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optimal sensor placement for railway vehicle bogie frame based on strain modal analysis

MEASUREMENT 2025年 253卷

作者： Zhang, Yadong Lu, Yaohui Yan, Bingqi Xue, Shuai Wang, Qiushi Liu, Xi Southwest Jiaotong Univ Sch Mech Engn Chengdu 610031 Sichuan Peoples R China Southwest Jiaotong Univ Tangshan Inst Tangshan Peoples R China

The optimal strain sensor placement on a high-speed train bogie frame was investigated using information entropy and strain modal analysis within Bayesian theory. The influence of prediction errors on sensor placement was examined, and modal strain energy was introduced to correct model errors, reduce measurement point clustering, and enhance the signal-to-noise ratio. A modal order selection method, combined with the Fisher Information Matrix (FIM), was proposed to determine the number of considered modes. Numerical analysis set the initial sensor count at 24, with an optimal correlation length of 24 mm. Four sensor arrangement schemes were compared: (A) without considering model error, (B) without correcting model error, (C) with model error correction, and (D) considering only model error. Results show that Scheme B exhibits the weakest aggregation effect and better modal independence, with an NND index of 123.9 mm and all non-diagonal elements of the MAC matrix below 0.5. The FIM determinant is 2.245 x 10-71, smaller than that of Scheme C but larger than A and D, indicating Scheme B provides sufficient information. Finally, sensor placement scheme B was validated based on literature, confirming that Scheme B effectively covers fatigue-prone regions. Frequency-domain analysis of signals from four measurement points using virtual prototyping revealed varying sensitivity to frequency bands, except at 32.2 Hz and 55.7 Hz. This study is significant for developing a damage index and achieving effective health monitoring of the high-speed train structure.

关键词： optimal sensor placement Strain modal analysis Bogie frame Information entropy Prediction error

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optimal sensor placement method for structural parameter identification considering nonlinear correlations under dynamic loadings

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 224卷

作者： Heng, Ouyang Wang, Haoyang Duan, Shuyong Shi, Zhaoyao Han, Xu Hebei Univ Technol Sch Mech Engn State Key Lab Reliabil & Intelligence Elect Equipm Tianjin 300401 Peoples R China Beijing Univ Technol Beijing Engn Res Ctr Precis Measurement Technol & Beijing 100124 Peoples R China

Structural parameter identification technology, using the structural responses measured by sensors and an accurate structural model to achieve the structural parameters to be determined (TBD), is widely applied in the structural damage detection, dynamic model updating and health monitoring. In practical engineering problems, the uncertainties and nonlinear correlations are commonly present in measurement data by sensors when a structure is subjected to dynamic loadings, which can significantly affect the stability and accuracy of identified results of the TBD parameter. To address the aforementioned issue, an optimal sensor placement (OSP) method for structural parameter identification considering nonlinear correlations under dynamic loadings is proposed in this paper. To start with, the OSP problem for structural parameter identification considering nonlinear correlations under dynamic loadings is discussed in detail and transformed into a forward uncertainty propagation problem. Then, a maximum independent mean variance criterion is proposed to determine the position and number of sensors for the OSP problem. In the framework of forward uncertainty propagation, Copula functions are then adopted to quantify the uncertainties and nonlinear correlations of TBD parameters, and the feature information of dynamic responses is extracted by the multi-layer discrete wavelet transform (MLDWT) method to convert the dynamic problem into a time-invariant problem. Subsequently, an improved principal component analysis and optimal polynomial chaos expansion method (IPCA-OPCE) is proposed to determine the OSP approach accurately and efficiently. Eventually, the structural parameters are accurately and stably identified by using the Markov chain Monte Carlo method. The accuracy and engineering applicability of the proposed method are demonstrated by a numerical example of a truss structure with 25 bars and an experimental example of a 4.55 MW compound planetary gearbox.

关键词： optimal sensor placement Inverse parameter identification Dynamic loading Nonlinear correlation Compound planetary gearbox

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Explainable Artificial Intelligence-Based Search Space Reduction for optimal sensor placement in the Pipeline Systems of Naval Ships

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STRUCTURAL CONTROL & HEALTH MONITORING 2025年第1期2025卷

作者： Kim, Chungeon Oh, Hyunseok Jung, Byung Chang Moon, Seok Jun Han, Bongtae Gwangju Inst Sci & Technol Sch Mech Engn Gwangju South Korea Korea Inst Machinery & Mat Dept Syst Dynam Daejeon South Korea Univ Maryland Dept Mech Engn College Pk MD USA

Pipeline damage in mission-critical systems, such as pipelines within naval ships, can result in substantial consequences. Compared to manual inspection of pipeline damage by crew members onboard, structural health monitoring of pipeline systems offers prompt identification of damage sites, enabling efficient damage mitigation. However, one challenge of this approach is deriving an optimal sensor placement (OSP) strategy, given the large and complex pipelines found in real-scale naval vessels. To address this issue, a search space reduction method is proposed for OSP suitable for the large and complex pipeline systems found in naval ships. In the proposed method, the original search space for sensor placement is reduced to a manageable scale using an explainable artificial intelligence (XAI) technique, namely, a gradient-weighted class activation map (Grad-CAM). Grad-CAM enables quantification and visualization of the contribution of individual pipeline nodes to classify damage scenarios. Noncritical sensor locations can be excluded from the candidate search space. Furthermore, a peak-finding algorithm is devised to select only a limited number of nodes with the highest Grad-CAM values;in this research, the algorithm is proven effective in reconstructing the search space. As a result, the original OSP problem-which has an extremely large search space-is reconstructed into a new OSP problem with a computationally manageable search space. The new OSP problem can be solved using either meta-heuristic methods or exhaustive search methods. The effectiveness of the proposed method is validated through a case study on a real-scale naval combat vessel, measuring 102 m in length and carrying a full load of 2300 tons. The results show that the proposed XAI-based search space reduction approach efficiently designs an optimal pipeline sensor network in real-scale naval combat vessels.

关键词： explainable artificial intelligence genetic algorithm optimal sensor placement sensor network design structural health monitoring

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Finite element model updating and response prediction of a frame structure based on optimal sensor placement

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ADVANCES IN STRUCTURAL ENGINEERING 2025年第1期28卷 55-67页

作者： Wang, Xiaoguang Liang, Peng Ma, Ming Zhou, Zhenwei Wu, Gang Song, Shuai Changan Univ Highway Sch Middle Sect Naner Huan Rd Xian 710064 Peoples R China CCCC First Highway Consultants Co Ltd Xian Peoples R China Zhongjiao Tongli Construct Co Ltd Xian Peoples R China East China Jiao Tong Univ Sch Civil Engn & Architecture Nanchang Peoples R China Qingdao Univ Technol Sch Civil Engn Qingdao Peoples R China

This paper proposes an approach for finite element (FE) model updating and response prediction of frame structures based on optimal sensor placement (OSP), which integrates sensor placement optimization, mode expansion, and model updating techniques. Firstly, sensor optimization layout and modal testing analysis are conducted on a bolted laboratory frame structure. The covariance-driven stochastic subspace identification (SSI-COV) method identifies the real-world structure's natural frequencies, modal damping, and mode shapes. Secondly, the complete mode shapes are expanded using the measured incomplete modal data from the limited number of sensors. Thirdly, a multi-objective function based on frequency and mode shapes is established to adjust the parameters of the FE model. This ensures that the updated model accurately represents the dynamic properties of the actual structure within a specific frequency range. Finally, the Rayleigh damping of the frame structure is estimated, and the damping matrix is assembled to enhance the accuracy of dynamic response prediction in the updated model. By comparing the response prediction results of the updated FE model with and without considering the updated damping effects to the measurement data of the real-world structure, it is demonstrated that the proposed method considering updated damping effects can more effectively predict the structural response.

关键词： finite element model updating optimal sensor placement operational modal analysis response prediction frame structure

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An improved vehicle dynamic load identification method with optimal sensor placement strategy based on augmented Kalman filter

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 225卷

作者： Zhou, Yabo Cai, Wubin Chi, Maoru Liang, Shulin Xu, Wentian Southwest Jiaotong Univ State Key Lab Rail Transit Vehicle Syst Chengdu 610031 Peoples R China Southwest Jiaotong Univ Sch Mech Engn Chengdu 610031 Peoples R China

Accurately assessing dynamic loads on railway vehicles is crucial for ensuring safety, refining vehicle design, enhancing passenger comfort, and streamlining maintenance procedures. However, direct load measurement methods often incur high costs due to challenges associated with precise force transducer positioning and the necessity for numerous sensors. Therefore, leveraging a limited set of accessible vibration response signals for real-time dynamic load identification proves to be a valuable approach. Real-time load identification algorithms, such as the augmented Kalman Filter (AKF), typically require a full-rank observability matrix to achieve stable results, which often involves measuring some or all displacements of each component. Nevertheless, accurately measuring absolute displacements is challenging due to the inherent mobility of railway vehicles along the track. To overcome this challenge, a state reconfiguration (SR) method has been developed within the state-space equation framework. This method transforms absolute displacements of all Degrees of Freedom (DOF) into readily measurable relative displacements, effectively meeting observability requirements. Furthermore, a refined optimal sensor placement strategy (OSPS) has been devised based on observability criteria and minimizing the normalized steady-state error covariance of the estimated loads. The proposed SRAKF combined with OSPS has been validated using a simple numerical vehicle model under three load conditions. Subsequently, a virtual test utilizing a detailed railway vehicle model was conducted, demonstrating the applicability and feasibility of the proposed method in engineering applications.

关键词： Augmented Kalman Filter Inverse load identification optimal sensor placement Observability Railway vehicle

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optimal sensor placement and structural health monitoring methods of ancient stone bridges based on an improved genetic algorithm: Taking Lugou Bridge as an example

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MEASUREMENT 2025年 241卷

作者： Zhang, Chengwen Chun, Qing Lin, Yijie Southeast Univ Sch Architecture Nanjing 210096 Peoples R China Southeast Univ Minist Educ Key Lab Urban & Architectural Heritage Conservat Nanjing 210096 Peoples R China

In this paper, a modified genetic algorithm (GA), Meta-GA, was developed to determine the optimal sensor placement (OSP). Then, the proposed OSP method was compared with the other two GA-based methods. Finally, a 15-month-long structural health monitoring was conducted for Lugou Bridge using the best sensor layout. The deformation monitoring results were compared with point cloud using a four-step method. The damage detection capability of the obtained sensor layout was also verified. The results show that Meta-GA has good computational efficiency and it can save 9.16 %similar to 28.24 % of optimization time compared to GA. Moreover, the damage sensitivity index obtained from Meta-GA is 12 %similar to 64 % higher than those of GA-based methods. Furthermore, the error between the monitoring deformation and the point cloud results is almost within 15 %. 90 % of apparent damage locations can be identified based on current sensor data. The research results can support for the structural health monitoring of masonry bridge.

关键词： Ancient bridge optimal sensor placement Long-term follow-up test Spatiotemporal variations Architectural heritage

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optimal sensor placement for Modal Identification in Multirotary-Joint Solar Power Satellite

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IEEE sensorS JOURNAL 2020年第13期20卷 7337-7346页

作者： Yang, Chen Ma, Ruize Ma, Rong China Acad Space Technol Qian Xuesen Lab Space Technol Beijing 100094 Peoples R China Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

In this study, optimal sensor placement (OSP) is investigated to select the best-suited sensor configurations for a multirotary-joint solar power satellite (MJ-SPS). To accurately realize the OSP and reduce the computational costs, three sensor specifications are considered, namely, number, edge effect, and measurement degree of freedom. As an important initial input for the sensor placement study, the dynamic analysis of the MJ-SPS is proposed. Six OSP methods are investigated to select the best sensor layout for MJ-SPS. The edge effect of the sensor location is noted in the final sensor placement results. In addition, three standards and two novel criteria i.e., sensor distribution, and similarity of sensor locations, have been added to evaluate the effectiveness of the sensor configurations. The OSP of the MJ-SPS is discussed and compared using the results of these assessments. Different numbers of sensors and orders of modal shape are compared, emphasizing the importance of this work for the MJ-SPS and OSP methods.

关键词： sensors Manganese Satellites Monitoring Shape Space vehicles Optimization optimal sensor placement structural health monitoring modal identification multirotary-joint solar power satellite placement criteria

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optimal sensor placement for leak localization in water distribution networks based on a novel semi-supervised strategy

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JOURNAL OF PROCESS CONTROL 2019年 82卷 13-21页

作者： Li, Juan Wang, Cong Qian, Zhihong Lu, Changgang Jilin Univ Nanhu Rd 5372 Changchun 130012 Jilin Peoples R China

optimal sensor placement (OSP) techniques are important to monitor water distribution networks (WDNs). However, these methods are only feasible under the premise of complete leak location information. In fact, partial leak locations may become lost or may not be recorded. Therefore, in this case, the previous OSP methods are not applicable. To overcome this problem, this paper proposes a new OSP strategy considering that some leak locations are unknown, meaning that they are under semi-supervised conditions. The proposed semi-supervised strategy and the original semi-JMI algorithm are applied to two benchmark networks. The results indicate that the monitoring nodes selected by the semi-JMI criterion will lead to the occurrence of monitoring blind zones, resulting in the degradation of the leak localization performance. The addition of the fuzzy c-means (FCM) clustering method will compensate for this problem and improve the accuracy and the stability of leak localization. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： optimal sensor placement Leak localization Water distribution networks Semi-supervised feature selection Fuzzy C-means Semi-JMI

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optimal sensor placement and motion coordination for target tracking

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AUTOMATICA 2006年第4期42卷 661-668页

作者： Martínez, S Bullo, F Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA Univ Calif Santa Barbara Dept Mech & Environm Engn Santa Barbara CA 93106 USA

This work studies optimal sensor placement and motion coordination strategies for mobile sensor networks. For a target-tracking application with range sensors, we investigate the determinant of the Fisher Information Matrix and compute it in the 2D and 3D cases, characterizing the global minima in the 2D case. We propose motion coordination algorithms that steer the mobile sensor network to an optimal deployment and that are amenable to a decentralized implementation. Finally, our numerical simulations illustrate how the proposed algorithms lead to improved performance of an extended Kalman filter in a target-tracking scenario. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： motion coordination optimal sensor placement Fisher Information Matrix Kalman filtering

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optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics

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OPTIMIZATION AND ENGINEERING 2018年第3期19卷 591-627页

作者： Herzog, Roland Riedel, Ilka Ucinski, Dariusz Tech Univ Chemnitz Fac Math Res Grp Numer Math Partial Differential Equat D-09107 Chemnitz Germany Univ Zielona Gora Inst Control & Computat Engn Ul Szafrana 2 PL-65516 Zielona Gora Poland

We consider large-scale dynamical systems in which both the initial state and some parameters are unknown. These unknown quantities must be estimated from partial state observations over a time window. A data assimilation framework is applied for this purpose. Specifically, we focus on large-scale linear systems with multiplicative parameter-state coupling as they arise in the discretization of parametric linear time-dependent partial differential equations. Another feature of our work is the presence of a quantity of interest different from the unknown parameters, which is to be estimated based on the available data. In this setting, we employ a simplicial decomposition algorithm for an optimal sensor placement and set forth formulae for the efficient evaluation of all required quantities. As a guiding example, we consider a thermo-mechanical PDE system with the temperature constituting the system state and the induced displacement at a certain reference point as the quantity of interest.

关键词： Data assimilation optimal sensor placement Simplicial decomposition Thermo-elastic model

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