Proposed System Identification Research Articles

Estimating the multivariable human ankle impedance in dorsi-plantarflexion and inversion-eversion directions using EMG signals and artificial neural networks

The use of a suitably designed ankle-foot prosthesis is essential for transtibial amputees to regain lost mobility. A desired ankle–foot prosthesis must be able to replicate the function of a healthy human ankle by transferring the ground reaction forces to the body, absorbing shock during contact, and providing propulsion. During the swing phase of walking, the human ankle is soft and relaxed; however, it hardens as it bears the body weight and provides force for push-off. The stiffness is one of the components of the mechanical impedance, and it varies with muscle activation (Stochastic estimation of human ankle mechanical impedance in medial-lateral direction, 2014, Stochastic estimation of the multivariable mechanical impedance of the human ankle with active muscles, 2010). This study defines the relationship between ankle impedance and the lower extremity muscle activations using artificial neural networks (ANN). We used the Anklebot, a highly backdrivable, safe, and therapeutic robot to apply stochastic position perturbations to the human ankle in the sagittal and frontal planes. A previously proposed system identification method was used to estimate the target ankle impedance to train the ANN. The ankle impedance was estimated with relaxed muscles and with lower leg muscle activations at 10 and 20% of the maximum voluntary contraction (MVC) of each individual subject. Given the root mean squared (rms) of the electromyography (EMG) signals, the proposed ANN effectively predicted the ankle impedance with mean accuracy of 89.8 ± 6.1% in DP and mean accuracy of 88.3 ± 5.7% in IE, averaged across three muscle activation levels and all subjects.

Application of System Identification for Modeling the Dynamic Behavior of Axial Flow Compressor Dynamics

Identification of a one-stage axial compressor system is addressed. In particular, we investigate the underlying dynamics of tip air injection and throttle activation to the overall compressor dynamics and the dynamics around the tip of the compressor blades. A proposed subspace system identification algorithm is used to extract three mathematical models: relating the tip air injection to the overall dynamics of the compressor and to the flow dynamics at the tip of the compressor blade and relating the movement of the throttle to the overall compressor dynamics. As the system identification relays on experimental data, concerns about the noise level and unmodeled system dynamics are addressed by experimenting with two model structures. The identification algorithm entails a heuristic optimization that allows for inspection of the results with respect to unmodeled system dynamics. The results of the proposed system identification algorithm show that the assumed model structure for the system identification algorithm takes on an important role in defining the coupling characteristics. A new measure for the flow state in the blade passage is proposed and used in characterizing the dynamics at the tip of the compressor blade, which allows for the inspection of the limits for the utilized actuation.

Bat Algorithm: Application to Adaptive Infinite Impulse Response System Identification

The problem of system identification concerns with the design of adaptive infinite impulse response (IIR) system by determining the optimal system parameters of the unknown system on the minimization of error fitness function. The conventional system identification techniques have stability issues and problem of degradation in performance when modeled using a reduced-order system. Hence, a meta-heuristic optimization method is applied to overcome such drawbacks. In this paper, a new meta-heuristic optimization algorithm, called bat algorithm (BA), is utilized for the design of an adaptive IIR system in order to approximate the unknown system. Bat algorithm is inspired from the echolocation behavior of bats combining the advantages of existing optimization techniques. A proper tuning of control parameter has been performed in order to achieve a balance between intensification and diversification phases. The proposed BA method for system identification is free from the problems encountered in conventional techniques. To valuate the performance of the proposed method, mean square error, mean square deviation and computation time are measured. Simulations have been carried out considering four benchmarked IIR systems using the same-order and reduced-order systems. The results of the proposed BA method have been compared to that of the well known optimization methods such as genetic algorithm, particle swarm optimization and cat swarm optimization. The simulation results confirm that the proposed system identification method outperforms the existing system identification methods.

An efficient numerical and experimental system identification approach for a flexible manipulator

Purpose – The purpose of this paper is to propose an efficient and straightforward approach for system identification of a rotating single link flexible manipulator (RSLFM). Also, the achieved results are experimentally validated through identification procedure. Design/methodology/approach – The proposed system identification approach is applied to a RSLFM with a tip mass. At first, the dynamic model of the system is derived using Lagrange method. Then, an efficient method is developed for identification of such a system. This method facilitates the nonlinear complicated identification problem of the RSLFM to a simplified root finding problem. Findings – The main advantage of the developed method is to convert a complicated system identification process to a simple nonlinear equation solution. This approach uses small-size input/output data set and requires a short-time interval of data acquisition, which gives important advantages in lower computational load and lower execution time. The investigated approach is studied on experimental system identification of a single link flexible manipulator. To demonstrate this fact, the developed method is successfully applied in identification of two other mechanical systems; the inverted pendulum on a cart and the ball and beam apparatus. Originality/value – In this work, the proposed identification approach has been originally applied to a RSLFM and two other mechanical examples. All obtained identification results show the performance and applicability of the developed method clearly. This approach is not restricted in using state space or transfer function. It has significant superiority in comparison with other known approaches including autoregressive with exogenous input (ARX) and Box-Jenkins (BJ).

Verification of system identification utilizing shaking table tests of a full‐scale 4‐story steel building

SummaryThis paper verifies the feasibility of the proposed system identification methods by utilizing shaking table tests of a full‐scale four‐story steel building at E‐Defense in Japan. The natural frequencies, damping ratios and modal shapes are evaluated by single‐input‐four‐output ARX models. These modal parameters are prepared to identify the mass, damping and stiffness matrices when the objective structure is modelled as a four degrees of freedom (4DOF) linear shear building in each horizontal direction. The nonlinearity in stiffness is expressed as a Bouc–Wen hysteretic system when it is modelled as a 4DOF nonlinear shear building. The identified hysteretic curves of all stories are compared to the corresponding experimental results. The simple damage detection is implemented using single‐input‐single‐output ARX models, which require only two measurements in each horizontal direction. The modal parameters are equivalent‐linearly evaluated by the recursive Least Squares Method with a forgetting factor. When the structure is damaged, its natural frequencies decrease, and the corresponding damping ratios increase. The fluctuation of the identified modal properties is the indirect information for damage detection of the structure. Copyright © 2015 John Wiley & Sons, Ltd.

System identification of high-rise buildings using shear-bending model and ARX model: Experimental investigation

System identification is regarded as the most basic technique for structural health monitoring to evaluate structural integrity. Although many system identification techniques extracting mode information (e.g., mode frequency and mode shape) have been proposed so far, it is also desired to identify physical parameters (e.g., stiffness and damping). As for high-rise buildings subjected to long-period ground motions, system identification for evaluating only the shear stiffness based on a shear model does not seem to be an appropriate solution to the system identification problem due to the influence of overall bending response. In this paper, a system identification algorithm using a shear-bending model developed in the previous paper is revised to identify both shear and bending stiffnesses. In this algorithm, an ARX (Auto-Regressive eXogenous) model corresponding to the transfer function for interstory accelerations is applied for identifying physical parameters. For the experimental verification of the proposed system identification framework, vibration tests for a 3-story steel mini-structure are conducted. The test structure is specifically designed to measure horizontal accelerations including both shear and bending responses. In order to obtain reliable results, system identification theories for two different inputs are investigated; (a) base input motion by a modal shaker, (b) unknown forced input on the top floor.

A new approach for online T-S fuzzy identification and model predictive control of nonlinear systems

This paper proposes a new unsupervised fuzzy clustering algorithm (NUFCA) to construct a novel online evolving Takagi–Sugeno (T-S) fuzzy model identification method and an adaptive predictive process control methodology. The proposed system identification approach consists of two main steps: antecedent T-S fuzzy model parameters identification and consequent parameters identification. The NUFCA combines the K-nearest neighbour and fuzzy C-means methods into a fuzzy modelling method for partitioning of the input–output data and identifying the antecedent parameters of the fuzzy system; then the recursive least squares method is exploited to obtain initialization type consequent parameters and to construct a method for on-line fuzzy model identification. The integration of the proposed adaptive identification method with the generalized predictive control results in an effective adaptive predictive fuzzy control methodology. For better demonstration of the robustness and efficiency of the proposed methodology, it is applied to the identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment plant (WWTP); and to control a simulated continuous stirred tank reactor (CSTR), and a real experimental setup composed of two coupled DC motors. The results show that the developed evolving T-S fuzzy model methodology can identify nonlinear systems satisfactorily and can be successfully used for a prediction model of the process for the generalized predictive controller. It is also shown that the algorithm is robust to changes in the initial parameters, and to unexpected disturbances.

A new design method based on firefly algorithm for IIR system identification problem

In this paper a population based evolutionary optimization methodology called firefly algorithm (FFA) is applied for the optimization of system coefficients of the infinite impulse response (IIR) system identification problem. FFA is inspired by the flash pattern and characteristics of fireflies. In FFA technique, behaviour of flashing firefly towards its competent mate is structured. In this algorithm attractiveness depends on brightness of light and a bright firefly feels more attraction for the brighter one. For this optimization problem, brightness varies inversely proportional to the error fitness value, so the position of the brightest firefly gives the optimum result corresponding to the least error fitness in multidimensional search space. Incorporation of different control parameters in basic movement equation results in balancing of exploration and exploitation of search space. The proposed FFA based system identification approach has alleviated from inherent drawbacks of premature convergence and stagnation, unlike genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed system identification approach using FFA over GA, PSO and DE in terms of convergence speed, identifying plant coefficients and mean square error (MSE) fitness values produced for both same order and reduced order models of adaptive IIR filters.

IIR system identification using differential evolution with wavelet mutation

In this paper an improved version of Differential Evolution (DE) technique called Differential Evolution with Wavelet Mutation (DEWM) is applied to the infinite impulse response (IIR) system identification problem. Instead of fixed value of scaling factor in standard DE, an iteration dependent scaling factor governed by the wavelet function during the mutation process is adopted in the proposed technique. This modification in the mutation process ensures not only the faster searching in the multidimensional search space but also the solution produced is very close to the global optimal solution. Apart from this, the proposed technique DEWM has alleviated from inherent drawbacks of premature convergence and stagnation, unlike Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed system identification approach using DEWM over GA, PSO and DE in terms of convergence speed, plant coefficients and mean square error (MSE) values produced for both the same order and reduced order models of adaptive IIR filters.

Identifying parameters of multi-degree-of-freedom nonlinear structural dynamic systems using linear time periodic approximations

The authors recently presented a new nonlinear system identification method, here dubbed the NL-LTP method, in which the system of interest is forced harmonically so that it responds in a stable periodic orbit, and then it is perturbed slightly and its response is recorded as it returns to the orbit. Under mild assumptions the response about the periodic orbit can be approximated using a linear time periodic system model, which can be identified from the measurements using techniques that are akin to linear modal analysis. While the prior work focused on simulated measurements from single degree-of-freedom systems, this work presents several tools that are needed in order to use this approach on multi-degree-of-freedom systems and focuses on applying the method to experimental hardware. The proposed system identification methodology is unique in that it identifies both the order of the nonlinear system and a mathematical model for the nonlinear restoring forces without assuming the mathematical form for the nonlinearities a priori. Towards these ends, this work explains how to extract the underlying nonlinear system model, or nonlinear restoring force versus displacement relationships, from the time periodic model that governs deviations of the system from its periodic orbit, and presents various metrics that can be used to determine which terms in the model are meaningful. These new tools are used to apply the identification method to a continuous, multi-degree-of-freedom structure with a discrete geometric nonlinearity, using both simulated and experimental measurements. The experimental hardware consists of a cantilever beam with a nonlinear spring attached to its tip, which is driven in a periodic limit cycle by an electromagnetic shaker.

Structural System Identification with Extended Kalman Filter and Orthogonal Decomposition of Excitation

Both the structural parameter and external excitation have coupling influence on structural response. A new system identification method in time domain is proposed to simultaneously evaluate structural parameter and external excitation. The method can be used for linear and hysteresis nonlinear structural condition assessment based on incomplete structural responses. In this method, the structural excitation is decomposed by orthogonal approximation. With this approximation, the strongly time-variant excitation identification is transformed to gentle time-variant, even constant parameters identification. Then the extended Kalman filter is applied to simultaneously identify state vector including the structural parameters and excitation orthogonal parameters in state space based on incomplete measurements. The proposed method is validated numerically with the simulation of three-story linear and nonlinear structures subject to external force. The external force on the top floor and the structural parameters are simultaneously identified with the proposed system identification method. Results from both simulations indicate that the proposed method is capable of identifing the dynamic load and structural parameters fairly accurately with contaminated incomplete measurement for both of the linear and nonlinear structural systems.

A novel social emotional optimisation algorithm for IIR system identification problem

In this paper an evolutionary optimisation methodology based on social emotional optimisation algorithm (SEOA) is applied to the infinite impulse response (IIR) system identification problem. In SEOA methodology, behaviour of human beings for achieving higher social status in society is structured. In this virtual world, the individual with the highest rank in society gives the optimal solution in multidimensional search space. Earning the highest social status by means of cooperation and competition with others not only results in better exploration and exploitation of problem space but also ensures faster convergence to optimal solution. The proposed SEOA based system identification approach has resolved the inherent drawbacks of premature convergence and stagnation, unlike genetic algorithm (GA), particle swarm optimisation (PSO) and differential evolution (DE). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed system identification approach using SEOA over GA, PSO and DE in terms of convergence speed, unknown plant coefficients and mean square error (MSE) values produced for both the same order and reduced order models of adaptive IIR filters.

Collective Animal Behaviour Based Optimization Algorithm for IIR System Identification Problem

In this paper a novel optimization technique which is developed on mimicking the collective animal behaviour (CAB) is applied to the infinite impulse response (IIR) system identification problem. Functionality of CAB is governed by occupying the best position of an animal according to its dominance in the group. Enrichment of CAB with the features of randomness, stochastic and heuristic search nature has made the algorithm a suitable tool for finding the global optimal solution. The proposed CAB has alleviated from the defects of premature convergence and stagnation, shown by real coded genetic algorithm (RGA), particle swarm optimization (PSO) and differential evolution (DE) in the present system identification problem. The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed system identification approach using CAB over RGA, PSO and DE in terms of convergence speed, unknown plant coefficients and mean square error (MSE) values produced for IIR system models of both the same order and reduced order.

Craziness based particle swarm optimization algorithm for IIR system identification problem

In this paper a variant of particle swarm optimization (PSO), called craziness based particle swarm optimization (CRPSO) technique is applied to the infinite impulse response (IIR) system identification problem. A modified version of PSO, called CRPSO adopts a number of random variables for having better and faster exploration and exploitation in multidimensional search space. Incorporation of craziness factor in the basic velocity expression of PSO not only brings diversity in particles but also ensures convergence to optimal solution. The proposed CRPSO based system identification approach has alleviated from the inherent drawbacks of premature convergence and stagnation, unlike real coded genetic algorithm (RGA), particle swarm optimization (PSO) and differential evolution (DE). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed system identification approach using CRPSO over RGA, PSO and DE in terms of convergence speed, unknown plant coefficients and mean square error (MSE) values produced for both the same order and reduced order models of adaptive IIR filters.

Modal Identification Based on Hilbert Transform for Time-Varying System

Modal identification methods based on the Hilbert Transform are applied to identify modal parameters of time-varying system using impulse response time histories. First, the response data are decomposed into modal responses through the empirical mode decomposition (EMD). Then, the Hilbert transform is applied to each modal response to obtain the instantaneous frequencies. The applications of the proposed methods are illustrated using a 3 degree-of-freedom (DOF) systems with time-varying dynamic characteristics. Numerical simulation results demonstrate that the proposed system identification methods yield good results.

SSA-based stochastic subspace identification of structures from output-only vibration measurements

In this study an output-only system identification technique for civil structures under ambient vibrations is carried out, mainly focused on using the Stochastic Subspace Identification (SSI) based algorithms. A newly developed signal processing technique, called Singular Spectrum Analysis (SSA), capable to smooth a noisy signal, is adopted for preprocessing the measurement data. An SSA-based SSI algorithm with the aim of finding accurate and true modal parameters is developed through stabilization diagram which is constructed by plotting the identified system poles with increasing the size of data matrix. First, comparative study between different approaches, with and without using SSA to pre-process the data, on determining the model order and selecting the true system poles is examined in this study through numerical simulation. Finally, application of the proposed system identification task to the real large scale structure: Canton Tower, a benchmark problem for structural health monitoring of high-rise slender structures, using SSA-based SSI algorithm is carried out to extract the dynamic characteristics of the tower from output-only measurements.

A novel approach to detecting breathing-fatigue cracks based on dynamic characteristics

During the service life of structures, breathing-fatigue cracks may occur in structural members due to dynamic loadings acting on them. These fatigue cracks, if undetected, might lead to a catastrophic failure of the whole structural system. Although a number of approaches have been proposed to detect breathing-fatigue cracks, some of them appear rather sophisticated or expensive (requiring complicated equipment), and others suffer from a lack of sensitivity. In this study, a simple and efficient approach to detecting breathing-fatigue cracks is developed based on dynamic characteristics of breathing cracks. First, considering that breathing cracks introduce bilinearity into structures, a simple system identification method for bilinear systems is proposed by taking best advantage of dynamic characteristics of bilinear systems. This method transfers nonlinear system identification into linear system identification by dividing impulse or free-vibration responses into different parts corresponding to each stiffness region according to the stiffness interface. In this way, the natural frequency of each region can be identified using any modal identification approach applicable to linear systems. Second, the procedure for identifying the existence of breathing fatigue cracks and quantifying the cracks qualitatively is proposed by looking for the difference in the identified natural frequency between regions. Third, through introducing Hilbert transform, the proposed procedure is extended to identify fatigue cracks in piecewise-nonlinear systems. The proposed system identification method and crack detection procedure have been successfully validated by numerical simulations and experimental tests.

Probing and diagnosis of slider–disk interactions in nanometer clearance regime using artificial neural network

This paper addresses the issue of system identification for an active-head slider used to form a stable and reliable head---disk interface with a spacing of sub 3 nm. A new identification method is proposed to fit the highly non-stationary and highly nonlinear slider dynamics. The estimated model can be used for design of a model based nonlinear controller to control the flying height within the desired range. The effectiveness of the proposed system identification method is verified with simulation examples.

The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization

In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the shaping parameters in NURB network are estimated using a particle swarm optimization (PSO) procedure. Then the remaining parameters are estimated by the method of the singular value decomposition (SVD). Numerical examples including a model based controller are utilized to demonstrate the efficacy of the proposed approach. The controller consists of computing the inverse of the nonlinear static function approximated by NURB network, followed by a linear pole assignment controller.

Nonlinear system identification using memetic differential evolution trained neural networks

Several gradient-based approaches such as back propagation (BP) and Levenberg Marquardt (LM) methods have been developed for training the neural network (NN) based systems. But, for multimodal cost functions these procedures may lead to local minima, therefore, the evolutionary algorithms (EAs) based procedures are considered as promising alternatives. In this paper we focus on a memetic algorithm based approach for training the multilayer perceptron NN applied to nonlinear system identification. The proposed memetic algorithm is an alternative to gradient search methods, such as back-propagation and back-propagation with momentum which has inherent limitations of many local optima. Here we have proposed the identification of a nonlinear system using memetic differential evolution (DE) algorithm and compared the results with other six algorithms such as Back-propagation (BP), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Genetic Algorithm Back-propagation (GABP), Particle Swarm Optimization combined with Back-propagation (PSOBP). In the proposed system identification scheme, we have exploited DE to be hybridized with the back propagation algorithm, i.e. differential evolution back-propagation (DEBP) where the local search BP algorithm is used as an operator to DE. These algorithms have been tested on a standard benchmark problem for nonlinear system identification to prove their efficacy. First examples shows the comparison of different algorithms which proves that the proposed DEBP is having better identification capability in comparison to other. In example 2 good behavior of the identification method is tested on an one degree of freedom ( 1DOF) experimental aerodynamic test rig, a twin rotor multi-input–multi-output system ( TRMS), finally it is applied to Box and Jenkins Gas furnace benchmark identification problem and its efficacy has been tested through correlation analysis.