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

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

doi:10.1016/j.neucom.2019.03.069

Cited by 9 publications

(6 citation statements)

References 31 publications

(104 reference statements)

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“…Further, it is interesting to note that the similar frequency response behavior was observed in the distinct NARX model identified for the same wave force data in our previous investigation [25].…”

Section: Identification Of Nonlinear Wave Forcessupporting

confidence: 83%

“…Hence, for these systems, the non-dominated structures identified by MOEAs can easily be evaluated. To this end, each non-dominated structure is 'qualitatively' evaluated following the search outcome definitions developed in our previous investigations [25,53].…”

Section: Qualitative Evaluation Of Search Outcomesmentioning

confidence: 99%

“…Consider the following subsets of NARX terms for this purpose, • ∅ : the null set • X model : the super-set containing all the NARX terms • X : the optimum structure or the set of system terms, X ⊂ X model • X k : k th non-dominated structure identified by an MOEA, X k ∈ Γ * • X spur k : set of spurious terms which are not present in the actual system but are included in X k , i.e., X spur k = X k \ X Following these definitions, each non-dominated structure can be categorized into one of the following search outcome [25]:…”

Section: Qualitative Evaluation Of Search Outcomesmentioning

confidence: 99%

“…It is worth noting that this study is a part of our broader investigation on alternative approaches for structure selection. 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.…”

Section: Introductionmentioning

confidence: 99%

“…These include OFR approaches with either new term evaluation criteria [17][18][19][20] or improved search strategies [21][22][23][24][25]. A detailed treatment on this subject can be found in the recent investigation by the authors [25]. It is worth noting that, while OFR and its extensions are quite effective in detecting the significant terms, these approaches typically require an auxiliary procedure to estimate the number of terms (cardinality).…”

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confidence: 99%

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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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Section: Identification Of Nonlinear Wave Forcessupporting

confidence: 83%

Section: Qualitative Evaluation Of Search Outcomesmentioning

confidence: 99%

Section: Qualitative Evaluation Of Search Outcomesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

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

Cited by 9 publications

References 31 publications

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

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

ARTINALI#: An Efficient Intrusion Detection Technique for Resource-Constrained Cyber-Physical Systems

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

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