Sensor Placement Method Research Articles

Multi-objective and risk-based optimal sensor placement for leak detection in a water distribution system

The optimal sensor placement for leak detection in a water supply network has been studied extensively. The previous studies usually assume that each node of the water distribution network has the same importance. However, this assumption does not consider the difference in the impact when a leak occurs at the different nodes on the water distribution network. When the number of sensors is limited, the detection of only leakage events that can cause serious consequences is usually prioritized. This study proposes a multi-objective optimization method for sensor placement while taking into consideration the differences in the risk of leakage for the different nodes. First, five types of risk-based leakage functions are obtained based on the impact on the water distribution network when a leakage occurs at each node. The pressure at the node drops, which causes the water demand and pipe pressure to decrease while the flow rate increases. The multi-objective optimization method is then used to obtain the Pareto front according to the various risk-based leakage functions. Finally, the multi-criteria decision analysis method is used to rank and cluster the Pareto fronts, the optimal solution for each cluster is obtained, and these solutions are compared and analyzed. This study contains a case study that is based on the example water distribution network model C-town. When the number of sensors is limited, a more reasonable optimal sensor placement scheme can be obtained by considering the different risk-based leakage functions of the nodes, with a smaller impact on the water distribution network when a leakage occurs. • A multi-objective optimization sensor placement for leak detection in water distribution system. • Five types of risk-based leakage functions are obtained based on the impact of each leakage. • The impacts of the leakage occurring at each node of the pipe network are compared.

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.

Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems: A New Approach Using Secants

Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable solution of an inverse problem. Most real-world systems of interest are nonlinear, yet the majority of available techniques for feature selection and sensor placement rely on assumptions of linearity or simple statistical models. We show that when these assumptions are violated, standard techniques can lead to costly over-sensing without guaranteeing that the desired information can be recovered from the measurements. In order to remedy these problems, we introduce a novel data-driven approach for sensor placement and feature selection for a general type of nonlinear inverse problem based on the information contained in secant vectors between data points. Using the secant-based approach, we develop three efficient greedy algorithms that each provide different types of robust, near-minimal reconstruction guarantees. We demonstrate them on two problems where linear techniques consistently fail: sensor placement to reconstruct a fluid flow formed by a complicated shock–mixing layer interaction and selecting fundamental manifold learning coordinates on a torus.

A multi-objective optimization strategy of load-dependent sensor number determination and placement for on-orbit modal identification

A load-dependent sensor placement method comprised of the estimated error of modal coordinates and redundancy elimination model of sensor distribution was developed for on-orbit modal identification. The first optimization objective was the selection of the optimum matching level of the full model according to the estimated error between the sub-modal coordinates obtained by sensor placement and the full case. A redundancy elimination was designed based on the distance and distribution of each sensor, as well as the effect of load position distance, which can overcome the dense distribution of sensors and interference caused by placing sensors near the loading. A multi-objective optimization strategy was proposed to determine the optimum number of sensors and corresponding positions based on the interval possibility. This method was applied to a solar-powered satellite for modal identification to monitor the load case of docking during the process of on-orbit service.

Time-varying frequency parameter identification of space solar power satellites based on an improved recursive subspace algorithm and optimal sensor placement

This study focuses on the time-varying modal frequency identification of space solar power satellites. Accordingly, an improved recursive subspace identification algorithm based on the variable forgetting factor is proposed to enhance the tracking adaptability of the original method in time-varying systems. Considering the changes in the structural configuration induced by the rotation of the solar concentrator mirror, a time-varying attitude-vibration coupling dynamic model of a space solar power satellite with an integrated symmetrical concentrator configuration is developed based on the modal synthesis technology and the substructure method. Moreover, based on the projection subspace theory, the time-varying forgetting factor is determined by minimizing the mean square deviation of the system estimator. Subsequently, the variable forgetting factor subspace algorithm is adopted to recursively identify the time-varying pseudo modal frequency parameters. A finite element model of the space solar power satellite is established via numerical simulations, and several optimal sensor placement methods are applied to determine the positions of the vibration sensors. Based on the output signals obtained from the optimal sensor placement results, the time-varying frequency parameters of the system are obtained using the proposed algorithm. The computational results reveal that a decrease in the average relative error by 4.2% compared with that obtained via the conventional recursive subspace method is observed when the signal-to-noise-ratio of the measured output is selected as 15 dB. In addition, the results also reveal that an average relative error reduction of approximately 0.4%–1.4%, over two other methods with a fixed forgetting factor, can be achieved using the proposed algorithm when the rotation speed of the solar concentrator mirror is increased. The findings of this study confirm that the proposed algorithm demonstrates a high noise-immune ability and tracking performance for fast time-varying systems.

Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory

This paper presents an optimal sensor placement method for vibration signal acquisition in the field of industrial robot health monitoring and fault diagnosis. Based on the general formula of Bayes and relative entropy, the evaluation function of sensor placement is deduced, and the modal confidence matrix is used to express the redundancy of sensor placement. The optimal placement of vibration sensors is described as a discrete variable optimization problem, which is defined as whether the existing sensor layout can obtain joint state information efficiently. The initial layout of the sensor was obtained from the structural simulation results of the industrial robots, and the initial layout was optimized by the derived objective function. The efficiency of the optimized layout in capturing joint state information is proven by the validation experiment with a simulation model. The problem of popularizing the optimization method in engineering is solved by a verification experiment without a simulation model. The optimal sensor placement method provides a theoretical basis for industrial robots to acquire vibration data effectively.

Robustness of Optimal Sensor Methods in Dynamic Testing–Comparison and Implementation on a Footbridge

One of the objectives of structural health monitoring (SHM) is to maximize the information while keeping the number of sensors, and consequently the cost of the sensor system, to a minimum. Besides, the sensor configurations must be robust in the sense that the feasibility of small errors inherent to the process must not lead to large variations in the final results. This paper presents novelties regarding the robustness evaluation to model and measurement errors of four of the most influential optimal sensor placement (OSP) methods: the modal kinetic energy (MKE) method; the effective independence (EFI) method; the information entropy index (IEI) method; and the MinMAC method. The four OSP methods were implemented on the Streicker Bridge, a footbridge located on the Princeton University Campus, to identify five mode shapes of the bridge. The mode shapes, obtained in a FE model’s modal analysis, were used as input data for the OSP analyses. The study indicates that the MKE method seems to be the most suitable method to estimate the optimal sensor positions: it provides a relatively large amount of information with the lowest computational time, and it outperforms the other three methods in terms of robustness in the usual range of number of sensors.

Optimal Sensor Placement for Modal-Based Health Monitoring of a Composite Structure.

Optimal sensor placement is one of the important issues in monitoring the condition of structures, which has a major influence on monitoring system performance and cost. Due to this, it is still an open problem to find a compromise between these two parameters. In this study, the problem of optimal sensor placement was investigated for a composite plate with simulated internal damage. To solve this problem, different sensor placement methods with different constraint variants were applied. The advantage of the proposed approach is that information for sensor placement was used only from the structure’s healthy state. The results of the calculations according to sensor placement methods were subsets of possible sensor network candidates, which were evaluated using the aggregation of different metrics. The evaluation of selected sensor networks was performed and validated using machine learning techniques and visualized appropriately. Using the proposed approach, it was possible to precisely detect damage based on a limited number of strain sensors and mode shapes taken into consideration, which leads to efficient structural health monitoring with resource savings both in costs and computational time and complexity.

Optimal Number and Location of Sensors for Structural Damage Detection using the Theory of Geometrical Viewpoint and Parameter Subset Selection Method

The recorded responses at predefined sensor placements are used as input to solve an inverse structural damage detection problem. The error rate that noise causes from the recorded responses of the sensors is a significant issue in damage detection methods. Therefore, an optimal number and location of sensors is a goal to achieve the lowest error rate in structural damage detection. To overcome this problem, an algorithm (GVPSS) based on a Geometrical Viewpoint (GV) of optimal sensor placement and Parameter Subset Selection (PSS) method is proposed. The goal of the GVPSS algorithm is to minimize the effect of noise on damage detection problem. Therefore, the fitness function based on error in damage detection is minimized by GVPSS. In this method, the degrees of freedom are arranged to place sensors using a fitness function based on GV theory. Then, the optimal number and location of sensors are found on these arranged the degrees of freedom using the objective function. The efficiency of the proposed method is studied in a 52-bar dome structure under static and dynamic loadings. In the examples, damages are detected in two states: 1) using responses recorded at all DOFs, 2) using responses recorded at the optimal number and location of sensors obtained by GVPSS. The results showed that the damage detection error in state 2 is approximately equal to the error in state 1. Therefore, the GVPSS have the high performance to find the optimal number and location of sensors for structural damage detection.

A method for quantitative damage identification in a high-piled wharf based on modal strain energy residual variability

Damage may occur in the pile foundations of high-pile wharfs due to the complex and diverse working conditions. To identify the damage in pile foundations in early stage is very important for the operation and maintenance on wharfs. Research on pile damage identification based on modal strain energy is one of the hot research topics. This study presents the concept of the modal strain energy residual variability using the characteristics of sensor placement and pile mode shapes of high-pile wharfs, which provide a simple, accurate and practical method to identify the damage in pile foundations of high-pile wharfs in early stage. The qualitative and quantitative relationships between the modal strain energy residual variability and element damage extent are deduced. This concept not only enhances the sensitivity of the modal strain energy to damage but also realizes the decoupling of damage element identification, which is easy to calculate in practical engineering. A damage identification method is constructed base on the concept, and the accuracy of the method is verified by a finite element numerical simulation and model test. A sensor placement method for engineering detection is studied by comparing the damage identification effect in different sampling intervals. The results show that this method can accurately locate a damage area and accurately identify the damage extent in numerical simulation and model test, which provides a new method for the practice of pile foundation damage identification of high-pile wharfs.

A novel two-step strategy of non-probabilistic multi-objective optimization for load-dependent sensor placement with interval uncertainties

Conventional optimal sensor placement methods use structural dynamic characteristics such as mode shapes to determine sampling positions for extracting information. However, these approaches have not considered actual load cases or structural responses. Relevant mode shapes in the responses are important for sensor configurations and damage detection. Because the sensor layouts under specific load cases and free vibrations are completely different from them in free vibration, using current sensor placement theories may lead to errors or even failure. In studies that consider both the dynamic characteristics and load cases, a novel uncertain load-dependent sensor placement method is developed using the non-probabilistic theory for response reconstruction, which has a two-step strategy. Based on the unbiased estimate of modal coordinates with a reduced and full model in the deterministic case, this study treats uncertainties as interval numbers, and the propagation of uncertain modal coordinates is proposed based on non-probabilistic theory. Provided uncertain but bounded responses are obtained, the uncertain modal coordinates are calculated easily without requiring the complex process of uncertainty quantification using statistical methods. Furthermore, a two-step strategy is used to select the optimum displacement sensor configurations. The non-probabilistic multi-objective optimization consists of deterministic and uncertain parts that can be solved using NSGA-II (Non-dominated Sorting Genetic Algorithm II) to obtain the preliminary Pareto front in the first step. For conveniently determining the final sensor configuration from a large number of candidate solutions located at the Pareto front, a novel interval time series model is constituted based on the ratio of reduced and full intervals. Therefore, the obtained solutions can be applied to reconstruct responses of the full structures from the deterministic and uncertain parts simultaneously. Two engineering examples are applied to verify the effectiveness and accuracy of the proposed method, accompanied by comprehensive discussions.

Optimal sensor placement method for wastewater treatment plants based on discrete multi-objective state transition algorithm

Parameters monitoring is essential to maintain the stability and efficiency of the wastewater treatment process, which has spurred ubiquitous installation of sensors in wastewater treatment plants (WWTPs). As the rich process data of WWTPs is not effectively transformed into actionable knowledge for system optimization due to improper sensor installation, the sensor placement scheme needs to be optimized. In this paper, a weighted sensor placement optimization model based on sensor cost, information richness and reliability is established to transform the sensor optimization problem to a nonlinear mathematical programming problem. Then a discrete multi-objective state transition algorithm is proposed to find the Pareto optimal solutions. Finally, an evaluation strategy is designed to select the most suitable solution for industrial application. The results of simulation experiments on three different WWTPs demonstrate the validity and superiority of the proposed method, increasing the degree of variable observability and measurement redundancy while keeping the sensor cost at a low level.

Pressure Sensor Placement for Leak Localization in Water Distribution Networks Using Information Theory.

This paper presents a method for optimal pressure sensor placement in water distribution networks using information theory. The criterion for selecting the network nodes where to place the pressure sensors was that they provide the most useful information for locating leaks in the network. Considering that the node pressures measured by the sensors can be correlated (mutual information), a subset of sensor nodes in the network was chosen. The relevance of information was maximized, and information redundancy was minimized simultaneously. The selection of the nodes where to place the sensors was performed on datasets of pressure changes caused by multiple leak scenarios, which were synthetically generated by simulation using the EPANET software application. In order to select the optimal subset of nodes, the candidate nodes were ranked using a heuristic algorithm with quadratic computational cost, which made it time-efficient compared to other sensor placement algorithms. The sensor placement algorithm was implemented in MATLAB and tested on the Hanoi network. It was verified by exhaustive analysis that the selected nodes were the best combination to place the sensors and detect leaks.

Pressure Sensor Placement in Water Supply Network Based on Graph Neural Network Clustering Method

Pressure sensor placement is critical to system safety and operation optimization of water supply networks (WSNs). The majority of existing studies focuses on sensitivity or burst identification ability of monitoring systems based on certain specific operating conditions of WSNs, while nodal connectivity or long-term hydraulic fluctuation is not fully considered and analyzed. A new method of pressure sensor placement is proposed in this paper based on Graph Neural Networks. The method mainly consists of two steps: monitoring partition establishment and sensor placement. (1) Structural Deep Clustering Network algorithm is used for clustering analysis with the integration of complicated topological and hydraulic characteristics, and a WSN is divided into several monitoring partitions. (2) Then, sensor placement is carried out based on burst identification analysis, a quantitative metric named “indicator tensor” is developed to calculate hydraulic characteristics in time series, and the node with the maximum average partition perception rate is selected as the sensor in each monitoring partition. The results showed that the proposed method achieved a better monitoring scheme with more balanced distribution of sensors and higher coverage rate for pipe burst detection. This paper offers a new robust framework, which can be easily applied in the decision-making process of monitoring system establishment.

Region-Restricted Sensor Placement Based on Gaussian Process for Sound Field Estimation

Sensor placement methods for field estimation based on Gaussian processes are proposed. Generally, sensor placement methods determine the appropriate placement positions by selecting them from predefined candidate positions. Many criteria for the selection have been proposed, with which the quality of the placements is evaluated with regard to the field at the candidate positions. This means that these sensor placement methods seek to find the positions that can estimate the field at the candidate positions accurately. In practical situations, however, the candidate sensor placement region can be different from the target region for field estimation. In this paper, to make sensor placement methods applicable to this situation, we propose two sensor placement methods based on the mean squared error and on conditional entropy that can be applied to cases in which the sensor placement region is arbitrarily restricted. After formulating the sensor placement problems, two approximate algorithms are derived: the greedy algorithm and the convex-relaxation-based algorithm. The application of the proposed methods to sound field estimation is also illustrated, and their effectiveness was confirmed through numerical experiments.

A new method for optimal sensor placement considering multiple factors and its application to deepwater riser monitoring systems

Various optimal sensor placement (OSP) methods have been developed and widely used in structural health monitoring (SHM). Among them, the effective independence-energy (EI-energy) methods integrating modal observability and system energy, have been attracting growing interest nowadays. However, the EI-energy techniques normally focus on a single energy factor, lacking consideration of the combined effects of multiple energy factors, especially for the large-scale structure with severe vibration and large deformation. To overcome this limitation, a novel multi-factor OSP strategy, namely effective independence-acceleration amplitude-total displacement (EI-AA-TD), is proposed in this study. This new method combines two typical energy indexes, kinetic energy and strain energy, into the classic EI method. The contribution matrixes associated with these two energy indexes are emphatically discussed. Then, the resulting contribution matrixes from energy perspective, and the EI coefficient vector from modal observability perspective are integrated together to formulate a multi-factor optimization framework for sensor placement. Furthermore, a comprehensive scoring evaluation technique is proposed to assess the quality of sensor layout. Finally, the proposed OSP method and evaluation approach are validated through a study case of deepwater riser monitoring systems. The proposed EI-AA-TD method gets an excellent score of 47 (total 50) with the comprehensive scoring evaluation technique. The related results illustrate the effectiveness and superiorities of the proposed methods.

Optimal Sensor Placement for Estimation of Center of Plantar Pressure Based on the Improved Genetic Algorithms

Plantar pressure analysis can be used for clinical diagnosis, exercise guidance and daily monitoring. In actual use, the CoP trajectory is an important parameter for dynamic analysis, which is generally obtained with an in-shoe system in outdoor and daily monitoring. Therefore, it is a critical issue to design the sensor placement to obtain accurate CoP estimation in a low-cost sensing insole. In this paper, a new sensor placement method, an improved genetic algorithm, was proposed, driven by a large amount of plantar pressure distribution data, with the objectives of reducing the trajectory estimation error and increasing the amount of information, and abstract the placement problem as a combinatorial optimization problem under multiple objectives. Through optimization iterations, a set of optimized sensor placements are determined and applied to practical use. Six subjects wore the optimal placement insoles and the mean absolute error was 3.81 mm (medial-lateral direction) and 8.61 mm (anterior-posterior direction) for comparison with the CoP trajectory provided by the measurement platform. Compared with previous results, the method proposed in this paper provides a more accurate CoP estimation with a 9.7% improvement. This study provides new guidelines for the selection of plantar pressure sensor placements and incorporates intelligent optimization algorithms into new ways to improve the accuracy of wearable device analysis.

Pareto-Based Bi-Objective Optimization Method of Sensor Placement in Structural Health Monitoring

For a practical structural health monitoring (SHM) system, the traditional single objective methods for optimal sensor placement (OSP) cannot always obtain the optimal result of sensor deployment without sacrificing other targets, which creates obstacles to the efficient use of the sensors. This study mainly focuses on establishing a bi-objective optimization method to select the sensor placement positions. The practical significance of several single-objective criteria for OSP is firstly discussed, based on which a novel bi-objective optimization method is proposed based on the Pareto optimization process, and the corresponding objective functions are established. Furthermore, the non-dominated sorting genetic algorithm is introduced to obtain a series of the Pareto optimal solutions, from which the final solution can be determined based on a new defined membership degree index. Finally, a numerical example of a plane truss is applied to illustrate the proposed method. The Pareto optimization-based bi-objective OSP framework presented in this study could be well suited for solving the problem of multi-objective OSP, which can effectively improve the efficiency of the limited sensors in SHM system.

Multi-objective optimization for sensor placement: An integrated combinatorial approach with reduced order model and Gaussian process

We develop a novel sensor placement method that maximizes monitoring performance while minimizing deployment cost. Our method integrates a reduced order model and multi-objective combinatorial optimization. We first decompose the spatio-temporal state field to be monitored by proper orthogonal decomposition (POD), and we use the Gaussian Process to model the uncertainty in each POD mode. Next, we develop a lazy greedy (LG)-∊-constraint optimization to derive the Pareto-optimal sensor configurations. We further design a branch and bound algorithm to calculate the global optimum and validate the correctness of select configurations on the LG-derived Pareto frontier. We evaluate and benchmark our algorithm in computational experiments based on the temperature dataset of the Berkeley Intel Lab. The computational results demonstrate that our algorithm places sensors at locations of large magnitude in the POD modes, and that our method achieves better state estimation accuracy and smaller reconstruction errors compared with alternative methods.

Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors.

Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show that under the A-optimality criterion, the optimization problem can be transferred to be a diagonalizing process on the AOA-based Fisher information matrix (FIM). Secondly, we prove that the FIM follows the invariance property of the 3D rotation, and the Gaussian covariance matrix of the FIM can be diagonalized via 3D rotation. Based on this finding, an optimal sensor placement method using 3D rotation was created for when prior information exists as to the target location. Finally, several simulations were carried out to demonstrate the effectiveness of the proposed method. Compared with the existing methods, the mean squared error (MSE) of the maximum a posteriori (MAP) estimation using the proposed method is lower by at least when the number of sensors is between 3 and 6, while the estimation bias remains very close to zero (smaller than 0.15 m).