Optimal Sensor Placement Problem Research Articles

A Study of Sensor Placement Optimization Problem for Guided Wave-Based Damage Detection.

Guided waves (GW) allow fast inspection of a large area and hence have attracted research interest from the structural health monitoring (SHM) community. Thus, GW-based SHM is ideal for thin structures such as plates, pipes, etc., and is finding applications in several fields like aerospace, automotive, wind energy, etc. The GW propagate along the surface of the sample and get reflected from discontinuities in the structure in the form of boundaries and damage. Through proper signal processing of the reflected waves based on their time of arrival, the damage can be detected and isolated. For complex structures, a higher number of sensors may be required, which increases the cost of the equipment, as well as the mass. Thus, there is an effort to reduce the number of sensors without compromising the quality of the monitoring achieved. It is of utmost importance that the entire structure can be investigated. Hence, it is necessary to optimize the locations of the sensors in order to maximize the coverage while limiting the number of sensors used. A genetic algorithm (GA)-based optimization strategy was proposed by the authors for use in a simple aluminum plate. This paper extends the optimization methodology for other shape plates and presents experimental, analytical, and numerical studies. The sensitivity studies have been carried out by changing the relative weights of the application demands and presented in the form of a Pareto front. The Pareto front allows comparison of the relative importance of the different application demands, and an appropriate choice can be made based on the information provided.

Greedy Sensor Placement With Cost Constraints

The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments. We consider a relaxation of the full optimization formulation of this problem and then extend a well-established greedy algorithm for the optimal sensor placement problem without cost constraints. We demonstrate the effectiveness of this algorithm on the datasets related to facial recognition, climate science, and fluid mechanics. This algorithm is scalable and often identifies sparse sensors with near-optimal reconstruction performance, while dramatically reducing the overall cost of the sensors. We find that the cost-error landscape varies by application, with intuitive connections to the underlying physics. In addition, we include experiments for various pre-processing techniques and find that a popular technique based on the singular value decomposition is often suboptimal.

Optimal sensor placement based on relaxation sequential algorithm

Aiming at the large tension of the solution obtained by sequential algorithm for optimal sensor placement problem, a novel relaxation sequential algorithm is proposed by introducing the idea of edge relaxation operation of Dijkstra’s algorithm into sequential algorithm. An initial solution set is generated by sequential algorithm, and improved by relaxation till the relaxation operation terminates. The proposed algorithm takes modal assurance criterion (MAC) matrix as the objective fitness function. A truss structure and a rigid-framed arch bridge are applied as examples to verify the effectiveness of the new algorithm for optimal sensor placement. The result indicates that the relaxation sequential algorithm requires fewer sensors and can reach better maximum off-diagonal element of MAC matrix in OSP problem.

Optimal Citizen-Centric Sensor Placement for Air Quality Monitoring: A Case Study of City of Cambridge, the United Kingdom

Air quality monitoring plays an increasingly important role in providing accurate air pollution data for assessing the impacts of air pollution on public health. Development of proper sensor networks, by deploying the right air pollution sensors at the right place, in order to meet the needs of different groups in the city and provide the much needed public services, deserves careful attention, especially when smart city development is being considered. However, air quality monitoring can be a costly measure. To tackle such a challenge, air pollution sensor placement can be carefully designed to achieve certain optimal citizen-centric objectives in the absence of field information, which can be formulated as an optimal sensor placement problem. In this paper, we propose three citizen-centric objectives for the optimal sensor placement problem, which does not require the prior deployment of pollution sensors for obtaining any field information. By citizen-centric, we mean that sensor placement puts the citizens' welfare at the center of attention and be able to fulfill the following objectives: 1) better assessing the vulnerable people's exposure to air pollution; 2) maximizing overall satisfaction of obtaining public information on existing air quality; and 3) better monitoring traffic emissions. We formulate the optimization problem for each scenario and propose an effective method to solve the problem accordingly. Last but not least, we conduct a case study in the city of Cambridge to evaluate the feasibility and effectiveness of our proposed methods. Our case study has shown that in order to optimize our citizen-centric objectives, there is a need to re-orient the current sensor placement strategies in the city of Cambridge, U.K.

Comparison of model order reduction methods for optimal sensor placement for thermo-elastic models

ABSTRACTIn this article an optimal sensor placement problem for a thermo-elastic solid body model is considered. Temperature sensors are placed in a near-optimal way so that their measurements allow an accurate prediction of the thermally induced displacement of a point of interest (POI). Low-dimensional approximations of the transient thermal field are used which allows for efficient calculations. Four model order reduction (MOR) methods are applied and subsequently compared with respect to the accuracy of the estimated POI displacement and the location of the sensors obtained.

Multiple underwater target positioning with optimally placed acoustic surface sensor networks

In an increasing number of scientific and commercial mission scenarios at sea, it is required to simultaneously localize a group of underwater targets. The latter may include moored systems, autonomous vehicles, and even human divers. For reasons that have to do with the unavailability of Global Positioning System underwater, cost reduction, and simplicity of operation, there is currently a surge of interest in the development of range-based multiple target localization systems that rely on the computation of the distances between the targets and a number of sensor nodes deployed at the ocean surface, equipped with acoustic range measuring devices. In the case of a single target, there is a wealth of literature on the problem of optimal acoustic sensor placement to maximize the information available for target localization using trilateration methods. In the case of multiple targets, however, the literature is scarce. Motivated by these considerations, we address the problem of optimal sensor placement for multiple underwater target positioning. In this setup, we are naturally led to a multiple objective optimization problem, the solution of which allows for the analysis of the trade-offs involved in the localization of the targets simultaneously. To this end, we resort to tools from estimation theory and multi-objective optimization. For each target, the function to be minimized (by proper choice of the sensor configuration) is related to the determinant of the corresponding Fisher information matrix, which yields information on the minimum possible covariance of the error with which the position of the target can be estimated using any non-biased estimator. To deal with the fact that more than one target is involved, we exploit the concept of multiple objective Pareto-optimal solutions to characterize the best possible accuracy with which each of the targets can be positioned, given constraints on the desired positioning accuracy of the other targets. Simulation examples illustrate how, for a three-sensor network and two targets, it is possible to define an optimal sensor configuration that yields large positioning accuracy for both targets simultaneously, using convex optimization tools. When more than two targets are involved, however, more than three sensors are required to exploit an adequate trade-off of the accuracy with which each target can be positioned by resorting to non-convex and Pareto-optimization tools. We show how in this case the optimal sensor configurations depend on the Pareto weights assigned to each of the targets, as well as on the number of sensors, the number of targets, and the uncertainty with which the positions of the targets are known a priori.

Compressed sensing based optimal sensor placement for leak localization in water distribution networks

Abstract The performance of model-based leak detection and localization techniques heavily depends on the configuration of a limited number of sensors. This paper presents a sensor placement optimization strategy that guarantees sufficient diagnosability while satisfying the budget constraint. Based on the theory of compressed sensing, the leak localization problem could be transformed into acquiring the sparse leak-induced demands from the available measurements, and the average mutual coherence is devised as a diagnosability criterion for evaluating whether the measurements contain enough information for identifying the potential leaks. The optimal sensor placement problem is then reformulated as a {0, 1} quadratic knapsack problem, seeking an optimal sensor placement scheme by minimizing the average mutual coherence to maximize the degree of diagnosability. To effectively handle the complicated real-life water distribution networks, a validated binary version of artificial bee colony algorithm enhanced by genetic operators, including crossover and swap, is introduced to solve the binary knapsack problem. The proposed strategy is illustrated and validated through a real-life water distribution network with synthetically generated field data.

Sensor placement for calibration of spatially varying model parameters

This paper presents a sensor placement optimization framework for the calibration of spatially varying model parameters. To account for the randomness of the calibration parameters over space and across specimens, the spatially varying parameter is represented as a random field. Based on this representation, Bayesian calibration of spatially varying parameter is investigated. To reduce the required computational effort during Bayesian calibration, the original computer simulation model is substituted with Kriging surrogate models based on the singular value decomposition (SVD) of the model response and the Karhunen–Loeve expansion (KLE) of the spatially varying parameters. A sensor placement optimization problem is then formulated based on the Bayesian calibration to maximize the expected information gain measured by the expected Kullback–Leibler (K–L) divergence. The optimization problem needs to evaluate the expected K–L divergence repeatedly which requires repeated calibration of the spatially varying parameter, and this significantly increases the computational effort of solving the optimization problem. To overcome this challenge, an approximation for the posterior distribution is employed within the optimization problem to facilitate the identification of the optimal sensor locations using the simulated annealing algorithm. A heat transfer problem with spatially varying thermal conductivity is used to demonstrate the effectiveness of the proposed method.

Acceleration sensor placement technique for vibration test in structural health monitoring using microhabitat frog-leaping algorithm

In this article, a microhabitat frog-leaping algorithm is proposed based on original shuffled frog-leaping algorithm and effective independence method to make the algorithm more efficient to optimize the 3-axis acceleration sensor configuration in the vibration test of structural health monitoring. Optimal sensor placement is a vital component of vibration test in structural health monitoring technique. Acceleration sensors should be placed such that all of the important information is collected. The resulting sensor configuration should be optimal such that the testing resources are saved. In addition, sensor configuration should be calculated automatically to facilitate engineers. However, most of the previous methods focus on the sensor placement of 1-axis sensors. Then, the 3-axis acceleration sensors are calculated by the method of 1-axis sensors, which results in non-optimal placement of many 3-axis acceleration sensors. Moreover, the calculation precisions and efficiencies of most of the previous methods cannot meet the requirement of practical engineering. In this work, the microhabitat frog-leaping algorithm is proposed to solve the optimal sensor placement problems of 3-axis acceleration sensors. The computation precision and efficiency are improved by microhabitat frog-leaping algorithm. Finally, microhabitat frog-leaping algorithm is applied and compared with other algorithms using Dalian South Bay Cross-sea Bridge.

Influence of multi-valued diagnostic signals on optimal sensor placement

In this paper the comparison of results of optimal sensor placement with the use of binary and multi-valued diagnostic signals is given. The exoneration assumption was introduced and its effects were discussed. The influence of multi-valued diagnostic signals on several fault isolability metrics were discussed. The optimal sensor placement problem under budgetary constraints is formulated. A branch-and-bound algorithm solving this problem is described. It is used in context of three tanks system with 25 possible diagnostic signals.

Efficient Sensor Placement for Leak Localization Considering Uncertainties

Losses in water distribution systems can be between several percent in well maintained systems up to more than 50 percent in developing countries. Most of the losses originate from leaks. Therefore, a fast detection and localization of leaks is crucial for effectively reducing this losses in water distribution networks. Model-based leak localization has become increasingly popular in recent years. Certainly, the performance of these methods is linked to 1) the measurement locations in the system and 2) uncertainties at these locations. This paper provides a methodology that incorporates uncertainties of different types and sources in the optimal sensor placement problem for leak localization shown by the example of the effect of demand uncertainties on potential pressure measurement points. The problem is solved for different numbers of sensors and different strengths of uncertainties are taken into account. Additionally, to describe the relation between the number of sensors and the leak localization quality, a cost-benefit function is derived based on the different sensor placement results and GoF statistics. It was found that the function follows a power law. Results show that incorporating uncertainties leads to other optimal positions than without uncertainties, but the power law behavior still stays true. Additionally, more sensors are needed than without uncertainties.

Sensor Configuration Optimizing in Modal Identification by Siege ant Colony Algorithm

AbstractProper monitor planning is a vital component of structural health monitoring (SHM) project. An extremely important part of the monitor planning is the placement of sensors, usually in the form of acceleration sensors. For the placement of three-dimensional acceleration sensors, the state of practice is to select the sensor configuration by previous experiences. However, this results in a waste of many sensors. A novel method called siege ant colony algorithm (SAC) is proposed in this paper. This method is built on the previous ant colony optimization (ACO) in the direction of improving efficiency and accuracy when applied to optimal sensor placement (OSP) problems in large-scale structure monitoring. This method is applied and compared with standard approaches using the Hanjiang transmission tower.

An Integrated Framework for Binary Sensor Placement and Inhabitants Location Tracking

This correspondence paper deals with the sensor placement optimization problem in the context of indoor multiple inhabitants location tracking to solve ambient assisted living problems. Binary sensors, like passive infrared (PIR) sensors, are used to guaranty specific coverage requirements and allow privacy respecting. Moreover, within real home environments, different kinds of obstacles (like walls, high furniture, etc.) can affect the detection capacity of PIR sensors. This paper proposes an integrated framework devoted to optimize the placement of sensors and PIR sensors in smart homes by taking into account physical topologies and coverage precision constraints. An integer linear programming problem is formalized and a case study illustrates the applicability of the proposed approach and the scalability of the optimization method.

Sensor placement for fault location identification in water networks: A minimum test cover approach

This paper focuses on the optimal sensor placement problem for the identification of pipe failure locations in large-scale urban water systems. The problem involves selecting the minimum number of sensors such that every pipe failure can be uniquely localized. This problem can be viewed as a minimum test cover (MTC) problem, which is NP-hard. We consider two approaches to obtain approximate solutions to this problem. In the first approach, we transform the MTC problem to a minimum set cover (MSC) problem and use the greedy algorithm that exploits the submodularity property of the MSC problem to compute the solution to the MTC problem. In the second approach, we develop a new augmented greedy algorithm for solving the MTC problem. This approach does not require the transformation of the MTC to MSC. Our augmented greedy algorithm provides in a significant computational improvement while guaranteeing the same approximation ratio as the first approach. We propose several metrics to evaluate the performance of the sensor placement designs. Finally, we present detailed computational experiments for a number of real water distribution networks.

Optimal Sensor Placement for Acoustic Underwater Target Positioning With Range-Only Measurements

This paper addresses the problem of optimal acoustic sensor placement for underwater target localization in 3-D using range measurements only. By adopting an estimation theoretical framework, the optimal geometric sensor formation that will yield the best achievable performance in terms of target positioning accuracy is computed by maximizing the determinant of an appropriately defined Fisher information matrix (FIM). For mathematical tractability, it is assumed that the measurements of the ranges between the target and a set of acoustic sensors are corrupted with white Gaussian noise. For the sake of completeness, an explicit analytical result for a generic $n$ -sensor network is first obtained for the case when there is no uncertainty in the prior knowledge about the target position. The result is then extended to the practical case where the target is known to lie inside a region of uncertainty. The optimal sensor configuration thus obtained lends itself to an interesting and useful geometrical interpretation. In addition, the “spreading” of the configuration is shown to depend on the number of range measurements, target depth, and the probability distribution function that characterizes the prior knowledge about the target position. Results are also obtained for the problem of optimal sensor placement with constraints, namely, by considering that the sensors can be either located at the sea surface or distributed between the surface and the seabed. The connection between 2-D and 3-D scenarios is clarified. Simulation examples illustrate the key results derived.

On optimal sensing and actuation design for an industrial scale steam methane reformer furnace

The spatial temperature distribution in the highly energy‐intensive furnace unit in a steam reforming‐based hydrogen manufacturing plant determines the energy efficiency of the plant. While the fuel distribution among the burners can be manipulated to control the furnace temperature distribution, adequate temperature measurements is a prerequisite. Typical furnaces have hundreds of tubes and burners, and economic considerations dictate that the number of temperature sensors and flow actuators required for automatic temperature optimization be minimized. In this article, we investigate several formulations for the design of the optimal sensor and actuation configurations for an industrial furnace. We initially formulate the optimal sensor placement problem as a bi‐level optimization problem, and exploit the problem structure to obtain an equivalent mixed‐integer linear program formulation. We then provide an extension to the combined sensor and actuator placement. We demonstrate the efficacy of our approach through simulation case studies based on industrial data. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3225–3237, 2016

On the Minimum Differentially Resolving Set Problem for Diffusion Source Inference in Networks

In this paper we theoretically study the minimum Differentially Resolving Set (DRS) problem derived from the classical sensor placement optimization problem in network source locating. A DRS of a graph G = (V, E) is defined as a subset S ⊆ V where any two elements in V can be distinguished by their different differential characteristic sets defined on S. The minimum DRS problem aims to find a DRS S in the graph G with minimum total weight Σv∈S w(v). In this paper we establish a group of Integer Linear Programming (ILP) models as the solution. By the weighted set cover theory, we propose an approximation algorithm with the Θ(ln n) approximability for the minimum DRS problem on general graphs, where n is the graph size.

Optimal sensor placement in structural health monitoring using discrete optimization

The objective of optimal sensor placement (OSP) is to obtain a sensor layout that gives as much information of the dynamic system as possible in structural health monitoring (SHM). The process of OSP can be formulated as a discrete minimization (or maximization) problem with the sensor locations as the design variables, conditional on the constraint of a given sensor number. In this paper, we propose a discrete optimization scheme based on the artificial bee colony algorithm to solve the OSP problem after first transforming it into an integer optimization problem. A modal assurance criterion-oriented objective function is investigated to measure the utility of a sensor configuration in the optimization process based on the modal characteristics of a reduced order model. The reduced order model is obtained using an iterated improved reduced system technique. The constraint is handled by a penalty term added to the objective function. Three examples, including a 27 bar truss bridge, a 21-storey building at the MIT campus and the 610 m high Canton Tower, are investigated to test the applicability of the proposed algorithm to OSP. In addition, the proposed OSP algorithm is experimentally validated on a physical laboratory structure which is a three-story two-bay steel frame instrumented with triaxial accelerometers. Results indicate that the proposed method is efficient and can be potentially used in OSP in practical SHM.

Optimal sensor placement for long-span cable-stayed bridge using a novel particle swarm optimization algorithm

In health monitoring of long-span structures, proper arrangement of sensors is a key point because of the need to acquire effective structural health information with limited testing resources. This study proposes a novel approach called dual-structure coding and mutation particle swarm optimization (DSC-MPSO) algorithm for the sensor placement. The cumulative effective modal mass participation factor is firstly derived to select the main contributions modes. A novel method combining dual-structure coding with the mutation operator is then utilized to determine the optimal sensors configurations. Finally, the feasibility of the DSC-MPSO algorithm is verified by optimizing the sensors locations for a long-span cable-stayed bridge. The effective independence method, genetic algorithm and standard particle swarm optimization algorithm are taken as contrast experiments. The simulation results show that the proposed algorithm in this paper could improve the convergence speed and precision. Accordingly, the method is effective in solving optimal sensor placement problems.

Gyroscopic sensing in the wings of the hawkmoth Manduca sexta: the role of sensor location and directional sensitivity

The wings of the hawkmoth Manduca sexta are lined with mechanoreceptors called campaniform sensilla that encode wing deformations. During flight, the wings deform in response to a variety of stimuli, including inertial-elastic loads due to the wing flapping motion, aerodynamic loads, and exogenous inertial loads transmitted by disturbances. Because the wings are actuated, flexible structures, the strain-sensitive campaniform sensilla are capable of detecting inertial rotations and accelerations, allowing the wings to serve not only as a primary actuator, but also as a gyroscopic sensor for flight control. We study the gyroscopic sensing of the hawkmoth wings from a control theoretic perspective. Through the development of a low-order model of flexible wing flapping dynamics, and the use of nonlinear observability analysis, we show that the rotational acceleration inherent in wing flapping enables the wings to serve as gyroscopic sensors. We compute a measure of sensor fitness as a function of sensor location and directional sensitivity by using the simulation-based empirical observability Gramian. Our results indicate that gyroscopic information is encoded primarily through shear strain due to wing twisting, where inertial rotations cause detectable changes in pronation and supination timing and magnitude. We solve an observability-based optimal sensor placement problem to find the optimal configuration of strain sensor locations and directional sensitivities for detecting inertial rotations. The optimal sensor configuration shows parallels to the campaniform sensilla found on hawkmoth wings, with clusters of sensors near the wing root and wing tip. The optimal spatial distribution of strain directional sensitivity provides a hypothesis for how heterogeneity of campaniform sensilla may be distributed.