Low complexity adaptive forgetting factor for online sequential extreme learning machine (OS-ELM) for application to nonstationary system estimations

Lim, Jun‐Seok; Lee, Seokjin; Pang, H.

doi:10.1007/s00521-012-0873-x

Cited by 51 publications

(27 citation statements)

References 22 publications

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“…Comparatively, a more universal RLS algorithm with adaptive FF (AFF-RLS) was presented in [21], in which the FF is adaptively tuned using a gradient based method without need for much a priori knowledge. At present, the AFF-RLS has been successfully applied to the OSELM for time-varying nonlinear system identification [22] and fault prediction [24], and it has shown good tracking performance in time-varying environment. However, the AFF-RLS algorithm is originally derived in the situation of the special exponential forgetting regularization, which is not applicable in the generalized regularization scenario.…”

Section: Adaptive Forgetting Scheme For Fgr-oselmmentioning

confidence: 99%

“…In this case, the objective is to calculate the FF that optimizes the mean square of the a priori estimation error [21,22]; that is, the optimized cost function is written as…”

Section: Adaptive Forgetting Scheme For Fgr-oselmmentioning

confidence: 99%

“…Since the computational complexity of the AFGR-OSELM algorithm is mainly decided by matrix multiplication, by using Strassen's matrix multiplication method [25], the number of multiplications can be reduced to ( 2.807 ); that is, the computational complexity of the AFGR-OSELM algorithm can also be reduced to ( 2.807 ). Moreover, with a proper approximation approach [22], the computational complexity of AFGR-OSELM may be further reduced, and we take it as future work.…”

Section: Computational Complexity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Analogously, the concept of FF has also been introduced into the OSELM for dynamic system estimation and prediction [22][23][24]. In [22], a low complexity adaptive forgetting factor OSELM (LAFF-OSELM) algorithm was proposed for time-varying nonlinear system identification, and it was found that the proposed algorithm can deal with the variation effectively by adaptive forgetting mechanism. In [23], the authors presented a new variable forgetting factor OSELM using the directional FF method (DFF-OSELM), which achieved superior prediction performance in industrial applications when compared to the OSELM algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Online Sequential Extreme Learning Machine with Generalized Regularization and Adaptive Forgetting Factor for Time-Varying System Prediction

Wei

Tang

et al. 2018

Mathematical Problems in Engineering

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Many real world applications are of time-varying nature and an online learning algorithm is preferred in tracking the realtime changes of the time-varying system. Online sequential extreme learning machine (OSELM) is an excellent online learning algorithm, and some improved OSELM algorithms incorporating forgetting mechanism have been developed to model and predict the time-varying system. But the existing algorithms suffer from a potential risk of instability due to the intrinsic ill-posed problem; besides, the adaptive tracking ability of these algorithms for complex time-varying system is still very weak. In order to overcome the above two problems, this paper proposes a novel OSELM algorithm with generalized regularization and adaptive forgetting factor (AFGR-OSELM). In the AFGR-OSELM, a new generalized regularization approach is employed to replace the traditional exponential forgetting regularization to make the algorithm have a constant regularization effect; consequently the potential illposed problem of the algorithm can be completely avoided and a persistent stability can be guaranteed. Moreover, the AFGR-OSELM adopts an adaptive scheme to adjust the forgetting factor dynamically and automatically in the online learning process so as to better track the dynamic changes of the time-varying system and reduce the adverse effects of the outdated data in time; thus it tends to provide desirable prediction results in time-varying environment. Detailed performance comparisons of AFGR-OSELM with other representative algorithms are carried out using artificial and real world data sets. The experimental results show that the proposed AFGR-OSELM has higher prediction accuracy with better stability than its counterparts for predicting time-varying system.

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Section: Adaptive Forgetting Scheme For Fgr-oselmmentioning

confidence: 99%

“…In this case, the objective is to calculate the FF that optimizes the mean square of the a priori estimation error [21,22]; that is, the optimized cost function is written as…”

Section: Adaptive Forgetting Scheme For Fgr-oselmmentioning

confidence: 99%

Section: Computational Complexity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Online Sequential Extreme Learning Machine with Generalized Regularization and Adaptive Forgetting Factor for Time-Varying System Prediction

Wei

Tang

et al. 2018

Mathematical Problems in Engineering

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Combining dynamic XFEM with machine learning for detection of multiple flaws

Jiang

Zhao

2021

Numerical Meth Engineering

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A novel methodology for multiple flaw detection is presented in this study. It combines the dynamic extended finite element method (XFEM) with machine learning for the first time. The extreme learning machine (ELM) is chosen as a learning rule for modeling and prediction. The XFEM is employed to overcome the issues associated with the large quantity of input data required for ELM network training, whereas the ELM itself is used to bypass the time-consuming repeated analyses ordinarily required for the detection of multiple flaws. A large amount of potential flaw data for a structure is quasi-randomly generated by a Sobol sequence. For each effective flaw datum, the dynamic XFEM with circular/elliptical void enrichment is used to compute the structural dynamic characteristics (i.e., frequencies and displacement mode shapes), which is possible because re-meshing is not required for each flaw. The available data generated from the results of XFEM analyses are used for ELM network training. According to the measured dynamic characteristics, the trained ELM is then utilized to predict the size and location of flaws. The results show that the proposed novel methodology can identify accurately the location and size of circular or elliptical structural flaws. The method also is more efficient than previously proposed approaches, as it can avoid time-consuming iterative analyses, and it is robust against noise.

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The Parameter Updating Method Based on Kalman Filter for Online Sequential Extreme Learning Machine

Wen

Chen

et al. 2018

Proceedings in Adaptation, Learning and Optimization

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Low complexity adaptive forgetting factor for online sequential extreme learning machine (OS-ELM) for application to nonstationary system estimations

Cited by 51 publications

References 22 publications

Online Sequential Extreme Learning Machine with Generalized Regularization and Adaptive Forgetting Factor for Time-Varying System Prediction

Online Sequential Extreme Learning Machine with Generalized Regularization and Adaptive Forgetting Factor for Time-Varying System Prediction

Combining dynamic XFEM with machine learning for detection of multiple flaws

The Parameter Updating Method Based on Kalman Filter for Online Sequential Extreme Learning Machine

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