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< Page ,Total 33 >
A Hierarchical Coarse-to-Fine Fault Diagnosis Method for Industrial Processes Based on Decision Fusion of Class-Specific Stacked Autoencoders SCIE
期刊论文 | 2024 , 73 | IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
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Abstract :

Fault diagnosis (FD) is crucial for ensuring the safety and stability of industrial processes. In real industrial processes, fault features in measurement data are prone to be misidentified due to the feature overlap, which hinders the effective FD. Besides, the large-scale characteristic of industrial processes also poses challenges for FD. To solve the above problems, a hierarchical coarse-to-fine FD method based on decision fusion of class-specific stacked autoencoders (DFCSSAEs) is proposed to achieve accurate FD by identifying overlapping features. The entire FD process is divided into three stages: sub-block division, coarse diagnosis, and fine diagnosis. In the sub-block division stage, for the large-scale characteristic, a sub-block division method based on prior knowledge and mutual information (MI) is proposed to divide the whole process into several new sub-blocks. On this basis, the faults with overlapping features in each sub-block are identified by leveraging the feature visualization technique and summarized into a new composite class. In the coarse diagnosis stage, several SAE-Softmax-based coarse FD models are established to achieve the targeted diagnosis of individual faults and the composite class fault. At the fine diagnosis stage, a weighted Dempster-Shafer (D-S) evidence theory is proposed to solve decision conflicts among different coarse FD models by assigning reasonable weights. Moreover, a new SAE-Softmax is established to diagnose the unclassifiable faults after the decision fusion and ultimately improve diagnostic accuracy. Finally, the effectiveness and advantages of our method are validated by the Tennessee Eastman process (TEP) and the real dataset of the PRONTO process. Experimental results demonstrate that our method achieves high FD rates of 0.962 and 0.997.

Keyword :

Fault diagnosis Fault diagnosis Principal component analysis Principal component analysis Feature extraction Feature extraction Accuracy Accuracy industrial process industrial process Mutual information Mutual information large scale large scale stacked autoencoder (SAE) stacked autoencoder (SAE) Dempster-Shafer (D-S) evidence theory Dempster-Shafer (D-S) evidence theory Numerical models Numerical models Evidence theory Evidence theory fault diagnosis (FD) fault diagnosis (FD)

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GB/T 7714 Gao, Huihui , Zhang, Xiaoran , Gao, Xuejin et al. A Hierarchical Coarse-to-Fine Fault Diagnosis Method for Industrial Processes Based on Decision Fusion of Class-Specific Stacked Autoencoders [J]. | IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT , 2024 , 73 .
MLA Gao, Huihui et al. "A Hierarchical Coarse-to-Fine Fault Diagnosis Method for Industrial Processes Based on Decision Fusion of Class-Specific Stacked Autoencoders" . | IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 73 (2024) .
APA Gao, Huihui , Zhang, Xiaoran , Gao, Xuejin , Li, Fangyu , Han, Honggui . A Hierarchical Coarse-to-Fine Fault Diagnosis Method for Industrial Processes Based on Decision Fusion of Class-Specific Stacked Autoencoders . | IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT , 2024 , 73 .
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A Data-Driven Key Performance Indicator-Related Monitoring Scheme for Dynamic Nonlinear Systems SCIE
期刊论文 | 2024 , 71 (4) , 2074-2078 | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
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Abstract :

This brief addresses the data-driven fault monitoring issues for nonlinear systems with dynamic operations by taking into account the key performance indicators (KPIs). To reach this objective, the KPIs related to the other variables of the nonlinear systems are first established by means of the Takagi-Sugeno fuzzy technique. Then, the input/output data model of the KPIs is constructed in fuzzy form. By applying the subspace-aided method, a fuzzy-model-based KPI predictor is obtained. On this basis, a data-driven realization algorithm of the KPI prediction residual generator is proposed with available system measurements. Towards KPI-related fault monitoring purpose, the control limit is computed by utilizing the kernel density estimation method, with which an online KPI-related monitoring scheme for dynamic nonlinear systems is presented. Compared with the existing methods, the merits of this scheme lie in that it can handle the nonlinear and dynamic characteristics of data, so as to improve the detection performance of KPI-related faults. Meanwhile, the KPI prediction model can achieve interpretability by introducing the fuzzy modeling. An experimental study on the ship propulsion system is finally given to demonstrate the developed results.

Keyword :

data-driven data-driven ship propulsion system ship propulsion system fuzzy-model-based key performance indicators fuzzy-model-based key performance indicators dynamic nonlinear systems dynamic nonlinear systems Fault monitoring Fault monitoring

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GB/T 7714 Han, Huayun , Zhao, Dong , Gao, Xuejin . A Data-Driven Key Performance Indicator-Related Monitoring Scheme for Dynamic Nonlinear Systems [J]. | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS , 2024 , 71 (4) : 2074-2078 .
MLA Han, Huayun et al. "A Data-Driven Key Performance Indicator-Related Monitoring Scheme for Dynamic Nonlinear Systems" . | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 71 . 4 (2024) : 2074-2078 .
APA Han, Huayun , Zhao, Dong , Gao, Xuejin . A Data-Driven Key Performance Indicator-Related Monitoring Scheme for Dynamic Nonlinear Systems . | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS , 2024 , 71 (4) , 2074-2078 .
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Multi-timescale attention residual shrinkage network with adaptive global-local denoising for rolling-bearing fault diagnosis SCIE
期刊论文 | 2024 , 304 | KNOWLEDGE-BASED SYSTEMS
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Abstract :

In actual engineering scenarios, bearing fault signals are inevitably overwhelmed by strong background noise from various sources. However, most deep-learning-based diagnostic models tend to broaden the feature extraction scale to extract rich fault features for bearing-fault identification under noise interference, with little attention paid to multi-timescale discriminative feature mining with adaptive noise rejection, which affects the diagnostic performance. Thus, a multi-timescale attention residual shrinkage network with adaptive global-local denoising (AMARSN) was proposed for rolling-bearing fault diagnosis by learning discriminative multi-timescale fault features from signals and fully eliminating noise components in the multi-timescale fault features. First, a multi-timescale attention learning module (MALMod) was developed to capture multi-timescale fault features and enhance their discriminability under noise interference. Subsequently, an adaptive global-local denoising module (AGDMod) was constructed to fully eliminate noise in multiscale fault features by constructing specific global-local denoising thresholds and designing an adaptive smooth soft thresholding function. Finally, end-toend bearing fault diagnosis tasks were realized using a softmax classifier located at the end of the AMARSN. The AMARSN was validated using two bearing datasets. The extensive results demonstrated that the AMARSN can mine more effective fault features from signals and achieve average diagnostic accuracies of 85.24% and 80.09% under different noise with different levels.

Keyword :

Global-local noise elimination Global-local noise elimination Adaptive soft thresholding function Adaptive soft thresholding function Attention mechanism Attention mechanism Rolling-bearing fault diagnosis Rolling-bearing fault diagnosis Multi-timescale feature extraction Multi-timescale feature extraction

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GB/T 7714 Gao, Huihui , Zhang, Xiaoran , Gao, Xuejin et al. Multi-timescale attention residual shrinkage network with adaptive global-local denoising for rolling-bearing fault diagnosis [J]. | KNOWLEDGE-BASED SYSTEMS , 2024 , 304 .
MLA Gao, Huihui et al. "Multi-timescale attention residual shrinkage network with adaptive global-local denoising for rolling-bearing fault diagnosis" . | KNOWLEDGE-BASED SYSTEMS 304 (2024) .
APA Gao, Huihui , Zhang, Xiaoran , Gao, Xuejin , Li, Fangyu , Han, Honggui . Multi-timescale attention residual shrinkage network with adaptive global-local denoising for rolling-bearing fault diagnosis . | KNOWLEDGE-BASED SYSTEMS , 2024 , 304 .
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Data Visualization and Fault Detection Using Bi-Kernel t-Distributed Stochastic Neighbor Embedding in Semiconductor Etching Processes SCIE
期刊论文 | 2022 , 35 (3) , 522-531 | IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING
WoS CC Cited Count: 1
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Abstract :

In semiconductor etching processes, fault detection monitors the quality of wafers. However, the detailed dynamics in batch data are ignored in many traditional methods. In this paper, sequential image-based data visualization and fault detection, using bi-kernel t-distributed stochastic neighbor embedding (t-SNE), is proposed for semiconductor etching processes. In the proposed method, multi-modals, multi-phases, and abnormal samples in batches are visualized in two-dimensional maps. First, the batch data are restructured into sequential images and input to a convolutional autoencoder (CAE) to learn the abstract representation. Then, bi-kernel t-SNE is applied to visualize the CAE codes in two-dimensional maps. To reduce the computational burden and overcome the out-of-sample projection diffusion in bi-kernel t-SNE, data subsampling is used in the training procedure. Finally, a one-class support vector machine is employed to calculate the visualization control boundary, and a batch-wise index is presented for fault wafer detection. To demonstrate the feasibility and effectiveness of the proposed method, it was applied to two wafer etching datasets. The results indicate that the proposed method outperforms state-of-the-art methods in data visualization and fault detection.

Keyword :

Etching Etching Transforms Transforms Convolutional autoencoder (CAE) Convolutional autoencoder (CAE) Kernel Kernel Indexes Indexes fault detection fault detection Training Training Data visualization Data visualization data visualization data visualization t-distributed stochastic neighbor embedding (t-SNE) t-distributed stochastic neighbor embedding (t-SNE) Fault detection Fault detection semiconductor manufacturing semiconductor manufacturing

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GB/T 7714 Zhang, Haili , Wang, Pu , Gao, Xuejin et al. Data Visualization and Fault Detection Using Bi-Kernel t-Distributed Stochastic Neighbor Embedding in Semiconductor Etching Processes [J]. | IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING , 2022 , 35 (3) : 522-531 .
MLA Zhang, Haili et al. "Data Visualization and Fault Detection Using Bi-Kernel t-Distributed Stochastic Neighbor Embedding in Semiconductor Etching Processes" . | IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING 35 . 3 (2022) : 522-531 .
APA Zhang, Haili , Wang, Pu , Gao, Xuejin , Qi, Yongsheng , Gao, Huihui . Data Visualization and Fault Detection Using Bi-Kernel t-Distributed Stochastic Neighbor Embedding in Semiconductor Etching Processes . | IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING , 2022 , 35 (3) , 522-531 .
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Fault Detection Approach for Nonlinear Systems via Nonlinear Factorization and Fuzzy Models SCIE
期刊论文 | 2022 , 69 (8) , 3425-3429 | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
WoS CC Cited Count: 4
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Abstract :

This brief aims to propose an effective fault detection method for general class of nonlinear systems in the context of the closed-loop system stability. To this end, the nonlinear factorization technique is first used to model the faulty nonlinear systems, which can be represented by the so-called stable kernel representation with a stable parameterization of the system changes triggered by faults. Then, the closed-loop system stability is discussed according to the internal stability definition and the small gain theorem, respectively, to present the design framework of the fault detection system. Different from the traditional fault detection schemes, the proposed fault detection approach focuses on detecting whether the system closed-loop stability is damaged by faults utilizing the online measurable system and controller residual signals. Furthermore, for the implementation of the proposed fault detection framework, Takagi-Sugeno fuzzy models are applied to approximate the nonlinear systems and thus the fault detection system design methods can be provided by taking advantage of the linear matrix inequality technique. Finally, a case study is used to verify the achieved results.

Keyword :

Stability criteria Stability criteria Takagi-Sugeno fuzzy models Takagi-Sugeno fuzzy models Analytical models Analytical models Circuits and systems Circuits and systems Circuit stability Circuit stability nonlinear systems nonlinear systems nonlinear factorization nonlinear factorization internal stability internal stability Fault detection Fault detection Uncertainty Uncertainty Nonlinear systems Nonlinear systems

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GB/T 7714 Han, Huayun , Han, Honggui , Zhao, Dong et al. Fault Detection Approach for Nonlinear Systems via Nonlinear Factorization and Fuzzy Models [J]. | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS , 2022 , 69 (8) : 3425-3429 .
MLA Han, Huayun et al. "Fault Detection Approach for Nonlinear Systems via Nonlinear Factorization and Fuzzy Models" . | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 69 . 8 (2022) : 3425-3429 .
APA Han, Huayun , Han, Honggui , Zhao, Dong , Gao, Xuejin . Fault Detection Approach for Nonlinear Systems via Nonlinear Factorization and Fuzzy Models . | IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS , 2022 , 69 (8) , 3425-3429 .
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A Novel Radial Basis Function Neural Network with High Generalization Performance for Nonlinear Process Modelling SCIE
期刊论文 | 2022 , 10 (1) | PROCESSES
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Abstract :

A radial basis function neural network (RBFNN), with a strong function approximation ability, was proven to be an effective tool for nonlinear process modeling. However, in many instances, the sample set is limited and the model evaluation error is fixed, which makes it very difficult to construct an optimal network structure to ensure the generalization ability of the established nonlinear process model. To solve this problem, a novel RBFNN with a high generation performance (RBFNN-GP), is proposed in this paper. The proposed RBFNN-GP consists of three contributions. First, a local generalization error bound, introducing the sample mean and variance, is developed to acquire a small error bound to reduce the range of error. Second, the self-organizing structure method, based on a generalization error bound and network sensitivity, is established to obtain a suitable number of neurons to improve the generalization ability. Third, the convergence of this proposed RBFNN-GP is proved theoretically in the case of structure fixation and structure adjustment. Finally, the performance of the proposed RBFNN-GP is compared with some popular algorithms, using two numerical simulations and a practical application. The comparison results verified the effectiveness of RBFNN-GP.

Keyword :

generation performance generation performance convergence analysis convergence analysis local generalization error bound local generalization error bound radial basis function neural network (RBFNN) radial basis function neural network (RBFNN) self-organizing structure method self-organizing structure method

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GB/T 7714 Yang, Yanxia , Wang, Pu , Gao, Xuejin . A Novel Radial Basis Function Neural Network with High Generalization Performance for Nonlinear Process Modelling [J]. | PROCESSES , 2022 , 10 (1) .
MLA Yang, Yanxia et al. "A Novel Radial Basis Function Neural Network with High Generalization Performance for Nonlinear Process Modelling" . | PROCESSES 10 . 1 (2022) .
APA Yang, Yanxia , Wang, Pu , Gao, Xuejin . A Novel Radial Basis Function Neural Network with High Generalization Performance for Nonlinear Process Modelling . | PROCESSES , 2022 , 10 (1) .
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Dynamic channel pruning via activation gates SCIE
期刊论文 | 2022 , 52 (14) , 16818-16831 | APPLIED INTELLIGENCE
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Abstract :

Dynamic channel pruning has been proved to be an effective method by dynamically adjusting the inference path to reduce the computing costs. However, in most existing work, the classification performance decreases rapidly with the increase of pruning rate because their pruning strategy weakens the representation ability of the model to a certain extent. To resolve this problem, a dynamic channel pruning method based on activation gate (DCPAG) is proposed, which can better maintain the classification performance while reducing the computing costs. First, a pipeline aiming for generating pruning strategy, namely channel pruning auxiliary (CPA) is proposed, which considers both the representation ability and computing costs. Second, the pruning strategy generated by CPA is embedded into dynamic rectifying linear unit (DyReLU) to form the embedded dynamic rectifying linear unit (EB-DyReLU), which achieves dynamic channel pruning while maintaining the representation capability. Third, each input sample was self-classified according to its identification difficulty during pruning, and additional training was given to hard samples to achieve better classification performance. Finally, some experiments are carried out on CIFAR-10 and ImageNet respectively to verify the effectiveness of DCPAG in accuracy and floating point of per second (FLOPs). The results show that the proposed method achieves better performance than other similar channel-based methods at the same pruning rate. Specifically, this method not only achieves 0.5-1.5% improvement in classification accuracy, but also reduces the computational costs by 5%-20%.

Keyword :

Gates Gates ReLU-Activation ReLU-Activation Channel Channel Pruning-Dynamic Pruning-Dynamic

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GB/T 7714 Liu, Shun-Qiang , Yang, Yan-Xia , Gao, Xue-Jin et al. Dynamic channel pruning via activation gates [J]. | APPLIED INTELLIGENCE , 2022 , 52 (14) : 16818-16831 .
MLA Liu, Shun-Qiang et al. "Dynamic channel pruning via activation gates" . | APPLIED INTELLIGENCE 52 . 14 (2022) : 16818-16831 .
APA Liu, Shun-Qiang , Yang, Yan-Xia , Gao, Xue-Jin , Cheng, Kun . Dynamic channel pruning via activation gates . | APPLIED INTELLIGENCE , 2022 , 52 (14) , 16818-16831 .
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Phase partition and KPI-related process monitoring for batch processes using a novel canonical correlation analysis strategy SCIE
期刊论文 | 2022 , 101 (4) , 1967-1985 | CANADIAN JOURNAL OF CHEMICAL ENGINEERING
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Abstract :

Key performance indicators (KPI)-related process monitoring has been of great significance to ensure product quality and economic benefits for batch processes. Considering that different phases exhibit different characteristics, one of the key issues is how to partition the whole batch process into different phases and characterize them separately by multiple phase models. In order to model and monitor batch processes more accurately and efficiently, a novel canonical correlation analysis (CCA) strategy is proposed in this paper. The phase partition algorithm is designed based on the joint canonical variable matrix (JCVM). Different from previous methods, it considers the time sequence of operation phases and can distinguish the phase switches from dynamics anomalies. Using this algorithm, phases are separated in order from a KPI-related perspective, revealing high correlation among variables. After phase partition, a novel multi-phase local neighbourhood standardization CAA (MPLNSCCA) method focusing on KPI is set up for online monitoring, which could further address the misclassification problems. The advantages of the proposed method are illustrated by two case studies, a penicillin simulation platform and an industrial application of Escherichia coli fermentation, respectively.

Keyword :

key performance indicator key performance indicator process monitoring process monitoring batch process batch process phase partition phase partition

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GB/T 7714 Gao, Xuejin , He, Zihe , Gao, Huihui et al. Phase partition and KPI-related process monitoring for batch processes using a novel canonical correlation analysis strategy [J]. | CANADIAN JOURNAL OF CHEMICAL ENGINEERING , 2022 , 101 (4) : 1967-1985 .
MLA Gao, Xuejin et al. "Phase partition and KPI-related process monitoring for batch processes using a novel canonical correlation analysis strategy" . | CANADIAN JOURNAL OF CHEMICAL ENGINEERING 101 . 4 (2022) : 1967-1985 .
APA Gao, Xuejin , He, Zihe , Gao, Huihui , Qi, Yongsheng . Phase partition and KPI-related process monitoring for batch processes using a novel canonical correlation analysis strategy . | CANADIAN JOURNAL OF CHEMICAL ENGINEERING , 2022 , 101 (4) , 1967-1985 .
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Takagi-Sugeno Fuzzy Realization of Stability Performance-Based Fault-Tolerant Control for Nonlinear Systems SCIE
期刊论文 | 2022 , 30 (10) , 4249-4261 | IEEE TRANSACTIONS ON FUZZY SYSTEMS
WoS CC Cited Count: 8
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Abstract :

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi-Sugeno (T-S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T-S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the L-2 input-output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results.

Keyword :

fault-tolerant control fault-tolerant control Takagi-Sugeno fuzzy models Takagi-Sugeno fuzzy models Uncertainty Uncertainty Observers Observers stability performance stability performance Takagi-Sugeno model Takagi-Sugeno model stable image and kernel representations stable image and kernel representations Fault tolerant systems Fault tolerant systems Actuators Actuators Fault detection system Fault detection system Fault tolerance Fault tolerance Nonlinear systems Nonlinear systems

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GB/T 7714 Han, Huayun , Han, Honggui , Zhao, Dong et al. Takagi-Sugeno Fuzzy Realization of Stability Performance-Based Fault-Tolerant Control for Nonlinear Systems [J]. | IEEE TRANSACTIONS ON FUZZY SYSTEMS , 2022 , 30 (10) : 4249-4261 .
MLA Han, Huayun et al. "Takagi-Sugeno Fuzzy Realization of Stability Performance-Based Fault-Tolerant Control for Nonlinear Systems" . | IEEE TRANSACTIONS ON FUZZY SYSTEMS 30 . 10 (2022) : 4249-4261 .
APA Han, Huayun , Han, Honggui , Zhao, Dong , Gao, Xuejin , Yang, Ying . Takagi-Sugeno Fuzzy Realization of Stability Performance-Based Fault-Tolerant Control for Nonlinear Systems . | IEEE TRANSACTIONS ON FUZZY SYSTEMS , 2022 , 30 (10) , 4249-4261 .
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Research and application of RBF neural network based on modified Levenberg-Marquardt
期刊论文 | 2022 , 22 (5) , 1597-1619 | JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING
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Radial basis function neural network (RBFNN) has been widely used in industrial process modeling because of its strong approximation ability. However, many existing modeling methods aim at accuracy, but ignore the stability of mode. Therefore, this paper proposes a parameter optimization method of RBF neural network based on modified Levenberg-Marquardt (MLM-RBFNN) to ensure the stability of the network. Firstly, a typical sample mechanism with variance reduction is proposed, which can reduce the error of gradient estimation and use accurate gradient information to guide learning. Secondly, a modified LM optimization algorithm is proposed to optimize the parameters, which not only improve the convergence speed of the network, but also ensure the stability of the model. Finally, a multi-step updating rule based on a typical sample and a single sample is designed, which effectively reduces the sample bias introduced by a single sample. In order to prove the advantages of the MLM-RBFNN method proposed in this paper, experiments are carried out on three benchmark data sets and a practical wastewater treatment process application problem and compared with several existing methods. The results show that the proposed MLM-RBFNN method has good performance in both learning speed and stability.

Keyword :

second-order online learning second-order online learning Levenberg-Marquardt algorithm Levenberg-Marquardt algorithm Radial basis function neural network Radial basis function neural network typical sample typical sample gradient approximation gradient approximation

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GB/T 7714 Yang, Yanxia , Wang, Pu , Gao, Xuejin et al. Research and application of RBF neural network based on modified Levenberg-Marquardt [J]. | JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING , 2022 , 22 (5) : 1597-1619 .
MLA Yang, Yanxia et al. "Research and application of RBF neural network based on modified Levenberg-Marquardt" . | JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 22 . 5 (2022) : 1597-1619 .
APA Yang, Yanxia , Wang, Pu , Gao, Xuejin , Gao, Huihui , Qi, Zeyang . Research and application of RBF neural network based on modified Levenberg-Marquardt . | JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING , 2022 , 22 (5) , 1597-1619 .
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