Journal of The Franklin Institute-engineering and Applied Mathematics最新文献

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Periodic event-triggered predictive formation control of networked mobile robots under unknown disturbances

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-21 DOI: 10.1016/j.jfranklin.2025.107581

Chengyu Zhu , Xiurui Lin , Dongdong Qin , Andong Liu , Wen-An Zhang , Jason J.R. Liu

This paper proposes an Extended State Observer (ESO)-based periodic event-triggered predictive formation control algorithm for networked mobile robots under unknown disturbances with system constraints. The aim is to efficiently reduce the computational load and communication burden in the presence of unknown disturbances. First, our approach employs an improved virtual structure method, which divides the formation problem into two subtasks: path-following and formation coordination. Moreover, a periodic event-triggered distributed model predictive control (PETDMPC) strategy is proposed to enhance the implementation of discrete linear systems in computer control systems. This strategy incorporates cooperation constraints related to the parameterized variables in the cost function as coupling terms. Additionally, to reduce the adverse effects of disturbances, a disturbance compensation mechanism based on ESO is incorporated into the periodic event-triggered predictive formation control strategy. Finally, the feasibility of the algorithm and the stability of the closed-loop systems are derived using the discrete Gronwall–Bellman inequality for networked mobile robots under unknown disturbances. Simulation results show the effectiveness of the proposed strategy.

{"title":"Periodic event-triggered predictive formation control of networked mobile robots under unknown disturbances","authors":"Chengyu Zhu , Xiurui Lin , Dongdong Qin , Andong Liu , Wen-An Zhang , Jason J.R. Liu","doi":"10.1016/j.jfranklin.2025.107581","DOIUrl":"10.1016/j.jfranklin.2025.107581","url":null,"abstract":"<div><div>This paper proposes an Extended State Observer (ESO)-based periodic event-triggered predictive formation control algorithm for networked mobile robots under unknown disturbances with system constraints. The aim is to efficiently reduce the computational load and communication burden in the presence of unknown disturbances. First, our approach employs an improved virtual structure method, which divides the formation problem into two subtasks: path-following and formation coordination. Moreover, a periodic event-triggered distributed model predictive control (PETDMPC) strategy is proposed to enhance the implementation of discrete linear systems in computer control systems. This strategy incorporates cooperation constraints related to the parameterized variables in the cost function as coupling terms. Additionally, to reduce the adverse effects of disturbances, a disturbance compensation mechanism based on ESO is incorporated into the periodic event-triggered predictive formation control strategy. Finally, the feasibility of the algorithm and the stability of the closed-loop systems are derived using the discrete Gronwall–Bellman inequality for networked mobile robots under unknown disturbances. Simulation results show the effectiveness of the proposed strategy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107581"},"PeriodicalIF":3.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

L1-based virtual guidance and robust adaptive event-triggered control of large-scale USV for a narrow channel maneuver

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-21 DOI: 10.1016/j.jfranklin.2025.107586

Guoqing Zhang , Zhu Sun , Jiqiang Li , Weidong Zhang

This note proposes a robust adaptive control strategy for the narrow channel maneuvering mission of the large-scale underactuated surface vessel (USV). The proposed strategy consists of the guidance module and control module. For the former, a L1-based virtual guidance is developed to generate the reference signal and guide the large-scale USV to execute the narrow channel maneuver, which aims to overcome the overshoot problem near waypoints. For the latter, a robust adaptive control algorithm with a novel dynamic event-triggered mechanism is designed. In particular, the model uncertainties and external disturbances are addressed with a new approach called “robust bounded compensating technique”, leading to a lower design complexity while the robustness is increasing. Furthermore, the output-based dynamic event-triggered control (DETC) mechanism without preset parameters tuning is introduced to reduce the transmission frequency from controller to actuator. Besides, considerable efforts have done to prove the stability of the proposed algorithm via the Lyapunov theorem. Finally, the effectiveness and superiorities of the proposed method are demonstrated with two numerical examples, where the satisfied tracking accuracy and low transmission frequency are achieved in presence of the marine environment.

{"title":"L1-based virtual guidance and robust adaptive event-triggered control of large-scale USV for a narrow channel maneuver","authors":"Guoqing Zhang , Zhu Sun , Jiqiang Li , Weidong Zhang","doi":"10.1016/j.jfranklin.2025.107586","DOIUrl":"10.1016/j.jfranklin.2025.107586","url":null,"abstract":"<div><div>This note proposes a robust adaptive control strategy for the narrow channel maneuvering mission of the large-scale underactuated surface vessel (USV). The proposed strategy consists of the guidance module and control module. For the former, a L1-based virtual guidance is developed to generate the reference signal and guide the large-scale USV to execute the narrow channel maneuver, which aims to overcome the overshoot problem near waypoints. For the latter, a robust adaptive control algorithm with a novel dynamic event-triggered mechanism is designed. In particular, the model uncertainties and external disturbances are addressed with a new approach called “robust bounded compensating technique”, leading to a lower design complexity while the robustness is increasing. Furthermore, the output-based dynamic event-triggered control (DETC) mechanism without preset parameters tuning is introduced to reduce the transmission frequency from controller to actuator. Besides, considerable efforts have done to prove the stability of the proposed algorithm via the Lyapunov theorem. Finally, the effectiveness and superiorities of the proposed method are demonstrated with two numerical examples, where the satisfied tracking accuracy and low transmission frequency are achieved in presence of the marine environment.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 5","pages":"Article 107586"},"PeriodicalIF":3.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

New controllability conditions for multi-layer networked systems

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-20 DOI: 10.1016/j.jfranklin.2025.107579

Longkun Tang, Quan Shen, Lixin Jiang

The controllability of networked system with high-dimensional nodes is far lack of understanding. From the perspective of the eigenvectors, based on the decoupled idea and dimensionality reduction technique, this paper investigates the controllability of multi-layer networks with high-dimensional nodes where the network topology is described by multiple connection structures with different coupling modes, and proposes some new necessary and sufficient conditions of the controllability for two intra-layer topology cases of simultaneously block diagonalization (SBD) and simultaneously diagonalization (SD), which are represented by the small-size units of intra-layer topologies and node dynamics. Furthermore, an easy-to-use algorithm is developed to check the controllability of multi-layer networked system, and two examples are used for illustration and verification, and then these conditions are specified for four cases of special intra-layer topologies. These findings provide a new and insight understandings for the controllability of multi-layer networks, and reveal the affect of multi-layer connections (outer topologies and inner couplings) on network controllability, particularly the impressive result that either one of two-layer networks being uncontrollable implies the two-layer networked system being uncontrollable when the two-layer network structures have the common left eigenvectors.

{"title":"New controllability conditions for multi-layer networked systems","authors":"Longkun Tang, Quan Shen, Lixin Jiang","doi":"10.1016/j.jfranklin.2025.107579","DOIUrl":"10.1016/j.jfranklin.2025.107579","url":null,"abstract":"<div><div>The controllability of networked system with high-dimensional nodes is far lack of understanding. From the perspective of the eigenvectors, based on the decoupled idea and dimensionality reduction technique, this paper investigates the controllability of multi-layer networks with high-dimensional nodes where the network topology is described by multiple connection structures with different coupling modes, and proposes some new necessary and sufficient conditions of the controllability for two intra-layer topology cases of simultaneously block diagonalization (SBD) and simultaneously diagonalization (SD), which are represented by the small-size units of intra-layer topologies and node dynamics. Furthermore, an easy-to-use algorithm is developed to check the controllability of multi-layer networked system, and two examples are used for illustration and verification, and then these conditions are specified for four cases of special intra-layer topologies. These findings provide a new and insight understandings for the controllability of multi-layer networks, and reveal the affect of multi-layer connections (outer topologies and inner couplings) on network controllability, particularly the impressive result that either one of two-layer networks being uncontrollable implies the two-layer networked system being uncontrollable when the two-layer network structures have the common left eigenvectors.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107579"},"PeriodicalIF":3.7,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Corrigendum to "Dynamical analysis of a stochastic delayed epidemic model with Lévy jumps and regime switching" [Journal of the Franklin Institute 360 (2023) 1252–1283]

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.jfranklin.2025.107582

Jasmina Đorđević, Bojana Jovanović

The authors correct part of the proof of Theorem 1 in the above-titled paper [1], in order to avoid using of the estimate

I (t) \geq 1 \Leftrightarrow \frac{1}{I (t)} \leq 1

, which is not justified. For the same reason, the proofs of Theorems 2 and 3 were corrected, while the idea remained the same. The authors apologize for any inconvenience that may have been caused.

引用次数: 0

Stochastic resonance of a fractional-order bistable system driven by corrected non-Gaussian noise and Gaussian noise

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.jfranklin.2025.107593

Haoyu Chen , Yongfeng Guo , Qingzeng Song , Qin Yu

In this paper, we study the phenomenon of stochastic resonance(SR) in a fractional-order bistable system including a periodic signal caused by terms of the colored cross-correlated multiplicative non-Gaussian noise and additive Gaussian noise. Applying the fractional-order minimum mean square error criterion, path integral approach and two-state model theory, the expression for signal-to-noise ratio(SNR) is derived theoretically. The effectiveness of these theoretical methods is also verified through numerical simulations. The results show that the SNR curves all exhibit a maximum value, indicating the occurrence of SR within the system. Larger values of self-correlation time and amplitude enhance the generation of SR. The effects of correlation strength, non-Gaussian parameter and fractional order on SR vary with the intensity of multiplicative noise and additive noise.

引用次数: 0

Rapid dynamical learning from neural control of sampled-data nonlinear systems via pseudo-inverse regression filter vector signal

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.jfranklin.2025.107585

Dengxiang Liang, Min Wang

In this paper, a rapid neural learning control method utilizing a pseudo-inverse regression filter vector signal strategy is developed for sampled-data strict-feedback nonlinear systems, targeting enhancements in both neural learning speed and output tracking performance. Firstly, the consistency condition is proposed to ensure the stability of the sampled-data system, which is derived from the stability framework of the approximate model. Subsequently, a pseudo-inverse regression filter vector signal-based adaptive neural dynamic surface control (PIRFVB-ANDSC) is proposed by integrating digital first-order filter, regression filter and pseudo-inverse technique. Specially, a new form of NN weight updating law is built upon the pseudo-inverse regression filter vector signal. The persistent excitation (PE) level of the pseudo-inverse regression filter signal is verified to be independent of the system control gain function and PE level of Gaussian activation function which is convenient for performance analysis. Then, it is verified that PIRFVB-ANDSC effectively accelerates convergence of NN estimated weights and reduces the consumption of computing resources. The convergent weights are utilized to develop a disturbance observer-based neural learning dynamic surface control (DOB-NLDSC) to improve robustness. Finally, the simulation comparison demonstrates several key advantages of the scheme with some merits including the rapid NN learning speed, the enhanced tracking performance, and the strong robustness.

{"title":"Rapid dynamical learning from neural control of sampled-data nonlinear systems via pseudo-inverse regression filter vector signal","authors":"Dengxiang Liang, Min Wang","doi":"10.1016/j.jfranklin.2025.107585","DOIUrl":"10.1016/j.jfranklin.2025.107585","url":null,"abstract":"<div><div>In this paper, a rapid neural learning control method utilizing a pseudo-inverse regression filter vector signal strategy is developed for sampled-data strict-feedback nonlinear systems, targeting enhancements in both neural learning speed and output tracking performance. Firstly, the consistency condition is proposed to ensure the stability of the sampled-data system, which is derived from the stability framework of the approximate model. Subsequently, a pseudo-inverse regression filter vector signal-based adaptive neural dynamic surface control (PIRFVB-ANDSC) is proposed by integrating digital first-order filter, regression filter and pseudo-inverse technique. Specially, a new form of NN weight updating law is built upon the pseudo-inverse regression filter vector signal. The persistent excitation (PE) level of the pseudo-inverse regression filter signal is verified to be independent of the system control gain function and PE level of Gaussian activation function which is convenient for performance analysis. Then, it is verified that PIRFVB-ANDSC effectively accelerates convergence of NN estimated weights and reduces the consumption of computing resources. The convergent weights are utilized to develop a disturbance observer-based neural learning dynamic surface control (DOB-NLDSC) to improve robustness. Finally, the simulation comparison demonstrates several key advantages of the scheme with some merits including the rapid NN learning speed, the enhanced tracking performance, and the strong robustness.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 5","pages":"Article 107585"},"PeriodicalIF":3.7,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic self-triggered control for positive fuzzy Markov jump systems with switching transition rates

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.jfranklin.2025.107583

Congxue Gao , Wenhai Qi , Jinde Cao , Jun Cheng , Kaibo Shi

This paper studies the dynamic self-triggered

L_{1}

-gain control for positive T-S fuzzy Markov jump systems subject to switching transition rates. Bearing in mind the positivity of Markov jump models, a dynamic self-triggered mechanism is crafted based on the 1-norm, wherein the subsequent execution time is precalculated to rely solely on the latest sampled information, thus eliminating the requirement for continual system state monitoring with additional hardware. By utilizing matrix decomposition technique and constructing linear co-positive Lyapunov function, sufficient conditions for the positivity and the exponential stability are derived under average dwell time switching. A detailed analysis of

L_{1}

-gain performance is conducted. All the mentioned conditions are amenable to being solved through linear programming. Finally, the validity of the obtained results is verified through two examples.

{"title":"Dynamic self-triggered control for positive fuzzy Markov jump systems with switching transition rates","authors":"Congxue Gao , Wenhai Qi , Jinde Cao , Jun Cheng , Kaibo Shi","doi":"10.1016/j.jfranklin.2025.107583","DOIUrl":"10.1016/j.jfranklin.2025.107583","url":null,"abstract":"<div><div>This paper studies the dynamic self-triggered <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-gain control for positive T-S fuzzy Markov jump systems subject to switching transition rates. Bearing in mind the positivity of Markov jump models, a dynamic self-triggered mechanism is crafted based on the 1-norm, wherein the subsequent execution time is precalculated to rely solely on the latest sampled information, thus eliminating the requirement for continual system state monitoring with additional hardware. By utilizing matrix decomposition technique and constructing linear co-positive Lyapunov function, sufficient conditions for the positivity and the exponential stability are derived under average dwell time switching. A detailed analysis of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-gain performance is conducted. All the mentioned conditions are amenable to being solved through linear programming. Finally, the validity of the obtained results is verified through two examples.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 5","pages":"Article 107583"},"PeriodicalIF":3.7,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust consensus protocols of multi-agent systems with unknown but bounded measurement errors

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-19 DOI: 10.1016/j.jfranklin.2025.107580

Quchao Ma, Cheng Song

This paper revisits the consensus problem for multi-agent systems (MASs) in the presence of unknown but bounded (UBB) measurement errors. Unlike existing works, the proposed approach accommodations agents with different upper bounds for their measurement errors. A distributed estimation algorithm is employed to estimate the state differences between neighboring agents using the inaccurate state measurements. Building on this estimation algorithm, a distributed robust consensus protocol is developed. It is demonstrated that the proposed protocol drives the MAS to a neighborhood of consensus, effectively mitigating or even eliminating the influence of UBB measurement errors on multi-agent consensus. The analysis is further extended to address the positive consensus problem for MASs with UBB measurement errors. Finally, numerical simulations confirm the effectiveness of the proposed consensus protocols.

引用次数: 0

Watermarking-Aided dimensionality reduction encryption for distributed fusion estimation against eavesdropping

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-17 DOI: 10.1016/j.jfranklin.2025.107594

Yuhang Yang, Shenmin Song

The existing defense strategies offer robust protection against eavesdropping attacks. However, in practical engineering scenarios, the system must navigate numerous challenges, particularly when communication resources are limited. Under such constraints, the estimator performance can suffer significantly, especially when faced with both eavesdropping attacks and resource limitations. This decline is due to the lack of effective adaptation mechanisms. To remedy this issue, we propose an encryption method that incorporates watermarking signals and dimensionality reduction techniques. The core principle of this method aims to find a balanced compromise between the performance demands and the resource constraints. Specifically, dimensionality reduction strategy is applied to reduce the information density of the transmitted signal, which alleviates the burden on network bandwidth. Additionally, the incorporation of the watermarking signal not only enhances the complexity of the signal but also maximizes the estimation error for potential eavesdroppers, which ensures the secure transmission of information. A compensation mechanism, which incorporates techniques for watermarking removal and prediction, has been specifically developed for users at the fusion center. This mechanism undergoes rigorous feasibility and boundedness analyses to ensure the robustness of the encryption strategy and estimator. Extensive simulation experiments conduct to validate the effectiveness and superiority of the developed algorithm.

{"title":"Watermarking-Aided dimensionality reduction encryption for distributed fusion estimation against eavesdropping","authors":"Yuhang Yang, Shenmin Song","doi":"10.1016/j.jfranklin.2025.107594","DOIUrl":"10.1016/j.jfranklin.2025.107594","url":null,"abstract":"<div><div>The existing defense strategies offer robust protection against eavesdropping attacks. However, in practical engineering scenarios, the system must navigate numerous challenges, particularly when communication resources are limited. Under such constraints, the estimator performance can suffer significantly, especially when faced with both eavesdropping attacks and resource limitations. This decline is due to the lack of effective adaptation mechanisms. To remedy this issue, we propose an encryption method that incorporates watermarking signals and dimensionality reduction techniques. The core principle of this method aims to find a balanced compromise between the performance demands and the resource constraints. Specifically, dimensionality reduction strategy is applied to reduce the information density of the transmitted signal, which alleviates the burden on network bandwidth. Additionally, the incorporation of the watermarking signal not only enhances the complexity of the signal but also maximizes the estimation error for potential eavesdroppers, which ensures the secure transmission of information. A compensation mechanism, which incorporates techniques for watermarking removal and prediction, has been specifically developed for users at the fusion center. This mechanism undergoes rigorous feasibility and boundedness analyses to ensure the robustness of the encryption strategy and estimator. Extensive simulation experiments conduct to validate the effectiveness and superiority of the developed algorithm.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 5","pages":"Article 107594"},"PeriodicalIF":3.7,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic analysis of three-dimensional stochastic resonance and its application in signal analysis

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-17 DOI: 10.1016/j.jfranklin.2025.107595

Qiumei Xiao, Wenxin Yu

In response to the difficulty of blind source separation of characteristic signals for mixed signals with severe noise pollution under uncertain observation signals, this paper constructs a multifunctional three-dimensional stochastic resonance (3DSR) system, which can simultaneously perform signal denoising, amplification, and feature restoration processing. The research improves the Ensemble Empirical Mode Decomposition (EEMD) algorithm through the 3DSR system, resulting in obtaining the 3DSR-Ensemble Empirical Mode Decomposition (3DSR-EEMD) algorithm. During the process of signal decomposition, the 3DSR-EEMD algorithm utilizes the 3DSR system to denoise and restore features of the signal, and timely smooth out transient noise interference. This paper proposes a components analysis method of noisy mixed signal based on 3DSR-EEMD. Firstly, the noisy mixed signal is decomposed using the 3DSR-EEMD algorithm. Then, the principal components in the decomposed signals are extracted using the principal component analysis algorithm. Finally, the principal components are processed through the independent component analysis algorithm to obtain the unmixing signals. Apply this method to the component analysis of noisy mixed signals and rolling bearing fault signals. The experimental results show that the components analysis method of noisy mixed signal based on 3DSR-EEMD has good separation performance and noise robustness.

{"title":"Dynamic analysis of three-dimensional stochastic resonance and its application in signal analysis","authors":"Qiumei Xiao, Wenxin Yu","doi":"10.1016/j.jfranklin.2025.107595","DOIUrl":"10.1016/j.jfranklin.2025.107595","url":null,"abstract":"<div><div>In response to the difficulty of blind source separation of characteristic signals for mixed signals with severe noise pollution under uncertain observation signals, this paper constructs a multifunctional three-dimensional stochastic resonance (3DSR) system, which can simultaneously perform signal denoising, amplification, and feature restoration processing. The research improves the Ensemble Empirical Mode Decomposition (EEMD) algorithm through the 3DSR system, resulting in obtaining the 3DSR-Ensemble Empirical Mode Decomposition (3DSR-EEMD) algorithm. During the process of signal decomposition, the 3DSR-EEMD algorithm utilizes the 3DSR system to denoise and restore features of the signal, and timely smooth out transient noise interference. This paper proposes a components analysis method of noisy mixed signal based on 3DSR-EEMD. Firstly, the noisy mixed signal is decomposed using the 3DSR-EEMD algorithm. Then, the principal components in the decomposed signals are extracted using the principal component analysis algorithm. Finally, the principal components are processed through the independent component analysis algorithm to obtain the unmixing signals. Apply this method to the component analysis of noisy mixed signals and rolling bearing fault signals. The experimental results show that the components analysis method of noisy mixed signal based on 3DSR-EEMD has good separation performance and noise robustness.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107595"},"PeriodicalIF":3.7,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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