Structure Selection of Polynomial NARX Models Using Two Dimensional (2D) Particle Swarms

Hafiz, Faizal; Swain, Akshya; Mendes, Eduardo M. A. M.; Patel, Nitish

doi:10.1109/cec.2018.8477782

Cited by 11 publications

(10 citation statements)

References 15 publications

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“…In several comparative investigations [18,26], the Bayesian Information Criterion (BIC) was found to be comparatively robust among the existing information criteria. Therefore, for the remainder of the study, the cardinality corresponding to the minimum BIC is selected as the model order.…”

Section: Selection Of Subset Cardinality (Model Order Selection)mentioning

confidence: 99%

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Orthogonal Floating Search Algorithms: From the perspective of nonlinear system identification

2019

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The present study proposes a new Orthogonal Floating Search framework for structure selection of nonlinear systems by adapting the existing floating search algorithms for feature selection. The proposed framework integrates the concept of orthogonal space and consequent Error-Reduction-Ratio (ERR) metric with the existing floating search algorithms. On the basis of this framework, three well-known feature selection algorithms have been adapted which include the classical Sequential Forward Floating Search (SFFS), Improved sequential Forward Floating Search (IFFS) and Oscillating Search (OS). This framework retains the simplicity of classical Orthogonal Forward Regression with ERR (OFR-ERR) and eliminates the nesting effect associated with OFR-ERR. The performance of the proposed framework has been demonstrated considering several benchmark non-linear systems. The results show that most of the existing feature selection methods can easily be tailored to identify the correct system structure of nonlinear systems.

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Section: Selection Of Subset Cardinality (Model Order Selection)mentioning

confidence: 99%

“…In comparison, if GA (or any suitable algorithm) is applied directly to select term subset the search space reduces from n! to 2 n [18]. The 'iterative OFR' (iOFR) algorithm [15] uses each term in the initial term subset as a pivot to identify new, and possibly better, term subsets in the secondary search.…”

Section: Introductionmentioning

confidence: 99%

Orthogonal Floating Search Algorithms: From the perspective of nonlinear system identification

2019

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“…The proof of concept of this algorithm as an alternate method of structure selection of nonlinear systems has been reported in [38]. The present investigation significantly differs from [38] in the following aspects:…”

Section: Introductionmentioning

confidence: 81%

“…Note that the 2D-learning was originally developed by the authors for the 'feature selection' problem in machine learning [37]. The proof of concept of this algorithm as an alternate method of structure selection of nonlinear systems has been reported in [38]. The present investigation significantly differs from [38] in the following aspects:…”

Section: Introductionmentioning

confidence: 90%

Two-Dimensional (2D) particle swarms for structure selection of nonlinear systems

2019

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The present study proposes a new structure selection approach for non-linear system identification based on Two-Dimensional particle swarms (2D-UPSO). The 2D learning framework essentially extends the learning dimension of the conventional particle swarms and explicitly incorporates the information about the cardinality, i.e., number of terms, into the search process. This property of the 2D-UPSO has been exploited to determine the correct structure of the non-linear systems. The efficacy of the proposed approach is demonstrated by considering several simulated benchmark nonlinear systems in discrete and in continuous domain. In addition, the proposed approach is applied to identify a parsimonious structure from practical non-linear wave-force data. The results of the comparative investigation with Genetic Algorithm (GA), Binary Particle Swarm Optimization (BPSO) and the classical Orthogonal Forward Regression (OFR) methods illustrate that the proposed 2D-UPSO could successfully detect the correct structure of the non-linear systems.

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“…In the first part of this investigation [25], the orthogonal floating search algorithms have been proposed to alleviate the nesting effects of the classical OFR. Subsequently, a new two-dimensional structure selection approach was developed in [52,53], which explicitly integrates the information about subset cardinality (number of terms) into a probabilistic learning framework to balance the bias-variance dilemma. These approaches have been shown to be very effective on both simulated and practical nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

2020

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The present study proposes a multi-objective framework for structure selection of nonlinear systems which are represented by polynomial NARX models. This framework integrates the key components of Multi-Criteria Decision Making (MCDM) which include preference handling, Multi-Objective Evolutionary Algorithms (MOEAs) and a posteriori selection. To this end, three well-known MOEAs such as NSGA-II, SPEA-II and MOEA/D are thoroughly investigated to determine if there exists any significant difference in their search performance. The sensitivity of all these MOEAs to various qualitative and quantitative parameters, such as the choice of recombination mechanism, crossover and mutation probabilities, is also studied. These issues are critically analyzed considering seven discretetime and a continuous-time benchmark nonlinear system as well as a practical case study of non-linear wave-force modeling. The results of this investigation demonstrate that MOEAs can be tailored to determine the correct structure of nonlinear systems. Further, it has been established through frequency domain analysis that it is possible to identify multiple valid discrete-time models for continuous-time systems. A rigorous statistical analysis of MOEAs via performance sweet spots in the parameter space convincingly demonstrates that these algorithms are robust over a wide range of control parameters.of correct terms which captures the system dynamics is one of the major challenges of the system identification [6,7], and, therefore, is the main focus of this investigation.The exhaustive search to solve the structure selection problem is intractable even for moderate number of terms 'n', as this would require an evaluation of 2 n term subsets/structures. The structure selection problem is often 'NP-Hard' [13] and therefore requires an efficient search strategy. Since the search for system structure is primarily dependent on the limited number of observed data, it involves bias-variance trade-off [2, 3, 7], i.e., too sparse a structure may yield a high bias error (under-fitting) whereas a very complex structure may yield a high variance error (over-fitting). Further, earlier investigations [14,15] show that the over-fitted structures tend to induce 'ghost' dynamics which are not present in the actual system. Pursuing these arguments, it is clear that determination of the size of the identified structure (i.e., number of terms or 'cardinality') is a critical aspect of the structure selection process. However, this issue has received relatively less attention in the existing investigations.Among the existing structure selection approaches, the Orthogonal Forward Regression (OFR) proposed by Billings and Korenberg [16] has extensively been studied. It is a sequential model building approach in which the most significant term is added in each step, which is determined on the basis of a statistical criterion. Over the years, this notion of the original OFR approach has been refined to further improve the search performance. These include OFR approaches...

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Structure Selection of Polynomial NARX Models Using Two Dimensional (2D) Particle Swarms

Cited by 11 publications

References 15 publications

Orthogonal Floating Search Algorithms: From the perspective of nonlinear system identification

Orthogonal Floating Search Algorithms: From the perspective of nonlinear system identification

Two-Dimensional (2D) particle swarms for structure selection of nonlinear systems

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

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