A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement

In recent decades, structural health monitoring (SHM) has gained increased importance for ensuring the sustainability and serviceability of large and complex structures. To design an SHM system that delivers optimal monitoring outcomes, engineers must make decisions on numerous system specifications, including the sensor types, numbers, and placements, as well as data transfer, storage, and data analysis techniques. Optimization algorithms are employed to optimize the system settings, such as the sensor configuration, that significantly impact the quality and information density of the captured data and, hence, the system performance. Optimal sensor placement (OSP) is defined as the placement of sensors that results in the least amount of monitoring cost while meeting predefined performance requirements. An optimization algorithm generally finds the "best available" values of an objective function, given a specific input (or domain). Various optimization algorithms, from random search to heuristic algorithms, have been developed by researchers for different SHM purposes, including OSP. This paper comprehensively reviews the most recent optimization algorithms for SHM and OSP. The article focuses on the following: (I) the definition of SHM and all its components, including sensor systems and damage detection methods, (II) the problem formulation of OSP and all current methods, (III) the introduction of optimization algorithms and their types, and (IV) how various existing optimization methodologies can be applied to SHM systems and OSP methods. Our comprehensive comparative review revealed that applying optimization algorithms in SHM systems, including their use for OSP, to derive an optimal solution, has become increasingly common and has resulted in the development of sophisticated methods tailored to SHM. This article also demonstrates that these sophisticated methods, using artificial intelligence (AI), are highly accurate and fast at solving complex problems.

Monitoring of Damage in Composite Structures Using an Optimized Sensor Network: A Data-Driven Experimental Approach

Due to the complexity of the fracture mechanisms in composites, monitoring damage using a vibration-based structural response remains a challenging task. This is also complex when considering the physical implementation of a health monitoring system with its numerous uncertainties and constraints, including the presence of measurement noise, changes in boundary and environmental conditions of a tested object, etc. Finally, to balance such a system in terms of efficiency and cost, the sensor network needs to be optimized. The main aim of this study is to develop a cost- and performance-effective data-driven approach to monitor damage in composite structures and validate this approach through tests performed on a physically implemented structural health monitoring (SHM) system. In this study, we combined the mentioned research problems to develop and implement an SHM system to monitor delamination in composite plates using data combined from finite element models and laboratory experiments to ensure robustness to measurement noise with a simultaneous lack of necessity to perform multiple physical experiments. The developed approach allows the implementation of a cost-effective SHM system with validated predictive performance.

Sensor Placement Optimization for Shape Sensing of Plates and Shells Using Genetic Algorithm and Inverse Finite Element Method

This paper reports the first investigation of the inverse finite element method (iFEM) coupled with the genetic algorithm (GA) to optimize sensor placement models of plate/shell structures for their real-time and full-field deformation reconstruction. The primary goal was to reduce the number of sensors in the iFEM models while maintaining the high accuracy of the displacement results. Here, GA was combined with the four-node quadrilateral inverse-shell elements (iQS4) as the genes inherited through generations to define the optimum positions of a specified number of sensors. Initially, displacement monitoring of various plates with different boundary conditions under concentrated and distributed static/dynamic loads was conducted to investigate the performance of the coupled iFEM-GA method. One of these case studies was repeated for different initial populations and densities of sensors to evaluate their influence on the accuracy of the results. The results of the iFEM-GA algorithm indicate that an adequate number of individuals is essential to be assigned as the initial population during the optimization process to ensure diversity for the reproduction of the optimized sensor placement models and prevent the local optimum. In addition, practical optimization constraints were applied for each plate case study to demonstrate the realistic applicability of the implemented method by placing the available sensors at feasible sites. The iFEM-GA method's capability in structural dynamics was also investigated by shape sensing the plate subjected to different dynamic loadings. Furthermore, a clamped stiffened plate and a curved shell were also considered to assess the applicability of the proposed method for the shape sensing of complex structures. Remarkably, the outcomes of the iFEM-GA approach with the reduced number of sensors agreed well with those of the full-sensor counterpart for all of the plate/shell case studies. Hence, this study reveals the superior performance of the iFEM-GA method as a viable sensor placement strategy for the accurate shape sensing of engineering structures with only a few sensors.

Derivative-Free Observability Analysis for Sensor Placement Optimization of Bioinspired Flexible Flapping Wing System

Observability analysis of a bioinspired flexible flapping wing system provides a measure of how well the states of flexible flapping wing micro-aerial vehicles can be estimated from real-time measurements during high-speed flight. However, the traditional observability analysis approaches have trouble in terms of lack of quantitative analysis index, high computational complexity, low accuracy, and unavailability in stochastic systems with memory, including bioinspired flexible flapping wing systems. Therefore, a novel derivative-free observability analysis method is proposed here based on the generalized polynomial chaos expansion. By formulating a surrogate model to represent the relationship between the cumulative measurement and the random initial state, the observability coefficient matrix is calculated and the observability rank condition is stated. Consequently, several observability indices are proposed to quantity the observability of the system. Altogether, the proposed method avoids the disadvantages of the traditional approaches, especially in assessing the observability degree of each state and the effect of stochastic noise on observability. The validation of the proposed method is first provided by demonstrating the equivalence between the traditional and proposed methods and subsequently by comparing the observability of the Lorenz system calculated via three different approaches. Finally, the proposed method is applied on a bioinspired flexible wing system to optimize the placement of sensors, which is consistent with the natural configuration of campaniform sensilla on the wing of the hawkmoth.

Genetic Algorithm to Solve Optimal Sensor Placement for Underwater Vehicle Localization with Range Dependent Noises

In source localization problems, the relative geometry between sensors and source will influence the localization performance. The optimum configuration of sensors depends on the measurements used for the source location estimation, how these measurements are affected by noise, the positions of the source, and the criteria used to evaluate the localization performance. This paper addresses the problem of optimum sensor placement in a plane for the localization of an underwater vehicle moving in 3D. We consider sets of sensors that measure the distance to the vehicle and model the measurement noises with distance dependent covariances. We develop a genetic algorithm and analyze both single and multi-objective problems. In the former, we consider as the evaluation metric the arithmetic average along the vehicle trajectory of the maximum eigenvalue of the inverse of the Fisher information matrix. In the latter, we estimate the Pareto front of pairs of common criteria based on the Fisher information matrix and analyze the evolution of the sensor positioning for the different criteria. To validate the algorithm, we initially compare results with a case with a known optimal solution and constant measurement covariances, obtaining deviations from the optimal less than 0.1%. Posterior, we present results for an underwater vehicle performing a lawn-mower maneuver and a spiral descent maneuver. We also present results restricting the allowed positions for the sensors.

An Optimal Sensor Layout Using the Frequency Response Function Data within a Wide Range of Frequencies

This study presents iterative optimal sensor placement (OSP) techniques using the modal assurance criterion (MAC) and the effective independence (EI) algorithm. The algorithms use the proper orthogonal mode (POM) extracted from the frequency response functions (FRFs) of dynamic systems within a wide range of frequencies. The FRF-based OSP method proposed in this study has the merit of reflecting dynamic characteristics, unlike the mode shape-based method. Evaluating the MAC values and the EI indices at each iteration, the DOFs of low contribution to the objective function of candidate sensor DOFs are deleted from master DOFs and moved to slave DOFs. This process is repeated until the sensor number corresponds with the master DOFs. The validity of the proposed methods is illustrated in an example, the sensor layouts by the proposed methods are compared, and the layout inconsistency between the MAC and the EI techniques is analyzed.

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.

Damage Detection and Localization under Variable Environmental Conditions Using Compressed and Reconstructed Bayesian Virtual Sensor Data

Structural health monitoring (SHM) with a dense sensor network and repeated vibration measurements produces lots of data that have to be stored. If the sensor network is redundant, data compression is possible by storing the signals of selected Bayesian virtual sensors only, from which the omitted signals can be reconstructed with higher accuracy than the actual measurement. The selection of the virtual sensors for storage is done individually for each measurement based on the reconstruction accuracy. Data compression and reconstruction for SHM is the main novelty of this paper. The stored and reconstructed signals are used for damage detection and localization in the time domain using spatial or spatiotemporal correlation. Whitening transformation is applied to the training data to take the environmental or operational influences into account. The first principal component of the residuals is used to localize damage and also to design the extreme value statistics control chart for damage detection. The proposed method was studied with a numerical model of a frame structure with a dense accelerometer or strain sensor network. Only five acceleration or three strain signals out of the total 59 signals were stored. The stored and reconstructed data outperformed the raw measurement data in damage detection and localization.

Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors

Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show that under the A-optimality criterion, the optimization problem can be transferred to be a diagonalizing process on the AOA-based Fisher information matrix (FIM). Secondly, we prove that the FIM follows the invariance property of the 3D rotation, and the Gaussian covariance matrix of the FIM can be diagonalized via 3D rotation. Based on this finding, an optimal sensor placement method using 3D rotation was created for when prior information exists as to the target location. Finally, several simulations were carried out to demonstrate the effectiveness of the proposed method. Compared with the existing methods, the mean squared error (MSE) of the maximum a posteriori (MAP) estimation using the proposed method is lower by at least 25% when the number of sensors is between 3 and 6, while the estimation bias remains very close to zero (smaller than 0.15 m).

Training Data Selection and Optimal Sensor Placement for Deep-Learning-Based Sparse Inertial Sensor Human Posture Reconstruction

Although commercial motion-capture systems have been widely used in various applications, the complex setup limits their application scenarios for ordinary consumers. To overcome the drawbacks of wearability, human posture reconstruction based on a few wearable sensors have been actively studied in recent years. In this paper, we propose a deep-learning-based sparse inertial sensor human posture reconstruction method. This method uses bidirectional recurrent neural network (Bi-RNN) to build an a priori model from a large motion dataset to build human motion, thereby the low-dimensional motion measurements are mapped to whole-body posture. To improve the motion reconstruction performance for specific application scenarios, two fundamental problems in the model construction are investigated: training data selection and sparse sensor placement. The problem of deep-learning training data selection is to select independent and identically distributed (IID) data for a certain scenario from the accumulated imbalanced motion dataset with sufficient information. We formulate the data selection into an optimization problem to obtain continuous and IID data segments, which comply with a small reference dataset collected from the target scenario. A two-step heuristic algorithm is proposed to solve the data selection problem. On the other hand, the optimal sensor placement problem is studied to exploit most information from partial observation of human movement. A method for evaluating the motion information amount of any group of wearable inertial sensors based on mutual information is proposed, and a greedy searching method is adopted to obtain the approximate optimal sensor placement of a given sensor number, so that the maximum motion information and minimum redundancy is achieved. Finally, the human posture reconstruction performance is evaluated with different training data and sensor placement selection methods, and experimental results show that the proposed method takes advantages in both posture reconstruction accuracy and model training time. In the 6 sensors configuration, the posture reconstruction errors of our model for walking, running, and playing basketball are 7.25°, 8.84°, and 14.13°, respectively.

Optimal Flow Sensing for Schooling Swimmers

Fish schooling implies an awareness of the swimmers for their companions. In flow mediated environments, in addition to visual cues, pressure and shear sensors on the fish body are critical for providing quantitative information that assists the quantification of proximity to other fish. Here we examine the distribution of sensors on the surface of an artificial swimmer so that it can optimally identify a leading group of swimmers. We employ Bayesian experimental design coupled with numerical simulations of the two-dimensional Navier Stokes equations for multiple self-propelled swimmers. The follower tracks the school using information from its own surface pressure and shear stress. We demonstrate that the optimal sensor distribution of the follower is qualitatively similar to the distribution of neuromasts on fish. Our results show that it is possible to identify accurately the center of mass and the number of the leading swimmers using surface only information.

Efficient Sensor Placement Optimization for Shape Deformation Sensing of Antenna Structures with Fiber Bragg Grating Strain Sensors

This paper investigates the problem of an optimal sensor placement for better shape deformation sensing of a new antenna structure with embedded or attached Fiber Bragg grating (FBG) strain sensors. In this paper, the deformation shape of the antenna structure is reconstructed using a strain–displacement transformation, according to the measured discrete strain data from limited FBG strain sensors. Moreover, a two-stage sensor placement method is proposed using a derived relative reconstruction error equation. In this method, the initial sensor locations are determined using the principal component analysis based on orthogonal trigonometric (i.e., QR) decomposition, and then a new location is sequentially added into the initial sensor locations one by one by minimizing the relative reconstruction error considering information redundancy. The numerical simulations are conducted, and the comparisons show that the proposed method is advantageous in terms of the sensor distribution and computational cost. Experimental validation is performed using an antenna experimental platform equipped with an optimal FBG strain sensor configuration, and the reconstruction results show good agreements with those measured directly from displacement sensors. The proposed method has a large potential for the strain sensor placement of complex structures, and the proposed antenna structure with FBG strain sensors can be applied to the future wing-skin antenna or flexible space-based antenna.

On the Design of Smart Parking Networks in the Smart Cities: An Optimal Sensor Placement Model

Smart parking is a typical IoT application that can benefit from advances in sensor, actuator and RFID technologies to provide many services to its users and parking owners of a smart city. This paper considers a smart parking infrastructure where sensors are laid down on the parking spots to detect car presence and RFID readers are embedded into parking gates to identify cars and help in the billing of the smart parking. Both types of devices are endowed with wired and wireless communication capabilities for reporting to a gateway where the situation recognition is performed. The sensor devices are tasked to play one of the three roles: (1) slave sensor nodes located on the parking spot to detect car presence/absence; (2) master nodes located at one of the edges of a parking lot to detect presence and collect the sensor readings from the slave nodes; and (3) repeater sensor nodes, also called “anchor” nodes, located strategically at specific locations in the parking lot to increase the coverage and connectivity of the wireless sensor network. While slave and master nodes are placed based on geographic constraints, the optimal placement of the relay/anchor sensor nodes in smart parking is an important parameter upon which the cost and efficiency of the parking system depends. We formulate the optimal placement of sensors in smart parking as an integer linear programming multi-objective problem optimizing the sensor network engineering efficiency in terms of coverage and lifetime maximization, as well as its economic gain in terms of the number of sensors deployed for a specific coverage and lifetime. We propose an exact solution to the node placement problem using single-step and two-step solutions implemented in the Mosel language based on the Xpress-MPsuite of libraries. Experimental results reveal the relative efficiency of the single-step compared to the two-step model on different performance parameters. These results are consolidated by simulation results, which reveal that our solution outperforms a random placement in terms of both energy consumption, delay and throughput achieved by a smart parking network.