Infinite Impulse Response Model Research Articles

Reduced order infinite impulse response system identification using manta ray foraging optimization

This article presents a useful application of the Manta Ray Foraging Optimization (MRFO) algorithm for solving the adaptive infinite impulse response (IIR) system identification problem. The effectiveness of the proposed technique is validated on four benchmark IIR models for reduced order system identification. The stability of the proposed estimated IIR system is assured by incorporating a pole-finding and initialization routine in the search procedure of the MRFO algorithm and this algorithmic modification contributes to the MRFO algorithm when seeking stable IIR filter solutions. The absence of such a scheme, which is primarily the case with the majority of the recently published literature, may lead to the generation of an unstable IIR filter for unknown real-world instances (particularly when the estimation order increases). Experiments conducted in this study highlight that the proposed technique helps to achieve a stable filter even though large bounds for the design variables are considered. The convergence rate, robustness, and computational speed of MRFO for all the considered problems are investigated. The influence of the control parameters of MRFO on the design performances is evaluated to gain insight into the interaction between the three foraging strategies of the algorithm. Extensive statistical performance analyses employing various non-parametric hypothesis tests concerning the design consistency and convergence are conducted for comparison of the proposed MRFO-based approach with six other metaheuristic search procedures to investigate the efficiency. The results on the mean square error metric also highlight the improved solution quality of the proposed approach compared to the various techniques published in the literature.

An improved artificial rabbits optimization for accurate and efficient infinite impulse response system identification

Identifying models with Infinite Impulse Response (IIR) is crucial in signal processing and system identification. This paper addresses the challenges of IIR model identification by proposing an improved version of the Artificial Rabbits Optimization (ARO) algorithm called improved ARO (IARO). The IARO algorithm integrates an adaptive local search mechanism and an experience-based perturbed learning strategy as two key enhancements to improve the effectiveness of ARO. These additions aim to address the loss of accuracy during iterations and improve the algorithm’s ability to exploit promising areas. Four benchmark examples of different IIR plants are considered, and the performance of the proposed IARO algorithm is compared to existing competitive methods. The results consistently demonstrate that IARO outperforms ARO in accuracy and convergence for system identification across all orders of IIR systems. Visual analysis, convergence curves, coefficient comparison, and statistical metrics comparison all validate the superiority of the IARO algorithm. Additionally, the Wilcoxon signed-rank test results provide further statistical evidence supporting the superior performance of IARO. The comprehensive analysis showcases the efficacy and effectiveness of the IARO algorithm in accurately identifying IIR systems. This work represents a significant advancement in IIR system identification, offering a superior methodology for accurate and efficient system modeling.

Artificial hummingbird optimizer as a novel adaptive algorithm for identifying optimal coefficients of digital IIR filtering systems

ABSTRACT This paper introduces the artificial hummingbird algorithm (AHA) as a novel and efficient algorithm for designing digital infinite impulse response (IIR) filtering systems. IIR filters are commonly used in various applications, and their design often involves complex error surfaces and coefficients. The AHA aims to address these challenges by optimizing the IIR model using mean squared error (MSE) cost function. Four benchmark examples are considered for evaluation by comparing both the same and reduced order cases of the IIR model. The results are compared against recent and efficient algorithms named prairie dog optimization, whale optimization algorithm, and artificial bee colony algorithm. The evaluation includes an analysis of the obtained coefficients, statistical measures, and convergence profiles. The findings show that the AHA outperforms the competing algorithms, achieving more accurate models and providing better statistical performance. Additionally, the AHA consistently converges to the lowest MSE values for each case. Further assessments are conducted using various examples from the literature, which validate the AHA's superior ability in digital IIR filtering design. The algorithm demonstrates more accurate identification and achieves lower MSE values compared to alternative methods which highlight the promising potential of the AHA for efficient and precise digital IIR filtering system design.

Application of Slime Mould Algorithm to Infinite Impulse Response System Identification Problem

Recently, the researchers working in the field of science and engineering have paid a considerable attention to the concept of the system identification to tackle with complex optimization problems. It is feasible to achieve more accurate models of physical plants with the infinite impulse response (IIR) models compared to their finite counterparts (FIR). To get the most out of the IIR models for the system identification, metaheuristic optimization algorithms can be used as efficient solutions. This work, therefore, aims to demonstrate more promising performance of a new metaheuristic algorithm named slime mould algorithm. In this regard, a comparative assessment is performed using different metaheuristic optimization techniques and different IIR model identification problems are considered. The slime mould algorithm is shown to achieve better accuracy and robustness in terms of IIR model identification with the help of obtained statistical results.

Real Time Computationally Efficient MIMO System Identification Algorithm

MIMO system identification is a fundamental concern in a variety of applications. Various iterative and recursive MIMO system identification algorithms exist in the literature. The iterative algorithms suffer from high computational cost due to large matrix computations and recursive algorithms suffer from slow convergence speed. This paper proposes a fast recursive exact least squares algorithm for MIMO system identification with fast convergence speed and low computational cost. The recursions of the algorithm give rise to a lattice structure. The lattice structure is less sensitive to round-off errors, coefficients variations and can also be used for model order reduction. Although in this work we estimate an FIR (finite impulse response) model of the MIMO system, the framework can also be used for IIR (infinite impulse response) models, and for estimating linear periodically time varying (LPTV) and multivariable systems. The theory proposed is validated using simulation results.

Linear Time-Periodic System Identification with Grouped Atomic Norm Regularization

This paper proposes a new methodology in linear time-periodic (LTP) system identification. In contrast to previous methods that totally separate dynamics at different tag times for identification, the method focuses on imposing appropriate structural constraints on the linear time-invariant (LTI) reformulation of LTP systems. This method adopts a periodically-switched truncated infinite impulse response model for LTP systems, where the structural constraints are interpreted as the requirement to place the poles of the non-truncated models at the same locations for all sub-models. This constraint is imposed by combining the atomic norm regularization framework for LTI systems with the group lasso technique in regression. As a result, the estimated system is both uniform and low-order, which is hard to achieve with other existing estimators. Monte Carlo simulation shows that the grouped atomic norm method does not only show better results compared to other regularized methods, but also outperforms the subspace identification method under high noise levels in terms of model fitting.

Modified Whale Optimization Algorithm for Infinitive Impulse Response System Identification

System identification based on infinite impulse response (IIR) models has received much attention because it is used in a variety of real-world applications. However, an IIR model might have a multimodal error surface. To attain an ideal identification, an efficient and robust method is necessary. In this study, a modified whale optimization algorithm (WOA) with a ranking-based mutation operator, called the RWOA, is presented to solve the IIR system identification problem. The RWOA integrates a ranking-based mutation operator into the basic WOA to enhance performance by speeding up the convergence rate and then enhances the exploitation capability. The experimental results of actual and reduced-order identification for a standard system using our proposed RWOA were superior to those of five state-of-the-art algorithms (including the basic WOA), in terms of improving the quality and stability of the results, in most cases, and significantly speeding up convergence.

Prediction-error identification of LPV systems: A nonparametric Gaussian regression approach

In this paper, a Bayesian nonparametric approach is introduced to estimate multi-input multi-output (MIMO) linear parameter-varying (LPV) models under the general noise model structure of Box–Jenkins (BJ) type. The approach is based on the estimation of the one-step-ahead predictor of general LPV-BJ structures. Parts of the predictors associated with the input and output signals are modeled as asymptotically stable infinite impulse response (IIR) models. Then, these IIR models are identified in a completely nonparametric sense: not only the coefficients are estimated as functions, but also the whole time evolution of the impulse response w.r.t. the scheduling signal of the LPV system. In this Bayesian setting, the estimate of the one-step-ahead predictor is a realization from a zero-mean Gaussian random field, where the covariance function is a multidimensional Gaussian kernel that encodes both the possible structural dependencies and the stability of the predictor. Two different kernel formulations are presented for the LPV setting, namely a diagonal (DI) like and tuned/correlated (TC) like kernels, where the TC-like kernel is able to describe the correlation between coefficient functions associated with different time indices. The unknown hyperparameters that parameterize the DI or TC kernel are tuned by maximizing the marginal likelihood w.r.t. the observed data. Moreover, we provide a nonparametric realization scheme to recover the original process and noise IIRs from the identified one-step-ahead predictor. The performance of the presented identification approach is tested on a MIMO LPV-BJ simulation example by means of an extensive Monte-Carlo study.

Improving particle swarm optimization via adaptive switching asynchronous – synchronous update

Particle swarm optimization (PSO) is a population-based metaheuristic optimization algorithm that solves a problem through iterative operations. Traditional PSO iteration strategies can be categorized into two groups: synchronous (S-PSO) or asynchronous (A-PSO) update. In S-PSO, the performance of the entire swarm is evaluated before the particles’ velocities and positions are updated, whereas in A-PSO, each particle's velocity and position are updated immediately after an individual's performance is evaluated. Previous research claimed that S-PSO is better in exploitation and has fast convergence, whereas A-PSO converges at a slower rate and is stronger at exploration. Exploration and exploitation are important in ensuring good performance for any population-based metaheuristic. In this paper, an adaptive switching PSO (Switch-PSO) algorithm that uses a hybrid update sequence is proposed. The iteration strategy in Switch-PSO is adaptively switched between the two traditional iteration strategies according to the performance of the swarm's best member. The performance of Switch-PSO is compared with existing S-PSO, A-PSO and three state-of-the-art PSO algorithms using CEC2014's benchmark functions. The results show that Switch-PSO achieves superior performance in comparison to the other algorithms. Switch-PSO is then applied for infinite impulse response model identification, where Switch-PSO is found to rank the best among all the algorithms applied.

Distributed machine learning strategies for efficient development of direct and inverse nonlinear and IIR models

This paper makes an in depth study on the applications of distributed machine learning based techniques for parameter estimation of infinite impulse response (IIR) systems and as well as inverse modeling of nonlinear systems or sensors. The bio-inspired learning algorithms such as particle swarm optimization (PSO) and differential evolution (DE) are used as incremental and diffusion based distributed learning strategies to estimate the pole-zero parameters of a feed forward-feedback systems. The same distributed learning algorithms are also employed to generate inverse model of nonlinear systems. The performance of these learning algorithms in terms of accuracy of estimation are compared under different additive noise conditions. The ranking based on accuracy of direct estimation demonstrates that the proposed Incremental DE (IDE) based model performs the best than Diffusion DE (DDE) counter part. It is then followed by IPSO, DPSO, ILMS and DLMS based models. The same ranking is also valid for inverse modeling problem. The proposed distributed bioinspired learning can also be applied to various forecasting and classification tasks.

Lévy Flight Trajectory-Based Whale Optimization Algorithm for Global Optimization

The whale optimization algorithm (WOA) has been shown to be powerful in searching for an optimal solution. This paper proposes an improvement to the whale optimization algorithm that is based on a Levy flight trajectory and called the Levy flight trajectory-based whale optimization algorithm (LWOA). The LWOA makes the WOA faster and more robust and avoids premature convergence. The Levy flight trajectory is helpful for increasing the diversity of the population against premature convergence and enhancing the capability of jumping out of local optimal optima. This method helps obtaining a better tradeoff between the exploration and exploitation of the WOA. The proposed algorithm is characterized by quick convergence and high precision, and it can effectively get rid of a local optimum. The LWOA is further compared with other well-known nature-inspired algorithms on 23 benchmarks and solving infinite impulse response model identification. The statistical results on the benchmark functions show that the LWOA can significantly outperform others on a majority of the benchmark functions, especially in solving an optimization problem that has high dimensionality. Additionally, the superior identification capability of the proposed algorithm is evident from the results obtained through the simulation study compared with other algorithms. All the results prove the superiority of the LWOA.

System identification application using Hammerstein model

Generally, memoryless polynomial nonlinear model for nonlinear part and finite impulse response (FIR) model or infinite impulse response model for linear part are preferred in Hammerstein models in literature. In this paper, system identification applications of Hammerstein model that is cascade of nonlinear second order volterra and linear FIR model are studied. Recursive least square algorithm is used to identify the proposed Hammerstein model parameters. Furthermore, the results are compared to identify the success of proposed Hammerstein model and different types of models.

Closed-loop identification of unstable systems using noncausal FIR models

ABSTRACTNoncausal finite impulse response (FIR) models are used for closed-loop identification of unstable multi-input, multi-output plants. These models are shown to approximate the Laurent series inside the annulus between the asymptotically stable pole of the largest modulus and the unstable pole of the smallest modulus. By delaying the measured output relative to the measured input, the identified FIR model is a noncausal approximation of the unstable plant. We present examples to compare the accuracy of the identified model obtained using least squares, instrumental variables methods, and prediction error methods for both infinite impulse response (IIR) and noncausal FIR models under arbitrary noise that is fed back into the loop. Finally, we reconstruct an IIR model of the system from its stable and unstable parts using the eigensystem realisation algorithm.

A Comparison of Evolutionary Computation Techniques for IIR Model Identification

System identification is a complex optimization problem which has recently attracted the attention in the field of science and engineering. In particular, the use of infinite impulse response (IIR) models for identification is preferred over their equivalent FIR (finite impulse response) models since the former yield more accurate models of physical plants for real world applications. However, IIR structures tend to produce multimodal error surfaces whose cost functions are significantly difficult to minimize. Evolutionary computation techniques (ECT) are used to estimate the solution to complex optimization problems. They are often designed to meet the requirements of particular problems because no single optimization algorithm can solve all problems competitively. Therefore, when new algorithms are proposed, their relative efficacies must be appropriately evaluated. Several comparisons among ECT have been reported in the literature. Nevertheless, they suffer from one limitation: their conclusions are based on the performance of popular evolutionary approaches over a set of synthetic functions with exact solutions and well-known behaviors, without considering the application context or including recent developments. This study presents the comparison of various evolutionary computation optimization techniques applied to IIR model identification. Results over several models are presented and statistically validated.

IIR model identification via evolutionary algorithms

Infinite impulse response (IIR) filters are often preferred to FIR filters for modeling because of their better performance and reduced number of coefficients. However, IIR model identification is a challenging and complex optimization problem due to multimodal error surface entanglement. Therefore, a practical, efficient and robust global optimization algorithm is necessary to minimize the multimodal error function. In this paper, recursive least square algorithm, as a popular method in classical category, is compared with two well-known optimization techniques based on evolutionary algorithms (genetic algorithm and particle swarm optimization) in IIR model identification. This comparative study illustrates how these algorithms can perform better than the classical one in many complex situations.

IIR GRAPPA for parallel MR image reconstruction

Accelerated parallel MRI has advantage in imaging speed, and its image quality has been improved continuously in recent years. This paper introduces a two-dimensional infinite impulse response model of inverse filter to replace the finite impulse response model currently used in generalized autocalibrating partially parallel acquisitions class image reconstruction methods. The infinite impulse response model better characterizes the correlation of k-space data points and better approximates the perfect inversion of parallel imaging process, resulting in a novel generalized image reconstruction method for accelerated parallel MRI. This k-space-based reconstruction method includes the conventional generalized autocalibrating partially parallel acquisitions class methods as special cases and has a new infinite impulse response data estimation mechanism for effective improvement of image quality. The experiments on in vivo MRI data show that the proposed method significantly reduces reconstruction errors compared with the conventional two-dimensional generalized autocalibrating partially parallel acquisitions method, particularly at the high acceleration rates.

Hankel-Norm Approximation of IIR by FIR Models: A Constructive Method

This paper presents a constructive method for (sub)optimal finite-impulse response (FIR) approximation of infinite-impulse response (IIR) models. The method minimizes the Hankel norm of the approximation error by using an explicit solution to the norm-preserved dilation problem. It has advantages over the existing methods in that it is a unified method for both single-input single-output and multiple-input multiple-output systems which allows direct tradeoff between the least-squares and Chebyshev error criteria by using a single tuning parameter, and that the approximation algorithm is constructive and only involves algebraic manipulations rather than iteration and convex optimization procedures. The lower and upper bounds on the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and Chebyshev norms of the approximation error are derived and are related to the tuning parameter. The problem of approximating noncausal IIR models by causal FIR models is also formulated and solved. The effectiveness and properties of the proposed algorithms are demonstrated by examples.

Modeling and simulation of a stand-alone photovoltaic system using an adaptive artificial neural network: Proposition for a new sizing procedure

This paper presents an adaptive artificial neural network (ANN) for modeling and simulation of a Stand-Alone photovoltaic (SAPV) system operating under variable climatic conditions. The ANN combines the Levenberg–Marquardt algorithm (LM) with an infinite impulse response (IIR) filter in order to accelerate the convergence of the network. SAPV systems are widely used in renewable energy source (RES) applications and it is important to be able to evaluate the performance of installed systems. The modeling of the complete SAPV system is achieved by combining the models of the different components of the system (PV-generator, battery and regulator). A global model can identify the SAPV characteristics by knowing only the climatological conditions. In addition, a new procedure proposed for SAPV system sizing is presented in this work. Different measured signals of solar radiation sequences and electrical parameters (photovoltaic voltage and current) from a SAPV system installed at the south of Algeria have been recorded during a period of 5-years. These signals have been used for the training and testing the developed models, one for each component of the system and a global model of the complete system. The ANN model predictions allow the users of SAPV systems to predict the different signals for each model and identify the output current of the system for different climatological conditions. The comparison between simulated and experimental signals of the SAPV gave good results. The correlation coefficient obtained varies from 90% to 96% for each estimated signals, which is considered satisfactory. A comparison between multilayer perceptron (MLP), radial basis function (RBF) network and the proposed LM–IIR model is presented in order to confirm the advantage of this model.

Linear and decision-feedback per tone equalization for DMT-based transmission over IIR channels

The per-tone equalizer (PTEQ) has been presented as an attractive alternative for the classical time-domain equalizer (TEQ) in discrete multitone (DMT) based systems, such as ADSL systems. The PTEQ is based on a linear minimum mean-square-error (L-MMSE) equalizer design for each separate tone. In this paper, we reconsider DMT modulation and equalization in the ADSL context under the realistic assumption of an infinite impulse response (IIR) model for the wireline channel. First, optimum linear zero-forcing (L-ZF) block equalizers for arbitrary IIR model orders and cyclic prefix (CP) lengths are developed. It is shown that these L-ZF block equalizers can be decoupled per tone, hence they lead to an L-ZF PTEQ. Then, based on the L-ZF PTEQ, low-complexity L-MMSE PTEQ extensions are developed: the linear PTEQ extension exploits frequency-domain transmit redundancy from pilot and unused tones; alternatively, a closely related decision-feedback PTEQ extension can be applied. The PTEQ extensions then add flexibility to a DMT-based system design: the CP overhead can be reduced by exploiting frequency-domain transmit redundancy instead, so that a similar bitrate as with the original PTEQ is achieved at a lower memory and computational cost or, alternatively, a higher bitrate is achieved without a considerable cost increase. Both PTEQ extensions are also shown to improve the receiver's robustness to narrow-band interference.

Orthogonal Rational Functions: A Transformation Analysis

Finite impulse response (FIR) models are among the most basic tools in control theory and signal processing and are routinely used in almost all fields of application. The connections to orthogonal polynomials are well known. However, infinite impulse response (IIR) models often provide much more compact descriptions and in many cases give improved performance. The objective of this paper is to present a simple framework for the derivation and analysis of orthogonal IIR transfer functions, which are directly related to orthogonal rational functions. Orthogonality simplifies approximation analysis and leads to improved numerical properties. The basic idea is to use a fractional transformation to map the problem to a new domain, where an FIR description is most appropriate. This FIR representation is then mapped back to the original domain to give an orthogonal IIR representation. It is then straightforward to extend many results for FIR models to IIR model structures with arbitrary stable poles; i.e., properties of orthogonal polynomials are easily generalized to orthogonal rational functions. Much of the theory to be presented is classical, e.g., Laguerre and Kautz functions, and we will make use of well-known results in orthogonal filter theory. However, our main contribution is to present a uniform and transparent theory which also covers more novel results that have mainly been presented in the signals, systems, and control literature in the last decade.