Least-squares Identification Method Research Articles

Research on Direct Lift Carrier-Based Unmanned Aerial Vehicle Landing Control Based on Performance Index Intelligent Optimization/Dynamic Optimal Allocation

High-precision control problems for carrier-based UAVs are challenging due to the requirements for safety, high-performance operation and uncertain ocean environments. To address such problems, this paper proposes a direct lift landing control method that can ensure the safe operation of UAVs using intelligent optimization of control performance indicators and dynamic optimal allocation methods. The direct lift control (DLC) scheme is adopted to improve the operability of the control by introducing flap channels to achieve the fast correction of vertical disturbances. To improve the landing control performance, an intelligent optimization method for DLC gain is proposed, and a neural network relationship between parameter uncertainty and optimal DLC gain is established. In addition, a recursive least-squares identification method is used to estimate the uncertain parameters in real time, so that the established neural network can be used to generate the optimal DLC commands online, and the generated control commands can be assigned to multiple actuators of the carrier-based UAV through a dynamic optimal assignment algorithm. Finally, the superiority of the method is verified using simulation comparison.

Regularised Volterra series models for modelling of nonlinear self-excited forces on bridge decks

Volterra series models are considered an attractive approach for modelling nonlinear aerodynamic forces for bridge decks since they extend the convolution integral to higher dimensions. Optimal identification of nonlinear systems is a challenging task since there are typically many unknown variables that need to be determined, and it is vital to avoid overfitting. Several methods exist for identifying Volterra kernels from experimental data, but a large class of them put restrictions on the system inputs, making them infeasible for section model tests of bridge decks. A least-squares identification method does not restrict the inputs, but the identified model often struggles with noisy (non-smooth) kernels, which is deemed to be unphysical and a sign of overfitting. In this work, regularised least-squares identification is introduced to improve the performance of model identification using least-squares. Standard Tikhonov regularisation and other penalty techniques that impose decaying kernels are also explored. The performance of the methodology is studied using experimental data from wind tunnel tests of a twin deck section. The regularised Volterra models show equal or better results in terms of modelling the self-excited forces, and the regularisation makes the models less prone to overfitting.

A novel analog controller design scheme for LLC resonant converter used in battery charging application

A new generation of batteries must be charged according to the charging curves recommended by battery manufacturers. For high reliability, low cost, high speed, and pulse by pulse protection ability, the controller of these chargers are commonly designed by analog circuits. Analog controllers can be implemented by internal circuits of analog controller ICs with additional passive elements. This paper proposes a controller design approach for battery charger applications with an LLC converter. The proposed approach stands on a novel method for applying the well-known least-squares (LS) identification method for designing the classic controller with changing the identification problem to the design problem. Compared with other methods, the proposed approach benefits from design a controller with desired structure and desired performance, simultaneously. Here, modelling of LLC converter has been carried out by the first harmonic approximation (FHA) method. For controller design, the linear model has been extracted by linearizing the non-linear FHA model. In addition, for providing the reduced switching losses and increased efficiency, the passive elements of the resonance tank and isolation transformer ratio have been designed to operate the converter in the zero-voltage switching (ZVS) region. To verify the controller and designed converter, some simulation and experimental results are provided.

A least squares method for identification of unknown groundwater pollution source

Abstract The identification of unknown groundwater pollution sources is one of the most important premises in groundwater pollution prevention and remediation. In this paper, an exploratory application of a least squares method to identify the unknown groundwater pollution source is conducted. Supported by a small amount of observation data and the analytical solutions of the pollutant transport model, the initial concentration, the leakage location and the pollutant mass are identified by using the least squares method under a sand tank experiment and a gas station area. In the sand tank experiment, it is found that the fitting errors of three cross-sections are within 6%. In the gas station area, it is found that the results are nearly consistent with the site investigation information. The results indicate that the least squares method has considerable application values in the identification of groundwater pollution sources.

Least Squares Method for Identification of IGBT Thermal Impedance Networks Using Direct Temperature Measurements

State-of-the-art methods for determining thermal impedance networks for IGBT (Insulated Gate Bipolar Transistor) modules usually involves the establishment of the relationship between the measured transistor or diode voltage and temperature under homogenous temperature distribution across the IGBT module. The junction temperature is recomputed from the established voltage–temperature relationship and used in determining the thermal impedance network. This method requires accurate measurement of voltage drop across the transistors and diodes under specific designed heating and cooling profiles. Validation of the junction temperature is usually done using infrared camera or sensors placed close to the transistors or diodes (in some cases and open IGBT module) so that the measured temperature is as close to the junction as possible. In this paper, we propose an alternative method for determining the IGBT thermal impedance network using the principles of least squares. This method uses measured temperatures for defined heating and cooling cycles under different cooling conditions to determine the thermal impedance network. The results from the proposed method are compared with those obtained using state-of-the-art methods.

Experimental study of structural change detection using data-driven reduced-order models

This paper presents a comparison of the effectiveness of three different data-driven vibration-based approaches in detecting and locating structural changes in a 1/4 scale six-storey single-bay steel frame laboratory structure from measured experimental input-output data obtained from band-limited white-noise base-excitation tests. The implemented methodologies are based on reduced-order models obtained using three input-output system identification approaches: a system realisation algorithm using information matrices, a general time-domain least-squares identification method, and a non-parametric chain-like system identification approach. Variations in the estimated reduced-order models are then used to indicate the presence and infer the location of actual structural changes in the test structure. The results of this experimental study show that even though the changes introduced by the various levels of damage in the structure were robustly detected in the presence of modelling, measurement, and data processing errors using reduced-order representations, the identified change locations in the reduced-order model could not be, in some cases, reliably correlated with the actual damage location in the structure.

Phase-based order separation for Volterra series identification

ABSTRACT This article addresses the identification of nonlinear systems represented by Volterra series. To improve the robustness of some existing methods, we propose a pre-processing stage that separates nonlinear homogeneous order contributions from which Volterra kernels can be identified independently. Unlike existing separation methods that use amplitude relations between test signals, we propose another order separation method based on phase. This method gives access to a new type of complex-valued output signals, which can be used to improve kernel identification. First, the underlying ideas are introduced via the presentation of a theoretical method using complex-valued test signals. Second, the proposed order separation method using real-valued signals is described. Third, a new identification process is given, combining existing least-squares identification method with the previous results. Finally, numerical experiments are used to compare the proposed order separation method with state-of-the-art, as well as to evaluate the new Volterra series identification process.

Identification of continuous-time hybrid “Box–Jenkins” systems with multiple unknown time delays using two-stage parameter estimation algorithm

PurposeThis study/paper aims to present a separable identification algorithm for a multiple input single output (MISO) continuous time (CT) hybrid “Box–Jenkins”.Design/methodology/approachThis paper proposes an optimal method for the identification of MISO CT hybrid “Box–Jenkins” systems with unknown time delays by using the two-stage recursive least-square (TS-RLS) identification algorithm.FindingsThe effectiveness of the proposed scheme is shown with application to a simulation example.Originality/valueA two-stage recursive least-square identification method is developed for multiple input single output continuous time hybrid “Box–Jenkins” system with multiple unknown time delays from sampled data. The proposed technique allows the division of the global CT hybrid “Box–Jenkins” system into two fictitious subsystems: the first one contains the parameters of the system model, including the multiple unknown time delays, and the second contains the parameters of the noise model. Then the TS-RLS identification algorithm can be applied easily to estimate all the parameters of the studied system.

Adaptive Unified Monitoring System Design for Tire-Road Information

Knowledge of the tire-road information is not only very crucial in many active safety applications but also significant for self-driving cars. The tire-road information mainly consists of tire-road friction coefficient and road-tire friction forces. However, precise measurement of tire-road friction coefficient and tire forces requires expensive equipment. Therefore, the monitoring of tire-road information utilizing either accurate models or improved estimation algorithms is essential. Considering easy availability and good economy, this paper proposes a novel adaptive unified monitoring system (AUMS) to simultaneously observe the tire-road friction coefficient and tire forces, i.e., vertical, longitudinal, and lateral tire forces. First, the vertical tire forces can be calculated considering vehicle body roll and load transfer. The longitudinal and lateral tire forces are estimated by an adaptive unified sliding mode observer (AUSMO). Then, the road-tire friction coefficient is observed through the designed mode-switch observer (MSO). The designed MSO contains two modes: when the vehicle is under driving or brake, a slip slope method (SSM) is used, and a recursive least-squares (RLS) identification method is utilized in the SSM; when the vehicle is under steering, a comprehensive friction estimation method is adopted. The performance of the proposed AUMS is verified by both the matlab/simulinkCarSim co-simulation and the real car experiment. The results demonstrate the effectiveness of the proposed AUMS to provide accurate monitoring of tire-road information.

Gyro Error Compensation in Optoelectronic Platform Based on a Hybrid ARIMA-Elman Model

As an important angle sensor of the opto-electric platform, gyro output accuracy plays a vital role in the stabilization and track accuracy of the whole system. It is known that the generally used fixed-bandwidth filters, single neural network models, or linear models cannot compensate for gyro error well, and so they cannot meet engineering needs satisfactorily. In this paper, a novel hybrid ARIMA-Elman model is proposed. For the reason that it can fully combine the strong linear approximation capability of the ARIMA model and the superior nonlinear compensation capability of a neural network, the proposed model is suitable for handling gyro error, especially for its non-stationary random component. Then, to solve the problem that the parameters of ARIMA model and the initial weights of the Elman neural network are difficult to determine, a differential algorithm is initially utilized for parameter selection. Compared with other commonly used optimization algorithms (e.g., the traditional least-squares identification method and the genetic algorithm method), the intelligence differential algorithm can overcome the shortcomings of premature convergence and has higher optimization speed and accuracy. In addition, the drift error is obtained based on the technique of lift-wavelet separation and reconstruction, and, in order to weaken the randomness of the data sequence, an ashing operation and Jarque-Bear test have been added to the handle process. In this study, actual gyro data is collected and the experimental results show that the proposed method has higher compensation accuracy and faster network convergence, when compared with other commonly used error-compensation methods. Finally, the hybrid method is used to compensate for gyro error collected in other states. The test results illustrate that the proposed algorithm can effectively improve error compensation accuracy, and has good generalization performance.

Multi-innovation based Identification of Output Error Model with Time Delay under Load Disturbance

In this paper, a robust output error model identification method is proposed for industrial processes with time delay subject to load disturbance. By viewing the load disturbance response as a time-variant parameter to be estimated, an extended recursive least-squares (RLS) identification method is established to simultaneously estimate the model parameters and the disturbance response, based on a multi-innovation fitting strategy. The integer type time delay parameter is determined by using a one-dimensional searching approach. An auxiliary model is used to estimate the noise-free output against stochastic noise. Besides, two adaptive forgetting factors are introduced to improve the convergence rates of estimating the time-invariant model parameters and the time-variant disturbance response, respectively. The effectiveness and merit of the proposed method is demonstrated by an illustrative example.

Correlation analysis-based error compensation recursive least-square identification method for the Hammerstein model

ABSTRACTIn this paper, the correlation analysis based error compensation recursive least-square (RLS) identification method is proposed for the Hammerstein model. Firstly, the covariance matrix between input and output data points of the Hammerstein model is derived by using separable signal to realize that the unmeasurable internal variable is replaced by the covariance matrix of input. Thus, the correlation analysis method can be accordingly used to estimate parameters of the linear part, which results in the identification problem of the nonlinear part separated from the linear part. In addition, a correction term is added to least-square estimation to compensate error caused by output noise, further the error compensation-based RLS method is obtained for the observed data from the Hammerstein model. As a result, the least-square identification method, which generates error in the presence of noise distribution, can be compensated. Finally, simulation experiments are conducted to illustrate the performance of the proposed identification method.

Iterative identification of output error model for industrial processes with time delay subject to colored noise

To deal with colored noise and unexpected load disturbance in identification of industrial processes with time delay, a bias-eliminated iterative least-squares (ILS) identification method is proposed in this paper to estimate the output error model parameters and time delay simultaneously. An extended observation vector is constructed to establish an ILS identification algorithm. Moreover, a variable forgetting factor is introduced to enhance the convergence rate of parameter estimation. For consistent estimation, an instrumental variable method is given to deal with the colored noise. The convergence and upper bound error of parameter estimation are analyzed. Two illustrative examples are used to show the effectiveness and merits of the proposed method.

A Least Squares Method for Identification of Feedback Cascade Systems

The problem of identification of systems in dynamic networks is considered. Although the prediction error method (PEM) can be applied to the overall system, the non-standardmodel structure requires solving a non-convex optimization problem. Alternative methods have been proposed, such as instrumental variables and indirect PEM. In this paper, we first consider acyclic cascade systems, and argue that these methods have different ranges of applicability. Then, for a network with feedback connection, we propose an approach to deal with the fact that indirect PEM yields a non-convex problem in that case. A numerical simulation may indicate that this approach is competitive with other existing methods.

Trajectory Optimization for Well-Conditioned Parameter Estimation

When attempting to estimate parameters in a dynamical system, it is often beneficial to strategically design experimental trajectories that facilitate the estimation process. This paper presents an optimization algorithm which improves conditioning of estimation problems by modifying the experimental trajectory. An objective function which minimizes the condition number of the Hessian of the least-squares identification method is derived and a least-squares method is used to estimate parameters of the nonlinear system. A software-simulated example demonstrates that an arbitrarily designed trajectory can lead to an ill-conditioned least-squares estimation problem, which in turn leads to slower convergence to the best estimate and, in the presence of experimental uncertainties, may lead to no convergence at all. A physical experiment with a robot-controlled suspended mass also shows improved estimation results in practice in the presence of noise and uncertainty using the optimized trajectory.

Structural Identification of Fuzzy Model

The purpose of this paper is to present a mathematical tool to build a fuzzy model of a nonlinear system using its input-output data. The phase plane of system is divided into sub-regions and a linear model is assigned for each of these regions. This linear model is represented either in state-space form. To determine the pre-selected parameters of the linear system model under study, least-square identification method is used. Then these linear models are arranged in a fuzzy manner to characterize the overall system behavior. The proposed methodology is verified through simulation on a numeric example.

3B22 Dynamic Modeling and Control System Design of Stewart Platform for Vibration Isolation(The 12th International Conference on Motion and Vibration Control)

Stewart platform in cubic configuration is of great application in the prospect of vibration control. However, the twist and torque between the conjunction of the strut and plate and the special characteristics of piezo would enhance the nonlinearity of cubic configuration, and influence the tracking accuracy and efficiency of the platform. Therefore, in this paper, an adaptive control based on least-square identification method of the dynamics model of piezoelectric Stewart Platform is proposed. Regarding that the force matrix can represent all the nonlinear influence and the real model can be identified accurately, the controller is designed to replace the original force matrix of the linear model of the cubic configuration with the identification outcome. Then simulation is implemented to confirm the feasibility of this method. Results show that the adaptive control law is able to remedy the influence of nonlinearity of the dynamic model and be efficient in isolation vibration.

Two‐stage parameter estimation algorithms for Box–Jenkins systems

A two-stage recursive least-squares identification method and a two-stage multi-innovation stochastic gradient method are derived for Box-Jenkins (BJ) systems. The key is to decompose a BJ system into two subsystems, one containing the parameters of the system model and the other containing the parameters of the noise model, and then to estimate the parameters of the system model and the noise model, respectively. The simulation examples indicate that the proposed algorithms can generate highly accurate parameter estimates and require small computational burden.

Parameters Recursive Identification of Minimum Variance Control

we discuss the problem of parameters recursive identification and designing of optimal input signal for minimum variance control from the point of system identification. we propose multi-innovation recursive least-squares identification method and separable iterative recursive least-squares identification method to identify and estimate it on line. Finally, the efficiency and possibility of the proposed strategy can be confirmed by the simulation example results.

METANET Model Validation using a Genetic Algorithm

This paper aims to describe a black box approach to traffic model validation. A genetic algorithm is utilised with a least-squares method for parameter identification. The procedure developed requires no knowledge of the model, just the model output and some reference data. Testing is done by applying the method to the second order macroscopic simulator METANET. This produces a valid model fitted to real data for a stretch of UK motorway. The optimal parameter set found is valid for data from different days and remains accurate when turning rates are estimated either as a 15-minute average or a constant rate.