Nonlinear Identification Research Articles

Study of nonlinear effects in a bolted joint using the base excitation as an input

In this paper, the nonlinearity detection, characterization and identification of a bolted beam assembly is presented. The methodology utilized in this work is based on the force reconstruction using the base excitation as an input and the nonlinear system identification. The force reconstruction procedure was carried out by exciting the bolted beam assembly at very low excitation with fully tightened bolt condition. The nonlinear effect in the bolted beam assembly was induced by reducing the bolt clamping loads. A collection of frequency response functions (FRFs) are shown at different clamping loads to detect and characterize the nonlinearities. Once the nonlinearities are detected and characterized, the restoring force surface method using the reconstructed force was used to identify the nonlinear parameters in the modal space. Four different base excitation (energy) levels with three different tightening torques were considered in the tests in order to study the energy dependence of the damping nonlinearities. In all the cases, the nonlinear system identification methodology employed was successful in identifying the damping and stiffness nonlinearities.

ON-LINE DETECTION OF CERASUS HUMILIS FRUIT BASED ON VIS/NIR SPECTROSCOPY COMBINED WITH VARIABLE SELECTION METHODS AND GA-BP MODEL

In order to realize the rapid and non-destructive detection of fresh Cerasus Humilis’ (CH) classification, and promote the deep-processing of post-harvest fresh fruit and improve market competitiveness, this study proposed a nonlinear identification method based on genetic algorithm (GA) optimized back propagation (BP) neural network of different varieties of fresh CH fruit. “Nongda-4”, “Nongda-5”, and “Nongda-7” fresh CH fruit were selected as research objects to collect their visible/near-infrared spectral data dynamically. The original spectra were preprocessed by moving smoothing (MS) and standard normal variate (SNV) methods, for the characteristic wavelengths were extracted with four dimension-reducing methods, namely principal components analysis (PCA), competitive adaptive reweighed sampling (CARS), CARS-mean impact value (CARS-MIV), and random frog (RF) algorithm. Finally, the BP prediction models were established based on full-spectrum and characteristic wavelengths. At the same time, the GA optimization was used to optimize the initial weight and threshold of the BP neural network and compared with the partial least squares’ discrimination analysis (PLS-DA) linear model. Through comparing the MS (7)+SNV was proved to be the best preprocessing method, the CARS-MIV-GA-BP model had the best discriminant accuracy, the prediction set accuracy was 98.76%, of which the variety “Nongda-4” and “Nongda-5” recognition rate were 100%, the variety “Nongda-7” recognition rate was 96.29%. The results show that the GA can effectively optimize the initial weights and threshold randomization of the BP neural network, improve the discrimination accuracy of CH varieties, and the CARS-MIV algorithm can effectively reduce the number of input nodes of the BP neural network model, simplify the structure of BP neural network. This study provides a new theoretical basis for the detection of fresh CH fruit classification.

Parameter identification of nonlinear structural systems through frequency response sensitivity analysis

Nonlinearity is ubiquitously encountered in structural systems, and it may have a great and complicated influence on the dynamic behaviours, including bifurcation, internal resonance, load history dependence, etc. Identifying the nonlinear system parameters is essential for analysis and design of the structure. To this end, a new approach is developed in this paper for nonlinear system parameter identification from frequency response sensitivity analysis. At first, the harmonic balance equation is established to govern the frequency response of the nonlinear system, upon which the frequency response and sensitivity analysis can be conducted. A remarkable feature is that the harmonic balance equation is algebraic so that the sensitivity analysis, pertaining to a linearized equation, is rather simple and straightforward. Then, parameter identification is modelled as a nonlinear least-squares problem, and the sensitivity approach is adopted in conjunction with the trust-region constraint for convergent solution. Numerical examples are conducted to demonstrate the feasibility and performance of the proposed approach.

Modeling of weld penetration control system in GMAW-P using NARMAX methods

Abstract This study introduces the nonlinear identification of a weld penetration control system in pulsed gas metal arc welding system (GMAW-P) characterized with the fused characteristic signal. It was found that both the change in arc voltage during the peak current period and the average arc voltage during the peak current period can be used for condition monitoring of weld pool surface and thus for the estimation of weld penetration depth in GMAW-P. By fusing these two signals through a Kalman filter, filtered fluctuation of arc voltage during peak current period, Δ U k f , is proposed to estimate weld penetration more reasonably. A second order NARMAX (nonlinear autoregressive moving average model with exogenous inputs) model is identified thorough forward regression orthogonal least squares (FROLS) algorithm and the error reduction ratio (ERR) criterion, and then validated in statistical validation. After simplification, the obtained model structure is a bilinear model, and is proved to be superior than linear models thorough model prediction tests. The proposed bilinear model is used to design a gain-scheduled model predictive controller, which shows the ability in weld penetration control in an experiment with a set point change.

Application of a long short-term memory neural network for modeling transonic buffet aerodynamics

In the present work, a reduced-order modeling (ROM) framework based on a long short-term memory (LSTM) neural network is applied for the prediction of transonic buffet aerodynamics. This type of network has a high potential for modeling sequential data, which is favorable for capturing the time-delayed effects associated with unsteady aerodynamics. Therefore, the nonlinear identification procedure as well as the generalization of the resulting ROM are presented. Further, a Monte-Carlo-based training procedure is performed in order to estimate statistical errors. The training data set for the ROM is provided by means of forced-motion unsteady Reynolds-averaged Navier Stokes (URANS) simulation. Subsequent to the training process, the ROM is applied for the computation of time-varying integral quantities such as aerodynamic force and moment coefficients. The most challenging aspect when considering buffet aerodynamics is given by the reproduction of the self-sustained unsteadiness of the buffeting flow. Even without any external excitation, the flow is characterized by large shock-boundary layer interaction, resulting in shock movement and flow separation. Finally, the performance of the trained network is demonstrated by predicting the aerodynamic loads of the NACA0012 airfoil considered at transonic freestream conditions. Therefore, the airfoil is excited by a forced pitching motion beyond the buffet-critical angle of attack. A comparison with a full-order computational fluid dynamics (CFD) solution shows that the essential characteristics of the nonlinear buffet phenomenon are captured by the ROM method.

Simultaneous Regression and Selection in Nonlinear Modal Model Identification

High fidelity finite element (FE) models are widely used to simulate the dynamic responses of geometrically nonlinear structures. The high computational cost of running long time duration analyses, however, has made nonlinear reduced order models (ROMs) attractive alternatives. While there are a variety of reduced order modeling techniques, in general, their shared goal is to project the nonlinear response of the system onto a smaller number of degrees of freedom. Implicit Condensation (IC), a popular and non-intrusive technique, identifies the ROM parameters by fitting a polynomial model to static force-displacement data from FE model simulations. A notable drawback of these models, however, is that the number of polynomial coefficients increases cubically with the number of modes included within the basis set of the ROM. As a result, model correlation, updating and validation become increasingly more expensive as the size of the ROM increases. This work presents simultaneous regression and selection as a method for filtering the polynomial coefficients of a ROM based on their contributions to the nonlinear response. In particular, this work utilizes the method of least absolute shrinkage and selection (LASSO) to identify a sparse set of ROM coefficients during the IC regression step. Cross-validation is used to demonstrate accuracy of the sparse models over a range of loading conditions.

Frequency-Geometric Identification of Magnetization Characteristics of Switched Reluctance Machine

Accurate modeling of electrical drives for online testing is a relevant problem. Switched Reluctance Machine (SRM) has lately attracted significant attention because it has several advantages compared to conventional engines. It is simple, free of rare-earth and fault-tolerant machine. An analytical model of a SRM has not been reported yet due to the dynamic and strong nonlinearity of SRM. The most SRM control and applications are based on several assumptions and simplifications. Therefore, it is convenient to develop an accurate approach to identify the SRM characteristics. In this paper, an analytical modeling and identification method of magnetization characteristics of Switched Reluctance Machine (SRM) is proposed. Presently, an exact mathematical model of SRM is established. Unlike several previous studies, in this approach the system nonlinearities of SRM are allowed to be hysteresis (i.e. the hysteresis effect is considered) and taking account the inherent magnetic nonlinearity. Indeed, the SRM is considered as highly nonlinear which makes the modeling of these machines difficult to achieve. Then, it is convenient to develop an accuracy model of SRM because it is always operated in the magnetically saturated mode to maximize the energy transfer. The developed model can be used in control, simulation and design development. Furthermore, an identification method, at standstill test, based on frequency technics is developed allowing the identification of SRM nonlinearities (considering the saturation and the hysteresis effects). In this respect, it is shown that the nonlinear behavior of SRM can be exactly described by a block-oriented nonlinear structure. Specifically, the SRM can be described by a Wiener nonlinear model. Compared to the existing methods, the proposed study gives good accuracy of flux-linkage value characteristics and enjoys the simplicity of implementation.

Hierarchical recursive signal modeling for multifrequency signals based on discrete measured data

AbstractThis paper studies the problem of parameter estimation for the multifrequency sine signals, which have multiple characteristic parameters such as the amplitudes, phases, and frequencies. It is noted that the signal output is nonlinear with respect to the phase and frequency parameters while it is linear with respect to the amplitude parameters. This feature inspires us to separate all of the characteristic parameters into a linear parameter set and a nonlinear parameter set, where the linear set is composed of the amplitude parameters and the nonlinear set is composed of the phase parameters and the frequency parameters. After the parameter separation, two identification submodels are constructed for optimizing the linear parameter set and the nonlinear parameter set. Then the nonlinear identification model becomes a linear identification submodel and a nonlinear identification submodel. Therefore, the nonlinear optimization for minimizing the objective function is converted into the combination of the quadratic optimization and nonlinear optimization. Based on the separable identification submodels, a recursive least squares subalgorithm and a recursive gradient subalgorithm are proposed for identifying the linear parameters and nonlinear parameters, respectively. Moreover, an interactive estimation algorithm is designed to remove the related parameter sets between the subalgorithms and a hierarchical identification method is presented by combining the subalgorithms. For the purpose of tracking the time‐varying, a forgetting factor is introduced to improve the convergence speed. The numerical examples are provided to qualify the performance of the proposed method based on some performance measures.

Nonlinear Identification for 4-DOF Ship Maneuvering Modeling via Full-Scale Trial Data

This research involves a 4-DOF ship maneuvering modeling with full-scale trial data. In order to avert the inversion of the multi-innovation matrix in the traditional multi-innovation least squares algorithm, a new novel is proposed based on the recognition concept new multi-innovation least squares algorithm to identify the innovation of the stochastic gradient hyperbolic tangent nonlinearity. A lot of work and efforts have been made to ensure the consistency and final convergence. Combined with relevant data and statistical indicators, the author derives a more effective hyperbolic tangent nonlinear innovation identification scheme to identify ship maneuvering motion. Compared with the previous results, this design scheme has significant computational advantages, with higher accuracy, faster identification speed, higher computational efficiency, and requiring fewer parameters. At the same time, the example is given to illustrate the effectiveness of the algorithm, especially for identification applications with full-scale trial data.

An improved nonlinear innovation-based parameter identification algorithm for ship models

AbstractTo solve the problem of identifying ship model parameters quickly and accurately with the least test data, this paper proposes a nonlinear innovation parameter identification algorithm for ship models. This is based on a nonlinear arc tangent function that can process innovations on the basis of an original stochastic gradient algorithm. A simulation was carried out on the ship Yu Peng using 26 sets of test data to compare the parameter identification capability of a least square algorithm, the original stochastic gradient algorithm and the improved stochastic gradient algorithm. The results indicate that the improved algorithm enhances the accuracy of the parameter identification by about 12% when compared with the least squares algorithm. The effectiveness of the algorithm was further verified by a simulation of the ship Yu Kun. The results confirm the algorithm's capacity to rapidly produce highly accurate parameter identification on the basis of relatively small datasets. The approach can be extended to other parameter identification systems where only a small amount of test data is available.

Research and dynamic analysis based on nonlinear identification of sports goods Econometrics

On the basis of literature research, this paper analyses the sports econometric analysis method, discusses the contribution of sports goods sales and economic growth in China, and analyses the dynamic relationship between them. In this paper, a nonlinear identification algorithm based on the econometric economics of sporting goods is proposed, and a nonlinear identification model based on the econometrics of sporting goods is established. Finally, through the MATLAB simulation analysis, the results show that: sports goods econometric nonlinear identification method is suitable for the coordinated development of regional economy, social environment and sports industry. The simulation results verify the feasibility and effectiveness of the nonlinear identification method of sports econometrics, and provide reference for the stable development of sports economy.

Research and Analysis of Nonlinear Model Identification Control Algorithm Based on Improved Neural RBF For Short Term Heat Load Forecasting of Heat Supply Network

Aiming at the mismatch between heat supply and demand of heating system, a nonlinear model identification control algorithm based on improved neural network for short-term heat load prediction of heat supply network is proposed by using the characteristics that heat load and temperature of heating system will not change dramatically in a short period of time By using MATLAB simulation, short-term heat load rolling prediction is realized. From the experimental results, this algorithm is better than the traditional RBF neural network in the prediction accuracy, and can accurately predict the trend of heat load.

Identification of static nonlinearities by sinusoidal excitation with variable DC offsets.

When identifying nonlinear systems with input-output measurements, a suitable test signal must be selected. Nonlinear systems are almost always in a cascade with linear systems, i.e., a Wiener-Hammerstein type system cascade. A suitable test signal is preferably less influenced by the linear systems and is therefore sinusoidal, if time-varying signals are required for the measurement principle, e.g., for induction or vibration measurements. Then, a sinusoidal excitation with different DC offsets is a suitable signal to analyze a static nonlinear system in a Wiener-Hammerstein type cascade by measuring the cascade output at higher harmonics of the input frequency in a steady state, e.g., by using sensitive lock-in techniques. To calculate the cascade output given the input signal or to reconstruct the static nonlinear system also given the output signal, the transfer function of the DC offset at the nonlinear system input to the higher harmonics at the nonlinear system output is required. Those transfer functions are calculated here with emphasis on the first harmonic component. The reconstruction of a static nonlinear system is demonstrated in a simple simulation scenario by inverse filtering, i.e., deconvolution, with the derived transfer function. It is pointed out that a commonly made small signal assumption to the test signal is bypassed with the deconvolution method, which can lead to more precise measurements in applications due to a higher signal-to-noise ratio at the cascade output.

An Alternative Procedure to Produce a P-Spline Small Area Estimation Model Based on Partial Residual Plot and Significance Test of Spline Term

This study provides an alternative procedure to produce the penalized spline small area estimation (P-Spline SAE) model by plotting each of auxiliary variable and variable interest as a simple nonlinearity identification and performing the iterative procedure: by estimating the model, producing partial residual plots to check model adequacy and also identify the nonlinearity, and testing the significance of spline term using Restricted Likelihood Ratio Test (RLRT). These procedures are applied to estimate the monthly average per-capita expenditure of district level in the Province of Bali, 2014 using direct survey estimates from the National Socio-Economic Survey (Susenas 2014) and auxiliary variables from the administrative record of village data (PODES 2014). The Fay-Herriot (FH) model (M1) as a benchmark and four P-Spline SAE model, i.e. the P-Spline SAE with spline term: x2 and x3 (M2), x3 and x4 (M3), x2, x3 and x4 (M4), and x1, x2, x3 and x4 (M5), are obtained. From RLRT, the spline term of M3, M4, and M5 are statistically significant. According to the parametric bootstrap of mean squared prediction error (MSPE) and coefficient of variation (CV), the M4 and M5 show a significant improvement with the CV values range from about 1%-6% compared to M1 with a range from about 4%-17%, shows that these two models more efficient. The M3 model shows the opposite performance even though has the smallest AIC value. More detail, the MSPE and CV produced by M4 are slightly better than M5 makes the M4 is the best model in this study.

The impact of static output nonlinearities on the control strategies that humans use in command-following tasks

The results of a human-in-the-loop experiment are used to investigate the control strategies that humans use to interact with nonlinear dynamic systems. Two groups of human subjects interact with a dynamic system and perform a command-following task. The first group interacts with a linear time-invariant (LTI) dynamic system. The second group interacts with a Wiener system, which consists of the same LTI dynamics cascaded with a static output nonlinearity. Both groups exhibit improved performance over the trials, but the average of the linear group’s performance is better on more than three-fourths of the trials. A new nonlinear subsystem identification algorithm is presented and used to identify the feedback and feedforward control strategies used by the subjects in both groups. The identification results for the linear group agree with prior studies suggesting that adaptive feedforward inversion is a primary control strategy used by humans for command-following tasks. The main results of this paper address an open question of whether a similar control strategy is used for nonlinear systems. The identification results for the nonlinear group suggest that those subjects also use adaptive feedforward inversion. However, the static output nonlinearity inhibits the human’s ability to approximate the inverse.

Eriyik yığma modelleme ile üretilen PLA parçalarının kuru sürtünmeli aşınma davranışlarının tanılanması.

In this study, wear behavior of Poly Lactic Acid (PLA) parts manufactured by one of the additive manufacturing techniques Fused Deposition Modelling (FDM) is investigated and modelled via linear and non-linear identification. Transfer Function, Process Model and Nonlinear Autoregressive with Exogenous Input (NARX) model are used as modelling. Identified wear models are established according to wear tests conducted on Pin-on-disc test apparatus under constant load and constant sliding distance. Two different manufacturing orientations are chosen for the PLA pin specimens and wear tests are performed against steel and cast iron discs. Obtained results from the identified models are compared with the experimental results to select most efficient and reliable model structure.

Nonlinear vibration suppression of composite laminated beam embedded with NiTiNOL-steel wire ropes

NiTiNOL-steel wire rope (NiTi-ST) is a new vibration absorber with nonlinear stiffness and hysteretic damping. Although there are many studies on NiTi-ST nonlinear identification, there are few studies on vibration suppression for laminated structures with NiTi-ST. In the present work, the NiTi-ST is integrated with a composite laminated beam for structural vibration suppression for the first time. A coupling model of the composite laminated beam embedded with NiTi-ST is proposed. The nonlinear restoring force and hysteretic damping force of NiTi-ST are processed into polynomial form. The responses of the beam embedded with different NiTi-ST are investigated by the Galerkin discretization together with the harmonic balance method (HBM). The terms of the polynomial model are discussed. Two numerical methods are utilized for steady-state responses and numerical validations. Simulation results demonstrate the effectiveness of NiTi-ST. This vibration suppression method can be popularized for other laminated structures and contribute to vibration control in engineering fields.

Joint Fiber Nonlinear Noise Estimation, OSNR Estimation and Modulation Format Identification Based on Asynchronous Complex Histograms and Deep Learning for Digital Coherent Receivers.

In this paper, asynchronous complex histogram (ACH)-based multi-task artificial neural networks (MT-ANNs), are proposed to realize modulation format identification (MFI), optical signal-to-noise ratio (OSNR) estimation and fiber nonlinear (NL) noise power estimation simultaneously for coherent optical communication. Optical performance monitoring (OPM) is demonstrated with polarization mode multiplexing (PDM), 16 quadrature amplitude modulation (QAM), PDM-32QAM, as well as PDM-star 16QAM (S-16QAM) for the first time. The range of launched power is −3 to −2 dBm with a fiber link of 160–1600 km. Then, the accuracy of MFI reaches 100%. The average root mean square error (RMSE) of OSNR estimation can reach 0.37 dB. The average RMSE of NL noise power estimation can reach 0.25 dB. The results show that the monitoring scheme is robust to the increase of fiber length, and the solution can monitor more optical network parameters with better performance and fewer training data, simultaneously. The proposed ACH MT-ANN has certain reference significance for the future long-haul coherent OPM system.

Deep State Space Models for Nonlinear System Identification

Abstract Deep state space models (SSMs) are an actively researched model class for temporal models developed in the deep learning community which have a close connection to classic SSMs. The use of deep SSMs as a black-box identification model can describe a wide range of dynamics due to the flexibility of deep neural networks. Additionally, the probabilistic nature of the model class allows the uncertainty of the system to be modelled. In this work a deep SSM class and its parameter learning algorithm are explained in an effort to extend the toolbox of nonlinear identification methods with a deep learning based method. Six recent deep SSMs are evaluated in a first unified implementation on nonlinear system identification benchmarks.

Study on control methods based on identification of unmanned vehicle model

This paper presents the results of nonlinear model identification of an unmanned vehicle in the Gazebo simulator based on a neural network autoregressive model. The dynamic characteristics of the control object can vary significantly that complicates the problem. The training sample of movement along the spatial path was obtained at the Robotics Center of the FRC CSC RAS. The model parameters were found by the particle swarm optimization method. Using the identified model, real-time control methods were experimentally compared. For a more accurate assessment of the methods, the model was subjected to random disturbances, and the tracking path of the control object was significantly complicated.