Effective Independence Research Articles

A novel data-driven sensor placement optimization method for unsupervised damage detection using noise-assisted neural networks with attention mechanism

Optimization of sensor placement (OSP) is one of the important steps in structural health monitoring to reduce the instrumentation cost, and improve damage detection. Although modal analysis is an optional intermediate process in terms of damage detection, conventional OSP methods for damage detection are mostly dependent on mode shapes. In this case, the sensor placement and damage detection are highly relying on the accuracy of modal analysis, and the results may not be adapted to different type of excitations. In this article, a novel noise-assisted neural network with attention mechanism is proposed based on the above challenges. This method which can be used to optimize sensor placement in an unsupervised and data-driven manner, is verified using a dataset simulated from the ASCE benchmark and an experimental dataset obtained from shake table tests. The results from the simulated dataset show that the percentage of the sensors that could be removed are higher than the conventional effective independence (EFI) method, with a highest of 62.5% for cases with low noise levels. In the meantime, the occurrence and the level of damage can still be well detected with a reduced number of sensors. Most importantly, in the proposed approach the optimal sensor placement configurations can be determined adaptively to account for different forms of excitations and noise levels, which is impossible for conventional model-driven methods. The results obtained from the experimental dataset show that the proposed method is also effective for real-world applications. As a result, the proposed data-driven OSP method skips the conventional model analysis process and directly focuses on the sensor arrangement that enables accurate detection of damage. It also has the potential for application in related fields, such as the monitoring of aerospace and mechanical infrastructures.

An Optimal Strain Gauge Layout Design for the Measurement of Truss Structures

Sensor measurements diagnose and evaluate the structural health state. A sensor configuration with a limited number of sensors must be designed to monitor sufficient information about the structural health state. The diagnosis of a truss structure composed of axial members can begin with a measurement by the strain gauges attached to the truss members or by the accelerometers and displacement sensors at the nodes. This study considered the layout design of the displacement sensors at the nodes for the truss structure by using the effective independence (EI) method based on the mode shapes. The validity of the optimal sensor placement (OSP) methods depending on their synthesis with the Guyan method was investigated by the mode shape's data expansion. The Guyan reduction technique rarely affected the final sensor design. A modified EI algorithm based on the strain mode shape of the truss members was presented. A numerical example was analyzed, showing that the sensor placements were affected depending on the displacement sensors and strain gauges. Numerical examples illustrated that the strain-based EI method without the Guyan reduction method has the advantage of reducing the number of sensors and providing more data related with the displacements at the nodes. The measurement sensor should be selected when considering structural behavior, as it is crucial.

LSTM-Autoencoder for Vibration Anomaly Detection in Vertical Carousel Storage and Retrieval System (VCSRS).

Industry 5.0, also known as the "smart factory", is an evolution of manufacturing technology that utilizes advanced data analytics and machine learning techniques to optimize production processes. One key aspect of Industry 5.0 is using vibration data to monitor and detect anomalies in machinery and equipment. In the case of a vertical carousel storage and retrieval system (VCSRS), vibration data can be collected and analyzed to identify potential issues with the system's operation. A correlation coefficient model was used to detect anomalies accurately in the vertical carousel system to ascertain the optimal sensor placement position. This model utilized the Fisher information matrix (FIM) and effective independence (EFI) methods to optimize the sensor placement for maximum accuracy and reliability. An LSTM-autoencoder (long short-term memory) model was used for training and testing further to enhance the accuracy of the anomaly detection process. This machine-learning technique allowed for detecting patterns and trends in the vibration data that may not have been evident using traditional methods. The combination of the correlation coefficient model and the LSTM-autoencoder resulted in an accuracy rate of 97.70% for detecting anomalies in the vertical carousel system.

Comparing Instrumentation Selection Techniques for Vibration Testing

Abstract Vibration testing of complex aerospace structures requires substantial pretest planning. Ground and flight testing of structures can be costly to execute in terms of time and money, so it is pertinent that tests are properly set up to capture mode shapes or dynamics of interest. One of the most important planning tasks is the placement of sensors to acquire measurements for control and characterization of the results. In this paper, we will examine two techniques that can leverage available output from finite element modeling to intelligently place accelerometers for a vibration test to capture the structural dynamics throughout a specified frequency range with a data acquisition channel budget. These two techniques are effective independence (EI) and optimal experimental design (OED). Both methods will be applied to an aerospace structure. Effects of the chosen sets on system equivalent reduction and expansion process (SEREP) are detailed alongside simpler comparison metrics, like the auto-modal assurance criterion (auto-MAC). In addition to comparing the resulting instrumentation sets, the application of the two approaches will be compared in terms of the inputs required, the information obtained from their application, and the computation time requirements. Both OED and EI offer an effective method for selecting an instrumentation set for a given vibration test. EI is a straightforward, computationally inexpensive approach that provides effective instrumentation sets. OED provides an effective alternative that is less sensitive to the impact of local modes and leads to a natural ranking of importance for each chosen degree-of-freedom (DOF).

Robustness of Optimal Sensor Methods in Dynamic Testing–Comparison and Implementation on a Footbridge

One of the objectives of structural health monitoring (SHM) is to maximize the information while keeping the number of sensors, and consequently the cost of the sensor system, to a minimum. Besides, the sensor configurations must be robust in the sense that the feasibility of small errors inherent to the process must not lead to large variations in the final results. This paper presents novelties regarding the robustness evaluation to model and measurement errors of four of the most influential optimal sensor placement (OSP) methods: the modal kinetic energy (MKE) method; the effective independence (EFI) method; the information entropy index (IEI) method; and the MinMAC method. The four OSP methods were implemented on the Streicker Bridge, a footbridge located on the Princeton University Campus, to identify five mode shapes of the bridge. The mode shapes, obtained in a FE model’s modal analysis, were used as input data for the OSP analyses. The study indicates that the MKE method seems to be the most suitable method to estimate the optimal sensor positions: it provides a relatively large amount of information with the lowest computational time, and it outperforms the other three methods in terms of robustness in the usual range of number of 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.

Optimum reduction of sensing electrodes for delamination identification with electrical resistance tomography

Electrical resistance tomography (ERT) is a non-destructive evaluation (NDE) technique that measures the voltages when electric current is injected in a body where damage induced electrical conductivity changes occur. Accurate and efficient damage identification in carbon fiber reinforced polymer (CFRP) composites using ERT requires the optimal selection of the sensing sites. The present work uses an effective independence (EI) measure for selecting the optimally reduced set of measurements among all possible for ERT damage identification. Finite element analyses (FEA) are used to calculate the electrical potential in two CFRP laminate layups with 14 electrodes given a set of specified delamination cases that span the space of possible damage states. Measurement reduction uses two strategies based on individual or group selection about the injection site. A third strategy performs complete electrode exclusion. Inverse identification of delamination cases for the full and the reduced sets after applying the strategies estimates the effectiveness of EI reduction. Results show the lowest errors come from individual measurement elimination. Electrode elimination is attainable with acceptable accuracy loss. This work shows that the EI measure optimally reduces electrode and electrode combinations in ERT-based damage identification.

Convex relaxation for efficient sensor layout optimization in large‐scale structures subjected to moving loads

AbstractThis paper proposes a computationally effective framework for load‐dependent optimal sensor placement in large‐scale civil engineering structures subjected to moving loads. Two common problems are addressed: selection of modes to be monitored and computational effectiveness. Typical sensor placement methods assume that the set of modes to be monitored is known. In practice, determination of such modes of interest is not straightforward. A practical approach is proposed that facilitates the selection of modes in a quasi‐automatic way based on the structural response at the candidate sensor locations to typical operational loads. The criterion used to assess sensor placement is based on Kammer's Effective Independence (EFI). However, in contrast to typical implementations of EFI, which treat the problem as a computationally demanding discrete problem and use greedy optimization, an approach based on convex relaxation is proposed. A notion of sensor density is applied, which converts the original combinatorial problem into a computationally tractable continuous optimization problem. The proposed framework is tested in application to a real tied‐arch railway bridge located in central Poland.

New Sensor Placement Method Based on Remodeling Innovation

Owing to an increased interest in damage identification and structural health monitoring during dynamic testing, sensor placement optimization has been a challenging research subject over the past decades. As the most influential method developed thus far, the effective independence (EI) method for sensor placement is discussed extensively in the present paper. Specifically, it was observed that, in the computation of the EI index, the sum of each retained row in the eigenvalue contribution matrix is a constant during each iteration. To reveal the significance of this property, a matrix transformation was employed, the form of which is similar to the orthogonal-triangular (QR) decomposition of the EI method previously proposed by the authors. In this regard, the physical significance of the re-orthogonalization of the modes through QR decomposition based on the computation of the EI method can be clearly seen from a new perspective. In view of this, a new sensor placement method, which is referred to as the remodeling innovation (RI) method, is proposed in this paper. The RI method avoids the existing problems in a conventional EI method in that, during each iterative calculation, the row with the least norm is removed without taking into account the effects of the structural mass redistribution. Furthermore, the RI method achieves better sensor placement in terms of the different evaluation criteria applied. Finally, to demonstrate the above observations, the proposed RI method was applied to the Hangzhou Nanshan Bridge.

A step excitation optimization method for intensive modal identification of cable net structures

Compared with the direct force measurement of cables, dynamic modal testing is more economic and applicable in engineering for monitoring the stiffness change of cable net structures caused by pretension deviation. Normally, it is sufficient to detect the variation of structural key stiffness by testing a few modes (target modes) that are, however, likely located in the region of dense modes. To effectively evaluate the stiffness of an existing cable net structure, the identification accuracy of these target modes should be improved when using conventional time-domain methods, e.g., the eigensystem realization algorithm (ERA). Structural free vibration can be induced by a step excitation that is generated by simultaneously releasing loads hung on the cable net. In this paper, the modal energy in the structural free vibration response is expounded to be determined by the work done by the step excitation loads in the direction of this mode shape. Therefore, the identification accuracy of a target mode can be improved by optimizing the layout and magnitude of the suspended loads to increase its energy proportion in the structural free vibration response and suppress those of its adjacent modes. For a certain set of degrees of freedom (DOFs) that loads are allowed to be suspended, a method is put forward to construct a step excitation load that can guarantee that the suppressed modes do not have an energy contribution to its induced free vibration. Referring to the effective independence (EI) method, an iterative algorithm is developed to select a given number of DOFs for the suspension of the step excitation loads that can ensure the target mode has a relatively large energy proportion. With the solution of generalized Rayleigh entropy, the magnitude of the loads suspended from the selected DOFs is further optimized to achieve the maximum energy proportion of the target mode. An illustrative saddle-shaped cable net roof is employed to validate the accuracy and validity of the proposed method by comparing the modal identification results under the optimized step excitation, conventional impact excitation and random excitation, respectively.

Development of a stochastic effective independence (SEFI) method for optimal sensor placement under uncertainty

Abstract Finding optimal sensor placement for data acquisition is an essential initial stage in the development of many engineered systems. For this purpose, the effective independence (EFI) method was developed and has been widely used. In this method, sensor locations are selected to maximize the linear independency of the target mode shape matrix. However, the EFI method lacks consideration of the uncertainty that is present in real applications. To overcome this limitation, in this study, a new stochastic EFI method is derived. The resultant equation is composed of the conventional deterministic term and an additional random term. Using the derived equation, optimal sensor locations are found. The results of stochastic EFI give the best linear independency of the mode shape matrix in the mean sense. In this paper, stochastic EFI is also extended to the energy-based EFI method. In the energy-based EFI method, the mass or stiffness matrix is weighted to have the kinetic or strain energy form of the EFI method. By decomposing the weighted matrix, the same form is obtained as in the EFI method; thus, its stochastic version follows naturally, as in the stochastic EFI method. Further, the stochastic sensor placement method is also derived for a different optimization criterion called the A-optimality criterion, which uses a matrix trace for its measure. Finally, the proposed method is validated using a truss bridge case. Its results are compared with the Monte Carlo simulation based method, which is another approach used to handle the system uncertainty. The case study indicates that the suggested method shows higher linear independency than the EFI method and the energy-based EFI method; it is also better with different optimality conditions.

Optimum Electrode Configurations for Two-Probe, Four-Probe and Multi-Probe Schemes in Electrical Resistance Tomography for Delamination Identification in Carbon Fiber Reinforced Composites

Internal damage in Carbon Fiber Reinforced Polymer (CFRP) composites modifies the internal electrical conductivity of the composite material. Electrical Resistance Tomography (ERT) is a non-destructive evaluation (NDE) technique that determines the extent of damage based on electrical conductivity changes. Implementation of ERT for damage identification in CFRP composites requires the optimal selection of the sensing sites for accurate results. This selection depends on the measuring scheme used. The present work uses an effective independence (EI) measure for selecting the minimum set of measurements for ERT damage identification using three measuring schemes: two-probe, four-probe and multi-probe. The electrical potential field in two CFRP laminate layups with 14 electrodes is calculated using finite element analyses (FEA) for a set of specified delamination damage cases. The measuring schemes consider the cases of 14 electrodes distributed on both sides and seven electrodes on only one side of the laminate for each layup. The effectiveness of EI reduction is demonstrated by comparing the inverse identification results of delamination cases for the full and the reduced sets using the measuring schemes and electrode sets. This work shows that the EI measure optimally reduces electrode and electrode combinations in ERT based damage identification for different measuring schemes.

Multi-scale model updating of a timber footbridge using experimental vibration data

PurposeThe purpose of this paper is to capture the actual structural behavior of the longest timber footbridge in Spain by means of a multi-scale model updating approach in conjunction with ambient vibration tests.Design/methodology/approachIn a first stage, a numerical pre-test analysis of the full bridge is performed, using standard beam-type finite elements with isotropic material properties. This approach offers a first structural model in which optimal sensor placement (OSP) methodologies are applied to improve the system identification process. In particular, the effective independence (EFI) method is used to determine the optimal locations of a set of sensors. Ambient vibration tests are conducted to determine experimentally the modal characteristics of the structure. The identified modal parameters are compared with those values obtained from this preliminary model. To improve the accuracy of the numerical predictions, the material response is modeled by means of a homogenization-based multi-scale computational approach. In a second stage, the structure is modeled by means of three-dimensional solid elements with the above material definition, capturing realistically the full orthotropic mechanical properties of wood. A genetic algorithm (GA) technique is adopted to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.FindingsAn overall good agreement is found between the results of the updated numerical simulations and the corresponding experimental measurements. The longitudinal and transverse Young's moduli, sliding and rolling shear moduli, density and natural frequencies are computed by the present approach. The obtained results reveal the potential predictive capabilities of the present GA/multi-scale/experimental approach to capture accurately the actual behavior of complex materials and structures.Originality/valueThe uniqueness and importance of this structure leads to an intensive study of its structural behavior. Ambient vibration tests are carried out under environmental excitation. Extraction of modal parameters is obtained from output-only experimental data. The EFI methodology is applied for the OSP on a large-scale structure. Information coming from several length scales, from sub-micrometer dimensions to macroscopic scales, is included in the material definition. The strong differences found between the stiffness along the longitudinal and transverse directions of wood lumbers are incorporated in the structural model. A multi-scale model updating approach is carried out by means of a GA technique to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

On the physical significance of the Effective Independence method for sensor placement

Optimally deploy sparse sensors for better damage identification and structural health monitoring is always a challenging task. The Effective Independence(EI) is one of the most influential sensor placement method and to be discussed in the paper. Specifically, the effect of the different weighting coefficients on the maximization of the Fisher information matrix(FIM) and the physical significance of the re-orthogonalization of modal shapes through QR decomposition in the EI method are addressed. By analyzing the widely used EI method, we found that the absolute identification space put forward along with the EI method is preferable to ensuring the maximization of the FIM, instead of the original EI coefficient which was post-multiolied by a weighting matrix. That is, deleting the row with the minimum EI coefficient can’t achieve the objective of maximizing the trace of FIM as initially conceived. Furthermore, we observed that in the computation of EI method, the sum of each retained row in the absolute identification space is a constant in each iteration. This potential property can be revealed distinctively by the product of target mode and its transpose, and its form is similar to an alternative formula of the EI method through orthogonal-triangular(QR) decomposition previously proposed by the authors. With it, the physical significance of re-orthogonalization of modal shapes through QR decomposition in the computation of EI method can be obviously manifested from a new perspective. Finally, two simple examples are provided to demonstrate the above two observations.

Optimal Electrode Selection for Electrical Resistance Tomography in Carbon Fiber Reinforced Polymer Composites.

Electrical Resistance Tomography (ERT) offers a non-destructive evaluation (NDE) technique that takes advantage of the inherent electrical properties in carbon fiber reinforced polymer (CFRP) composites for internal damage characterization. This paper investigates a method of optimum selection of sensing configurations for delamination detection in thick cross-ply laminates using ERT. Reduction in the number of sensing locations and measurements is necessary to minimize hardware and computational effort. The present work explores the use of an effective independence (EI) measure originally proposed for sensor location optimization in experimental vibration modal analysis. The EI measure is used for selecting the minimum set of resistance measurements among all possible combinations resulting from selecting sensing electrode pairs. Singular Value Decomposition (SVD) is applied to obtain a spectral representation of the resistance measurements in the laminate for subsequent EI based reduction to take place. The electrical potential field in a CFRP laminate is calculated using finite element analysis (FEA) applied on models for two different laminate layouts considering a set of specified delamination sizes and locations with two different sensing arrangements. The effectiveness of the EI measure in eliminating redundant electrode pairs is demonstrated by performing inverse identification of damage using the full set and the reduced set of resistance measurements. This investigation shows that the EI measure is effective for optimally selecting the electrode pairs needed for resistance measurements in ERT based damage detection.

Determining the Optimal Placement of Sensors on a Concrete Arch Dam Using a Quantum Genetic Algorithm

Structural modal identification has become increasingly important in health monitoring, fault diagnosis, vibration control, and dynamic analysis of engineering structures in recent years. Based on an analysis of traditional optimization algorithms, this paper proposes a novel sensor optimization criterion that combines the effective independence (EFI) method with the modal strain energy (MSE) method. Considering the complex structure and enormous degrees of freedom (DOFs) of modern concrete arch dam, a quantum genetic algorithm (QGA) is used to optimize the corresponding sensor network on the upstream surface of a dam. Finally, this study uses a specific concrete arch dam as an example and determines the optimal sensor placement using the proposed method. By comparing the results with the traditional optimization methods, the proposed method is shown to maximize the spatial intersection angle among the modal vectors of sensor network and can effectively resist ambient perturbations, which will make the identified modal parameters more precise.

An Effective Independence-Improved Modal Strain Energy Method for Optimal Sensor Placement of Bridge Structures

In this study, an effective independence-improved modal strain energy (EI-IMSE) method is proposed for the optimal sensor placement (OSP) problem in the field of the structural health monitoring and moving force identification. The improved modal strain energy (IMSE) is used to modify optimal sensor placement results obtained by the effective independence (EI) method. The EI-IMSE OSP method is verified by some numerical simulations on a 2D planar truss bridge model. Based on the criteria of modal assurance criterion (MAC), trace of fisher matrix, matrix condition number, and the least mean square error, the EI-IMSE OSP method is assessed through comparing with those of EI, EI-driving point residue (EI-DPR), EI-average driving DOF velocity (EI-ADDOFV), and EI-average acceleration amplitude (EI-AAA). The illustrated results show that the proposed EI-IMSE OSP method is feasible with a higher accuracy.

Optimal sensor placement for structural response estimation

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.

Optimal Sensor Placement Based on Tabu Search Algorithms

In this study, the Tabu search (TS) algorithm is introduced into the optimal sensor placement (OSP) problem in the field of the structural health monitoring and moving force identification. A TS-based OSP procedure is proposed and further evaluated by some numerical simulations on a 2D planar truss model. The mean values of off-diagonal elements in a modal assurance criterion (MAC) matrix are used as the optimization objective function. Based on the criteria of MAC, determinant of fisher matrix, matrix condition number, and the least mean square error, the TS-based OSP procedure is evaluated through comparing with ones due to both of the energy coefficient-effective independence (ECEFI) and the effective independence (EFI) algorithms. The results show that the proposed TS-based OSP procedure is feasible with a higher accuracy.

Sensor placement optimisation for Dalian international trade mansion focusing on application demands

The research on optimal locating sensors was carried on the Dalian International Trade Mansion (DITM), the tallest building in the north of China, with the aim of maximising the data information so that structural dynamic behaviour may be fully characterised. Since the sensors can only be arranged in the translational degrees of freedom (DOF) of the structure in the state-of-the-practice, a method based on the simplified finite element (FE) model which is able to avoid distinguishing the translational and rotational DOFs is presented. To demonstrate the effectiveness of the proposed approach and compare the different sensor placement techniques, the effective independence (EfI) method, EfI-DPR (the driving-point residue, DPR) and Uniform methods were employed. The calculation results show that the presented approach is easy in understanding and could be used practically by civil engineers. EfI method provides a more effective method for optimal sensor placement than other ones to identify the vibration characteristics of the studied building.