Dual-type sensor placement optimization by fully utilizing structural modal information

2018 ◽  
Vol 22 (3) ◽  
pp. 737-750 ◽  
Author(s):  
Xue-Yang Pei ◽  
Ting-Hua Yi ◽  
Hong-Nan Li
Keyword(s):  
Mode Shape ◽  
Sensor Placement ◽  
Estimation Method ◽  
Mode Shapes ◽  
Strain Gauges ◽  
Shape Estimation ◽  
Modal Assurance Criterion ◽  
Strain Mode ◽  
Placement Method ◽  
Displacement Mode

Strain gauges and accelerometers are widely used in bridge structural health monitoring systems. Generally, the strain gauges are placed on the key locations to obtain local structural deformation information; the accelerometers are used to obtain the structural modal information. However, the modal information contained in the measured strains is not taken into account. In this article, to fully utilize the modal information contained in strains, a mode shape estimation method is proposed that the strain mode shapes of the strain locations are used to obtain the displacement mode shapes of some positions without accelerometers. At first, to simulate the practical situation, some positions with large structural deformations are selected as the strain gauge locations. Using the proposed mode shape estimation method, the displacement mode shapes of some locations without accelerometers are estimated by the strain mode shapes using the least squares method, and the locations with the smallest estimation error are finally determined as the estimated locations. Then, accelerometers are added to the existing sensor placement. Here, the modal assurance criterion is used to evaluate the distinguishability of the displacement mode shapes obtained from the strain gauges and accelerometers. The accelerometer locations that bring the smallest modal assurance criterion values are selected. In addition, a redundancy can be set to avoid the adjacent sensors containing similar modal information. Through the proposed sensor placement method, the deformation and modal information contained in the strain gauges is fully utilized; the modal information contained in the strain gauges and accelerometers is comprehensively utilized. Numerical experiments are carried out using a bridge benchmark structure to demonstrate the sensor placement method.

scholarly journals A Multiobjective Perspective to Optimal Sensor Placement by Using a Decomposition-Based Evolutionary Algorithm in Structural Health Monitoring

2020 ◽  
Vol 10 (21) ◽  
pp. 7710
Author(s):  
Tsung-Yueh Lin ◽  
Jin Tao ◽  
Hsin-Haou Huang
Keyword(s):  
Structural Health Monitoring ◽  
Evolutionary Algorithm ◽  
Health Monitoring ◽  
Sensor Placement ◽  
Frame Structure ◽  
Mode Shapes ◽  
Beam Model ◽  
Optimal Sensor Placement ◽  
Modal Assurance Criterion ◽  
Structural Health

The objective of optimal sensor placement in a dynamic system is to obtain a sensor layout that provides as much information as possible for structural health monitoring (SHM). Whereas most studies use only one modal assurance criterion for SHM, this work considers two additional metrics, signal redundancy and noise ratio, combining into three optimization objectives: Linear independence of mode shapes, dynamic information redundancy, and vibration response signal strength. A modified multiobjective evolutionary algorithm was combined with particle swarm optimization to explore the optimal solution sets. In the final determination, a multiobjective decision-making (MODM) strategy based on distance measurement was used to optimize the aforementioned objectives. We applied it to a reduced finite-element beam model of a reference building and compared it with other selection methods. The results indicated that MODM suitably balanced the objective functions and outperformed the compared methods. We further constructed a three-story frame structure for experimentally validating the effectiveness of the proposed algorithm. The results indicated that complete structural modal information can be effectively obtained by applying the MODM approach to identify sensor locations.

scholarly journals Damage identification using modal strains identified from operational fiber-optic Bragg grating data

2017 ◽  
Vol 17 (6) ◽  
pp. 1441-1459 ◽  
Author(s):  
Dimitrios Anastasopoulos ◽  
Maure De Smedt ◽  
Lucie Vandewalle ◽  
Guido De Roeck ◽  
Edwin P.B. Reynders
Keyword(s):  
Fiber Optic ◽  
Early Stage ◽  
Structural Characteristics ◽  
Mode Shapes ◽  
Dynamic Strain ◽  
Bragg Grating ◽  
Local Damage ◽  
Strain Mode ◽  
Displacement Mode ◽  
Strain Mode Shapes

Vibration-based structural health monitoring of civil structures relies on the repeated identification of dynamic structural characteristics of the structure from output-only vibration data. Natural frequencies and displacement mode shapes are the most commonly employed dynamic characteristics; yet their sensitivity to local damage of moderate severity is rather low with respect to their sensitivity to other factors such as temperature, necessitating data normalization. Strain mode shapes offer a higher sensitivity to local damage, but their accurate identification in a dense grid is challenging given the very small dynamic strain levels that are encountered under ambient excitation. In this article, a method is presented for tackling this challenge. It consists of three stages. First, fiber-optic Bragg grating strain sensors are attached to the structure and interrogated with a tunable laser performing a wavelength sweep. In this way, the measured strain amplitudes have the required accuracy but synchronization errors are introduced between the different Bragg sensors. Second, a modal analysis is performed on the dynamic strain data using an accurate parametric system identification technique. This is followed by a synchronization step which compensates for the delays introduced by the wavelength sweep. Finally, the synchronized strain mode shapes are employed as damage-sensitive features, either directly or via a newly proposed quantity, the top-to-bottom strain ratio. The method is validated by progressive damage testing of a complex, prestressed concrete “roof” beam, reinforced with steel fibers. It is observed that the proposed method can identify both the presence and the location of the damage in a relatively early stage.

scholarly journals Robust Baseline-Free Damage Localization by Using Locally Perturbed Dynamic Equilibrium and Data Fusion Technique

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5964
Author(s):  
Shancheng Cao ◽  
Huajiang Ouyang ◽  
Chao Xu
Keyword(s):  
Data Fusion ◽  
Mode Shape ◽  
Structural Damage ◽  
Dynamic Equilibrium ◽  
Experimental Studies ◽  
Measurement Noise ◽  
Mode Shapes ◽  
Damage Localization ◽  
Shape Estimation ◽  
Fusion Approach

Mode shape-based structural damage identification methods have been widely investigated due to their good performances in damage localization. Nevertheless, the evaluation of mode shapes is severely affected by the measurement noise. Moreover, the conventional mode shape-based damage localization methods are normally proposed based on a certain mode and not effective for multi-damage localization. To tackle these problems, a novel damage localization approach is proposed based on locally perturbed dynamic equilibrium and data fusion approach. The main contributions cover three aspects. Firstly, a joint singular value decomposition technique is proposed to simultaneously decompose several power spectral density transmissibility matrices for robust mode shape estimation, which statistically deals better with the measurement noise than the traditional transmissibility-based methods. Secondly, with the identified mode shapes, an improved pseudo-excitation method is proposed to construct a baseline-free damage localization index by quantifying the locally damage perturbed dynamic equilibrium without the knowledge of material/structural properties. Thirdly, to circumvent the conflicting damage information in different modes and integrate it for robust damage localization, a data fusion scheme is developed, which performs better than the Bayesian fusion approach. Both numerical and experimental studies of cantilever beams with two cracks were conducted to validate the feasibility and effectiveness of the proposed damage localization method. It was found that the proposed method outperforms the traditional transmissibility-based methods in terms of localization accuracy and robustness.

Gaussian Stochastic Process Modeling of Blend Repaired Airfoil Modal Response Using Reduced Basis Mode Shape Approach

2021 ◽  
Author(s):  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Daniel L. Gillaugh ◽  
Emily B. Carper ◽  
Joseph A. Beck
Keyword(s):  
Stochastic Process ◽  
Mode Shape ◽  
Training Data ◽  
Mode Shapes ◽  
Shape Variation ◽  
Reduced Basis ◽  
Gaussian Stochastic Process ◽  
Modal Assurance Criterion ◽  
Validation Data ◽  
Full Factorial

Abstract A machine learning (ML) approach is developed to predict the effect of blend repairs on airfoil frequency, modal assurance criterion (MAC), and modal displacement vectors. The method is demonstrated on a transonic research rig compressor rotor airfoil. A parametric definition of blend geometry is developed and shown to be capable of encompassing a large range of blend geometry. This blend repair geometry is used to modify the airfoil surface definition and a mesh morphing process transforms the nominal finite element model (FEM) to the repaired configuration. A multi-level full factorial sampling of the blend repair design space provides training data to a Guassian stochastic process (GSP) regressor. The frequency and MAC results create a vector of training data for GSP calibration, but the airfoil mode shapes require further mathematical manipulation to avoid creating GSP models for each nodal displacement. This paper develops a method to significantly reduce blended airfoil mode shape emulation cost by transforming the mode shape training data into a reduced basis space using principal component analysis (PCA). The coefficients of this reduced basis are used to train a GSP that can then predict the values for new blended airfoils. The emulated coefficients are used with the reduced basis vectors in a reconstruction of blended airfoil mode shape. Validation data is computed at a full-factorial design that maximizes the distance from training points. It is found that large variations in modal properties from large blend repairs can be accurately emulated with a reasonable number of training points. The reduced basis approach of mode shape variation is shown to more accurately predict MAC variation when compared to direct MAC emulation. The added benefit of having the full modal displacement field also allows determination of other influences such as tip-timing limits and modal force values.

Damage Detection of Cantilever Beams Based on Derivatives of Mode Shapes

2014 ◽  
Vol 488-489 ◽  
pp. 817-820
Author(s):  
Jin Quan Guo ◽  
Fen Lan Ou ◽  
Jian Feng Zhong ◽  
Shun Cong Zhong ◽  
Xiao Xiang Yang ◽  
...  
Keyword(s):  
Mode Shape ◽  
Crack Detection ◽  
Shape Change ◽  
Approximation Error ◽  
Mode Shapes ◽  
Difference Approximation ◽  
Cantilever Beams ◽  
Crack Location ◽  
Displacement Mode ◽  
Derivatives Of

For the small crack detection (crack ration less than 5%), the derivatives of mode shapes of cantilever beams were used for crack detection in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small discontinuity in the response at the crack location. It is hard to detect small cracks in beams using the direct data of mode shape change. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked cantilever beam provide a progressively better indication of the presence of a crack. However, `noise' effects due to the difference approximation error also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives of mode shapes. For the intact beam, these derivatives are smooth curves. So the local peaks or discontinuity on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and intact cantilever beams used were computed using the finite element method.

Research on the Beam Damage Diagnosis Method for a High-Speed Transplanter Based on the Strain Mode

2021 ◽  
Vol 37 (1) ◽  
pp. 25-32
Author(s):  
Jiangtao Ji ◽  
Kaikang Chen ◽  
Xin Jin ◽  
Jing Pang ◽  
Xing Chen ◽  
...  
Keyword(s):  
Mode Shape ◽  
High Speed ◽  
Operating Conditions ◽  
Agricultural Machinery ◽  
Damage Diagnosis ◽  
Change Rate ◽  
Strain Mode ◽  
Mode Change ◽  
Displacement Mode ◽  
Beam Damage

Abstract. The vibration of agricultural machinery significantly influences driving comfort and operation reliability. In recent years, research on the vibrational characteristics of agricultural machinery has gradually expanded. To solve the problem of the obvious vibration of a high-speed transplanter under operating conditions, this article examines the method of beam damage diagnosis for high-speed transplanters based on the strain mode. Based on the modal theory, the displacement and strain modal analysis of the beam of the high-speed transplanter is performed. The analysis shows that the relative deviation of the modal frequencies of the same order before and after the beam is damaged is small. There is no obvious abrupt change in the displacement mode shape, while the strain mode shape has a sudden change peak after the beam is damaged. Thus, the strain mode change rate is constructed as a diagnostic index for beam damage. The analysis results show that the strain mode change rate increases with the increase in beam damage degree. Finally, the least squares method is used to fit the corresponding relationship between the two quantities. The results show that the strain mode change rate is sensitive and reliable as an index of damage diagnosis, which can better determine the location and degree of damage to the beam. Keywords: Beam, Damage, Diagnosis, Rice transplanter, Strain mode.

scholarly journals One-Step FE Model Updating Using Local Correspondence and Mode Shape Orthogonality

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Martin Ø. Ø. Jull ◽  
Sandro D. R. Amador ◽  
Anders Skafte ◽  
Jannick B. Hansen ◽  
Manuel L. Aenlle ◽  
...  
Keyword(s):  
Mode Shape ◽  
Model Updating ◽  
Low Frequency ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Assurance Criterion ◽  
Mass Scaling ◽  
The Matrix ◽  
One Step ◽  
Fe Model Updating

In this paper, it is described how the matrix mixing model updating technique can be combined with the local correspondence (LC) mode shape expansion algorithm, to give a new finite element (FE) model updating method. The matrix mixing method uses that the inverse mass and stiffness matrices can be expressed as a linear combination of outer products of FE mode shape vectors, where the low-frequency part of these sums are substituted with expanded test modes. The approach is meant to update FE models in one-step and is exact, except for the following two approximations: the mode shape smoothing and the mass scaling of the expanded experimental mode shapes. A simulation study illustrates the errors from the two approximations and shows the ability of the technique to improve the modal assurance criterion (MAC) values so that they get very close to unity. Finally, the performance of the proposed updating method is assessed by means of an application example in which the FE model is updated based on the test modes of a real structure.

Novel Sensor Placement for Damage Identification in a Cracked Complex Structure With Structural Variability

2010 ◽  
Author(s):  
Sung-Kwon Hong ◽  
Bogdan I. Epureanu ◽  
Matthew P. Castanier
Keyword(s):  
Crack Length ◽  
Damage Identification ◽  
Complex Structure ◽  
Sensor Placement ◽  
Mode Shapes ◽  
Complex Structures ◽  
Structural Dynamic ◽  
Placement Method ◽  
Structural Variability ◽  
Sensor Locations

The focus of this work is on sensor placement for structural dynamic analysis and damage detection. In particular, novel sensor placement techniques are presented for the detection of cracks in ground vehicles and other complex structures. These techniques are designed to provide vibration characteristics for complex structures that have both cracks and structural variability (such as uncertainty in the geometry or the material properties). Such techniques are needed because structural variability affects the mode shapes of a structure, and thus the optimal sensor locations for detecting cracks are affected. Two approaches are developed and used: (a) parametric reduced order models (PROMs), and (b) bilinear mode approximation (BMA). Based on PROMs and BMA, a novel sensor placement method (which uses a derivative of the effective independent distributed vector algorithm) is used to determine the optimal sensor locations for complex structures with cracks and structural variability. The approach can also be used to estimate the crack length. The length is identified by using a few mode shapes and only a few selected measurement locations. The information from the sensors can be used to determine variations in mode shapes of the structure (between healthy and cracked states) for different crack lengths. The variation in mode shapes can then be used to identify the crack length. Numerical results are presented for a ground vehicle frame. The sensor placement method is applied first to find the optimal sensor locations for a structure with a crack and parameter variability, and then to identify the length of a crack.

Experimental Verification and Comparison of Mode Shape-Based Damage Detection Methods

2009 ◽  
Vol 413-414 ◽  
pp. 699-706 ◽  
Author(s):  
Maciej Radzieński ◽  
Marek Krawczuk ◽  
Wiesław M. Ostachowicz
Keyword(s):  
Damage Detection ◽  
Mode Shape ◽  
Experimental Verification ◽  
Median Filter ◽  
Laser Doppler Vibrometer ◽  
Detection Methods ◽  
Mode Shapes ◽  
Laplacian Operator ◽  
Beam Length ◽  
Modal Assurance Criterion

This paper presents experimental verification and comparison of damage detection methods based on changes in mode shapes such as: mode shape curvature (MSC), modal assurance criterion (MAC), strain energy (SE), modified Laplacian operator (MLO), generalized fractal dimension (GFD) and Wavelets Transform (WT). The object of the investigation is to determine benefits and drawbacks of the aforementioned methods and to develop data preprocessing algorithms for increasing damage assessment effectiveness by using signal processing techniques such as interpolation and extrapolation measured points. Noise reduction algorithms based on moving average, median filter and wavelet decomposition are also tested. The experiments were performed on a 1m long steal cantilever beam. Damage was introduced in form of 10% and 20% deep saw cut, placed in 10%, 30%, 50%, 70% and 90% beam length. Measurements were made using non-contact Scanning Laser Doppler Vibrometer at 125 points equally spaced along beam length.

An Acceleration Sensor Placement Method Considering Network Life Cycle for Vibration Monitoring of Bridges

2013 ◽  
Vol 361-363 ◽  
pp. 1264-1271
Author(s):  
Wei Dong Zhang ◽  
Jun Wan ◽  
Yi Bo Ai ◽  
Bin Yang
Keyword(s):  
Life Cycle ◽  
Health Monitoring ◽  
Sensor Placement ◽  
Vibration Monitoring ◽  
Wireless Sensor ◽  
Multiple Objective Optimization ◽  
Acceleration Sensor ◽  
Modal Assurance Criterion ◽  
Placement Method ◽  
Battery Energy

Vibration is a very important signal for the health monitoring of bridge. Wireless sensor network powered by batteries are widely used in the monitoring system. How to prolong the network life cycle becomes an important problem due to the limitation of battery energy. This paper presents a new method of optimal acceleration sensor placement for monitoring the vibration of bridges, the method considers network life cycle as the second target on the basis of traditional modal assurance criterion (MAC). And multiple-objective optimization is performed by using a genetic algorithm. The simulation result shows that when the sensors number is less than 30, the networks life cycle can be greatly extended with the addition of only the little cost of MAC indicators.

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