Nonlinear Identification Method Research Articles

Nonlinear Parameter Identification of the Franka Emika PANDA Robot

This research addresses the problem of dynamic parameter identification for robot manipulators. As the complex manipulation of tasks increases, traditional control methods become insufficient, necessitating accurate model-based control. Previous studies have explored various parameter identification methods for robot manipulators. Still, the impact of different friction models on dynamic parameter identification, particularly for the Franka Emika PANDA robot, is yet to be comprehensively investigated. The linear and nonlinear parameter identification methods and nonlinear friction models (Lugre, Stribeck, and Sigmoidal) were studied on the PANDA robot. A linear inverse dynamic model was developed using the Newton-Euler method. Identification and validation trajectories were designed. Nonlinear constraints and bounds were applied for easier convergence, ensuring a positive definite inertia tensor in the center of mass (COM) frame. Using constrained least squares with Lasso regularisation, model-estimated torques comparison to measurements was done to estimate the physical parameters, considering the PANDA robot’s hand as a payload. We obtained the PANDA robot’s physical parameters, including the hand’s mass, without a friction model where discrepancies in joint torques were observed. Incorporating friction models reduced these discrepancies, validated by another trajectory comparison between the measured and the model’s predicted joint torques. Stribeck friction model exhibited the best performance in estimating parameters from its Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), indicating its effectiveness in capturing nonlinearities in the PANDA robot.

A subspace parameter identification method for nonlinear structures under oversampling conditions

In engineering practice, sampling frequencies much higher than the Nyquist frequency are often used to obtain accurate measurements of the dynamic characteristics of nonlinear systems. However, it may lead to oversampling when using the nonlinear subspace identification method (NSIM). This study proposes a subspace parameter identification method to address the identification of nonlinear structures under oversampling conditions. The proposed method first employs the prediction error method (PEM) to estimate the linear part of the state space model. In noisy environments, the PEM can achieve more accurate results than the NSIM by minimizing an error criterion function. The initial values fed into the PEM are obtained by the stochastic subspace identification method. The nonlinear part of the state space model is estimated by solving a linear regression equation. The proposed method effectively reduces the impact of high sampling frequencies on identification accuracy by combining data with different sampling frequencies to construct the linear regression equation. Among them, the low sampling frequency data is obtained by downsampling the high sampling frequency measurement data. The proposed method effectively reduces the effect of high sampling frequencies and environmental noise on identification accuracy by accurately estimating both the linear and nonlinear parts of the state space model. The identification accuracy of the proposed method is numerically verified by a chain-type structure with five degrees of freedom and a cantilever beam structure. Additionally, experimental verification is carried out on a two degrees of freedom floor structure with local nonlinearities. The results show that the proposed method achieves high identification accuracy in oversampling conditions and noisy environments.

High-precision identification and compensation of nonlinear error in hemispherical resonator gyro

This paper presents a novel nonlinear error identification and compensation method for the Hemispherical Resonator Gyro (HRG) from the signal processing perspective. Firstly, the paper establishes an HRG nonlinear error model that reveals the quantitative correlation between angle measurement error and the amplitude-gap ratio. Subsequently, a dynamic analysis model for gyro drift is developed using nonlinear motion equations. Based on this, a scalar factor nonlinear identification model encompassing assembly and nonlinear errors is proposed. Nonlinear optimization is then used to identify error parameters accurately. Finally, a joint compensation method is devised to mitigate assembly and nonlinear error issues. Empirical findings provide concrete validation for the precision of the identification and compensation method. The experimental results demonstrate that reductions of 97%, 89%, and 40% after the joint compensation are achieved in the fourth harmonic component, scale factor nonlinearity, and bias instability of the gyro, respectively.

A novel time-domain approach for identifying nonlinear structural dynamical system with explicit model based on observer/Kalman filter identification method

In this paper, a novel time-domain method for identifying nonlinear structural dynamical system with explicit model is proposed. By exploiting the observer/Kalman filter identification (OKID) and nonlinear feedback interpretation, the nonlinear parameters of the system are estimated accurately. The effectiveness of the proposed nonlinear OKID (NOKID) method is demonstrated through three numerical examples, namely a five degree-of-freedom system with one nonlinear spring, a three degree-of-freedom system with three nonlinear springs and a nonlinear rectangular membrane structure with all edges clamped. Comparing with the time-domain nonlinear subspace identification (TNSI) method, the proposed NOKID method can identify the nonlinear parameters without system order determination, and the identification results obtained by the proposed method are real numbers and have no dependency on frequency.

Nonlinear characteristics identification of an impact oscillator with a one-sided elastic constraint

Impacting systems are widely used in many engineering applications, such as self-propelled robots, energy harvesting and percussive drilling, which exhibit rich and complex nonlinear phenomena. Among these applications, predicting nonlinearities and estimating system parameters are of great interest of nonlinear dynamics research community. Backbone curve is an analytical tool that captures the frequency–amplitude dependence of nonlinear systems. In this paper, we estimate the impacting stiffness of a single-degree-of-freedom non-smooth dynamical system qualitatively by using the backbone curve. It was found that an increase of the impacting stiffness may lead to lowering the backbone curve. An adaptive differential evolution algorithm with the Metropolis criterion is proposed to identify the parameters of the impacting system quantitatively using experimental data, which are consistent with our theoretical predictions. Finally, the identified parameters are verified, and the limitations of the backbone curve are drawn. The nonlinear characteristics identification method studied in this paper can be extended to other vibro-impact systems and is potentially applicable to structural health monitoring and robotic sensing.

An intelligent identification method based on self-adaptive mechanism regulated neural network for chemical process

BackgroundThe complex characteristics of chemical process, such as multivariable, nonlinear, time-varying and strong coupling often lead to the poor effect of traditional identification theory in practical application. The development of deep learning in recent years has brought a breakthrough for nonlinear system identification, but more progress is still needed. MethodsThis paper proposes a nonlinear identification method based on self-adaptive mechanism regulated Long Short-Term Memory (LSTM) network for chemical process dynamic simulation. First, to increase the reliability of the application of neural network (NN) for chemical process identification and improve the generalization ability, the known differential equation describing the mechanism is taken as a regularization term to constrain the output of the NN. Then, a specific training method is proposed, which introduces trainable self-adaptive weights to force the neural network to focus on the regions with large training error. In addition, a semi-supervised network training method is proposed for the case that some parameters in the mechanism equation are unknown. Finally, a dynamic virtual device (VD) model is established, which can simulate the dynamic response of controlled objects. Significant findingsTo evaluate the efficiency of the developed identification method, various comparative experiments are conducted on pH neutralization and continuous stirred tank reactor (CSTR) processes. The experimental results show that the proposed identification method can obtain a nonlinear dynamic model with robustness, high accuracy and strong generalization ability.

Structural nonlinear damage identification based on the information distance of GNPAX/GARCH model and its experimental study

In the structural health monitoring (SHM) of civil engineering, most of the structural damage is nonlinear damage, such as breathing cracks and bolt looseness. Under the excitation of external loads, the time-domain response data of the structure produced by these nonlinear damages have nonlinear features. In order to solve the time-domain nonlinear damage identification problem of complex structures, this paper proposes a nonlinear damage identification method based on the information distance of GNPAX/GARCH (general expression of system identification for linear and nonlinear with polynomial approximation and exogenous inputs/generalized autoregressive conditional heteroskedasticity) model. First, an order determination method based on Bayesian optimization to select the order of the GNPAX/GARCH model was proposed, and the GNPAX/GARCH model was established for damage identification. Then, the redundant structural items of GNPAX/GARCH model were removed by the model optimization method based on the structural pruning algorithm. Finally, the information distance of the GNPAX/GARCH model conditional heteroscedasticity series between the baseline state and test state was derived, and the structural damage source locations were determined according to the information distance. A three-story frame structure experiment and a stand structure experiment were used to verify the effectiveness of the proposed method. The results show that the proposed method can effectively identify the nonlinear damages caused by the component breathing crack and joint bolt looseness, verifying its robustness to the nonlinear damage identification of the multi-story and multi-span complex structures.

Uranium-Bearing Layers of Sandstone Type Uranium Deposits Identification and Three-Dimensional Reconstruction in the Northern Ordos Basin, North-Central China

Sandstone type uranium is the most valuable and has the most potential for mining among the known uranium deposits. In the process of forming, the hydrolytic migration and enrichment of uranium require special basin sedimentary environment and tectonic background. Therefore, the mineralization process of sandstone type uranium deposits has certain layering characteristics and distribution rules in the underground vertical depth space. It is important to mine the spatial distribution characteristics of vertical uranium-bearing layers, and thus, reconstruct the three-dimensions of uranium orebodies. In this paper, according to the metallogenic law and distribution characteristics of sandstone type uranium in the underground vertical space, a nonlinear uranium-bearing layers identification (NULI) method of sandstone type uranium is proposed by using different types, resolutions and scales of borehole data. Then, the depth of uranium mineralization for the Daying uranium deposit within northern Ordos Basin is identified accurately and the spatial distribution characteristics of the uranium-bearing layer on the exploration line are obtained. Finally, the occurrence mode of the underground uranium orebodies are presented by using three-dimensional reconstruction analysis. It provides a basis for the prediction, exploration and mining of sandstone type uranium deposits within the Ordos Basin.

Novel nonlinear damping identification method: Simultaneous size, mass, charge and density measurements of a microparticle in quadrupole trap

In this paper, we present the nonlinear damping identification method for the fast and comprehensive study of individual microparticles localized in a quadrupole electrodynamic Paul trap. The measurement procedure is discussed in detail. The size, mass and charge of individual silica microspheres from the studied sample are determined simultaneously and non- destructively. Experimental results agree well with the results of independent microscopic examination and density reference values. The further development of the method are outlined.

Identification of multiple nonlinear lap joints using instantaneous power flow balance

PurposeThe purpose of this paper is to apply the novel instantaneous power flow balance (IPFB)-based identification strategy to a specific practical situation like nonlinear lap joints having single and double bolts. The paper also investigates the identification performance of the proposed power flow method over conventional acceleration-matching (AM) methods and other methods in the literature for nonlinear identification.Design/methodology/approachA parametric model of the joint assembly formulated using generic beam element is used for numerically simulating the experimental response under sinusoidal excitations. The proposed method uses the concept of substructure IPFB criteria, whereby the algebraic sum of power flow components within a substructure is equal to zero, for the formulation of an objective function. The joint parameter identification problem was treated as an inverse formulation by minimizing the objective function using the Particle Swarm Optimization (PSO) algorithm, with the unknown parameters as the optimization variables.FindingsThe errors associated with identified numerical results through the instantaneous power flow approach have been compared with the conventional AM method using the same model and are found to be more accurate. The outcome of the proposed method is also compared with other nonlinear time-domain structural identification (SI) methods from the literature to show the acceptability of the results.Originality/valueIn this paper, the concept of IPFB-based identification method was extended to a more specific practical application of nonlinear joints which is not reported in the literature. Identification studies were carried out for both single-bolted and double-bolted lap joints with noise-free and noise-contamination cases. In the current study, only the zone of interest (substructure) needs to be modelled, thus reducing computational complexity, and only interface sensors are required in this method. If the force application point is outside the substructure, there is no need to measure the forcing response also.

Automatic Nonlinear Subspace Identification Using Clustering Judgment Based on Similarity Filtering

Accurately determining system order plays a vital role in system identification directly related to the accuracy of identification results, especially for nonlinear system identification. Due to the need for human subjective judgment, the traditional sequence determination method easily causes uncertainty in the results; and the phenomenon of the virtual mode or omission occurs. An automatic nonlinear subspace identification method is proposed to address the aforementioned problems. When the eigenvalue decomposition of the constructed Hankel matrix is performed, the calculation range of the modal order of the system is estimated. The similarity coefficient and distance function are introduced to cluster the identified modal results, the poles of the false modes are removed to obtain the cluster stabilization diagram, and the best order of the system is received. Then, the modal parameters and nonlinear coefficients are obtained. Simulation examples are carried out to verify the effectiveness and robustness of the proposed method. An experimental study is carried out on a multilayer building with nonlinear characteristics. Compared with the traditional stabilization graph, the accuracy of the automatic order determination proposed in this paper is proven.

Structural Nonlinear Damage Identification Method Based on the Kullback–Leibler Distance of Time Domain Model Residuals

Under external load excitation, damage such as breathing cracks and bolt loosening will cause structural time domain acceleration to have nonlinear features. To solve the problem of time domain nonlinear damage identification, a damage identification method based on the Kullback–Leibler (KL) distance of time domain model residuals is proposed in this paper. First, an autoregressive (AR) model order was selected using the autocorrelation function (ACF) and Akaike information criterion (AIC). Then, an AR model was obtained based on the structural acceleration response time series, and the AR model residual was extracted. Finally, the KL distance was used as a damage indicator to judge the structural damage source location. The effectiveness of the proposed method was verified by using a multi-story, multi-span stand model experiment and a simulated eight-story shear structure. The results show that the proposed structural nonlinear damage identification method can effectively distinguish the structural damage location of multi-degree-of-freedom shear structures and complex stand structures, and it is robust enough to detect environmental noise and small damage.

Pulse response method for the Wiener-type nonlinear process identification

The Wiener-type nonlinear process where a nonlinear static block follows a linear dynamic subsystem is widely used to describe the dynamics of chemical processes. The present study proposes a new Wiener-type process identification method based on a narrow pulse response to cope with the relatively long process excitation requirement in the previous methods. The proposed identification method is developed based on the property of the Wiener-type nonlinear process that outputs of a linear dynamic subsystem is the same at two points when process outputs are equivalent at those points. The proposed method requires a relatively short process excitation (a single pulse response) but almost exactly estimates the Wiener-type nonlinear process. The simulation and experimental studies show the outstanding performance of the proposed method.

Research on Adaptive Prescribed Performance Control Method Based on Online Aerodynamics Identification

Wide-speed-range vehicles are characterized by high flight altitude and high speed, with significant changes in the flight environment. Due to the strong uncertainty of its aerodynamic characteristics, higher requirements are imposed on attitude control. In this paper, an adaptive prescribed performance control method based on online aerodynamic identification is proposed, which consists of two parts: an online aerodynamic parameter identification method and an adaptive attitude control method based on the pre-defined parameters of the control system. The aerodynamic parameter identification is divided into offline design and online design. In the offline design, neural networks are used to fit nonlinear aerodynamic characteristics. In the online design, a nonlinear recursive identification method is used to correct the errors of the offline fitted model. The adaptive attitude control is based on the conventional control method and updates the control gain in real time according to the desired system parameters to enhance the robustness of the controller. Finally, the effectiveness of the offline neural network and online discrimination correction is verified by mathematical simulations, and the effectiveness and robustness of the adaptive control proposed in this paper are verified by comparative simulation.

Robust Decomposition of Kernel Function-Based Nonlinear Robust Multimode Process Monitoring

With the rapid development of modern industry, actual production processes generally have a variety of complex characteristics including nonlinearity, multimodality, and contamination. Those characteristics, as well as the faults, bring great challenges to traditional process monitoring. To deal with all the above-mentioned three problems simultaneously, this paper develops a robust nonlinear multimode process monitoring scheme. First, the robust decomposition of kernel function (RDKF) algorithm is proposed to detect outliers. Then, a nonlinear mode identification method is presented by combining block diagonal kernel function matrix and spectral clustering. For the online sample, a mode indicator is derived from kernel function to judge whether it belongs to a fault or a certain mode. Finally, the effectiveness of the proposed method is validated by two cases in terms of both mode identification and fault detection.

Structural nonlinear damage identification based on Bayesian optimization GNAR/GARCH model and its experimental study

Cracks and bolt looseness are common damages in a steel structure. Under the time-history loading, nonlinear characteristics of variable stiffness exist in cracks, and bolt looseness has complex nonlinear characteristics of stiffness and damping. To effectively solve the problem of structural nonlinear damage identification, an output-only damage identification method based on the GNAR/GARCH (general expression for linear and nonlinear autoregressive/general autoregressive conditional heteroskedasticity) model with Bayesian optimization is proposed. First, the stationarity test and continuous difference processing was carried out on the measured acceleration data, and an order determination method based on Bayesian optimization was proposed to automatically select the optimal model order. Then, a model structure optimization method based on Bayesian optimization was proposed to select the optimal model structure of a GNAR/GARCH model, and a GNAR/GARCH model was established based on the measured acceleration data for damage identification. Finally, a new damage indicator PIDI (probabilistic Itakura distance indicator) was proposed to judge the structural healthy status. The nonlinear damage experiment of three-story frame and relay tower was used to verify the effectiveness of the proposed method. In addition, in order to illustrate the efficiency of the proposed method for nonlinear damage identification, a comparative study was carried out using other two damage identification methods. The results show that the nonlinear damage identification method based on the GNAR/GARCH model with Bayesian optimization can easily identify the nonlinear damage of the frame and relay tower structure, and it can effectively identify the structure damage with single or multiple nonlinear damage sources.

Closed-loop data-driven modeling and distributed control for islanded microgrids with input constraints

In this paper a new nonlinear identification method for microgrids based on neural networks is proposed. The system identification process can be done using the available closed-loop system input/output data recorded during normal operation without additional external excitation, while disturbances between different distributed energy resources are considered to improve the identification accuracy. Moreover, Based on the nonlinear identified model, a novel distributed frequency/voltage regulation and active/reactive power sharing control framework is developed. The new control strategy does not rely on the classical droop-based hierarchical control structure, such that improved transient performance and accurate power sharing for microgrid with mixed lines can be achieved. Furthermore, the anti-windup technique is incorporated into the controller design process to guarantee that the input constraints are satisfied and the voltage deviations are within an acceptable range. The effectiveness of the proposed method is demonstrated via simulations.

Nonlinear damage identification method of transmission tower structure based on general expression for linear and nonlinear autoregressive model and Itakura distance

Fatigue cracks and bolt looseness are two kinds of common nonlinear damage in a transmission tower structure. However, due to the complexity of the transmission tower structure, it is difficult to identify the nonlinear damage accurately by using traditional damage identification methods. To solve this problem effectively, a time domain damage identification method based on general expression for linear and nonlinear autoregressive model (GNAR model) and Itakura distance is proposed. To describe the stochastic characteristics of time series more concisely and accurately, the optimized structure of GNAR model was selected by the stochastic pruning algorithm based on greedy strategy. And Itakura distance was used as a damage indicator for nonlinear damage identification. The nonlinear damage experiment of three-story frame model in Los Alamos laboratory was used to verify the effectiveness of the proposed method, and this method was applied to the nonlinear damage identification experiment of a transmission tower steel frame model. In the transmission tower model experiment, two kinds of nonlinear damage types are considered: component breathing cracks and joint bolt loosening. The results show that the proposed nonlinear damage identification method can easily identify the nonlinear damage of the frame model and the transmission tower model effectively. The change of floor mass barely has effects on the damage identification results. The damage probability of the damaged stories calculated by the proposed method is significantly higher than that of the undamaged stories, so that it is helpful to find the location of the nonlinear damage source efficiently. And the proposed method is a damage identification method based on sub-structure story, which can identify the transmission tower model with two nonlinear damage sources at the same time.

A two-stage sparse algorithm for localization and characterization of local nonlinear structures

This paper considers the localization and characterization of nonlinear components in local nonlinear structures with noisy measurements, and a novel two-stage sparse identification method is proposed. In this algorithm, one set of candidate nonlinear basis functions are leveraged to characterize system nonlinearities. To effectively localize and characterize nonlinear components, the algorithm introduces two sparse stages. At the first sparse stage, the adaptive group Lasso is adopted to localize nonlinear components in structures. At the second sparse stage, the adaptive Lasso is used to further characterize the contributing nonlinear basis functions in the identified nonlinear positions. Since the first sparse stage can greatly decrease the number of candidate nonlinear basis functions, the contributing functions can be effectively selected and characterized at the second sparse stage. Compared with the one-stage sparse algorithms, the proposed algorithm is more robust to noise, i.e., the new method can correctly identify the local nonlinear structures with a lower Signal to Noise Ratio (SNR). In addition, many existed nonlinear identification methods, simultaneously require the synchronous data of vibration displacements, velocities and accelerations. If only vibration displacements are measured, the first and second order derivatives of displacement are conducted to estimate velocities and accelerations, respectively. Nevertheless, the noise mixed into the displacement measurement will be severely amplified in the process of derivative calculation, which will make the estimation of velocities and accelerations deviating from the actual value and reduce the identification accuracy. To avoid performing the second order derivative, the Duhamel's integral is adopted to rewrite the dynamic relationship between the system input and output. In addition, a non-parametric de-noising method based on reproducing kernel Hilbert space (RKHS) is further developed to reduce the effect of noise in vibration displacements and obtain vibration velocities, which can effectively reduce the effect of noise and improve the identification accuracy. The numerical and experimental studies verify the potential and effectiveness of the proposed algorithm in localizing and characterizing nonlinear components in local nonlinear structures.

A Nonlinear Friction Identification Method Combining Separable Least Squares Approach and Kinematic Orthogonal Property

A Nonlinear Friction Identification Method Combining Separable Least Squares Approach and Kinematic Orthogonal Property