Optimal Sensor Placement Method Research Articles

Sparse regularized graph pooling network optimal sensor placement method for diesel engine vibration fault perception system

Vibration sensor network optimization increases monitoring effectiveness and reduces sensor quantity and transmission burden. However, the traditional model-driven methods depend on precise finite element models, challenging for complex machinery. This paper presents a data-driven approach using the Sparse Regularized Graph Pooling Network (SRGPN), which conceptualizes sensor networks as graphs and uses graph pooling to identify optimal sensor combinations. A sparsity regularization term related to the number of sensors is included in the loss function, aiming for the minimal yet effective sensor combination. Additionally, a monitoring capability metric suited for diesel engines with multi-source impulse signals is proposed, reflecting the sensors’ monitoring capacity. Validated through simulations and tests on a diesel engine test bench, the results show that SRGPN optimally places sensors near excitation sources, balancing sensor count and monitoring needs. This approach shows potential for optimizing sensor placements in condition monitoring.

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

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 %∼28.24 % of optimization time compared to GA. Moreover, the damage sensitivity index obtained from Meta-GA is 12 %∼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.

An all-purpose method for optimal pressure sensor placement in water distribution networks based on graph signal analysis

Many researchers have addressed the challenge of optimal pressure sensor placement for different purposes, such as leakage detection, model calibration, state estimation, etc. However, pressure data often need to serve multiple purposes, and a method to optimize sensor locations with versatility for various objectives is still lacking. In this paper, a graph-based optimal sensor placement (GOSP) framework is proposed, which aims to provide a robust and all-purpose approach to identify critical points for pressure monitoring. By analysing the spatial variation frequencies of WDN pressures, the relationship between measurements and the global variation of original pressures is established. On this basis, the D-optimality criterion is adopted to formulate the objective of GOSP, which aims to maximize the information on the spatial distribution of pressures that can be obtained from measurements. The new-proposed objective ensures that the sensor locations are compatible with various application scenarios. The proposed method was applied to a real-life distribution network, and was compared with other optimal sensor placement methods oriented towards burst detection and pipe roughness calibration. Based on comparative studies in different scenarios including unknown pressure estimation, burst detection, and model calibration, the effectiveness and robustness of the proposed method have been proved.

Novel optimal sensor placement method towards the high-precision digital twin for complex curved structures

The complex shape of the structure and the new needs for high-precision in digital twin modeling pose challenges for sensor placement optimization. A novel optimal sensor placement towards the high-precision digital twin (OSP-HDT) method is proposed for complex curved structures. It comprises three key aspects. Firstly, leveraging the spatial dimensionality reduction method, the complex curved surface is simplified into a planar representation. Subsequently, candidate sensor placement points can be easily identified by dividing the background mesh in the plane and screening them within the curved surface. These candidate points are then binary encoded to facilitate the subsequent optimization. Secondly, the method collects result data from the finite element model, treating it as virtual sensor data. Using this data, a surrogate model is constructed and then the objective function is formulated based on both the global and local critical areas precision of the surrogate model. Thirdly, the sensor placement optimization model is constructed, followed by optimization design using the efficient multi-objective covariance matrix adaptive evolutionary strategy. Through the steps above, the optimal sensor placement can be identified. To validate the proposed OSP-HDT method, an experiment is conducted on an S-shaped variable cross-section stiffened shell, with the construction of the corresponding digital twin. Compared to the uniform placement with an equivalent number of sensors, the OSP-HDT method demonstrated a significant 9.0% improvement in global precision and a remarkable 62.1% enhancement in local precision of critical areas. Furthermore, when compared to the random sensor placement strategies, the OSP-HDT method exhibited a 20.5% increase in global precision, together with a 44.2% increase in the local precision. Notably, even when compared to the full sensor placement, the OSP-HDT method can maintain comparable local precision, while significantly reducing the number of sensors by 77.6%. The above comparison indicates that the proposed OSP-HDT method can build a digital twin model with higher global and local precision for complex structures.

Assessment of different optimal sensor placement methods for dynamic monitoring of civil structures and infrastructures

The optimal sensor placement is a critical aspect in the structural health monitoring of structures, as the number and layout of sensors directly impact the quality and usefulness of collected data. When developing a monitoring system, it is of paramount importance to use the minimum number of sensors to gain the maximum amount and quality of information. However, in the case of a limited number of sensors, their location on the structure becomes crucial. This study aims to assess the potential of several optimal sensor placement methods for the development of cost-efficient and well-dimensioned dynamic structural health monitoring systems to be implemented in a wide range of civil engineering structures and infrastructures. Indeed, the construction stock consists of a great variety of civil engineering structures and infrastructures that significantly differ from each other in terms of typology, historical period, construction techniques, materials, etc. Some of the most widely used optimal sensor placement methods are selected and applied in real case studies, and the obtained sensor configurations are discussed and compared. The results illustrated in this paper will contribute to defining good practice in the optimal sensor placement procedure for typical civil engineering structures and infrastructures.

Optimal sensor placement for ensemble-based data assimilation using gradient-weighted class activation mapping

We introduce an optimal sensor placement method using convolutional neural networks for ensemble-based data assimilation. The proposed method utilizes the gradient-weighted class activation mapping of the convolutional neural networks to identify important regions for assimilation processes. It is achieved by using the initial ensemble of samples for data assimilation as training data to construct a convolutional neural network-based surrogate model. In doing so, the method can estimate optimal sensor locations in an a priori manner, allowing for sensor placement before conducting data assimilation processing. Moreover, the gradient-weighted class activation mapping is used to alleviate the effect of error accumulation during the backpropagation process through global averaging. Further, these observation sensors are incorporated to reconstruct mean turbulent flow fields based on the ensemble Kalman method. The proposed optimal sensor placement method is applied to two flow applications with complex geometries, i.e., flows around periodic hills and an axisymmetric body of revolution. Both cases demonstrate that the proposed method can significantly reduce the number of sensors without sacrificing the accuracy of the reconstructed flow field.

A Novel Optimal Sensor Placement Method for Optimizing the Diagnosability of Liquid Rocket Engine

There are hundreds of various sensors used for online Prognosis and Health Management (PHM) of LREs. Inspired by the fact that a limited number of key sensors are selected for inflight control purposes in LRE, it is practical to optimal placement of redundant sensors for improving the diagnosability and economics of PHM systems. To strike a balance between sensor cost, real-time performance and diagnosability of the fault diagnosis algorithm in LRE, this paper proposes a novel Optimal Sensor Placement (OSP) method. Firstly, a Kernel Extreme Learning Machine-based (KELM) two-stage diagnosis algorithm is developed based on a system-level failure simulation model of LRE. Secondly, hierarchical diagnosability metrics are constructed to formulate the OSP problem in this paper. Thirdly, a Hierarchy Ranking Evolutionary Algorithm-based (HREA) two-stage OSP method is developed, achieving further optimization of Pareto solutions by the improved hypervolume indicator. Finally, the proposed method is validated using failure simulation datasets and hot-fire test-run experiment datasets. Additionally, four classical binary multi-objective optimization algorithms are introduced for comparison. The testing results demonstrate that the HREA-based OSP method outperforms other classical methods in effectively balancing the sensor cost, real-time performance and diagnosability of the diagnosis algorithm. The proposed method in this paper implements system-level OSP for LRE fault diagnosis and exhibits the potential for application in the development of reusable LREs.

A Sensor Placement Approach Using Multi-Objective Hypergraph Particle Swarm Optimization to Improve Effectiveness of Structural Health Monitoring Systems.

In this paper, a novel Multi-Objective Hypergraph Particle Swarm Optimization (MOHGPSO) algorithm for structural health monitoring (SHM) systems is considered. This algorithm autonomously identifies the most relevant sensor placements in a combined fitness function without artificial intervention. The approach utilizes six established Optimal Sensor Placement (OSP) methods to generate a Pareto front, which is systematically analyzed and archived through Grey Relational Analysis (GRA) and Fuzzy Decision Making (FDM). This comprehensive analysis demonstrates the proposed approach's superior performance in determining sensor placements, showcasing its adaptability to structural changes, enhancement of durability, and effective management of the life cycle of structures. Overall, this paper makes a significant contribution to engineering by leveraging advancements in sensor and information technologies to ensure essential infrastructure safety through SHM systems.

Efficient Modal Identification and Optimal Sensor Placement via Dynamic DIC Measurement and Feature-Based Data Compression

Full-field non-contact vibration measurements provide a rich dataset for analysing structural dynamics. However, implementing the identification algorithm directly using high-spatial resolution data can be computationally expensive in modal identification. To address this challenge, performing identification in a shape-preserving but lower-dimensional feature space is more feasible. The full-field mode shapes can then be reconstructed from the identified feature mode shapes. This paper discusses two approaches, namely data-dependent and data-independent, for constructing the feature spaces. The applications of these approaches to modal identification on a curved plate are studied, and their performance is compared. In a case study involving a curved plate, it was found that a spatial data compression ratio as low as 1% could be achieved without compromising the integrity of the shape features essential for a full-field modal. Furthermore, the paper explores the optimal point-wise sensor placement using the feature space. It presents an alternative, data-driven method for optimal sensor placement that eliminates the need for a normal model, which is typically required in conventional approaches. Combining a small number of point-wise sensors with the constructed feature space can accurately reconstruct the full-field response. This approach demonstrates a two-step structural health monitoring (SHM) preparation process: offline full-field identification of the structure and the recommended point-wise sensor placement for online long-term monitoring.

Interval Pareto front-based multi-objective robust optimization for sensor placement in structural modal identification

Considering the multi-performance development of complex systems and the requirement of structural modal identification with typical uncertainties, the nominal single-objective optimization method is not suitable for sensor placement. Therefore, by combining conventional optimal sensor placement with non-probabilistic theory, this study proposes an uncertainty-oriented multi-objective robust optimization method for optimal sensor placement. The Fisher information matrix and ill-posedness comprise one eigenvalue-based optimization objective, and the mean and minimum off-diagonal values in the modal assurance criterion comprise another. Considering the high-cost limitation of the statistical method for handling uncertainties, uncertainty propagations are realized by a dimension-wise analysis with better accuracy and efficiency, thus avoiding the overestimation incurred by the classical Taylor expansion method. The multi-objective robust optimization is established by uncertain eigenvalue- and eigenvector-based indices with interval numbers and solved using the multi-objective optimization algorithm. Considering the solution sets located at the Pareto front, an interval possibility was developed using interval Pareto fronts to determine the optimal number of sensors. A numerical example demonstrated the validity of the proposed method with an optimal number of sensors and corresponding configurations.

Optimal sensor placement for leak location in water distribution networks: A feature selection method combined with graph signal processing

Nowadays, real-time monitoring of smart water networks is essentially performed by Supervisory Control and Data Acquisition (SCADA) systems and through the use of sensors strategically positioned in the water distribution network (WDN). The purpose of sensor placement is to reasonably collect signals and thus improve the efficiency of subsequent leak diagnosis, while also limiting their deployment and operational costs. Most current sensor placement methods rely on well-calibrated hydraulic models for node selection and subsequent leak location evaluation. In this study, an efficient Optimal Sensor Placement (OSP) method for WDN is proposed, which avoids the reliance on the hydraulic model in the node selection step. It can be generalized as an optimization process, and the algorithm to solve the problem is a heuristic algorithm. We consider the user nodes in the WDN as features and propose a feature selection algorithm combined with graph signal processing. By this method, the importance of different nodes in the WDN is analyzed and the redundancy between different nodes is considered in the iterative selection process. A graph signal reconstruction method is applied to recover pressure data of all nodes using the data monitored by the selected nodes, and the relationship between the number of sensors and the reconstruction error is analyzed. The proposed method is tested on two benchmark networks of different sizes and types. A comparative analysis with other methods shows that the proposed OSP method can be easily extended to other WDNs. In addition, the proposed method achieves better monitoring results while selecting nodes quickly.

Multiobjective-Based Acoustic Sensor Configuration for Structural Health Monitoring of Compressor Blade

Structural health monitoring (SHM) is essential to maintain the stability and efficiency of compressor. Based on the characteristics of non-destructive evaluation, acoustic sensors are widely utilized for SHM of compressor blades. As the monitoring data of compressor blades is unable to effectively reflect damage under improper sensor configuration, the number and placements of acoustic sensors need to be optimized. In this paper, the optimal sensor placement (OSP) method is presented for multiple acoustic sensors based on the proposed multi-objective optimization (MOO) model and evaluation strategy. Specially, the proposed MOO model is established from five objectives by comprehensively considering the sensor cost and monitoring reliability. It can transform the OSP to the nonlinear mathematical MOO problem. Besides, an evaluation strategy is presented to select optimal solution from Pareto solution set through fully evaluating its performance. Finally, the compressor experiments are implemented to validate the effectiveness of the proposed method. Based on the experimental data collected at the OSP, the proposed method can reach the average accuracy of 97.74% under different working conditions. Through discussing and comparing with other methods, the reliability and superiority of the proposed method are verified for OSP searching and SHM. The results indicate that the proposed method can obtain reliable monitoring information and realize SHM with efficient sensor configuration.

Acoustic Sensor Placement Optimization for Compressor Based on Adversarial Transfer Learning and Vibro-Acoustic Simulation

Generally, the success of optimal sensor placement (OSP) method based on artificial intelligence highly depends on signals at all feasible placements, which may be unavailable or expensive. Therefore, the acoustic sensor placement optimization method is proposed based on adversarial transfer learning (ATL) and vibro-acoustic simulation. First, the vibro-acoustic simulation is applied to provide sufficient simulation signals for all feasible placements. To bridge the deviation of simulation and measured signals, the ATL-based conditional generative adversarial network (CGAN) is presented, which can transfer signals from limited measured placements to unmeasured placements. In addition, a multi objective optimization model is proposed to obtain the OSP from three aspects, and it is useful for structural health monitoring (SHM). The acoustic signals obtained from the experimental platform are utilized to explore the feasibility and effectiveness of the proposed method. It can accurately detect the fault with average accuracy of 98.35% under four working conditions. The comparison investigations demonstrate that the proposed method can obtain high-quality signals at all feasible placements, which can realize SHM with the optimal sensor placements and the least sensor cost.

Performance-based optimal sensor placement method for single-layer reticulated shells considering modal observability and damage identifiability

Structural health monitoring allows for the early detection of structural damage and provide valuable insight into structural performance. However, duo to numerous degrees of freedom and dense vibration modals, designing a sensor placement scheme for Single-Layer Reticulated Shells (SLRSs) is a challenging task. This paper introduces two performance indexes, namely the modal observability and damage identifiability, to quantitatively evaluate the efficiency of the sensor system. Subsequently, based on these indexes, the multi-objective optimization algorithm, as well as the performance-based design concepts, a novel performance-based optimal sensor placement (OSP) method for SLRSs is proposed. Two types of sensor placement performance curves, namely the sensor placement effect curve and the sensor placement proportion curve, are presented to determine the optimal number and placement of sensors in different directions. Numerical examples demonstrate that the proposed method can generate OSP schemes that meet various performance targets, and the performance-based OSP method is superior to the simple multi-objective OSP method. Furthermore, suggestion on selecting the total number of sensors for practical engineering applications is also provided.

A new optimal sensor placement method for virtual sensing of composite laminate

Identifying modal coordinates from output-only data is a key link of virtual sensing technology based on the modal extension method. It is also one of the goals of optimal sensor placement (OSP). Traditional OSP methods are based on the underlying assumption that the estimated values of modal coordinates are unbiased estimates of real values. However, due to uncertainty and the characteristics of an inverse problem, the unbiased estimation obtained from the output-only data may seriously deviate from the true value. This study proposes a new OSP method for composite virtual strain sensing, which can obtain the global unbiased estimation of modal coordinates. First, a Bayesian probabilistic model for virtual sensing considering model uncertainty and measurement error is formulated. Then, the K-L divergence, which measures the reduction in utility by removing sensors from the full configuration, is used to obtain the unbiased estimation of modal parameters. Finally, using the regularization mechanism in the Bayesian method, a new variance determination method is proposed to improve the stability of the solution. Considering both unbiasedness and stability, NSGA-II multi-objective optimization algorithm and two OSP evaluation criteria are used to obtain the final optimal sensor placement. To illustrate the effectiveness of the proposed method, an example involving a laminate plate is considered, accompanied by comprehensive discussions.

A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement.

In recent decades, structural health monitoring (SHM) has gained increased importance for ensuring the sustainability and serviceability of large and complex structures. To design an SHM system that delivers optimal monitoring outcomes, engineers must make decisions on numerous system specifications, including the sensor types, numbers, and placements, as well as data transfer, storage, and data analysis techniques. Optimization algorithms are employed to optimize the system settings, such as the sensor configuration, that significantly impact the quality and information density of the captured data and, hence, the system performance. Optimal sensor placement (OSP) is defined as the placement of sensors that results in the least amount of monitoring cost while meeting predefined performance requirements. An optimization algorithm generally finds the "best available" values of an objective function, given a specific input (or domain). Various optimization algorithms, from random search to heuristic algorithms, have been developed by researchers for different SHM purposes, including OSP. This paper comprehensively reviews the most recent optimization algorithms for SHM and OSP. The article focuses on the following: (I) the definition of SHM and all its components, including sensor systems and damage detection methods, (II) the problem formulation of OSP and all current methods, (III) the introduction of optimization algorithms and their types, and (IV) how various existing optimization methodologies can be applied to SHM systems and OSP methods. Our comprehensive comparative review revealed that applying optimization algorithms in SHM systems, including their use for OSP, to derive an optimal solution, has become increasingly common and has resulted in the development of sophisticated methods tailored to SHM. This article also demonstrates that these sophisticated methods, using artificial intelligence (AI), are highly accurate and fast at solving complex problems.

An Optimal Strain Gauge Layout Design for the Measurement of Truss Structures

Sensor measurements diagnose and evaluate the structural health state. A sensor configuration with a limited number of sensors must be designed to monitor sufficient information about the structural health state. The diagnosis of a truss structure composed of axial members can begin with a measurement by the strain gauges attached to the truss members or by the accelerometers and displacement sensors at the nodes. This study considered the layout design of the displacement sensors at the nodes for the truss structure by using the effective independence (EI) method based on the mode shapes. The validity of the optimal sensor placement (OSP) methods depending on their synthesis with the Guyan method was investigated by the mode shape's data expansion. The Guyan reduction technique rarely affected the final sensor design. A modified EI algorithm based on the strain mode shape of the truss members was presented. A numerical example was analyzed, showing that the sensor placements were affected depending on the displacement sensors and strain gauges. Numerical examples illustrated that the strain-based EI method without the Guyan reduction method has the advantage of reducing the number of sensors and providing more data related with the displacements at the nodes. The measurement sensor should be selected when considering structural behavior, as it is crucial.

Seismic damage identification of moment frames based on random forest algorithm and enhanced gray wolf optimization

SummaryThe present study aims to identify damage in two‐dimensional (2‐D) moment frames using seismic responses by combining the random forest (RF) machine classifier and the enhanced gray wolf optimizer (EGWO) metaheuristic algorithm. First, a 2‐D moment frame for the dynamic analysis is simulated using the finite element method (FEM). Then, the placement of sensors is optimized using a proposed optimal sensor placement (POSP) method, which is a combination of the iterated improved reduced system (IIRS) and the binary differential evolution (BDE) optimization algorithm. The acceleration responses of the moment frame having damaged elements under 1995 Kobe earthquake are measured at the optimal sensor placement. Then, the natural frequencies and mode shapes of the structure are extracted using the auto‐regressive model with exogenous input method (ARX) as a system identification method. The natural frequencies are exploited to train an RF machine learning network that can find the damaged story of the moment frame. Then, EGWO is employed to accurately locate and quantify the damaged elements of the structure. The efficiency of the proposed method is assessed through considering a six‐story frame with 18 elements, a seven‐story frame with 49 elements, and the experimental data of an eight‐story frame for various conditions. The results show that the RF algorithm has an outstanding performance to correctly find a damaged story. Furthermore, the location and severity of damaged elements are precisely determined by EGWO algorithm. As a final outcome, it is demonstrated that the two‐step proposed method is very effective in seismically identifying damage to such structures.

A Novel Non-Probabilistic Sensor Placement Method for Structural Health Monitoring Using an Iterative Multiobjective Optimization Algorithm

A novel non-probabilistic sensor placement method for structural health monitoring is proposed with interval numbers based on the relationship of interval for sensor number (RISEN) index, and an iterative multiobjective optimization algorithm is constituted to optimize sensor placement. To avoid the limitation of scarce statistical information, the interval objectives of effective independence and eigenvalue vector product methods are derived. To overcome the inaccuracy of sensor number decisions using the determinate methods in uncertain cases, the novel RISEN index is defined to ascertain the best sensor number. Considering the number and locations of sensors as two types of design variables, two methods are regarded as optimization objectives, which are composed of the multiobjective optimal sensor placement methods. Based on the modified hypervolume evaluation index, an iterative multiobjective optimization algorithm is investigated using the updating process to improve the efficiency of the sensor placement. The validity of the method is proven using four examples.

Comparative Analysis between Genetic Algorithm and Simulated Annealing-Based Frameworks for Optimal Sensor Placement and Structural Health Monitoring Purposes

The arbitrary placement of sensors in concrete structures measures a considerable amount of unnecessary data. Optimal sensor placement methods are used to provide informative data with the least cost and maximum efficiency. In this study, a robust optimal sensor placement framework that combines an optimization-based algorithm, the simulated annealing (SA) algorithm, and the ensemble Kalman filter (EnKF) are presented for structural health monitoring and system identification. The SA algorithm randomly generates an initial population of sensor locations, while the framework undergoes a minimization process. The objective function used is the difference between the actual measured data and their corresponding EnKF predicted values. A comparative analysis between the genetic algorithm–ensemble Kalman filter (GA-EnKF) and the simulated annealing–ensemble Kalman filter (SA-EnKF) approaches is presented. The performance and computational burden of both algorithms, which converge to the best sensor locations for damage detection purposes, are tested on a 10-story building subjected to a seismic excitation. The results are compared to the optimal sensor locations of the brute-force search methodology. The GA-EnKF outperforms the SA-EnKF in terms of accuracy in converging to the optimal results, yet the computational cost of the SA-EnKF is considerably lower.