Performance-based optimal sensor placement method for single-layer reticulated shells considering modal observability and damage identifiability

The current work aims at determining optimal sensor configurations for the modal identification of a post-tensioned timber frame structure. The objective is to maximise the information gained from the structural testing, while keeping the number of necessary sensors to a minimum. Three different and widely used optimal sensor placement (OSP) methods are investigated and evaluated based on appropriate metrics, namely the effective independence method, the modal kinetic energy method and the information entropy (IE) method. An enhanced IE variant is adopted, which resolves the problem of close positioning of sensors, which forms a common issue when sensor positions are selected from a dense grid. In terms of the adopted metrics, three different options are investigated, namely, the information entropy index, the Modal Assurance Criterion and a newly introduced metric, the relative dispersion index. For the quantification of trade-offs among the selected metrics a Pareto Front scheme is realised. The study indicates that the evaluation of different OSP configurations is strongly dependent on the employed metric. It is therefore of vital importance to select the appropriate metric when determining optimal sensor positions.

Optimal sensor placement (OSP) method plays a key role in setting up a health monitoring system for large-scale structures. This paper describes the implementation of monkey algorithm (MA) as a strategy for the optimal placement of a predefined number of sensors. To effectively maintain the population diversity while enhancing the exploitation capacities during the optimization process, a novel niching monkey algorithm (NMA) by combining the MA with the niching techniques is developed in this paper. In the NMA, the dual-structure coding method is adopted to code the design variables and a chaos-based approach instead of a pure random initialization is employed to initialize the monkey population. Meanwhile, the niche generation operation and fitness sharing mechanism are modified and incorporated to alleviate the premature convergence problem while enhancing the exploration of new search domain. In addition, to promote interactions and share the available resources, the replacement scheme is proposed and adopted among the niches. Finally, numerical experiments are conducted on a high-rise structure to evaluate the performance of the proposed NMA. It is found that the innovations in the proposed NMA can effectively improve the convergence of algorithm and generate superior sensor configurations when compared to the original MA.

Optimal sensor placement and structural health monitoring methods of ancient stone bridges based on an improved genetic algorithm: Taking Lugou Bridge as an example

This study investigates the application of the inverse finite element method (iFEM) in fracture mechanics by developing a novel two‐dimensional six‐node triangular inverse crack‐tip element. With its simplified formulation, the proposed inverse element is computationally efficient and ensures strain singularity at the crack tip by repositioning midside nodes. Its displacement‐based stress intensity factor (SIF) computation methodology integrates seamlessly with the existing iFEM framework, making it highly suitable for real‐time health assessment of structures with pre‐existing cracks. The inverse element has been rigorously validated for shape‐sensing and mixed‐mode SIF calculations by considering various crack geometries and mixed‐mode loading conditions. The triangular inverse element demonstrates superior flexibility in handling structured and unstructured discretizations in mapping regular and complex geometries, particularly high‐stress gradient areas like crack tips. The study also explores the variational least squares method for optimal sensor placement within the inverse element domain, ensuring accurate shape‐sensing and SIF computations with fewer onboard strain sensors. The proposed inverse formulation, with its accurate shape‐sensing capabilities and precise reconstruction of fracture parameters, represents a significant advancement in the real‐time Structural Health Monitoring of engineering structures with pre‐existing cracks.

A methodology, termed estimation error minimization (EEM) method, was proposed to determine the optimal number and locations of sensors so as to better estimate the vibration response of the entire structure. Utilizing the limited sensor measurements, the entire structure response can be estimated based on the system equivalent reduction-expansion process (SEREP) method. In order to compare the capability of capturing the structural vibration response with other optimal sensor placement (OSP) methods, the effective independence (EI) method, modal kinetic energy (MKE) method and modal assurance criterion (MAC) method, were also investigated. A statistical criterion, root mean square error (RMSE), was employed to assess the magnitude of the estimation error between the real response and the estimated response. For investigating the effectiveness and accuracy of the above OSP methods, a 31-bar truss structure is introduced as a simulation example. The analysis results show that both the maximum and mean of the RMSE value obtained from the EEM method are smaller than those from other OSP methods, which indicates that the optimal sensor configuration obtained from the EEM method can provide a more accurate estimation of the entire structure response compared with the EI, MKE and MAC methods.

The response sensitivity method in time domain has been applied extensively for damage identification. In this paper, the relationship between the error of damage identification and the sensitivity matrix is investigated through perturbation analysis. An index is defined according to the perturbation amplify effect and an optimal sensor placement method is proposed based on the minimization of that index. A sequential sub-optimal algorithm is presented which results in consistently good location selection. Numerical simulations with a two-dimensional high truss structure are conducted to validate the proposed method. Results reveal that the damage identification using the optimal sensor placement determined by the proposed method can identify multiple damages of the structure more accurately.

Structural health monitoring (SHM) is gaining more attention, particularly for bridge structures to continuously evaluate their structural performance and assure their serviceability and safety throughout their service life. To assure reliable SHM systems, optimal sensor placement (OSP) is a cornerstone since it directly influences the quality of obtained data and, thus, the accuracy of the diagnosis. Hence, determining the optimal sensor configuration is a critical step to acquire the maximum information on the structural behavior. Of the available OSP methods, the effective independence method (EFI), which aims to assure that the mode shapes identified from the recorded vibrations are orthogonal to each other, is popular and widely used in literature. Despite its popularity, there are no clear guidelines on how to select the modes that will be included in the OSP application. This chapter evaluates the impact of various parameters including the selected number of mode shapes and sensors on the results of OSP using EFI.KeywordsOptimal sensor placementEffective independence methodStructural health monitoringFinite element modelingModal mass participation

Although intensive development continues on innovative sensor systems, there is still considerable uncertainty in deciding on the number of sensors required and their locations in order to obtain adequate information on structural behavior. This paper is concerned with the sensor locations on a beam-structure for prognostic structural health monitoring. The purpose of this study is to investigate how to determine optimal sensor placement(OSP) from the sensitivity information of a known failure mode. The sensitivity of the forced vibration response of a beam to the variation of stiffness due to a crack is calculated analytically and used to determine the optimal sensor locations for the specified failure mode. The results of this method compared with the results of different OSP methods. The results have shown that the proposed method on optimal sensor placement is very effective in structural health monitoring.

Structural health monitoring plays an increasingly significant role in detecting damages for large and complex structures to ensure their serviceability and sustainability. Optimal sensor placement is critical in the structural health monitoring system as the sensor configuration directly impacts the quality of collected data used for structural health diagnosis. Therefore, this study presents a comprehensive review of computational methodologies for optimal sensor placement in structural health monitoring. The problem formulation of optimal sensor placement is first introduced, including commonly used evaluation criteria for sensor configurations. Then, various existing optimization methodologies for sensor placement are summarized and introduced in detail, especially for the evolutionary algorithms and their improved variants. Finally, the suitability of computational methods for specific structural health monitoring applications is also discussed. The main goal of this study is to deliver a comprehensive reference of computational methodologies for optimal sensor placement in structural health monitoring studies and applications. This article is concluded by highlighting the most widely utilized evaluation criteria and optimization methodologies for sensor configuration determination.

Blasts can produce, in a very short time, an overload much greater than the design load of a building. The blast explosion nearby or within structures causes catastrophic damage to the building both externally and internally. This study intends to model a Cold-Formed Steel (CFS) building using Finite Element Method (FEM) in which material properties of the model are defined according to results of performed laboratory tests. Then accelerograph record of a standard blast was applied to the Finite Element (FE) model. Furthermore, various Optimal Sensor Placement (OSP) algorithms were used and Genetic Algorithm (GA) was selected to act as the solution of the optimization formulation in selection of the best sensor placement according to the blast loading response of the system. In this research a novel numerical algorithm was proposed for OSP procedure which utilizes the exact value of the structural response under blast excitation. Results show that with a proper OSP method for Structural Health Monitoring (SHM) can detect the weak points of CFS structures in different parts efficiently.

The optimal placement method of sensors is carried out based on improved genetic algorithm for solving the sensors optimal placement problem of the health monitoring system for long-span railway bridge. Dual structure coding method is introduced to improve the individual encoding method in the Genetic Algorithm. Adaptive partial matching crossover and inversus mutation method is adopted in the optimal preservation strategy, and the probabilities of crossover and mutation are changed automatically according to the fitness value for obtaining the global optimal solution of the sensor placement. So some defects in other Genetic Algorithm applied in the optimal placement of sensors for major bridge structure, such as slow convergence speed and easily falling into local optimum etc., are overcome, and the convergence is ensured. Then the optimal sensors placement of the health monitoring system for one certain long-span railway steel truss cable-stayed bridge is taken as the example to verify the proposed improved genetic algorithm. The result shows that the proposed method has better global optimization, computational efficiency and reliability in compare with the Simple Genetic Algorithm and General Genetic Algorithm, and can be applied to the actual railway cable-stayed bridge health monitoring system for the optimal sensors placement.

Accurate localization is a critical task in underwater navigation. Typical localization methods use a set of acoustic sensors and beacons to estimate relative position, whose geometric configuration has a significant impact on the localization accuracy. Although there is much effort in the literature to define optimal 2D or 3D sensor placement, the optimal sensor placement in irregular and constrained 3D surfaces, such as autonomous underwater vehicles (AUVs) or other structures, is not exploited for improving localization. Additionally, most applications using AUVs employ commercial acoustic modems or compact arrays, therefore the optimization of the placement of spatially independent sensors is not a considered issue. This article tackles acoustic sensor placement optimization in irregular and constrained 3D surfaces, for inverted ultra-short baseline (USBL) approaches, to improve localization accuracy. The implemented multi-objective memetic algorithm combines an evaluation of the geometric sensor's configuration, using the Cramer-Rao Lower Bound (CRLB), with the incidence angle of the received signal. A case study is presented over a simulated homing and docking scenario to demonstrate the proposed optimization algorithm.

A sensor (microphone) placement method based on mutual information for spatial sound field recording is proposed. The sound field recording methods using distributed sensors enable the estimation of the sound field inside a target region of arbitrary shape; however, it is a difficult task to find the best placement of sensors. We focus on the mutual-information-based sensor placement method in which spatial phenomena are modeled as a Gaussian process (GP). We propose the use of the sound-field-interpolation kernel for the covariance of measurements in a GP model to obtain the sensor placement suitable for sound field recording. We also extend the method to treat broadband signals and derive an efficient algorithm based on block matrix inversion. Numerical simulation results indicated that the proposed method achieves accurate sound field estimation compared with a method using the generally used Gaussian kernel.

We consider the problem of sensor placement (both spatial location and number) for a class of parameter-dependent diffusion-advection processes that model environmental processes. To distinguish between advection and diffusion dominated environmental processes, the Péclet number, Pe, which takes values over a set of a priori defined values, is utilized to optimize the number and spatial location of the sensors required. The minimum number of sensors is defined using system theoretic measures and essentially considers the smallest number of sensors that would render the system observable, thereby facilitating the design of a state observer. The optimization metric is defined with respect to the spatial H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm of the dominant system modes, which may differ for different values of Pe. For each value of Pe, a set of optimal sensor locations and number is found and the associated state estimator is designed. The supervisory scheme then schedules the sensors corresponding to the Péclet number that describes the process at a given time by pouting in sleep mode all sensors associated with a different value of Pe and activating the sensors that are optimal for the current value of Pe. At the same time, the state estimator also switches by using the filter gain corresponding to the current value of the Péclet number and the active sensors. Extensive simulation studies are included to provide further inside on parameter-dependent sensor and observer scheduling for environmental processes.

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.