Sensor Placement Methodology Research Articles

Enhancing source separation quality via optimal sensor placement in noisy environments

The paper aims to bridge a part of the gap between source separation and sensor placement studies by addressing a novel problem: “Predicting optimal sensor placement in noisy environments to improve source separation quality”. The structural information required for optimal sensor placement is modeled as the spatial distribution of source signal gains and the spatial correlation of noise. The sensor positions are predicted by optimizing two criteria as measures of separation quality, and a gradient-based global optimization method is developed to efficiently address this optimization problem. Numerical results exhibit superior performance when compared with classical sensor placement methodologies based on mutual information, underscoring the critical role of sensor placement in source separation with noisy sensor measurements. The proposed method is applied to actual electroencephalography (EEG) data to separate the P300 source components in a brain-computer interface (BCI) application. The results show that when the sensor positions are chosen using the proposed method, to reach a certain level of spelling accuracy, fewer sensors are required compared with standard sensor locations.

Design methodology for optimal sensor placement for cure monitoring and load detection of sensor-integrated, gentelligent composite parts

AbstractSelecting 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.

An optimal sparse sensing approach for scanning point selection and response reconstruction in full-field structural vibration testing

Non-contact vibration measurements, such as 3D scanning laser Doppler vibrometry (3D SLDV), are becoming more prevalent in testing next-generation lightweight aerospace structures. This approach reduces the impact of attached sensors and improves measurement reliability. Acquiring precise measurement data for the whole area is feasible, albeit it would demand a considerable amount of time and storage space for testing. The concept of compressed sensing has been recently approved as an effective way to exploit signal sparsity and achieve full response reconstruction with very few measurements. The objective of this work is to enhance the efficiency of non-contact vibration testing by utilizing the state-of-the-art compressive sensing approach. In contrast to conventional sensor placement methods that rely on effective independence, modal kinetic energy, or modal assurance criterion matrix as targets, this paper proposes a novel sensor placement methodology from the perspective of dynamic response reconstruction. The scanning points are chosen with a minimal number to reduce testing time and are well-placed such that full-field vibration responses of the test structure can be reconstructed accurately. This allows for the spatially-detailed vibration responses to be obtained efficiently and accurately with optimal sparse sensing placement and effective response reconstruction through ℓ1 algorithm. Two case studies will be presented in this work to demonstrate and validate the methodology. The first case study is focused on a simplified cantilever beam using the numerical data from the FE analysis to demonstrate the methodology. The second case study is focused on using 3D SLDV experimental testing data from a full-scale industrial fan blade. Based on the results, it is evident that the proposed approach can significantly decrease the scanning points required for a full-field dynamic response reconstruction during full-field vibration testing.

Optimal Sensor Placement for Vibration-Based Damage Localization Using the Transmittance Function.

A methodology for optimal sensor placement is presented in the current work. This methodology incorporates a damage detection framework with simulated damage scenarios and can efficiently provide the optimal combination of sensor locations for vibration-based damage localization purposes. A classic approach in vibration-based methods is to decide the sensor locations based, either directly or indirectly, on the modal information of the structure. While these methodologies perform very well, they are designed to predict the optimal locations of single sensors. The presented methodology relies on the Transmittance Function. This metric requires only output information from the testing procedure and is calculated between two acceleration signals from the structure. As such, the outcome of the presented method is a list of optimal combinations of sensor locations. This is achieved by incorporating a damage detection framework that has been developed and tested in the past. On top of this framework, a new layer is added that evaluates the sensitivity and effectiveness of all possible sensor location combinations with simulated damage scenarios. The effectiveness of each sensor combination is evaluated by calling the damage detection framework and feeding as inputs only a specific combination of acceleration signals each time. The final output is a list of sensor combinations sorted by their sensitivity.

Optimal sensor placement methodology of triaxial accelerometers using combined metaheuristic algorithms for structural health monitoring applications

Structural health monitoring applications present a valuable opportunity for cities to improve their infrastructures environmental life cycle, reduce operational maintenance cost and enhance their resiliency through early damage detection capabilities. The dilemma with structural health monitoring resides in balancing between the number of sensors to be installed and the amount of data that needs to be transferred, stored, and managed. These technical complications directly impact the cost efficiency of such solutions. Thus, limiting the wide range deployment of such technology. Henceforth, Optimal Sensor Placement (OSP) methodologies offers the possibility to optimize the sensor configuration that will ensure a proper and cost-efficient monitoring system to obtain the maximum modal information related to any infrastructure type.In this study, a novel “Modal Assurance Criterion (MAC)”-based methodology with the aim of the optimal sensor placement is presented using a 410 m high rise structure. The Modal Kinetic Energy (MKE) and a MAC-based objective function are combined in the suggested methodology. The optimization problem is solved using a new hybrid metaheuristic algorithm that combines Teaching–Learning-Based Optimization (TLBO), Artificial Bee Colonies (ABC), and Stochastic Paint Optimizer (SPO). With no user-defined parameters, the combination of algorithms exhibits up to 86% better fitness, avoids local optimums due to higher accuracy, and shows promising results for cost calculation optimization because it requires 50% to 70% fewer iterations compared to six evolutionary algorithms that are usually used.

SHM of historical buildings: The case study of Santa Maria in Via church in Camerino (Italy)

Historical buildings constitute a huge heritage for the Italian country, and they deserve to be preserved to be handed over in good condition for future generations. As well know, Italy is a prone earthquake country and many earthquakes occurred over time producing awful consequences in terms of human losses and building damage. Historical buildings are typically the most damaged ones since they were built often with poor materials and conceived to sustain only gravitational loads. The preservation of these buildings is not a trivial task as structural retrofits have to be carried out not only in a proper way, but also timely in case the actual conditions of the construction may worse over time. Since large-scale rapid interventions after an earthquake are almost impossible, instrumenting damaged structures with appropriate sensors and analyzing measured data become crucial to control the damage evolution. At the same time, the monitoring of secured structures is essential to evaluate the effectiveness of the interventions and the possible evolution of damage. This paper presents the Structural Health Monitoring (SHM) system installed in the Santa Maria in Via church in Camerino (Central Italy). The church, severely damaged after the seismic sequence that stroke Central Italy in 2016, was secured with a steel structural system aimed at preventing possible collapse of some peculiar components, as the overturning of the massive façade body and the collapse of the slender elliptical drum. The SHM system permanently installed is presented; the latter consists of several sensors of different typologies placed in specific positions to monitor the effectiveness of the securing steel structure and the behavior of the church. Also, the Optimal Sensor Placement (OSP) methodology is adopted to determine the best sensor layout (number and position) to develop the SHM of the case study. Finally, the numerical model developed to support the interpretation of the SHM data, is described.

Design of Digital Twin Sensing Strategies Via Predictive Modeling and Interpretable Machine Learning

Abstract This work develops a methodology for sensor placement and dynamic sensor scheduling decisions for digital twins. The digital twin data assimilation is posed as a classification problem, and predictive models are used to train optimal classification trees that represent the map from observed data to estimated digital twin states. In addition to providing a rapid digital twin updating capability, the resulting classification trees yield an interpretable mathematical representation that can be queried to inform sensor placement and sensor scheduling decisions. The proposed approach is demonstrated for a structural digital twin of a 12 ft wingspan unmanned aerial vehicle. Offline, training data are generated by simulating scenarios using predictive reduced-order models of the vehicle in a range of structural states. These training data can be further augmented using experimental or other historical data. In operation, the trained classifier is applied to observational data from the physical vehicle, enabling rapid adaptation of the digital twin in response to changes in structural health. Within this context, we study the performance of the optimal tree classifiers and demonstrate how they enable explainable structural assessments from sparse sensor measurements and also inform optimal sensor placement.

Optimal sensor placement methodology of hydraulic control system for fault diagnosis

During the state monitoring and fault diagnosis of hydraulic control system, different kinds of sensors are used to collect fault signals. The arrangement of a limited number of sensors in the most reasonable positions of the hydraulic system, that is, to solve the problem on the optimal placement of sensors, is the key to improving efficiency of fault diagnosis. Aiming at fault diagnosis of hydraulic control system, this paper proposes a sensor placement methodology of hydraulic control system to determine the optimal number and position of sensors based on a discrete particle swarm algorithm. First, the model of fault propagation and sensor response time is evaluated by a simulation model. Second, a discrete optimization model for sensor placement is established. Finally, a discrete particle swarm optimization algorithm is used to calculate the optimal solution for the optimal placement of sensors. In the iterative process, a Monte Carlo simulation-based comparison algorithm is used for the evaluation and comparison of particle. The simulation case of typical multi-circuit hydraulic control systems proves that the proposed method has fast convergence speed and optimization results. A real case of a subsea blowout preventer control system shows that the proposed method reduces the number of sensors and data redundancy effectively. Compared with the traditional method, the robustness of the proposed system under the optimal solution is improved.

Optimal Sensor Placement for Hybrid Source Localization Using Fused TOA-RSS-AOA Measurements

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 (TOA), received signal strength (RSS) and angle of arrival (AOA) measurements, the localization accuracy can be enhanced further by optimally designing the placements of the hybrid sensors. In this paper, we present an optimal sensor placement methodology, which is based on the principle of majorization-minimization (MM), for hybrid localization technique. We first derive the Cramer-Rao lower bound (CRLB) 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 paper 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 paper 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.

Incremental upgrading sensor placement methodology: Application to the leak localization in water networks

This paper presents a new methodology for sensor reallocation in large scale-systems considering fault isolation purposes. From an initial set consisting of a limited number of sensors already installed in certain locations of the system, the proposed methodology produces a new sensor placement where some of the sensors are strategically reallocated in different but available places of the system. The procedure is posed as an optimization problem where the performance index is specific of the fault isolation method to be used. The algorithm that solves the problem is an incremental upgrading approach based in the Sequential Forward Floating Search algorithm and it combines a forward phase (where sensors are added sequentially) with a backward phase (where sensors can be individually removed from the original sensor placement). The proposed methodology is illustrated by means of its application to the problem of leak localization in Water Distribution Networks (WDN), where the particular placement of the pressure sensors has a great impact in the ability to isolate the leaky node. Also, since only a limited number of pressure sensors can be installed in some nodes, space interpolation techniques must be used to estimate the pressure in the other network nodes. The performance of the localization process is measured in terms of pipe distance from the estimated leaky node candidate to the real leaky node. The proposed methodology is applied to two District Metered Areas of the WDN of a metropolitan area of Spain, in simulation and using real measurements and leak scenarios.

Sensor placement for model identification of multi-story buildings under unknown earthquake ground motion

The number of sensors and their position is very important for the acquisition of high-quality measurement data in structural health monitoring (SHM), where the detection and evaluation of structural health status under unknown seismic ground motion have been an important research area. It is undoubtedly that the identification of structural model parameters under unknown seismic ground motion or joint identification of model parameters and seismic time-history input depends on the effective placement of sensors on structures. At present, the investigation of sensor configuration is mainly intended for structural model or modal parameter identification without taking into account the seismic effect, which cannot guarantee the effective contribution of the dynamic measurement data to the joint identification of ground motion and model parameters. To the best of authors knowledge, the optimal sensor configuration for the purpose of model parameter identification under unknown seismic ground motion has not yet been reported in the current literature. In the framework of Bayes'theorem and information theory, this paper proposes an optimal sensor placement methodology targeting at model parameter identification under unknown seismic ground motion. Based on the joint identification of ground motion and structural model parameters, the optimal configuration scheme for a given number of sensors is determined by maximizing a proposed expected entropy measure formed by utilizing the marginal distribution of model parameters prior to the availability of the measurement data. In addition, to solve the combinatorial optimization problem arising from the optimal sensor configuration, this paper also proposes a simple yet efficient strategy for revising the fitness function of genetic algorithm, which converts the continuous variable representation of the sensor configuration vector into a binary string representation. This completely avoids the common approaches relying on modifying various genetic operators to ensure the mandatory constraint of always configuring a fixed number of sensors. The validity of the proposed methodology is fully validated by numerical and experimental case studies conducted respectively for a 20-story shear-building model and a laboratory 6-story shear-building model under shaking table test.

Voxel-based sensor placement for additive manufacturing applications

The manufacturing sector is experiencing a transformation to Industry 4.0. The authors are researching 3D printable sensors to measure operating conditions like wear, strain and temperature, as part of a project to develop a large-scale multi-material extrusion 3D printer to print a Gravity Separation Spiral—a piece of mining equipment that separates minerals from slurry. This paper proposes a sensor placement methodology for placing embedded sensors in large 3D printed objects. Voxels, the 3D equivalent of 2D pixels, are used to discretise the object and an optimisation routine optimally positions the 3D printable sensors into a 3D printed object. The optimisation objectives that are used during sensor placement include the information gain from the sensor, the ability to print the sensor using a robot, and the ability to discourage sensors being placed in important structural locations by penalising these voxels. Finite element analysis is employed to measure the information gain, while the robot arm’s manipulability measures the capability to print at each voxel location. The objectives are integrated using 3D kernels, which are represented by voxels shaped in the size of the sensor and different weights related to the intricate traces that need to be printed. Using a weighted objective function the best locations are chosen. A simulation environment has been developed to simulate the printing and Matlab is used to do the voxel-based calculations to identify the ideal location for sensor placement.

Uniformly optimal multi-sensor design in pipe networks for transient-based leakage localization

The design of sensor placement in water supply pipe networks for the purpose of transient-based leakage localization is investigated. Each sensor is placed at where the Fisher information of measurement concerning leaks is maximized; equivalently, the Cramér–Rao lower bound (CRLB) representing the lower limit of leak localization error is minimized. An explicit algorithm for computing the CRLB with respect to leak parameters in a general pipe network is developed. The presence of leak is considered as stochastic and modeled in a probabilistic framework by assuming that the leak location follows a probabilistic distribution with a support on the whole network. The optimal distribution of the sensors is then computed via a quasi-Monte-Carlo simulation, where the expectation of the CRLB of leak localization error is minimized. The proposed sensor placement methodology is optimal uniformly over all the leak localization methods, all the potential sensor locations and all the situations of leaks. Four examples from a simple single-pipe system to a complex pipe network are presented to illustrate the proposed methodology.

On a Sensor Placement Methodology for Monitoring the Vibrations of Horizontally Excited Ground.

In this paper, the problem of optimal sensor arrangement during vibration monitoring is analysed. The wave propagation caused by horizontal excitation is investigated to predict the areas of the largest ground and structure response. The equations of motion for a transversally isotropic elastic medium with appropriate absorbing boundary conditions are solved using the finite element method (FlexPDE software). The possibility of an amplified soil medium response is examined for points located on the ground surface and at various depths. The results are presented in the form of a dimensionless vibration reduction factor, defined as the ratio of the peak particle velocity observed at the selected depth to the corresponding value observed at the ground surface. Significant amplifications (≈50%) can be observed below the ground surface, especially in the case of a weak layer below a stiff layer. The effect of vibration amplification is most significant near the boundary surface of two layers. For the points located on the ground surface, the greatest peak particle velocities are observed in the direction perpendicular to the load direction. However, the greatest vertical velocity component at the ground surface is observed in front of the applied force.

Sensor placement methodology for spindle thermal compensation of machine tools

This paper presents a temperature sensor placement methodology for the thermal compensation of the tool center point of a machine tool. The methodology consisted of two phases: ranking and screening. With multiple temperature sensors attached to a targeted machine tool, principal component analysis and then principal component regression were employed to rank temperature sensors in phase I. In phase II, the temperature sensors, after they had been ranked in phase I, were screened using singular value decomposition to eliminate redundant sensors, which exhibited high collinearity to other sensors. Spindle thermal compensation was performed on a 3-axis machining center using conventional multiple regression (MR), back propagation neural network (BPNN), and random forest (RF). With only four sensors selected from 16 sensors, the results revealed that through the proposed ranking and screening processes, the accuracy levels of the thermal compensation models from MR, BPNN, and RF were all higher than those of models without ranking or screening. Accuracy improved in both BPNN and RF more than 40% from those using sensor ranking only. The compensation performance with only four sensors was even better than that with six sensors selected using importance from RF. Moreover, how to determine optimal sensor quantity was presented. This proposed methodology of spindle thermal compensation could be more cost effective in terms of lower numbers of sensors but with higher thermal compensation accuracy.

A methodology for measurement-system design combining information from static and dynamic excitations for bridge load testing

Managing infrastructure assets is challenging for developed countries because of demand for increases in capacity, the scarcity of economic and environmental resources as well as ageing. Due to conservative approaches to construction design and practice, infrastructure often has hidden reserve capacity and its estimation may improve asset-management decisions. Static and dynamic bridge load testing has the potential to support engineers in their evaluation of infrastructure reserve capacity if monitoring data are associated with a robust structural-identification methodology. As choices of sensor types and locations directly influence structural-identification outcomes, sensor-placement methodologies have recently been developed to ensure successful model-updating results. Due to the nature of static and dynamic measurements, sensor-placement methodologies are usually developed independently. However, both types of load testing are used to update the same bridge behavior model. Therefore, when sensor-placement strategies are established independently, redundant sensor information is likely. In this study, two measurement-system design methodologies are proposed. First, a new methodology for sensor-placement for dynamic load testing is presented, where expected information gain of natural frequencies is used to prioritize sensor-location selections. Then, a measurement-system-design methodology combining information of both static and dynamic load testing is proposed. Finally, the methodology is evaluated using a full-scale bridge. A well-designed measurement system based on expected information gain enhances system identification and reserve-capacity estimation.

A transfer operator methodology for optimal sensor placement accounting for uncertainty

Sensors in buildings are used for a wide variety of applications such as monitoring air quality, contaminants, indoor temperature, and relative humidity. These are used for accessing and ensuring indoor air quality, and also for ensuring safety in the event of chemical and biological attacks. It follows that optimal placement of sensors become important to accurately monitor contaminant levels in the indoor environment. However, contaminant transport inside the indoor environment is governed by the indoor flow conditions which are affected by various uncertainties associated with the building systems including occupancy and boundary fluxes. Therefore, it is important to account for all associated uncertainties while designing the sensor layout. The transfer operator based framework provides an effective way to identify optimal placement of sensors. Previous work has been limited to sensor placements under deterministic scenarios. In this work we extend the transfer operator based approach for optimal sensor placement while accounting for building systems uncertainties. The methodology provides a probabilistic metric to gauge coverage under uncertain conditions. We illustrate the capabilities of the framework with examples exhibiting boundary flux uncertainty.

Non-contact sensor placement strategy for condition monitoring of rotating machine-elements

Careful selection and location of sensors are of key importance in the construction and implementation of an effective condition monitoring system. There is a continual call for depletion of maintenance and operational costs of rotating machine elements. Health monitoring of bearings, which is regarded as a crucial component of rotating machinery, is expected to facilitate in the preclusion of machine breakdown and ensure the machine availability by maintenance actions in time. The effectiveness and reliability of measurement approaches for monitoring the condition of the bearing are influenced by both the signal processing techniques and locations of the sensors selected for fault characteristic extraction. This paper proposes a low cost Non-contact optimal sensor placement (NC-OSP) methodology in order to get information of high quality related to the dynamic features of the machines. Experiments were conducted using different bearing conditions under different operating conditions and sensor placement positions. Mathematical models have been proposed based on the response parameters and input variables experimentation using response surface methodology. Results indicate that the most effective input variable to control the response parameters viz. FFT vibration amplitude of characteristic frequency and RMS value of time domain was the shaft speed followed by load and angle of incidence. The responses proposed by the optimal models have been observed at 8° angle of incidence with maximum load and speed. The optimal outcomes have been validated experimentally which proved that the predicted results were in sync with the actual ones. The proposed work has significant potential in industrial environment with complex systems, where the condition monitoring approach with proper placement of sensors can play an important role.

An Entropy Based Bayesian Network Framework for System Health Monitoring

Oil pipeline network system health monitoring is important primarily due to the high cost of failure consequences. Optimal sensor selection helps provide more effective system health information from the perspective of economic and technical constraints. Optimization models confront different issues. For instance, many oil pipeline system performance models are inherently nonlinear, requiring nonlinear modelling. Optimization also confronts modeling uncertainties. Oil pipeline systems are among the most complicated and uncertain dynamic systems, as they include human elements, complex failure mechanisms, control systems, and most importantly component interactions. In this paper, an entropy-based Bayesian network optimization methodology for sensor selection and placement under uncertainty is developed. Entropy is a commonly used measure of information often been used to characterize uncertainty, particularly to quantify the effectiveness of measured signals of sensors in system health monitoring contexts. The entropy based Bayesian network optimization outlined herein also incorporates the effect that sensor reliability has on system information entropy content, which can also be related to the sensor cost. This approach is developed further by incorporating system information entropy and sensor costs in order to evaluate the performance of sensor combinations. The paper illustrates the approach using a simple oil pipeline network example. The so-called particle swarm optimization algorithm is used to solve the multi-objective optimization model, establishing the Pareto frontier.

Surface heat assessment for developed environments: Optimizing urban temperature monitoring

The urban heat island effect, exacerbated by rising average surface temperatures due to climate change, can lead to adverse impacts on city populations. Fine resolution modeling of the spatial and temporal distribution of extreme heat risk within a city can improve the strategies used to mitigate this risk, such as the issuance of targeted heat advisories to city residents. In this paper, we combine a recently developed method for probabilistic modeling of urban temperatures with previously developed vulnerability assessments, and then implement sensor placement optimization techniques to guide temperature monitoring in urban areas. A variety of metrics are used to optimize the placement of temperature measures to best support decision-making for monitoring and responding to extreme heat risk. This optimal sensor placement methodology is demonstrated for the city of Pittsburgh, PA, resulting in several proposed temperature monitoring schemes based on the various sensor performance metrics investigated. We quantitatively and qualitatively compare these schemes to identify the relative merits of each proposed metric.