Optimal Sensor Placement Strategy Research Articles

Advancements in Optimal Sensor Placement for Enhanced Structural Health Monitoring: Current Insights and Future Prospects

Structural health monitoring (SHM) is critical to maintaining safe and reliable civil infrastructure, but the optimal design of an SHM sensing system, i.e., optimal sensor placement (OSP), remains a complex challenge. Based on the existing literature, this paper presents a comprehensive review of OSP strategies for SHM. It covers the key steps in OSP, from evaluation criteria to efficient optimization algorithms. The evaluation criteria are classified into six groups, while the optimization algorithms are roughly categorized into three classes. The advantages and disadvantages of each group of methods have been summarized, aiming to benefit the OSP strategy selection in future projects. Then, the real-world implementation of OSP on bridges, high-rise buildings, and other engineering structures, is presented. Based on the current progress, the challenges of OSP are recognized; its future development directions are recommended. This study equips researchers/practitioners with an integrated perspective on state-of-the-art OSP. By highlighting key developments, persistent challenges, and prospects, it is expected to bridge the gap between theory and practice.

Methodologies and Challenges for Optimal Sensor Placement in Historical Masonry Buildings

As ageing structures and infrastructures become a global concern, structural health monitoring (SHM) is seen as a crucial tool for their cost-effective maintenance. Promising results obtained for modern and conventional constructions suggested the application of SHM to historical masonry buildings as well. However, this presents peculiar shortcomings and open challenges. One of the most relevant aspects that deserve more research is the optimisation of the sensor placement to tackle well-known issues in ambient vibration testing for such buildings. The present paper focuses on the application of optimal sensor placement (OSP) strategies for dynamic identification in historical masonry buildings. While OSP techniques have been extensively studied in various structural contexts, their application in historical masonry buildings remains relatively limited. This paper discusses the challenges and opportunities of OSP in this specific context, analysing and discussing real-world examples, as well as a numerical benchmark application to illustrate its complexities. This article aims to shed light on the progress and issues associated with OSP in masonry historical buildings, providing a detailed problem formulation, identifying ongoing challenges and presenting promising solutions for future improvements.

Merging experimental design and structural identification around the concept of modified Constitutive Relation Error in low-frequency dynamics for enhanced structural monitoring

This paper presents a novel Optimal Sensor Placement (OSP) strategy that is dedicated to model updating problems based on the modified Constitutive Relation Error (mCRE) functional in low-frequency dynamics. The mCRE is a credible alternative to model updating functionals that stands out by searching structural parameters alongside mechanical fields as the best trade-off between all available information from measured data, without any further a priori assumption. Considering damage detection problems, due to possible discrepancies in terms of parameters sensitivity with respect to mCRE, sensor locations provided by standard OSP algorithms may be irrelevant. The proposed approach uses the concept of Information Entropy by formulating a modified Fisher information matrix, in which the sensitivity of the mCRE mechanical fields with respect to the updated parameters is involved. The approach is legitimated by the strong connection between mCRE and Bayesian inference. A proof-of-concept involving an earthquake engineering inspired academic case study, where accelerometers are positioned on a two-story frame structure subjected to random ground motion, permits to illustrate the soundness and efficiency of the proposed methodology compared to other classical OSP techniques. The influence of critical mCRE parameters is shown, as well as the benefits of taking multiple scenarios into account so as to get an OSP that is relevant for a wider range of possible damage occurrences.

A data-driven sensor placement strategy for reconstruction of mode shapes by using recurrent Gaussian process regression

Current Optimal Sensor Placement (OSP) strategies for bridges mostly rely on data from a finite element model rather than from the real structure due to high cost in placing massive sensors for data collection. For large-scale bridges, however, it is difficult to formulate a precise model and thus the OSP strategies building upon a finite element model inevitably suffer from modelling errors. Besides, the finite element model cannot account for real measurement noise. Premised on the fact that it is not expensive to make in-situ trial measurements with a few sensors on a target bridge before deploying a structural health monitoring (SHM) system on it, a data-driven OSP strategy is proposed in this study which aims at accurately reconstructing mode shapes (to facilitate vibration-based structural damage detection) by using only a few vibration sensors to be included in the SHM system. The proposed OSP strategy is also applicable for the upgrade of a long-term SHM system currently deployed on a bridge, by using historical data collected from the current SHM system. To precisely reconstruct mode shapes, a two-stage OSP strategy in terms of Recurrent Gaussian Process Regression (RGPR) is developed, and its performance is validated on a simulation model and a real bridge. In the first stage, the greedy algorithm is leveraged to temporarily deploy sensors on the structure and train accurate RGPR models using the collected data, which are used to afford spatially complete mode shape data for optimization later. Starting from a few sensors temporarily deployed on the bridge, a one-by-one sensor adding procedure is performed to configure increasing sensors until the target is achieved. In the second stage, Cuckoo Search (CS) algorithm is pursued to obtain the globally optimal sensor placement solution, from which the temporarily deployed sensors can be re-configured to the optimum positions. Both the best sensor quantity and positions are obtained by the proposed OSP strategy.

Optimal Measurement of Drone Swarm in RSS-Based Passive Localization With Region Constraints

Passive geolocation by multiple unmanned aerial vehicles (UAVs) covers a wide range of military and civilian applications including rescue, wild life tracking and electronic warfare. The sensor-target geometry is known to significantly affect the localization precision. The existing optimal sensor placement strategies mainly work on the cases without any constraints on the sensor locations. However, UAVs cannot fly/hover simply in arbitrary region due to realistic constraints, such as the geographical limitations, the security issues, and the max flying speed. In this paper, optimal geometrical configurations of UAVs in received signal strength (RSS)-based localization under region constraints are investigated. Employing the D-optimal criteria, i.e., maximizing the determinant of Fisher information matrix (FIM), such optimal problem is formulated. Based on the rigorous algebra and geometrical derivations, optimal and also closed-form configurations of UAVs under different flying states are proposed. Finally, the effectiveness and practicality of the proposed configurations are demonstrated by simulation examples.

Evaluating the Robustness of Water Quality Sensor Placement Strategies of Water Distribution Systems Considering Possible Sensor Failures and System Changes

An early contamination warning system with deployed water quality sensors is often used to enhance the safety of a water distribution system (WDS). While algorithms have been developed to select an optimal water quality sensor placement strategy (WQSPS) for WDSs, many of them do not account for the influences caused by future uncertainties, such as sensor failures and system changes (e.g., demand variations and configuration/expansion changes in the WDS). To this end, this paper proposes a comprehensive framework to evaluate the robustness of WQSPSs to these possible uncertainties. This is achieved by considering five different performance objectives of WQSPSs as well as possible future demand and typology variations of WDSs under a wide range of sensor failure scenarios. More specifically, an optimization problem is formulated to evaluate the robustness of the WQSPSs, in which an evolutionary-based optimization approach coupled with an efficient data-archive method is used to solve this optimization problem. The framework is demonstrated on two real-world WDSs in China. The results show that: (1) the WQSPS’s robustness can be highly dependent on the performance objectives considered, implying that an appropriate objective needs to be carefully selected for each case driven by practical needs, (2) the WDS’s demand and configuration changes can have a significant influence on the WQSPS’s robustness, in which the solution with more sensors in or close to the affected area is likely to better cope with these system changes, and (3) the proposed framework enables critical sensors to be identified, which can then be targeted for prioritizing maintenance actions.

A Game-Theoretic Framework for Security-Aware Sensor Placement Problem in Networked Control Systems

This article studies the sensor placement problem in a leader–follower networked control system for improving its security against cyber-physical attacks. In a zero-sum game, the attacker selects <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f$</tex-math></inline-formula> nodes of the network to attack, and the detector places <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f$</tex-math></inline-formula> sensors to detect the presence of the attack signals. In our formulation, the attacker’s objective is to have a large impact on a target node in the network while being as little visible as possible to the detector. The detector, however, seeks to maximize the visibility of the attack signals. The effects of the attack signals on both the target node and the detector node are captured via the system <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_2$</tex-math></inline-formula> gain from the attack signals to the target node and deployed sensors’ outputs, respectively. The equilibrium strategy of the game determines the optimal locations of the sensors. The existence of Nash equilibrium for the single-attack single-sensor case is studied when the underlying connectivity graph is a directed or an undirected tree. We show that, under the optimal sensor placement strategy, an undirected topology provides a higher security level for a networked control system compared to its corresponding directed topology. For the multiple-attack multiple-sensor case, we show that the game does not necessarily admit a Nash equilibrium and introduce a Stackelberg game approach, where the detector acts as the leader. Finally, these results are used to study the sensor placement problem in a vehicle platooning application in the presence of bias injectionattacks.

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.

On statistical Multi-Objective optimization of sensor networks and optimal detector derivation for structural health monitoring

Sensor placement and structural health classifiers are fundamental components of Structural Health Monitoring (SHM) systems, as they largely define system detection (or classification) performance. Optimal sensor placement strategies are designed to maximize the ability to detect damage or to minimize lifetime costs, given limited resource availability. However, usually choosing one strategy over the other and non-optimal detector implementation may provide poorly performing solutions in terms of detection performance or total cost, even though both are critical objectives for a cost-effective SHM system implementation.The work proposes a unique and coherent framework for optimal detector and sensing network design for SHM. After an optimal detector is defined based on the Neyman-Pearson likelihood ratio test, classification performance indexes are used in a multi-objective optimization paradigm for optimal sensor placement. Specifically, the optimization considers maximizing the classification performances and, simultaneously, minimizing a measure of total cost or risk in a Bayesian sense.Even though the approach is general for any structure and sensor measurement process, the method is numerically verified with a cracked plate under tension and monitored by measurements of local strain serving as the surrogate SHM system. The results are also validated by comparing the multi-objective optimal design to engineering judgment and single-objective-based solutions in terms of probability of detection and costs. The advantages of an optimization scheme are emphasized with respect to an engineering scheme and, above all, how a multi-objective optimization strategy reflects a conjunct saving in costs and improvement in detection performances.

Advanced optimal sensor placement for Kalman-based multiple-input estimation

The direct measurement of the external loads acting on a mechanical component represents often a challenge in many engineering applications. In this context, the attention of many researchers is focused on the field of inverse load identification. Several techniques are proposed in literature to address this problem by means of experimental methodologies, often coupled with simulation solutions. In this paper, a Kalman-based methodology is considered, which solves the problem of inverse load identification in a predictive manner. The common issue of most of the techniques is the selection of an optimal set of sensors which gives the best load estimation. In the Kalman-filtering framework, an Optimal Sensor Placement (OSP) strategy has been proposed by the authors and it aims to find the best set of sensors in terms of system observability, which is the minimum requirement of a stable estimation. However, this does not guarantee the most accurate load estimation. In this contribution, two alternative metrics are proposed, based on: i) steady-state error covariance of the estimation, ii) estimator bandwidth, with respect to the available set of measurements. Both criteria will be included in the existing OSP to improve the sensors selection. A comparison of the three strategies for multiple input/state estimation is discussed on an industrial-scale Finite Element Model, in order to show the improvement in the accuracy of the estimated quantities.

A multi‐objective genetic algorithm strategy for robust optimal sensor placement

AbstractThe performance of a monitoring system for civil buildings and infrastructures or mechanical systems depends mainly on the position of the deployed sensors. At the current state, this arrangement is chosen through optimal sensor placement (OSP) techniques that consider only the initial conditions of the structure. The effects of the potential damage are usually completely neglected during its design. Consequently, this sensor pattern is not guaranteed to remain optimal during the whole lifetime of the structure, especially for complex masonry buildings in high seismic hazard zones. In this paper, a novel approach based on multi‐objective optimization (MO) and genetic algorithms (GAs) is proposed for a damage scenario driven OSP strategy. The aim is to improve the robustness of the sensor configuration for damage detection after a potentially catastrophic event. The performance of this strategy is tested on the case study of the bell tower of the Santa Maria and San Giovenale Cathedral in Fossano (Italy) and compared to other classic OSP strategies and a standard GA approach with a single objective function.

Deep neural network-based strategy for optimal sensor placement in data assimilation of turbulent flow

This paper focuses on the optimal sensor placement (OSP) strategy based on a deep neural network (DNN) for turbulent flow recovery within the data assimilation framework of the ensemble Kalman filter (EnKF). The assimilated flow field can be obtained using EnKF by optimizing the Reynolds-averaged Navier–Stokes (RANS) model constants. A feature importance layer was designed and used in a DNN to obtain the spatial sensitivity with respect to the RANS model constants. Two flow configurations experimentally measured using particle image velocimetry—i.e., a free round jet flow at Rej=6000 and a separated and reattached flow around a blunt plate at Reb=15 800—were selected as the benchmarks to demonstrate the effectiveness and robustness of the proposed strategy. The results indicated that the RANS models with EnKF augmentation were substantially improved over their original counterparts. A comprehensive investigation demonstrated that the selection of the five most sensitive sensors by DNN-based OSP can efficiently reduce the number of sensors and achieve a similar or better-assimilated performance over that obtained using all data in the entire flow field as observations.

Optimal Sensor Placement for Target Localization Using Hybrid RSS, AOA and TOA Measurements

This letter investigates the optimal sensor placement strategy for single static target localization using the hybrid received-signal-strength (RSS), angle-of-arrival (AOA) and time-of-arrival (TOA) measurements on the 2-dimensional (2D) plane. Firstly, the problem formulation is introduced. Secondly, the theoretical smallest trace of the Cramer-Rao lower bound (CRLB), which is equivalent to the smallest estimation mean-squared-error (MSE), is derived using the A-optimality criterion. Besides, we propose that the reachable smallest trace of the CRLB (tr(CRLB)) will be determined, once the number and characters of the sensors are selected. Thirdly, the corresponding optimal sensor placement strategies are proposed and concluded in two observations. Finally, the findings are demonstrated by simulation examples.

An optimal sensor placement strategy for reliable expansion of mode shapes under measurement noise and modelling error

Modal expansion techniques are typically used to expand the experimental modal displacements at sensor positions to all unmeasured degrees of freedom. Since in most cases, sensors can be attached only at limited locations in a structure, an expansion is essential to determine mode shapes, strains, stresses, etc. throughout the structure which can be used for structural health monitoring. Conventional sensor placement algorithms are mostly aimed to make the modal displacements at sensor positions of different modes as linearly independent as possible. However, under the presence of modelling errors and measurement noise, an optimal location based on this criterion is not guaranteed to provide an expanded mode shape which is close to the real mode shape. In this work, the expected value of normal distance between the real mode shape and the expanded mode shape is used as a measure of closeness between the two entities. Optimal sensor locations can be determined by minimizing this distance. This new criterion is applied on a simple cantilever beam and an industrial milling tower. In both cases, by using an exhaustive search of all possible sensor configurations it was possible to find sensor locations which resulted in a significant reduction in the distance when compared to a conventional optimal sensor placement strategy. Sufficiently accurate sub-optimal sequential sensor placement algorithm is also suggested as an alternative to the exhaustive search which is then compared with a genetic algorithm-based search. The efficiency of this new sensor placement criterion is further verified using Monte Carlo simulations for some realistic modelling error conditions.

Two-Stage Structural Damage Assessment by Combining Modal Kinetic Energy Change with Symbiotic Organisms Search

In the literature, modal kinetic energy (MKE) has been commonly utilized for optimal sensor placement strategies. However, there have been very few studies on its application to structural damage detection. This paper introduces a new two-stage structural damage assessment method by combining the modal kinetic energy change ratio (MKECR) and symbiotic organisms search (SOS) algorithm. In the first stage, an efficient damage indicator, named MKECR, is used to locate the potential damaged sites. Meanwhile, for the purpose of comparison with MKECR, three other indices are also used. In the second stage, an SOS-based finite element (FE) model updating strategy is adopted to estimate the damage magnitude of identified sites, while excluding false warnings (if any), where an objective function is proposed using a combination of the flexibility matrix and modal assurance criterion (MAC). The performance of the SOS algorithm is also verified by comparing with four other meta-heuristic algorithms. Finally, three numerical examples of 2D truss and frame structures with various hypothetical damage scenarios are carried out to investigate the capability of the proposed method. The numerical results indicate that the proposed method not only can accurately locate and quantify single- and multi-damage in the structures, but also shows a great saving in computational cost.

Optimal Sensor Placement for 3-D Time-of-Arrival Target Localization

This paper focuses on finding the optimal sensor placement strategies for circular time-of-arrival (TOA) localization in the three-dimensional (3D) space. The A-optimality criterion, minimizing the trace of the inverse Fisher information matrix (FIM), is applied to determine optimal sensor placements under the Gaussian measurement noise. A comprehensive analysis of optimal sensor-target geometries is provided in the general circumstance with no restriction on the number of sensors, sensor elevation angle and sensor-target range. The analysis is divided into two detailed sub-cases with uniform sensor measurement noise variance. The reachable minimum trace of Cramer-Rao lower bound (CRLB) $=\frac{9\sigma ^2}{4N}$ is derived. Two new closed-form solutions, i.e., the resistor network and special solution methods, are developed to quickly determine the optimal geometries. Furthermore, the theoretical smallest tr(CRLB) $=\frac{9}{4} (\sum _{i=1}^N\frac{1}{\sigma _{i}^{2}})^{-1}$ of using different noise variances is also presented. The analytical results are verified by simulation examples.

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

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.

Optimal Sensor-Target Geometries for 3-D Static Target Localization Using Received-Signal-Strength Measurements

This letter investigates how to place the received-signal-strength (RSS) sensors to improve the static target localization accuracy in the three-dimensional (3-D) space. By using the A-optimality criterion, i.e., minimizing the trace of the inverse Fisher information matrix (FIM), a new optimal RSS sensor placement strategy is developed when sensors can be placed freely in the 3-D space. The smallest reachable trace of Cramer–Rao lower bound, i.e., the inverse FIM, is derived with the corresponding optimal sensor-target geometries. Besides, a resistor network method and a special configuration strategy are proposed to quickly determine the optimal geometries. The findings are concluded in three remarks, which are used to evaluate and improve the estimation accuracy. Simulation examples verified these findings.

Kalman-based load identification and full-field estimation analysis on industrial test case

Abstract The potential of the Augmented Kalman Filter algorithm is tested in this paper for joint state-input estimation in structural dynamics field. In view of inverse load identification, the filter is compared with the Transfer Path Analysis Matrix Inversion technique, commonly used for industrial applications. An existing Optimal Sensor Placement strategy for Kalman Filter is adopted and validated on real experimental data. The advantages of the proposed methods, through strain measurements information, are identified in the effort needed for data-acquisition and data-processing. The effectiveness of the filter and the quality of the results are demonstrated in this paper for an industrial test-case, such as a rear twistbeam suspension.

Cable force monitoring and prediction for cable group of long-span cable-supported bridges

Cable force monitoring is an essential and critical part of structural health monitoring for long-span cable-supported bridges. Considering economical and efficient issues, the accuracy and quality of safety assessment depend considerably on a reasonable cable-monitoring scheme, especially the number and locations of limited sensors. This paper presents the optimal sensor placement for cable force monitoring and cable force prediction in non-sensor positions with optimal sensor arrangement. Bond-energy algorithm was used to obtain optimal sensor placement strategy, where mutual information was employed to describe the inherent spatial correlation of cable group. To maximize useful cable force information of cable group utilizing from optimal sensor arrangement, particle-swarm optimization-based Kernel Extreme Learning Machine model was employed for forecasting cable forces in non-sensor positions. The analysis results illustrated that the proposed kernel extreme learning machine can achieve better predictive performance than multiple linear regression model and multiple adaptive spline regression model with higher accuracy and generalization. The cable force monitoring and prediction with notable decrease of sensor number lays a comprehensive basis for bridge safety assessment and verified the effectiveness of the proposed method.