Optimal Sensor Placement Algorithm Research Articles

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.

Simultaneous seismic input and state estimation with optimal sensor placement for building structures using incomplete acceleration measurements

Simultaneous real-time input and state estimation and optimal sensor placements are investigated in this paper, focusing on systems without direct feedthrough, such as earthquake-excited building structures with absolute floor acceleration measurements. Current studies showed that system properties such as strong observability, strong* detectability (the asterisk distinguishes strong* detectability from strong detectability), and invertibility conditions are crucial to the stability and convergence of unknown input and state estimation, but they can often be violated in practice. Consequently, uncertainties such as modeling errors and measurement noise can greatly degrade the accuracy and stability of the estimations. Estimation in this case has remained challenging due to the above reasons. To fill this gap, this paper develops an optimal sensor placement algorithm (OSPA) for real-time unknown input and state estimation, which ensures the required system conditions are met. The developed OSPA is integrated with two optimal real-time Kalman-based filters, a minimum-variance unbiased input and state estimation filter (MVUIS) and an Augmented State Kalman Filter (ASKF), for simultaneous input and state estimation. In particular, the MVUIS is presented in a recursive three-step structure without using the arbitrary matrix in the gain, which makes no assumptions on the input but requires strong* detectability. To avoid the requirement, ASKF is derived from the MVUIS by incorporating prior knowledge of the input. The developed OSPA along with the MVUIS and ASKF provide the optimal input and state estimation in real-time without incurring low-frequency drift or unstable estimations. Notably, the OSPA improves the performance of MVUIS by reducing amplitude errors and enhances the accuracy of ASKF by reducing phase errors. The developed OSPA integrated with the MVUIS and ASKF are validated through numerical and experimental studies as well as a real-world instrumented building structure under earthquakes using incomplete absolute acceleration measurements.

Real-time assessment of asphalt pavement moduli and traffic loads using monitoring data from Built-in Sensors: Optimal sensor placement and identification algorithm

Asphalt pavement performance is gradually attenuated subjected to repeated traffic loads. Grasping the relationship between the repeated traffic loads and pavement modulus attenuation is crucial for understanding pavement mechanical behavior, improving pavement design methods, and guiding maintenance decisions. However, the current bottleneck is that neither the existing non-destructive testing nor monitoring methods can simultaneously obtain the information of traffic loads and pavement moduli. To fill this gap, an innovative real-time assessment method of asphalt pavement moduli and traffic loads from the aspect of structural health monitoring was proposed. On the one hand, the optimal sensor placement was determined by the theoretical relationships between moduli, loads, and mechanical responses based on elastic multi-layered theory. On the other hand, the corresponding algorithm for stepwise decoupling identification of asphalt pavement moduli and traffic loads to match the optimal sensor placement was developed. Therefrom, the validity of the proposed assessment method was theoretically verified, and the effects of the viscoelastic property of asphalt materials, measurement errors, and layer thickness on the identification accuracy were comprehensively discussed. The proposed assessment method was applied to the realistic pavement to further prove its applicability. Results show that the proposed assessment method can both evaluate pavement moduli and traffic loads accurately. The proposed assessment method has application prospects for simultaneous real-time monitoring of the pavement modulus attenuation and traffic loads, which helps understand the pavement damage behavior, improve pavement design methods, and guide maintenance decisions.

Distribution Systems AC State Estimation via Sparse AMI Data Using Graph Signal Processing

This work establishes and validates a Grid Graph Signal Processing (G-GSP) framework for estimating the state vector of a radial distribution feeder. One of the key insights from GSP is the generalization of Shannon’s sampling theorem for signals defined over the irregular support of a graph, such as the power grid. Using a GSP interpretation of Ohm’s law, we show that the system state can be well approximated with relatively few components that correspond to low-pass Graph Fourier Transform (GFT) frequencies. The target application of this theory is the formulation of a three-phase unbalanced Distribution System State Estimation (DSSE) formulation that recovers the GFT approximation of the system state vector from sparse Advanced Metering Infrastructure (AMI) measurements. To ensure convergence of G-GSP for DSSE, the proposed solution relies on a convex relaxation technique. Furthermore, we propose an optimal sensor placement algorithm for AMI measurements. Numerical results demonstrate the efficacy of the proposed method.

Early lumping observer design and sensor placement for transport-reaction systems

This paper deals with the observer design problem for a class of one-dimensional multi-species transport-reaction systems satisfying sector bounded nonlinearities and considering measurements distributed over the spatial domain. A design method is proposed based on a reduced-order model and a Lyapunov function, which provides sufficient conditions in terms of standard linear matrix inequalities (LMIs) to ensure the exponential convergence of the estimation error with a prescribed decay rate. The observer performance is further improved through an offline optimal sensor placement algorithm considering a parameterized reduced-order output matrix. A nonisothermal tubular reactor is presented to demonstrate the observer performance as well as the advantages of the proposed sensor placement optimization scheme.

Optimal Sensor Placement in Reduced-Order Models Using Modal Constraint Conditions.

Sensor measurements of civil structures provide basic information on their performance. However, it is impossible to install sensors at every location owing to the limited number of sensors available. Therefore, in this study, we propose an optimal sensor placement (OSP) algorithm while reducing the system order by using the constraint condition between the master and slave modes from the target modes. The existing OSP methods are modified in this study, and an OSP approach using a constrained dynamic equation is presented. The validity and comparison of the proposed methods are illustrated by utilizing a numerical example that predicts the OSPs of the truss structure. It is observed that the proposed methods lead to different sensor layouts depending on the algorithm criteria. Thus, it can be concluded that the OSP algorithm meets the measurement requirements for various methods, such as structural damage detection, system identification, and vibration control.

Optimal sensor placements using modified Fisher information matrix and effective information algorithm

This article presents an optimal sensor placement algorithm for modifying the Fisher information matrix and effective information. The modified Fisher information matrix and effective information are expressed using a dynamic equation constrained by the condensed relationship of the incomplete mode shape matrix. The mode shape matrix row corresponding to the master degree of freedom of the lowest-contribution Fisher information matrix and effective information indices is moved to the slave degree of freedom during each iteration to obtain an updated shape matrix, which is then used in subsequent calculations. The iteration is repeated until the target sensors attain the targeted number of modes. The numerical simulations are then applied to compare the optimal sensor placement results obtained using the number of installed sensors, and the contribution matrices using the Fisher information matrix and effective information approaches are compared based on the proposed parameter matrix. The mode-shape-based optimal sensor placement approach selects the optimal sensor layout at the positions to uniformly allocate the entire degree of freedom. The numerical results reveal that the proposed F-based and effective information–based approaches lead to slightly different results, depending on the number of parameter matrix modes; however, the resulting final optimal sensor placement is included in a group of common candidate sensor locations. However, the resulting final optimal sensor placement is included in a group of common candidate sensor locations.

Optimal sensor placement of bridge structure based on sensitivity‐effective independence method

Taking the optimal sensor placement problem in bridge structural health monitoring as the study object and relying on the engineering example of a simply supported steel truss bridge, the improved optimal sensor placement method based on sensitivity-effective independence method was proposed. Using the sensitivity coefficient reflecting structural damage, the proposed method could modify the effective independence method reflecting the maximum linear independence. The proposed method further optimizes the sensor placement method. A method for selecting the number of models based on modal closeness was proposed and makes the selection of the number of modes more objective. The example analysis shows that evaluations using this method are effective for multiple evaluation criteria. The method ensures observability of the mode vector and identifiability of structural damage. It is an effective optimal sensor placement algorithm for the bridge structure.

Minimizing observation spillover for pose control of elastic bodies using optimal sensor placement

The impact of elastic modes limits the performance of position control of elastic bodies in a significant way. Local dampers are a typical way to suppress this issue, but lead to non-proportional damping and complex oscillation modes with varying nodal lines. To this end, the placement of the sensors is of major importance in high-precision applications. In this contribution, we present an optimal sensor placement algorithm which uses Gramian-based observability measures to overcome this issue. Singular sensing configurations with respect to the pose are avoided by considering the mappings’ local invertibility explicitly. Furthermore, we are in the position to cope with the highly relevant issue of constrained installation space and to handle complex 2D and 3D geometries by using model order reduction techniques. By means of an illustrative example, the significantly reduced influence of the elastic deformations on the controller is demonstrated at last.

Serious Sensor Placement—Optimal Sensor Placement as a Serious Game

In this paper, we present a novel approach in water loss research combining two different topics: The optimal placement of pressure sensors to localize leaks in water distribution systems and Serious Gaming—games that are not only entertaining but that are also serving another purpose. The goal was to create a web interface, through which gamers could place sensors in a water distribution system model, in order to improve these sensor positions after they had been evaluated by a suitable algorithm. Two game objectives are to be pursued by the players: reaching a specified net coverage while not using more than a maximum number of sensors. For this purpose, an existing optimal sensor placement algorithm was extended and implemented, together with two hydraulic models taken from literature. The resulting Serious Game was then tested and rated in a case study. The results showed that human players are able to reach solutions that are similar regarding net coverage to those obtained by optimization, within in a short amount of time. Furthermore, it was shown that the implementation of the ideal sensor placement problem as a Serious Game motivates the players to get better and better results, while also providing them with an enjoyable gaming experience.

Evaluation of optimal sensor placement algorithms for the Structural Health Monitoring of architectural heritage. Application to the Monastery of San Jerónimo de Buenavista (Seville, Spain)

In recent years, Structural Health Monitoring (SHM) based on Operational Modal Analysis (OMA) and damage detection tools has become a popular non-destructive solution to assess the real-time integrity of any kind of structure. This technique is especially well-suited for the condition-based conservation of historical structures, where minimal invasiveness must be ensured owing to their high cultural and architectural value. Optimal Sensor Placement (OSP) techniques represent a valuable tool for efficiently designing the sensor layout in a SHM system in order to achieve an effective modal identification with a reduced number of sensors and, consequently, an improved cost efficiency. In this light, this paper proposes a design methodology of sensor networks based on OSP techniques suitable for historical structures. To do so, a preliminary extensive OMA campaign is conducted in order to construct a reliable finite element (FE) model by fitting the identified modal properties. Afterwards, an optimal sensor arrangement with a limited number of sensors is obtained by applying different model-based OSP techniques. In order to improve the robustness of the solution, material uncertainties are included in the model and the optimal sensor placement is conducted within a statistical framework. This methodology is presented and evaluated with a case study of a Spanish secular building: the Monastery of San Jerónimo de Buenavista in Seville (Spain). In particular, this paper presents the results of the preliminary ambient vibration test and the modal identification of the monastery, the updating process of the FE model, as well as a critical review of the different OSP techniques within a framework of material parameter uncertainty. The presented analysis demonstrate that OSP techniques based on the rank optimization of the kinetic energy matrix of the structure yield robust sensor layout.

An optimal sensor placement algorithm (O-SPA) for improving tracking precision of human activity in real-world healthcare systems

In this article, an Optimal Sensor Placement Algorithm (O-SPA) is designed for improving the precision of human activity. This placement algorithm is designed based on the fact of improving the Rate of Observation (RO) and sensing in the day-to-day activities of human. SPA for RO and sensing improves the analysis precision by accumulating and classifying useful sensor information. Useful sensor information is achieved by approximating the sensor data mitigating positioning errors. The analysis process differentiates useful and less preference information from the placed sensors to reduce complications in classification. This device positioning algorithm is more specific for the precision of data accumulation and manipulation by reducing sensing errors to improve the efficiency of healthcare systems The efficiency of healthcare systems with optimal sensor deployment is measured in terms of accuracy (98.9%), classification time (0.079s), replications (4.12), recall (96.29%), and error factor (0.000021). The efficiency results are the best compared to Hybrid sensing aided human activity recognition (HHAR), Multi-sensor fusion with ensemble pruning system (MSF-EP) and Activities of daily living Compressive sensing (ADL).

Coverage intensity of optimal sensors for common, isolated, and integrated steel structures using novel approach of FEM-MAC-TTFD

The coverage intensity of sensors is the most important issue on structural health monitoring technique. The geometric configuration of sensors must be optimized based on coverage intensity with proper objectives. In this article, a novel algorithm for optimal sensor placement in various steel frames was evaluated. These frames including moment-resisting frame, moment-resisting frame with base isolation, and moment-resisting frame with base isolation with steel shear wall were selected for case studies. This approach was proposed based on combination of common optimal sensor placement algorithm and nonlinear time history analysis. A new method called transformed time history to frequency domain approach was evaluated to transform nonlinear time history analysis results to frequency domain and then the effective frequencies according the maximum range of Fourier amplitude were selected. The modified type of modal assurance criterion values can be achieved from modal assurance criterion with the exact seismic displacement. All of novel optimal sensor placement processes were done through FEM-MAC-TTFD code modeled and developed in MATLAB by authors of this article. The results show that there is good relative correlation between the sensors number and coverage intensity obtained with modal and modified modal assurance criterion approaches for moment-resisting frame system, but for integrated frame such as moment-resisting frame with base isolation and moment-resisting frame with base isolation with steel shear wall, the modified modal assurance criterion approach is better approach. There is no significant difference between coverage intensity of sensors for top joints between modal assurance criterion and modified modal assurance criterion approaches for moment-resisting frame, moment-resisting frame with base isolation, and moment-resisting frame with base isolation with steel shear wall systems ( R2 = 0.994, 0.986, and 0.724, respectively). It was found that if reference point is located in center of frame, there is significant difference between modal assurance criterion and modified modal assurance criterion approaches, and modified modal assurance criterion generated slightly better results.

Optimal sensor placement and assessment for modal identification

A review is presented on a wide range of optimal sensor placement (OSP) strategies and ways of evaluation. An assessment-guided optimal sensor placement algorithm based on minimal root mean square is proposed to give quantitative comparison on these options. The algorithm is applied to an example of a cantilever beam, as well as to a jacket-platform where model uncertainty and measurement error are included simultaneously. The results reveal the influence of the number of desired sensors and the number of modes of interest. It is shown that the optimal sensor placement selected by the proposed strategy yields the best modal orthogonality of the corresponding mode shapes, and competitive results are derived on the other two assessment standards, i.e. the condition number of the reduced mode shape matrix and the determinant of the Fisher information matrix. The conclusions also show that the effective independence method keeps the largest determinant, and there seems no regular trend on the condition number but unexpected biased solutions can be derived when unreasonable combination for number of wanted sensors and modes of interest are chosen. The proposed minimal root mean square algorithm is capable of avoiding this drawback.

Reconstruction of unidirectional strain maps via iterative signal fusion for mesoscale structures monitored by a sensing skin

Abstract Flexible skin-like membranes have received considerable research interest for the cost-effective monitoring of mesoscale (large-scale) structures. The authors have recently proposed a large-area electronic consisting of a soft elastomeric capacitor (SEC) that transduces a structure’s change in geometry (i.e. strain) into a measurable change in capacitance. The SEC sensor measures the summation of the orthogonal strains (i.e. e x + e y ). It follows that an algorithm is required for the decomposition of the sensor signal into unidirectional strain maps. In this study, a new method enabling such decomposition, leveraging a dense sensor network of SECs and resistive strain gauges (RSGs), is proposed. This method, termed iterative signal fusion (ISF), combines the large-area sensing capability of SECs and the high-precision sensing capability of RSGs. The proposed ISF method adaptively fuses the different sources of signal information (e.g. from SECs and RSGs) to build a structure’s best fit unidirectional strain maps. Each step of ISF contains an update process for strain maps based on the Kriging model. To demonstrate the accuracy of the proposed method, an experimental test bench is developed, which is the largest deployment of the SEC-based sensing skin to date in terms of both size and sensor count. A network of 40 SECs deployed on a grid (5 × 8) is utilized and an optimal sensor placement algorithm is used to select the optimal RSG sensor locations within the network of SECs. Results show that the proposed ISF method is capable of reconstructing unidirectional strain maps for the experimental test plate. In addition to the experimental data, a numerical validation for the ISF method is provided through a finite element analysis model of the experimental test bench.

An online input force time history reconstruction algorithm using dynamic principal component analysis

Abstract The knowledge of dynamic loads acting on a structure is always required for many practical engineering problems, such as structural strength analysis, health monitoring and fault diagnosis, and vibration isolation. In this paper, we present an online input force time history reconstruction algorithm using Dynamic Principal Component Analysis (DPCA) from the acceleration time history response measurements using moving windows. We also present an optimal sensor placement algorithm to place limited sensors at dynamically sensitive spatial locations. The major advantage of the proposed input force identification algorithm is that it does not require finite element idealization of structure unlike the earlier formulations and therefore free from physical modelling errors. We have considered three numerical examples to validate the accuracy of the proposed DPCA based method. Effects of measurement noise, multiple force identification, different kinds of loading, incomplete measurements, and high noise levels are investigated in detail. Parametric studies have been carried out to arrive at optimal window size and also the percentage of window overlap. Studies presented in this paper clearly establish the merits of the proposed algorithm for online load identification.

Optimal sensor placement for maximum area coverage (MAC) for damage localization in composite structures

In this paper an optimal sensor placement algorithm for attaining the maximum area coverage (MAC) within a sensor network is presented. The proposed novel approach takes into account physical properties of Lamb wave propagation (attenuation profile, direction dependant group velocity due to material anisotropy) and geometrical complexities (boundary reflections, presence of openings) of the structure. A feature of the proposed optimization approach lies in the fact that it is independent of characteristics of the damage detection algorithm (e.g. probability of detection) making it readily up-scalable to large complex composite structures such as aircraft stiffened composite panel. The proposed fitness function (MAC) is independent of damage parameters (type, severity, location). Statistical analysis carried out shows that the proposed optimum sensor network with MAC results in high probability of damage localization. Genetic algorithm is coupled with the fitness function to provide an efficient optimization strategy.

Optimal sensor placement for time-domain identification using a wavelet-based genetic algorithm

This paper presents a wavelet-based genetic algorithm strategy for optimal sensor placement (OSP) effective for time-domain structural identification. Initially, the GA-based fitness evaluation is significantly improved by using adaptive wavelet functions. Later, a multi-species decimal GA coding system is modified to be suitable for an efficient search around the local optima. In this regard, a local operation of mutation is introduced in addition with regeneration and reintroduction operators. It is concluded that different characteristics of applied force influence the features of structural responses, and therefore the accuracy of time-domain structural identification is directly affected. Thus, the reliable OSP strategy prior to the time-domain identification will be achieved by those methods dealing with minimizing the distance of simulated responses for the entire system and condensed system considering the force effects. The numerical and experimental verification on the effectiveness of the proposed strategy demonstrates the considerably high computational performance of the proposed OSP strategy, in terms of computational cost and the accuracy of identification. It is deduced that the robustness of the proposed OSP algorithm lies in the precise and fast fitness evaluation at larger sampling rates which result in the optimum evaluation of the GA-based exploration and exploitation phases towards the global optimum solution.

Sensor Placement for Structural Monitoring of Transmission Line Towers

Transmission line towers are usually analyzed using linear elastic idealized truss models. Due to the assumptions used in the analysis, there are discrepancies between the actual results obtained from full scale prototype testing and the analytical results. Therefore, design engineers are interested in assessing the actual stress levels in transmission line towers. Since it is costly to place sensors on every member of a tower structure, the best locations for sensors need to be carefully selected. This study evaluates a methodology for sensor placement in transmission line towers. The objective is to find optimal locations for sensors such that the real behavior of the structure can be explained from measurements. The methodology is based on the concepts of entropy and model falsification. Sensor locations are selected based on maximum entropy such that there is maximum separation between model instances that represent different possible combinations of parameter values which have uncertainties. The performance of the proposed algorithm is compared to that of an intuitive method in which sensor locations are selected where the forces are maximum. A typical 220 kV transmission tower is taken as case study in this paper. It is shown that the intuitive method results in much higher number of non-separable models compared to the optimal sensor placement algorithm. Thus the intuitive method results in poor identification of the system.

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.