Parameter Identification Of Systems Research Articles

Identification of fractional order non– homogeneous Hammerstein-Wiener MISO continuous systems

Aiming at the problem of difficult identification of parameters in fractional non-homogeneous Hammerstein-Wiener nonlinear MISO time-delay continuous systems, an algorithm that can simultaneously identify coupled coefficients, orders, and time-delays in nonlinear fractional-order systems is designed. In this algorithm, a fractional order fitting model is constructed by using the Legendre wavelet operation matrix, and a full-parameter partial derivative model of the time-delay nonlinear system is derived. Second, the sequential quadratic programming (SQP) method is used to simultaneously estimate the non-homogeneous order, delay parameters, and coefficient parameters of the fractional order system. Finally, the effectiveness of the proposed algorithm is demonstrated through an academic example and a two-wall heat conduction system with a nonlinear fractional order system of MISO.

Data filtering based multi‐innovation gradient identification for bilinear systems with colored noise

SummarySystem identification is the powerful tool to establish the mathematical models of practical systems. This article considers the parameter identification for bilinear systems with colored noise. First, the bilinear system is transformed into an input‐output form by eliminating the state variables in the model. Then, based on the data filtering technique, the measured input‐output data is filtered using an estimated noise transfer function, and a filtering based generalized extended stochastic gradient (F‐GESG) algorithm is proposed to enhance the parameter estimation accuracy. Furthermore, the multi‐innovation identification theory is employed to improve the convergence speed of the proposed F‐GESG algorithm, and a filtering based multi‐innovation generalized extended stochastic gradient (F‐MI‐GESG) algorithm is developed to identify the parameters of bilinear systems. The GESG algorithm is given for comparison. Finally, a numerical simulation example is provided to illustrate the effectiveness and excellent performance of the proposed algorithms.

Editorial for the special issue “Control‐theoretic approaches for systems in the life sciences”

Editorial for the special issue “Control<scp>‐theoretic</scp> approaches for systems in the life sciences”

Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach

This work describes the parameter identification of servo systems using the least squares of orthogonal distances method. The parameter identification problem was reconsidered as data fitting to a plane, which in turn corresponds to a nonlinear minimization problem. Three models of a servo system, having one, two, and three parameters, were experimentally identified using both the classic least squares and the least squares of orthogonal distances. The models with two and three parameters were identified through numerical routines. The servo system model with a single parameter only considered the input gain. In this particular case, the analytical conditions for finding the critical points and for determining the existence of a minimum were presented, and the estimate of the input gain was obtained by solving a simple quadratic equation whose coefficients depended on measured data. The results showed that as opposed to the least squares method, the least squares of orthogonal distances method experimentally produced consistent estimates without regard for the classic persistency-of-excitation condition. Moreover, the parameter estimates of the least squares of orthogonal distances method produced the best tracking performance when they were used to compute a trajectory-tracking controller.

Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester

• An improved approximate Bayesian method is proposed. • The unknown parameters of chaotic VEH system are identified by improved approximate Bayesian method. • The 0-1 test is used to judge the chaotic occur based on the correlation of the response data In this paper, the approximate Bayesian computation combines the particle swarm optimization and sequential Monte Carlo methods, which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system. Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed, which verifies the effectiveness of the proposed method. Finally, a partial response sample of the regular and chaotic responses, determined by the maximum Lyapunov exponent, is applied to detect whether chaotic motion occurs in them by a 0-1 test. This paper can provide a reference for data-based parameter identification and chaotic prediction of chaotic vibration energy harvester systems.

Nonlinear adaptive sliding mode control with application to quadcopters

AbstractNonlinear adaptive sliding mode control (NASMC) has the capability to adequately control a system whose parameters are unknown to the controller designer. Conventional model-based controllers require a mathematical dynamic model of the system with known parameters. These system parameters are normally determined by extensive system identification experiments, which are expensive and time-consuming to perform. A NASMC approach that does not require known system parameters is proposed. Using NASMC, a controller designer can skip the expensive and time-consuming system parameter identification and fast-forward to the control implementation. In addition, once a controller is derived for a quadcopter using NASMC, the same controller will work on any quadcopter with the same equations of motion but different dynamic parameters. The formulation of the NASMC is presented for general second-order and fourth-order systems. Then, as an implementation example, the application of the general NASMC approach is demonstrated by applying it to a quadcopter unmanned aerial vehicle in simulation.

An improved Hammerstein system identification method using Stein Variational Inference and sampling technology

This paper considers the identification of the Hammerstein system with immeasurable process noise. The complexity of the Hammerstein system makes it difficult to obtain accurate mathematical expressions of the parameters, or even impossible to obtain accurate mathematical expressions at all. In this contribution, we cast the Hammerstein system parameter identification problem as a posterior parameter estimation problem and take a sampling and Stein variational inference viewpoint to solve it. Improved Stein variational gradient descent(ISVGD)algorithm is proposed in posterior parameter calculation. Compared with other methods, not only the prior distribution of parameters but also the proposal distribution of parameters is considered. In other words, The posterior information is enriched and the parameter identification accuracy is improved. At the same time, ISVGD and reversible jump markov chain monte carlo (RJMCMC) algorithms are used (called ISVGD-RJMCMC algorithm) in the structure detection problem. In the algorithm, the correct basis function number k can be found in the parameter estimation. It tends to be accurate but is slow to converge. Three simulation examples were given to demonstrate the proposed algorithm’s effectiveness. Furthermore, the performances of these approaches were analyzed, including parameter estimation accuracy and error, system order estimation and parameter convergence analysis.

Fast Detection Method on Water Tree Aging of MV Cable Based on Nonsinusoidal Response Measurement

A MV power cable will exhibit nonlinear impedance when dendritic defects appear. To solve the long time-consuming measurement of pure sinusoidal excitation and realize rapid and accurate evaluation of insulation conditions, a measurement and evaluation method based on nonsinusoidal excitation is proposed in this paper. Firstly, a nonsinusoidal excitation test system is established, which can obtain the high voltage dielectric response in the frequency range of 0.01 Hz–1 kHz. For parameterizing dielectric response characteristics of MV XLPE insulation under nonsinusoidal excitation, a Hammerstein-Wiener model is proposed to realize system parameter identification under non sinusoidal excitation with different aging degrees of water tree. The time-domain current response waveform based on the H-W model is more accurate than the traditional linear model, and the resulting fitting degree of the frequency-domain dielectric loss factor curve between the calculated H-W model and the measured curve was higher than 95%. The results show that the rotation and distortion of the u-i hysteresis ellipse under nonsinusoidal excitation can be used to diagnose the insulation defects of XLPE MV cables. The response model and its detection method proposed in this paper can improve the efficiency and accuracy of the field tests of cable insulation.

Parameter Estimation of Fractional-Order Chaotic Power System Based on Lens Imaging Learning Strategy State Transition Algorithm

Parameter identification of fractional-order chaotic power systems is a multidimensional optimization problem that plays a decisive role in the synchronization and control of fractional-order chaotic power systems. In this paper, a state transition algorithm based on the lens imaging learning strategy is proposed for parameter identification of fractional-order chaotic power systems. Taking a fractional-order six-dimensional chaotic power system mathematical model as an example, the mathematical model and chaotic state are analyzed. First, the Tent chaotic mapping is used to initialize the population, thus increasing population diversity. The randomness and ergodicity of the Tent chaotic sequence are used to enhance the global searching ability of the algorithm. Second, a maturity index is employed to determine population maturity. The lens imaging learning strategy is used to suppress the premature convergence of the state transition algorithm effectively and help the population jump out of local optima. Finally, the improved state transition algorithm is used to identify the parameters of the fractional-order six-dimensional chaotic power system model. The proposed improved state transition algorithm shows high estimation accuracy and convergence speed, and is superior to the traditional state transition and particle swarm optimization algorithms. The simulation results show that the parameters of the fractional-order chaotic power system are identified accurately even in the presence of white noise, demonstrating the strong robustness and versatility of the proposed algorithm.

Investigation on Characteristic Parameters Identification and Evolution of Supercapacitor Energy Storage System From Sparse and Fragmented Monitoring Data

Supercapacitors with advantages of high-power density, fast charging speed and long cycle life, have very promising application prospects in many fields such as transportation and energy storage. Usually, the onboard operation profiles will be recorded and sent to remote monitoring terminal for further study. As the working condition of onboard supercapacitor is complex and fluctuating, it requires high sampling frequency, accuracy, and continuous recording. However, the remote monitoring data usually has the problems of low sampling frequency and fragmented recording, making it difficult to extract the characteristic parameters by traditional parameter identification methods. To solve the problem, this paper makes an extensive investigation on the long-term remote monitoring data of a supercapacitor tram and proposes a set of data processing method that can extract the characteristic parameters of supercapacitors from the sparse and fragmented data. Firstly, a group of proper data segments considering thermal stability of supercapacitor system was selected as effective data from the fragmented daily monitoring data. Secondly, the parameters which can be used to study the aging indicators are extracted by interior point method. With this method, the simulated voltage error is within 0.3% with a sampling frequency of 0.1 Hz. Through analyzing 3.5 years of remote monitoring data, it is found that the characteristic parameters exhibit the feature of seasonal fluctuations, which is highly related to temperature. To further extract the aging trend, a linear fitting model which eliminates the effect of seasonal fluctuations is proposed which can be used for analyzing the evolution characteristic of the studied supercapacitor system.

Current Controller Based on Active Disturbance Rejection Control With Parameter Identification for PMSM Servo Systems

Current Controller Based on Active Disturbance Rejection Control With Parameter Identification for PMSM Servo Systems

DECENTRALIZED COORDINATED CONTROL OF CONTINUOUS MULTI-ZONE OBJECTS

Distributed continuous multi-zone objects are widespread both in production and in everyday life. Centralized and hierarchical control systems have a rigid relationship structure and are difficult to scale. This complicates their application to objects with frequent and rapid changes in its structure and requirements. The authors have proposed a new approach to the decentralized coordination of control of multi-zone thermal objects, however, the problem of coordination control of the state of continuous multi-zone distributed objects with a dynamic structure and variable requirements has not yet been effectively solved. The aim of the work is to generalize the approach to decentralized coordination of control of distributed systems with multi-zone objects of continuous type. The results of the work are based on the methods of the automatic control theory, heat engineering and simulation modeling. The methodology of decentralized coordination control, in particular the model of the distributed control system of a multi-zonal continuous object, the method of decentralized coordination based on the global-local criterion, the principle of close action, the approaches to active and passive identification of system parameters, the method of forecasting the state of the system based on analysis of spatial-time spectrum of object states were generalized in the work. Based on theoretical studies, a decentralized indoor microclimate control system was proposed. Further research is expected to be directed to the tasks of decentralized coordination by non-linear objects and to the expansion of the scope of practical application of decentralized coordination.

Design and Development of Structural Parameter Identification Software for Nonlinear Vibration Isolators

This paper developed an object-oriented software to facilitate parameter calibration of the quasi-zero stiffness (QZS) vibration isolator for engineering applications. Considering its advantages of convenient programming and high noise resistance, we employ the harmonic balance method to construct the identification core algorithm. The developed software consists of data pre-processing, parameter identification, and post-processing modules. The data pre-processing module imports and classifies all the required data. Then, the parameter identification module conducts preliminary nonlinearity analysis so that nonlinear structural parameter identification can be successfully carried out. After parameter identification, the data post-processing module displays and stores the identified results. The performance of the software is tested by a numerical example of a two-degree-of-freedom QZS vibration isolator, proving the software can give accurate identification results within a few user-friendly graphical interfaces. Based on this software, we hope that the application and promotion of nonlinear system parameter identification become more convenient.

Identification of Friction Coefficient of Controlled Wheel System Roller Racer Type Based on Experimental Data

The work studies the motion of the controlled wheel system to provide coordination of mathematical model de-scribing its motion and the experiment. The obtained results allow improving the accuracy of the mobile robot trajectory following. A mobile wheel system with a drive articulated frame and freely rotating wheels (Roller Racer) was chosen as the research object of the work. The paper presents a structural diagram of the research object, a mathematical model describing its motion with design constraints. The coordination of the motion model with experimental studies is provided by the identification of Roller Racer parameters. Identification of Roller Racer parameters is carried out due to the developed method of the controlled wheel system parameters identification. The proposed method of controlled wheel system identification allows determining the geometric and dynamic parameters of Roller Racer, which are considered in the motion model of the controlled wheel system. The results of the experimental trajectories captured on the motion capture system are compared with the simulated trajectories according to the motion model of the controlled wheel system. According to the obtained mismatch, the exact values of controlled wheel system parameters are determined. The paper presents expressions for calculating the mismatch based on experimental data from the motion capture system and theoretical data of the controlled wheel system motion model. An algorithm for identifying the value of the rolling friction coefficient based on experimental studies of the Roller Racer is presented. Conclusions about the possibility of using system parameter identification method are made.

Identification of inverse kinematic parameters in redundant systems: Towards quantification of inter-joint coordination in the human upper extremity.

Understanding and quantifying inter-joint coordination is valuable in several domains such as neurorehabilitation, robot-assisted therapy, robotic prosthetic arms, and control of supernumerary arms. Inter-joint coordination is often understood as a consistent spatiotemporal relation among kinematically redundant joints performing functional and goal-oriented movements. However, most approaches in the literature to investigate inter-joint coordination are limited to analysis of the end-point trajectory or correlation analysis of the joint rotations without considering the underlying task; e.g., creating a desirable hand movement toward a goal as in reaching motions. This work goes beyond this limitation by taking a model-based approach to quantifying inter-joint coordination. More specifically, we use the weighted pseudo-inverse of the Jacobian matrix and its associated null-space to explain the human kinematics in reaching tasks. We propose a novel algorithm to estimate such Inverse Kinematics weights from observed kinematic data. These estimated weights serve as a quantification for spatial inter-joint coordination; i.e., how costly a redundant joint is in its contribution to creating an end-effector velocity. We apply our estimation algorithm to datasets obtained from two different experiments. In the first experiment, the estimated Inverse Kinematics weights pinpoint how individuals change their Inverse Kinematics strategy when exposed to the viscous field wearing an exoskeleton. The second experiment shows how the resulting Inverse Kinematics weights can quantify a robotic prosthetic arm's contribution (or the level of assistance).

Parallel Algorithm for Parametric Identification of Dynamical Systems with Interval Parameters

The paper presents a parallel algorithm for the parametric identification of dynamical systems with interval parameters. The algorithm is based on the previously developed, substantiated and tested adaptive interpolation algorithm, which makes it possible to explicitly obtain the dependence of the states of a dynamic system on interval parameters. The solution of the problem of parametric identification is reduced to the problem of minimizing a certain objective function in the space of boundaries of interval parameter estimates. Due to the use of the adaptive interpolation algorithm when calculating the gradient of the objective function, there is no need for additional analysis and modeling of the original dynamic system, so it is convenient to use first-order methods for optimization. However, the task of calculating the objective function and the gradient includes a set of conditional minimization problems for explicit functions that can be solved independently of each other. The article discusses the main aspects and features of parallelization and implementation of the parametric identification algorithm and tests it on several representative examples. The acceleration and efficiency of parallelization are analyzed.

TUNNEL REACTION TO GROUND MOVEMENT USING A SIMPLIFIED MODEL

Purpose: the analysis is performed by modal superposition of the response of a simplified model containing connected bending and shear beams supported by Winkler-type springs.&#x0D; Objective: to present a simplified model using coupled Bernoulli and shear beams supported by Winkler-type springs for the systematic identification of tunnels subject to earthquake-induced ground motions. A model formulation is introduced and closed-form solutions for the modal characteristic equation and mode shape are derived.&#x0D; Research methods: the formulation of the model is introduced and closed-form solutions are derived for the equation of modal characteristic and mode shape. The latter are checked by the results of numerical models. A system identification algorithm is then presented, demonstrating its ability to recover the model parameters when the recorded acceleration time intervals along the tunnel are perturbed by noise and sensor locations change. The presented framework can be used for initial and simple recovery of tunnel response in the presence of monitoring data or for planning monitoring campaigns in newly constructed or existing tunnels.&#x0D; Main results: using a simple genetic algorithm and the proposed simplified model, it was shown that system identification can be performed for variable conditions. The model was tested for two different earthquakes of different frequencies, and the influence of the distribution of sensors along the length of the tunnel was also parametrically investigated. The test results were intentionally compromised by adding white Gaussian noise with a variance equal to that observed during ground motion. It was observed that for values ​​of α &gt;3.0 (ie, when the effect of the shear beam is significant), the model parameters can be successfully recovered. Therefore, for such conditions, the proposed approach can be used to recover important tunnel dynamic properties (e.g., T1 or α) as well as soil-structure interaction by tracking kb changes after earthquakes. For values ​​&lt; 3, a Bernoulli beam with a Winkler basis is a valid representation, while observing differences with a model involving a Pasternak basis are marginal.&#x0D; Scientific novelty: another approach to parametric system identification using simplified models. For tunnels, such models usually consist of beams on independent Winkler-type springs, including both numerical and analytical schemes. However, the seismic response of the continuum (i.e., soil) can be better modeled by including a transverse beam above the Winkler foundation, which allows interaction between individual springs, rather than using a single layer of independent springs. In geotechnical seismic resistance, a similar approach was used to assess the seismic response of pile foundations and retaining walls.&#x0D; Conclusions and practical challenge: different sensor distributions and reduced number of sensors did not lead to significant differences in the final results. This first shows that sensor position is not the dominant parameter for the case of five sensors along the length of the tunnel, fixed at both ends, and uniform soil conditions and other assumptions made in the paper. Further tests should be performed on real data and sensors to examine the impact of other aspects such as sensor noise.&#x0D; Key words: winkler springs, soil; soil; model; system identification algorithm is presented.

Local parameter identification with neural ordinary differential equations

The data-driven methods extract the feature information from data to build system models, which enable estimation and identification of the systems and can be utilized for prognosis and health management (PHM). However, most data-driven models are still black-box models that cannot be interpreted. In this study, we use the neural ordinary differential equations (ODEs), especially the inherent computational relationships of a system added to the loss function calculation, to approximate the governing equations. In addition, a new strategy for identifying the local parameters of the system is investigated, which can be utilized for system parameter identification and damage detection. The numerical and experimental examples presented in the paper demonstrate that the strategy has high accuracy and good local parameter identification. Moreover, the proposed method has the advantage of being interpretable. It can directly approximate the underlying governing dynamics and be a worthwhile strategy for system identification and PHM.

Two-step online identification of in-service cable-inertial mass damper systems under nonstationary wind excitations

Recently developed inertial mass dampers (IMDs) exhibit superior performances in vibration attenuation of stay cables due to the introduction of large inertial masses. However, physical parameters of in-service IMD systems tend to vary with operation time and inappropriate parameters would affect vibration mitigation effect. So far, very few researches have been conducted on the online parametric identification of in-service dampers using on-site monitoring data and such evaluation is essential for performances of dampers. To solve such a problem, a novel method is proposed in this paper for online parametric identification of in-service cable-IMD systems under nonstationary wind loads. The identification is a two-step and output-only approach. In the first step, an energy spectrum transmissibility (EST) approach is developed to detect system poles under nonstationary excitation and identification results are not influenced by inputs. By combining covariance-driven stochastic subspace identification (SSI-COV) method with the developed EST approach, spurious modes in SSI-COV estimation are eliminated to obtain reliable modal parameter identification results. In the second step, the errors between the identified modal parameters (i.e., frequencies and damping ratios) and the estimated modal parameters through complex modal analysis are used to construct objective function, and the modified directional bat algorithm (MDBA) recently developed by the authors is utilized to estimate the physical parameters of cable and IMD by minimizing the objective function. Online parametric identification results of a numerical cable-IMD system model under nonstationary wind loads using limited accelerometers demonstrate the effectiveness of the proposed method.

Parameter identification of dual-rate Hammerstein-Volterra nonlinear systems by the hybrid particle swarm-gradient algorithm based on the auxiliary model

This paper aims at the parameter estimation of dual-rate Hammerstein-Volterra (DR-HV) systems. The auxiliary model (AM) method is applied to solve the incomplete identification data caused by the dual-rate sampling. Besides, combining the particle swarm optimization (PSO) and the gradient search principle, this paper proposes an improved algorithm — the hybrid particle swarm-gradient based on the auxiliary model (AM-HPSG) algorithm, which is employed to the DR-HV identification. The AM-HPSG method converts the nonlinear identification issue into the optimization problem in the parameter space. Moreover, the application of the gradient mutation strategy in the AM-HPSG algorithm can not only improve the optimization speed and the identification accuracy, but also solve the premature problem of the basic PSO method. To verify the feasibility of the AM-HPSG algorithm, the second-order DR-HV model and the third-order DR-HV models are considered in simulation. And it can be easy to find that the AM-HPSG performs much better than the PSO and the gradient iterative (GI) methods through algorithm comparison.