,EKF is recommended to be adopted to establish battery model in real application among these three most widely used methods.

Identification of material parameters from punch stretch test

To accurately describe the mechanical properties of aluminium alloy sheet during deformation, an inverse identification was presented to deal with material parameters from the popular punch stretch test. In the identification procedure, the optimization strategy combines finite element method （FEM）, Latin hypercube sampling （LHS）, Kriging model and multi-island genetic algorithm （MIGA）. The proposed approach is used on material parameter identification of aluminium alloy sheet 2D12. The anisotropic yield criterion Hill’90 is discussed. The results show that the Hill’90 anisotropic yield criterion with identified anisotropic material parameters has a good potential in describing the anisotropic behaviours. It provides a way to obtain the material parameters for FE simulations of sheet metal forming.