Nonlinear Identification Method Research Articles

Non-linear structural parameter identification using instantaneous power flow balance approach

ABSTRACT In this paper, a non-linear parameter identification method for structures is presented, whereby the instantaneous power flow balance of the substructure of interest is enforced. The time-domain power flow into the non-linear substructure is balanced against the power transmitted to adjacent structures, damping and kinetic and strain energies. Enforcing this condition of matching the net power balance to zero, a numerical model is iteratively updated as an inverse problem. Here, the identification is carried out using a non-classical optimization search tool, particle swarm optimization algorithm. A cubic non-linearity in spring and a quadratic non-linearity in damper are modelled for non-linear parameter estimation using power flow concept and is a preliminary stage of non-linear joint parameter identification. Important numerical simulations are presented in this paper, which cover different load cases, measurement points and different combination of non-linearities under noise-free and noisy conditions. The identified results show significant improvements in non-linear identification accuracy compared to previous literature related to non-linear identification.

Control oriented data driven linear parameter varying model for proton exchange membrane fuel cell systems

Proton exchange membrane fuel cell systems are widely used to drive vehicles. It is indispensable to establish accurate and simple control oriented model of the system. However, this control oriented model is difficult to build due to the characteristic of strongly nonlinear, coupled and time - varying in proton exchange membrane fuel cell systems. To solve this problem, nonlinear subspace identification method is proposed to discover linear parameter varying model for the proton exchange membrane fuel cell system. The modeling process can be divided into two stages. In the first stage, algebraic transformation method is proposed to transform the nonlinear model to linear parameter varying model. In the second stage, kernel method based subspace identification is presented to identify parameter matrices of the proton exchange membrane fuel cell system. The established model is demonstrated by a 50 kW on board proton exchange membrane fuel cell system under real driving condition. The results show that mean absolute percent error and root mean squared error are as low as 9.6941e−06 and 0.0957, respectively. Therefore, the control oriented model perfectly agrees with real data. Compared with the prediction error method and recursive neural network nonlinear auto - regressive moving average model with exogenous method, modeling accuracy and speed of the proposed method are the best. Moreover, linear control theory can be employed to design controller based on the linear parameter varying model, which greatly simplifies controller design for proton exchange membrane fuel cell systems.

Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids

The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications.This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

Research on TE process fault diagnosis method based on DBN and dropout

AbstractIn recent years, deep learning has shown outstanding performance and potential in pattern recognition and feature extraction, which has attracted an increasing amount of attention from engineering researchers and academics. Fault diagnosis methods based on deep learning have also become the focus of a significant amount of research. In this paper, a nonlinear process fault diagnosis and identification method based on DBN‐dropout is proposed. The deep belief network (DBN) has significant advantages in dealing with nonlinear processes, and it can extract the abstract representation of nonlinear process data to build a deep network to achieve the real‐time monitoring of process operations. Dropout technology can reduce overfitting and improve the generalization ability of the model. Afterwards, the Tennessee Eastman (TE) process is employed to analyze the performance of the proposed approach.

Structural dynamic nonlinear model and parameter identification based on the stiffness and damping marginal curves

This paper presents a novel structural dynamic nonlinear model and parameter identification method based on the stiffness and damping marginal curves. The stiffness and damping marginal curves are first extracted from the structural dynamic responses. Then, nine nonlinear feature indices (NFIs) are defined based on the marginal curves to describe the characteristics of various nonlinear models. To reduce the dimension of NFIs and facilitate the subsequent calculation of the support vector machine (SVM), the principal component analysis (PCA) is implemented. Afterwards, the NFIs processed by PCA are employed as the training samples to SVM classifier, which is used to identify the structural nonlinear model. According to the identified nonlinear model corresponding to the type of nonlinearity, the parameters of the nonlinear model are further identified by the nonlinear least square method. The numerical results of a single degree of freedom (SDOF) system and a cantilever beam structure demonstrate that the proposed method can effectively identify both nonlinear model and corresponding parameters under various excitations even considering the noise effect. Subsequently, the proposed method is also verified by a benchmark system subjected to a semisinusoidal pulse load and a beam bridge structure subjected to an earthquake load. The proposed method is also applied to the experimental test of a bolted joint cantilever beam subjected to a random excitation in the laboratory. Both numerical and test results demonstrate that the proposed method can identify both nonlinear model and corresponding parameters within good accuracy and robustness.

Identification of physical nonlinearities of a hybrid aeroelastic\u2013pressure balance

This study has presented an improved method for determining physical nonlinearities of weakly nonlinear spring-suspension system and successfully applied to a novel hybrid aeroelastic–pressure balance (HAPB) system used in wind tunnel, which can be used for simultaneously obtaining the unsteady wind pressure and aeroelastic response of a test model. A nonlinear identification method of equivalent linearization approximation was firstly developed on the basis of the averaging method of Krylov–Bogoliubov to model the physical nonlinearity of a weakly nonlinear system. Subsequently, the nonlinear physical frequency and damping were identified using a modified Morlet wavelet transform method and a constant variant method. Using these methods, the physical nonlinear frequency and damping of the HAPB system with a vertical test model were determined and were validated by a time domain method and the Newmark-beta method. Finally, the nonlinear mechanical frequency and damping of the HAPB system with inclined test models were determined in a similar way. This study has not only provided an identification method for determining physical nonlinearities of weakly nonlinear system, but presented the detail for developing a hybrid aeroelastic–pressure balance used in wind tunnel.

The Nonlinear Filtering Feature Identification Methods for the Duffing Chaotic Fractal State

With the wide applications of weak signal detection techniques for Duffing system, it is important to study the fast and accurate identification methods for fractal state, such as in the field of all kinds of signals detections, by fractal state discriminant of Duffing, the target detections can be achieved under the conditions of extremely low signal-to-noise ratios. Aiming at the existing problems of the algorithm, a new idea is put forward, the Duffing oscillator is converted to the state equation of nonlinear filters, respectively by CKF(Cubature Kalman Filter,) PF(Particle Filter) and EKF(Extended Kalman Filter) three nonlinear filtering algorithm for recursive estimations, the inherent rules whose filtering parameters change with the system state changing will be researched, and a discrimination method of oscillator Fractal state is proposed; the experimental results show that the three kinds of filtering methods can all achieve the Duffing oscillator state tracking, and with the help of the filtering characteristics, the identification of the oscillator state can be distinguished and feature extraction can both realize the qualitative and quantitative detections.

Koopman-Based Lifting Techniques for Nonlinear Systems Identification

We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator. The key idea is to identify the linear (infinite dimensional) Koopman operator in the lifted space of observables, instead of identifying the nonlinear system in the state space, a process which results in a linear method for nonlinear systems identification. The proposed lifting technique is an indirect method that does not require to compute time derivatives and is therefore well-suited to low-sampling rate data sets. Considering different finite-dimensional subspaces to approximate and identify the Koopman operator, we propose two numerical schemes: a main method and a dual method. The main method is a parametric identification technique that can accurately reconstruct the vector field of a broad class of systems. The dual method provides estimates of the vector field at the data points and is well-suited to identify high-dimensional systems with small datasets. This paper describes the two methods, provides theoretical convergence results, and illustrates the lifting techniques with several examples.

Second Path Planning for Unmanned Surface Vehicle Considering the Constraint of Motion Performance

When utilizing the traditional path planning method for unmanned surface vehicles (USVs), ‘planning-failure’ is a common phenomenon caused by the inflection points of large curvatures in the planned path, which exceed the performances of USVs. This paper presents a second path planning method (SPP), which is an initial planning path optimization method based on the geometric relationship of the three-point path. First, to describe the motion performance of a USV in conjunction with the limited test data, a method of integral nonlinear least squares identification is proposed to rapidly obtain the motion constraint of the USV merely by employing a zig zag test. It is different from maneuverability identification, which is performed in combination with various tests. Second, the curvature of the planned path is limited according to the motion performance of the USV based on the traditional path planning, and SPP is proposed to make the maximum curvature radius of the optimized path smaller than the rotation curvature radius of the USV. Finally, based on the ‘Dolphin 1’ prototype USV, comparative simulation experiments were carried out. In the experiment, the path directly obtained by the initial path planning and the path optimized by the SPP method were considered as the tracking target path. The artificial potential field method was used as an example for the initial path planning. The experimental results demonstrate that the tracking accuracy of the USV significantly improved after the path optimization using the SPP method.

A modified time domain subspace method for nonlinear identification based on nonlinear separation strategy

Nonlinear factors existing in engineering structures have drawn considerable attention, and nonlinear identification is a competent technique to understand the dynamic characteristics of nonlinear structures. Therefore, in this paper, a novel nonlinear separation subspace identification (NSSI) algorithm based on subspace algorithm and nonlinear separation strategy is proposed to conduct nonlinear parameter identification of nonlinear structures. For the proposed NSSI algorithm, the low-level excitation test is firstly conducted to obtain the transfer matrix in the linear response formula. Then, the obtained transfer matrix is used in the high-level excitation test to calculate the nonlinear response part by the proposed nonlinear separation strategy, and the subspace algorithm is utilized to identify the nonlinear parameter on the modified state-space model including only the nonlinear part. The proposed NSSI algorithm can reduce the coupling error caused by simultaneously processing both the large number part (corresponding to the linear part) and small number part (corresponding to the nonlinear part) in the traditional nonlinear subspace identification (NSI) algorithm. At last, two numerical experiments are given to validate the effectiveness of the developed novel nonlinear identification method. Furthermore, some influence factors are discussed to show the stability of the identification algorithm, and some comparisons between the proposed NSSI method and traditional NSI method are also conducted to demonstrate the advantages of the novel method.

A new method for the accurate measurement of higher-order frequency response functions of nonlinear structural systems

Higher-order frequency response functions (FRFs) are important to the analysis and identification of structural nonlinearities. Though much research effort has been devoted recently to their potential applications, practical issues concerning the difficulty and accuracy of higher-order FRF measurement have not been rigorously assessed to date. This paper presents a new method for the accurate measurement of higher-order FRFs. The method is developed based on sinusoidal input, which is ideal for exciting a nonlinear structure into desired regimes with flexible control, and the correlation technique, which is a novel signal processing method capable of extracting accurate frequency components present in general nonlinear responses. The correlation technique adopted is a major improvement over Fourier transform based existing methods since it eliminates leakage and aliasing errors altogether and proves to be extremely robust in the presence of measurement noise. Extensive numerical case studies have been carried out to critically assess the capability and accuracy of the proposed method and the results achieved are indeed very promising. Interesting nonlinear behavior such as frequency shift and jump have been observed in first-, second- and third-order FRFs, as well as solitary islands which have been identified over which higher-order FRFs virtually do not change as input force amplitude varies. Higher-order FRFs over such solitary islands are essentially their theoretical counterparts of Volterra transfer functions which can be measured with very low input force and can be profitably employed for the identification of physical parameters of structural nonlinearities. Subsequently, a nonlinear parameter identification method has also been developed using measured higher-order FRFs and results are presented and discussed.

A nonlinear dynamic model and parameters identification method for predicting the shock pulse of rubber waveform generator

This paper proposed a highly accurate nonlinear dynamic model and parameters identification method to predict the shock pulses generated by rubber waveform generator (RWG) used in shock test. The establishment of the model is based on the primary results of the Duffing equation, Pan-Yang model and empirical stiffness formulae of cylindrical rubber isolator. We proposed a series of measures to eliminate the interferences in the drop shock test experiment, which are also of benefit to design, regulate and calibrate drop shock testers. The overall nonlinear system is solved in time domain with Runge–Kutta. And the parameters of the nonlinear dynamic model are identified by minimizing the holistic shape difference between experimental and predicted shock pulses with multiple population genetic algorithm. Meanwhile, the capacity of this model in characterizing the dynamic behavior of RWG under shock excitations is also investigated. Compared with previous work, our model considers nonlinear viscoelasticity of RWG, the geometric factor of RWG and the effect of initial shock velocity, which makes our model more accurate and general. Experimental results shown great agreements with the predictions and that the proposed method can determine the parameters conveniently and synergistically.

Nonlinear parameter identification of timber-concrete composite beams using long-gauge fiber optic sensors

A novel method for nonlinear parameter identification of partially composite beams using long-gauge strain responses is proposed in this paper. Firstly, theoretical analysis shows that neutral axis position of timber beam and concrete slab can be estimated by measured long-gauge strain and material properties. Then, distribution of curvature, bending stiffness, deflection and interface slip can be determined by identified neutral axis position. Secondly, timber-concrete composite beams connected by ductile connectors with different degree of composite action are designed to verify the presented method. Experimental results show that the estimated parameters (neutral axis position, bending stiffness and interface slip) can clearly reflect and quantify the deterioration process of partially composite beams. Meanwhile, both global and local responses can be predicted by long-gauge strain sensors. The predicted responses (deflection at mid-span and strain along the beam height) agree well with the test results when partially composite action is considered, the errors will be unacceptable without considering partially composite action. Hence, the presented method can be utilized for better understanding of mechanical properties of partially composite beams and performance assessment of existing composite structures.

Tremor severity rating by Markov chains

The paper deals with mathematical modeling tools for tremor quantification, a problem arising in e.g. clinical applications and sports. Tremor is an involuntary repetitive movement of extremities, head, or trunk that occurs in disease but also in health, due to e.g. strain or fatigue. Quantification of tremor is traditionally performed by ocular observation, while numerous technologies based on wearable accelerometer data exist and have been tested in medical practice. The currently available approaches rely on spectral analysis that reduces a fundamentally nonlinear and non-stationary phenomenon to a linear combination of harmonic components. The classical nonlinear identification methods are as well of limited use because the underlying system is essentially autonomous and produces sustained oscillations without exogenous excitation. An alternative view on tremor is therefore adopted that treats the problem from a severity rating perspective aligned with clinical practices. The tremor amplitude is modelled by a Markov chain, where the states represent the predefined intervals of severity. A comparison with a previously developed event-based method of tremor quantification is provided on data collected using a smart phone in a patient diagnosed with Parkinson disease and undergoing Deep Brain Stimulation therapy. The experimental procedure is unobtrusive and can be implemented in a way that is transparent to the patient.

A nonlinear subspace-prediction error method for identification of nonlinear vibrating structures

The industrial structural systems always contain various kinds of nonlinear factors. Recently, a number of new approaches have been proposed to identify those nonlinear structures. One of the promising methods is the nonlinear subspace identification method (NSIM). The NSIM is derived from the principals of the stochastic subspace identification method (SSIM) and the internal feedback formulation. First, the nonlinearities in the system are regarded as internal feedback forces to its underlying linear dynamic system. The linear and nonlinear components of the identified system can be decoupled. Second, the SSIM is employed to identify the nonlinear coefficients and the frequency response functions of the underlying linear system. A typical SSIM always consists of two steps. The first step makes a projection of certain subspaces generated from the data to identify the extended observability matrix. The second one is to estimate the system matrices from the identified observability matrix. Since the calculated process of the NSIM is non-iterative and this method poses no additional problems on the part of parameterization, the NSIM becomes a promising approach to identify nonlinear structural systems. However, the result generated by the NSIM has its deficiency. One of the drawbacks is that the identified results calculated by the NSIM are not the optimal solutions which reduce the identified accuracy. In this study, a new time-domain subspace method, namely the nonlinear subspace-prediction error method (NSPEM), is proposed to improve the identified accuracy of nonlinear systems. In the improved version of the NSIM, the prediction error method (PEM) is used to reestimate those estimated coefficient matrices of the state-space model after the application of NSIM. With the help of the PEM, the identified results obtained by the NSPEM can truly become the optimal solution in the least square sense. Two numerical examples with local nonlinearities are provided to illustrate the effectiveness and accuracy of the proposed algorithm, showing advantages with respect to the NSIM in a noise environment.

Identification of Preisach hysteresis model parameters using genetic algorithms

Preisach model is widely used to characterize ferromagnetic material’s hysteresis. Thus, it is necessary to identify its parameters in order to complete magnetic hysteresis modeling successfully. In this paper, a stochastic identification method, Genetic algorithm, is implemented. The procedure consists of the minimization of the error between measurements and program results. Obtained results are compared with the classical nonlinear least square identification method and experimental hysteresis of a fully-process non oriented Fe-3 wt%Si steel sheet.

Nonlinear vibrational response of a single edge cracked beam

The nonlinear vibrational response of a breathing cracked beam was investigated. The study was done by using a new crack stiffness model to examine some of the nonlinear behaviors of a cantilever beam with a breathing crack. The quadratic polynomial stiffness equation of the cracked beam was derived based on the hypothesis that the breathing process of a crack depends on the vibration magnitude. The Galerkin method combined with the stiffness equation was used to simplify the cracked beam into a Single-degree-of-freedom (SDOF) lumped system with nonlinear terms. The multi scale method was adopted to analyze the nonlinear amplitude frequency response of the beam. The applicability of the stiffness model was discussed and parameter sensitivity studies on the dynamic response were carried out by the SDOF model for a cantilever beam. Results indicate that the new stiffness model provides an efficient tool to study the vibrational nonlinearities introuduced by the breathing crack. Therefore, it might be used to develop a nonlinear identification method of a crack in a beam.

Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking

Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multiphases and multifields interactions with long time delay phenomena take place during its operation. In BF operation, the molten iron temperature as well as the Si content ([Si]), the phosphorus content ([P]), and the sulfur content ([S]) is the most essential quality (MIQ) indices. The measurement, modeling, and control of these indices have always been important issues in metallurgic engineering and automation. This paper proposes a novel data-driven nonlinear state-space modeling method for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques together. First, to improve modeling efficiency, a data-driven hybrid method that combines canonical correlation analysis and correlation analysis is established to identify the most influential controllable variables as the modeling inputs from multitudinous factors. Then, a Hammerstein model for the prediction of MIQ indices is established using the Least squares support vector machine-based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method. Compared with the original Hammerstein model, it has been shown that this simplified model can not only significantly reduce the computational complexity, but can also exhibit a good reliability and accuracy for a stable prediction of MIQ indices. In order to verify the practicability of the developed model, it is applied to the design of a genetic algorithm based nonlinear predictive controller for the multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approaches.

Development of pH sensitive polyacrylic acid grafted hemicellulose hydrogels for colon-specific controlled drug delivery

Boiler superheated steam temperature control is of great importance for the safety and economy of thermal power unit. This article presents a nonlinear model identification method for the superheated steam temperature system, based on the unit load as a time-varying parameter. The linear parameter varying (LPV) model, which has been established by using the unit historical data, is suitable for control studies, and it can reflect the global dynamic characteristics of the object. To solve the model parameters estimation in high-dimensional problem, the evolutionary acceleration factor is introduced to the quantum particle swarm optimization (A-QPSO) algorithm to optimize the model parameters. The validity of the modified algorithm A-QPSO is verified through optimizing several classical high-dimensional standard test functions. The A-QPSO improved the optimization efficiency, and optimized result is very close to the optimal value. Finally, the proposed method is applied to the identification of a power plant superheated steam temperature process, and the results show that the optimized superheated steam temperature model is of high accuracy and the proposed method is feasible.

Study on Nonlinear Identification SOFC Temperature Model Based on Particle Swarm Optimization–Least-Squares Support Vector Regression

In order to facilitate valid solid oxide fuel cell (SOFC) temperature control scheme, a nonlinear identification method of SOFC temperature dynamic behaviors is proposed using an autoregressive network with exogenous inputs (NARX) model, whose nonlinear function is described by a least-squares support vector regression (LSSVR) method with radial basis kernel function (RBF). During the identifying process, a particle swarm optimization (PSO) algorithm is introduced to optimize the parameters of LSSVR. On the other hand, a mechanism model is developed to sample the training data to regress the NARX model. Investigations are conducted to analyze the effects of training data size and PSO fitness function on the accuracy of the NARX model. The results demonstrate that the NARX model with tenfold cross-validation fitness function and large size data is precise enough in predicting the SOFC temperature dynamic behaviors. The maximum errors of cathode and anode outlet temperature are 0.3081 K and 0.3293 K, respectively. Furthermore, the simulation speed of NARX model is much faster than the mechanism model because NARX model avoids the internal complex computation process. The training time of the NARX model with large size data is about 1.2 s. For a 20,000 s simulation, the predicting time of the NARX model is about 0.2 s, while the mechanism model is about 36 s. In consideration of its high computational speed and accuracy, NARX model is a powerful candidate for valid multivariable model predictive control (MPC) schemes.