Optimal Sensor Place

This article addresses the problem of moving source localization in 3-D using the time-difference-of-arrival and frequency-difference-of-arrival measurements without accurate sensor location information. Different from the previous studies, we focus on improving the localization performance by introducing two approaches with a limited number of sensors, including optimal sensor placement and velocity configuration, as well as successive measurements for a time period. This article first determines the sensor placement and velocity (including speed and orientation) configuration to achieve optimal localization based on a criterion devised from the Fisher information matrix, in which the restrictions for the two-stage weighted-least-squares (TSWLS) positioning algorithm and the geographical conditions are taken into considerations. Then, to utilize successive measurements while the source is in motion, we separate the sensor velocity into two components for achieving the localization optimality and compensating the source motion, and propose a practical sensor placement and velocity configuration strategy. Finally, combining with the TSWLS-based prelocalization, Kalman filtering and the proposed sensor motion strategy, we develop a source tracking scheme that simultaneously obeys the optimal sensor placement and velocity configuration during tracking. Mathematical analyses and numerical simulations validate the optimal sensor placement and the efficiencies of the source tracking scheme.

Abstract Selecting right positions for composite-integrated sensors for monitoring cure during manufacturing and loads during product use presents challenges for engineering design. Since an optimal sensor placement (OSP) methodology for both phases is not emphasised enough in literature, a new methodology is proposed. This methodology is based on a Genetic Algorithm and strain gauges, temperature sensors and interdigitated electrode sensors for cure monitoring and physics-informed neural network-based load detection. Additionally, it includes sensor node positions optimization in a sensor network.

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.

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This paper focuses on static source localization employing different combinations of measurements, including time-difference-of-arrival (TDOA), received-signal-strength (RSS), angle-of-arrival (AOA), and time-of-arrival (TOA) measurements. Since sensor-source geometry significantly impacts localization accuracy, the strategies of optimal sensor placement are proposed systematically using combinations of hybrid measurements. Firstly, the relationship between sensor placement and source estimation accuracy is formulated by a derived Cramér-Rao bound (CRB). Secondly, the A-optimality criterion, i.e., minimizing the trace of the CRB, is selected to calculate the smallest reachable estimation mean-squared-error (MSE) in a unified manner. Thirdly, the optimal sensor placement strategies are developed to achieve the optimal estimation bound. Specifically, the specific constraints of the optimal geometries deduced by specific measurement, i.e., TDOA, AOA, RSS, and TOA, are found and discussed theoretically. Finally, the new findings are verified by simulation studies.

Structural health monitoring obtains data reflecting the service status of grid structures through sensors. One of the issues to consider in optimal sensor placement is how to obtain as much information as possible with a limited number of sensors. In this paper, a sensor placement method is proposed based on damage sensitivity and correlation analysis, which is based on strain energy calculation and is suitable for grid structures. Specifically, with the sensor locations as optimization variables, a mathematical optimization model is established by considering the damage sensitivity and redundancy of the monitoring scheme, and a genetic algorithm is employed for computation. Two examples, including a lattice shell and a flat grid, are provided to illustrate the method, followed by a discussion of the sensitivity of parameters such as stiffness reduction degree and load form. The results indicate that the redundancy of the optimized schemes for the two examples decreased by approximately 80% and 30%, respectively. The proposed method ensures a certain degree of damage sensitivity while significantly reducing redundancy, demonstrating its applicability and robustness in sensor placement for grid structures.

This study examines the impact of sensor placement and multimodal sensor fusion on the performance of a Long Short-Term Memory (LSTM)-based model for human activity classification taking place in an agricultural harvesting scenario involving human-robot collaboration. Data were collected from twenty participants performing six distinct activities using five wearable inertial measurement units placed at various anatomical locations. The signals collected from the sensors were first processed to eliminate noise and then input into an LSTM neural network for recognizing features in sequential time-dependent data. Results indicated that the chest-mounted sensor provided the highest F1-score of 0.939, representing superior performance over other placements and combinations of them. Moreover, the magnetometer surpassed the accelerometer and gyroscope, highlighting its superior ability to capture crucial orientation and motion data related to the investigated activities. However, multimodal fusion of accelerometer, gyroscope, and magnetometer data showed the benefit of integrating data from different sensor types to improve classification accuracy. The study emphasizes the effectiveness of strategic sensor placement and fusion in optimizing human activity recognition, thus minimizing data requirements and computational expenses, and resulting in a cost-optimal system configuration. Overall, this research contributes to the development of more intelligent, safe, cost-effective adaptive synergistic systems that can be integrated into a variety of applications.

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The estimation sound fields over space is of interest in sound field control and analysis, spatial audio, room acoustics and virtual reality. Sound fields can be estimated from a number of measurements distributed over space yet this remains a challenging problem due to the large experimental effort required. In this work we investigate sensor distributions that are optimal to estimate sound fields. Such optimization is valuable as it can greatly reduce the number of measurements required. The sensor positions are optimized with respect to the parameters describing a sound field, or the pressure reconstructed at the area of interest, by finding the positions that minimize the Bayesian Cramér-Rao bound (BCRB). The optimized distributions are investigated in a numerical study as well as with measured room impulse responses. We observe a reduction in the number of measurements of approximately 50% when the sensor positions are optimized for reconstructing the sound field when compared with random distributions. The results indicate that optimizing the sensors positions is also valuable when the vector of parameters is sparse, specially compared with random sensor distributions, which are often adopted in sparse array processing in acoustics.

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A new digital twin (DT) framework with optimal sensor placement (OSP) is proposed to accurately calculate the modal responses and identify the damage ratios of the offshore jacket platforms. The proposed damage identification framework consists of two models (namely one OSP model and one damage identification model). The OSP model adopts the multi-objective Lichtenberg algorithm (MOLA) to perform the sensor number/location optimization to make a good balance between the sensor cost and the modal calculation accuracy. In the damage identification model, the Markov Chain Monte Carlo (MCMC)-Bayesian method is developed to calculate the structural damage ratios based on the modal information obtained from the sensory measurements, where the uncertainties of the structural parameters are quantified. The proposed method is validated using an offshore jacket platform, and the analysis results demonstrate efficient identification of the structural damage location and severity.

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.

The construction of an efficient monitoring network is critical for the effective and safe management of urban drainage systems. This study developed a re-clustering methodology that incorporates additional perspectives beyond node similarity to improve the traditional clustering process for optimal sensor placement. Instead of targeting event-specific water quality or hydraulic monitoring, the method integrates the water hydraulic and quality characteristics of nodes in response to the demand for routine monitoring. The implementation of this method first applies model simulation to generate the attribute datasets required for clustering analysis, and then re-clusters the initial clustering result according to the constructed re-clustering potential indices. And the information theory-based evaluation metrics were introduced to quantitatively assess the sensor deployment scheme obtained by amalgamating the two clustering results. Two networks with different drainage systems and sizes were chosen as case studies to illustrate the application of the framework. The results demonstrate that the clustering process enables to expand the information contained in the monitoring network, and that the re-clustering strategy can generate more comprehensive and practical solutions upon this basis.

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In this article, new characterizations for functional observability, functional detectability, and structural functional observability (SFO) are developed, and based on them, the related optimal sensor placement problems are investigated. A novel concept of modal functional observability coinciding with the notion of modal observability is proposed. This notion introduces necessary and sufficient conditions for functional observability and detectability in a unified way without resorting to system observability decomposition, and facilitates the design of a functionally observable/detectable system. Afterward, SFO is redefined rigorously from a generic perspective, contrarily to the definition of structural observability. A complete graph-theoretic characterization for SFO is proposed. Based on these results, the problems of selecting the minimal sensors from a prior set to achieve functional observability and SFO are shown to be NP-hard. Nevertheless, supermodular set functions are established, leading to greedy heuristics that can find approximation solutions to these problems with provable guarantees in polynomial time. A closed-form solution along with a constructive procedure is also given for the unconstrained case on systems with diagonalizable state matrices. Notably, our results also yield a polynomial-time verifiable case for structural target controllability, a problem that may be hard otherwise.

Modern health and productivity concerns related to air pollutant exposure in buildings have sparked the need for occupant-centric monitoring and ventilation control. The existing personal exposure monitoring is often restricted to stationary air quality sensors and static occupancy. This study aims to identify optimal stationary sensor placement that best represents exposure to CO 2 , PM 2.5 , and PM 10 under static and dynamic office occu-pancies. A total of 48 controlled chamber experiments were executed in four office layouts with variation of occupant numbers (2, 4, 6 or 8), activities (sitting/standing and static/dynamic), ventilation strategies (mixing/ displacement) and air change rates (0.5 – 0.7 h (cid:0) 1 , 2.4 – 2.6 h (cid:0) 1 , and 3.8 – 4.2 h (cid:0) 1 ). The breathing zone concentration of a reference occupant was monitored with concurrent measurements at seven stationary locations: front edge of the desk, sides of two desks, two sidewalls, and two exhaust vents. The proximity of sensors to the reference occupant and ventilation rate/strategy were important determinants of personal exposure detection. Regression analyses showed that the wall-and desk-mounted CO 2 sensors near the occupant ( < 1 m) best captured CO 2 exposure under dynamic – standing activities (R 2 ~0.4). The wall immediately behind the seated occupant and the ceiling-mounted exhaust near the standing occupant ( < 1 – 1.5 m) were the best sensor placements for capturing exposure to particles (R 2 = 0.8 – 0.9). Separating static from dynamic occupancy activities resulted in improved exposure prediction by 1.4-6.1 × . This study is a step towards provision of practical guidelines on stationary air quality sensor placement indoors with the consideration of dynamic occupancy profiles.

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Deciding how to optimally deploy sensors in a large, complex, and spatially extended structure is critical to ensure that the surface pressure field is accurately captured for subsequent analysis and design. In some cases, reconstruction of missing data is required in downstream tasks such as the development of digital twins. This paper presents a data-driven sparse sensor selection algorithm, aiming to provide the most information contents for reconstructing aerodynamic characteristics of wind pressures over tall building structures parsimoniously. The algorithm first fits a set of basis functions to the training data, then applies a computationally efficient QR algorithm that ranks existing pressure sensors in order of importance based on the state reconstruction to this tailored basis. The findings of this study show that the proposed algorithm successfully reconstructs the aerodynamic characteristics of tall buildings from sparse measurement locations, generating stable and optimal solutions across a range of conditions. As a result, this study serves as a promising first step toward leveraging the success of data-driven and machine learning algorithms to supplement traditional genetic algorithms currently used in wind engineering.

Optimal sensor location methods are crucial to realize a sensor profile that achieves pre-defined performance criteria as well as minimum cost. In recent times, indoor cultivation systems have leveraged on optimal sensor location schemes for effective monitoring at minimum cost. Although the goal of monitoring in indoor cultivation system is to facilitate efficient control, most of the previously proposed methods are ill-posed as they do not approach optimal sensor location from a control perspective. Therefore in this work, a genetic programming-based optimal sensor placement for greenhouse monitoring and control is presented from a control perspective. Starting with a reference micro-climate condition (temperature and relative humidity) obtained by aggregating measurements from 56 dual sensors distributed within a greenhouse, we show that genetic programming can be used to select a minimum number of sensor locations as well as a symbolic representation of how to aggregate them to efficiently estimate the reference measurements from the 56 sensors. The results presented in terms of Pearson’s correlation coefficient (r) and three error-related metrics demonstrate that the proposed model achieves an average r of 0.999 for both temperature and humidity and an average RMSE value of 0.0822 and 0.2534 for temperate and relative humidity respectively. Conclusively, the resulting models make use of only eight (8) sensors, indicating that only eight (8) are required to facilitate the efficient monitoring and control of the greenhouse facility.

Sensor-based Human Activity Recognition facilitates unobtrusive monitoring of human movements. However, determining the most effective sensor placement for optimal classification performance remains challenging. This paper introduces a novel methodology to resolve this issue, using real-time 2D pose estimations derived from video recordings of target activities. The derived skeleton data provides a unique strategy for identifying the optimal sensor location. We validate our approach through a feasibility study, applying inertial sensors to monitor 13 different activities across ten subjects. Our findings indicate that the vision-based method for sensor placement offers comparable results to the conventional deep learning approach, demonstrating its efficacy. This research significantly advances the field of Human Activity Recognition by providing a lightweight, on-device solution for determining the optimal sensor placement, thereby enhancing data anonymization and supporting a multimodal classification approach.

Over the last decade, concepts such as industry 4.0 and the Internet of Things (IoT) have contributed to the increase in the availability and affordability of sensing technology. In this context, structural health monitoring (SHM) arises as an especially interesting field to integrate and develop these new sensing capabilities, given the criticality of structural application for human life and the elevated costs of manual monitoring. Due to the scale of structural systems, one of the main challenges when designing a modern monitoring system is the optimal sensor placement (OSP) problem. The OSP problem is combinatorial in nature, making its exact solution infeasible in most practical cases, usually requiring the use of metaheuristic optimization techniques. While approaches such as genetic algorithms (GAs) have been able to produce significant results in many practical case studies, their ability to scale up to more complex structures is still an area of open research. This study proposes a novel quantum-based combinatorial optimization approach to solve the OSP problem approximately, within the context of SHM. For this purpose, a quadratic unconstrained binary optimization (QUBO) model formulation is developed, taking as a starting point of the modal strain energy (MSE) of the structure. The framework is tested using numerical simulations of Warren truss bridges of varying scales. The results obtained using the proposed framework are compared against exhaustive search approaches to verify their performance. More importantly, a detailed discussion of the current limitations of the technology and the future paths of research in the area is presented to the reader.

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.

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in the sensor configuration and robust with respect to the source, yet relatively easy to compute in practice, compared to a direct evaluation of the error by a large number of samples. In particular, we consider the identification of a measure consisting of an unknown linear combination of point sources from a finite number of measurements contaminated by Gaussian noise. The statistical framework for recovery relies on two main ingredients: first, a convex but non-smooth variational Tikhonov point estimator over the space of Radon measures and, second, a suitable mean-squared error based on its Hellinger–Kantorovich distance to the ground truth. To quantify the error, we employ a non-degenerate source condition as well as careful linearization arguments to derive a computable upper bound. This leads to asymptotically sharp error estimates in expectation that are explicit in the sensor configuration. Thus they can be used to estimate the expected reconstruction error for a given sensor configuration and guide the placement of sensors in sparse inverse problems.

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This work presents an approach for optimal placement of strain sensors in composite circular cylindrical shells. The approach uses numerical strain values in longitudinal and transverse directions extracted from the top surface of the thin-walled composite cylindrical shell. Numerical model of composite cylindrical shell was modelled using the FE commercial solver ANSYS. The modal analysis was performed to determine the first 12 natural frequencies and corresponding mode shapes. Number of sensors and their locations were obtained taking into account physical constraints of strain sensors and optimization strategies. Finally, the optimal sensor placements were obtained. Maximal number of sensors in each direction equals 30.

The 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.

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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.

Source localization techniques incorporating hybrid measurements improve the reliability and accuracy of the location estimate. Given a set of hybrid sensors that can collect combined time of arrival, received signal strength, and angle of arrival measurements, the localization accuracy can be enhanced further by optimally designing the placements of the hybrid sensors. In this article, we present an optimal sensor placement methodology, which is based on the principle of majorization–minimization (MM), for the hybrid localization technique. We first derive the Cramer–Rao lower bound of the hybrid measurement model, and formulate the design problem using the A-optimal criterion. Next, we introduce an auxiliary variable to reformulate the design problem into an equivalent saddle-point problem, and then, construct simple surrogate functions (having closed form solutions) over both primal and dual variables. The application of MM in this article is distinct from the conventional MM (that is usually developed only over the primal variable), and we believe that the MM framework developed in this article can be employed to solve many optimization problems. The main advantage of our method over most of the existing state-of-the-art algorithms (which are mostly analytical in nature) is its ability to work for both uncorrelated and correlated noise in the measurements. We also discuss the extension of the proposed algorithm for the optimal placement designs based on D and E optimal criteria. Finally, the performance of the proposed method is studied under different noise conditions and different design parameters.