Finite Element Modeling Errors Research Articles

Damage localization and quantification for beam bridges based on frequency variation of parked vehicle-bridge systems

Frequency variations are normally employed for damage detection as frequencies possess the advantages of the high accuracy and high anti-noise capability. However, the validity and applicability of such methods are restricted due to the limited order of frequencies. A damage localization and quantification approach is proposed for beam bridges by using the frequency variation of parked vehicle-bridge systems. Firstly, the phenomenon of frequency variation of parked vehicle-bridge systems is briefly illustrated. Secondly, a damage location index (DLI) is defined by the frequency change rate (FCR) of the vehicle-bridge systems with the vehicle parked at different positions before and after damage. Then the relationship between the frequency-parameter change rate (FPCR) and damage severity is established via finite element model (FEM) and further employed to formulate a damage equation(s) for severity estimation. The dimension of coefficient matrix in damage equations is reduced to large extent as the damage locations are determined by DLI in advance, which is meaningful in enhancing the effectiveness of severity estimation. Results of numerical and experimental examples with different damage scenarios indicate that the proposed approach can localize and quantify damages with high accuracy and efficiency by using frequency information only. The effects of measurement noise and FEM error are discussed to examine the robustness of the proposed approach. The cases when damage occurs in neighbor elements are analyzed to investigate the feasibility and robustness of the proposed approach.

A reliability-based sieve technique: A novel multistage probabilistic methodology for the damage assessment of structures

A novel multistage probabilistic methodology called the “Reliability-Based Sieve Technique (RBST)” is presented in this paper for the reliable assessment of the functionality of structures. In this method, the structural damagedetectionproblem is defined as a multistage probabilistic optimization problem. The Holistic Objective Function (HOF) based on the combination of the inherent characteristics of the structure (i.e., the vibration frequencies and mode shapes) is incorporated into the Interactive Autodidactic School (IAS) optimization algorithm, for the first time, to solve the problem. In addition, the Latin Hypercube Sampling (LHS) techniqueis used to simulate and analyzethe probabilistic damage assessment problem. In each stage of the proposed methodology,the Probability of Damage Existence (PDE) is computed in each of the structural elementsthrough a probabilistic damage detection analysis. According to the results of the PDE inthe structural elements in each stage, the elements with low PDEsare gradually sieved inthe subsequent steps. The sifted elements ineach stage are considered asintactones in the next stage. This systematic filtration of the design variables can simultaneously decrease the dimensions and increase the speed of the optimization problem. To improve the performance of the RBST, the sizesof the sieves are regularly reduced for the next stages. This multistage procedure iscontinueduntil convergence to a precise structural damage location diagnosis and intensity prognosis is achieved. Finally, to investigate the efficiency and robustness of the proposed technique, it is examined on three benchmark structures by taking the high level of uncertainties associated with both finite element modeling errors and vibration data noises into account. The obtained results confirmed that the proposed technique correctly identifies the damage indices and has consummate capability compared with the single-stage probabilistic analysis. Likewise, it is observed that the RBST accurately sieves the intact elementsfromthe vector of the design variables in highly noisy conditions. Consequently, in the presence of both mentioned uncertainty sources, the RBST not only assesses the damage site and extent properly, but also shows a reliable performance in terms of PDE.

Structural damage identification with uncertain modelling error and measurement noise by clustering based tree seeds algorithm

This paper proposes a novel structural damage identification approach by using the clustering based Tree Seeds Algorithm, termed as C-TSA, taking into account of both the finite element modeling errors and measurement noise. In order to make the standard TSA more powerful and robust, K-means cluster technique is introduced into the standard TSA before starting the seeds search, which is beneficial to enhance the algorithm’s global optimization performance. The objective function based on the modal data is formulated for structural damage identification. Numerical studies on benchmark functions and a 61-bar truss structure are conducted to investigate the accuracy and robustness of the proposed approach. The finite element modelling errors and noises in the measurement data are considered. Experimental verifications on a laboratory steel frame structure model is conducted to further validate the accuracy of the proposed approach. The results from the numerical and experimental studies are compared with those obtained from several latest evolutionary algorithms. The identification results demonstrate that the proposed approach is more competitive and robust for structural damage identification even considering the modelling errors and measurement noises.

Numerical and experimental investigation of modal-energy-based damage localization for offshore wind turbine structures

Offshore wind turbine structures are prone to deterioration and damage during their service life in harsh marine environment. To explore highly efficient and robust damage detection methods for offshore wind turbine structures, three well-known modal strain energy indices are reviewed first and then a new index named total modal energy method is proposed. The innovation of the new index is the simultaneous use of modal strain energy and modal kinetic energy. To investigate the feasibility and robustness of the four modal-energy-based methods, numerical and experimental studies are conducted on a tripod-type offshore wind turbine structure with simulated and measured data. It is indicated that all the four modal-energy-based methods work well with limited incomplete modal data, especially for the single-damage cases. While for the cases of multiple damage locations, the new total modal energy index significantly outperforms the traditional modal strain energy indices. Moreover, high robustness is shown for the indices, when the measured mode shapes of undamaged and damaged structures are polluted with the same noise level. However, when their noise levels have some difference, two of the modal strain energy indices turn invalid, but the new total modal energy index still shows stronger robustness. As frequencies are also used in the total modal energy index, its robustness to the noise in modal frequencies is also studied. It is shown that the results are slightly affected by the measurement noise in modal frequencies. Besides, the influence of finite element modeling errors is also investigated with both simulated and experimental data. Results show that all the four modal-energy-based methods are all very stable and insensitive to certain modeling errors. So, finite element model updating is not necessary in the test structure herein.

Structural damage detection by a new iterative regularization method and an improved sensitivity function

A new sensitivity-based damage detection method is proposed to identify and estimate the location and severity of structural damage using incomplete noisy modal data. For these purposes, an improved sensitivity function of modal strain energy (MSE) based on Lagrange optimization problem is derived to adapt the initial sensitivity formulation of MSE to damage detection problem with the aid of new mathematical approaches. In the presence of incomplete noisy modal data, the sensitivity matrix is sparse, rectangular, and ill-conditioned, which leads to an ill-posed damage equation. To overcome this issue, a new regularization method named as Regularized Least Squares Minimal Residual (RLSMR) is proposed to solve the ill-posed damage equation. This method relies on Krylov subspace and exploits bidiagonalization and iterative algorithms to solve linear mathematical systems. For the majority of Krylov subspace methods, conventional direct methods for the determination of an optimal regularization parameter may not be proper. To cope with this limitation, a hybrid technique is introduced that depends on the residual of RLSMR method, the number of iterations, and the bidiagonalization algorithm. The accuracy and performance of the improved and proposed methods are numerically examined by a planner truss by incorporating incomplete noisy modal parameters and finite element modeling errors. A comparative study on the initial and improved sensitivity functions is conduced to investigate damage detectability of these sensitivity formulations. Furthermore, the accuracy and robustness of RLSMR method in detecting damage are compared with the well-known Tikhonov regularization method. Results show that the improved sensitivity of MSE is an efficient tool for using in the damage detection problem due to a high sensitivity to damage and reliable damage detectability in comparison with the initial sensitivity function. Additionally, it is observed that the RLSMR method with the aid of the hybrid technique successfully solves the ill-posed damage equation and provides better damage detection results compared with the Tikhonov regularization technique.

Multi-damage localization in plate structure using frequency response function-based indices

Vibration signal and its derivative have shown some promise in structural damage detection in previous research. However, the theoretical and practical difficulties of multi-damage detection in plate structures based on dynamic responses remain. In this paper, an efficient damage localization index based on frequency response function (FRF) is presented. The imaginary part of FRF (IFRF) is extracted to derive the new localization index due to its relation to modal flexibility. For avoiding the finite element model error, two-dimensional gapped smoothing method (GSM) is employed without the need for baseline data from a presumably undamaged structure. Experimental studies on a steel plate with two localized defects in different boundary conditions are performed. The results are compared with some typical damage indices in the literature, such as mode shapes, uniform load surface and IFRF. In order to mitigate the inherent disadvantages of GSM in anti-noise ability, a simple statistical treatment based on Thompson outlier analysis is finally used for noise suppression. The effect of damage level and boundary condition on the detection results is also investigated.

Experimental validation of Kalman filter-based strain estimation in structures subjected to non-zero mean input

Response estimation at unmeasured locations using the limited number of measurements is an attractive topic in the field of structural health monitoring (SHM). Because of increasing complexity and size of civil engineering structures, measuring all structural responses from the entire body is intractable for the SHM purpose; the response estimation can be an effective and practical alternative. This paper investigates a response estimation technique based on the Kalman state estimator to combine multi-sensor data under non-zero mean input excitations. The Kalman state estimator, constructed based on the finite element (FE) model of a structure, can efficiently fuse different types of data of acceleration, strain, and tilt responses, minimizing the intrinsic measurement noise. This study focuses on the effects of (a) FE model error and (b) combinations of multi-sensor data on the estimation accuracy in the case of non-zero mean input excitations. The FE model error is purposefully introduced for more realistic performance evaluation of the response estimation using the Kalman state estimator. In addition, four types of measurement combinations are explored in the response estimation: strain only, acceleration only, acceleration and strain, and acceleration and tilt. The performance of the response estimation approach is verified by numerical and experimental tests on a simply-supported beam, showing that it can successfully estimate strain responses at unmeasured locations with the highest performance in the combination of acceleration and tilt.

Experimental Study of Multi-damage Detection in a Plate Based on Non-modal Method

Many published damage localization indices require structural modal identification and mathematical model of the undamaged structure. However, it is somewhat inconvenient for use in practical engineering. In this study, an efficient localization index has been presented, named as image flexibility of frequency response function, for damage detection in plate-like structures. In order to avoid the finite element model error, two-dimensional gapped smoothing method is employed without the need for the baseline data from a presumably undamaged structure. To assess the effectiveness of the proposed scheme, experimental studies on a multi-damage steel plate are carried out. Meanwhile, the effects of damage magnitude and boundary condition on detection results are also discussed. The results show the effectiveness and robustness of the non-modal method compared to those found in the literature.

Error Location in Structural Dynamic Model of a Rocket Structure

Structural dynamic characteristics of the aerospace structures are essential to obtain the structural responses due to dynamic loads during its mission. The structural dynamic parameters of the aerospace structures are frequencies, associated mode shape and damping. Usually finite element (FE) model of the aerospace structures are generated to estimate the frequencies and the associated mode shape. These FE models are validated by modal survey/ground resonance tests to ensure its completeness and correctness. The modeling deficiencies, if any, in these FE models have to be corrected. This paper describes the method to locate the FE modeling errors using residual force method.

Seismic response prediction for cabinets of nuclear power plants by using impact hammer test

An effective method to predict the seismic response of electrical cabinets of nuclear power plants is developed. This method consists of three steps: (1) identification of the earthquake-equivalent force based on the idealized lumped-mass system of the cabinet, (2) identification of the state-space equation (SSE) model of the system using input–output measurements from impact hammer tests, and (3) seismic response prediction by calculating the output of the identified SSE model under the identified earthquake-equivalent force. A three-dimensional plate model of cabinet structures is presented for the numerical verification of the proposed method. Experimental validation of the proposed method is carried out on a three-story frame which represents the structure of a cabinet. The SSE model of the frame is accurately identified by impact hammer tests with high fitness values over 85% of the actual frame characteristics. Shaking table tests are performed using El Centro, Kobe, and Northridge earthquakes as input motions and the acceleration responses are measured. The responses of the model under the three earthquakes are predicted and then compared with the measured responses. The predicted and measured responses agree well with each other with fitness values of 65–75%. The proposed method is more advantageous over other methods that are based on finite element (FE) model updating since it is free from FE modeling errors. It will be especially effective for cabinet structures in nuclear power plants where conducting shaking table tests may not be feasible. Limitations of the proposed method are also discussed.

Shape Design Sensitivity and Optimization Using P-Version Design Modeling and Finite Element Analysis*

ABSTRACT A methodology that supports shape design modeling, structural shape design sensitivity analysis (DSA), and optimization of elastic solids, using p-version finite element analysis (FEA), is developed. The p-version FEA approach is attractive for shape design optimization, due to its high accuracy of analysis results, even with coarse mesh; ease of creation of design and finite element models; consistency between design and finite element models; insensitivity to finite element mesh distortion and aspect ratio; and tolerance for large shape changes during design optimization iterations. A continuum-based DSA method that is applicable to both planar and spatial structures is developed with an established p-version FEA code, STRESS CHECK. A shape design parameterization method that uses the geometric entities of STRESS CHECK is proposed and implemented. In STRESS CHECK, the shape design model is identical to the finite element model, so finite element modeling errors are eliminated. Design optimization is carried out by integrating the shape design parameterization, design velocity field computation; first-order shape design sensitivity computation, STRESS CHECK; and an optimization code, DOT. Examples are run successfully in full-batch mode to demonstrate the feasibility of the proposed integrated optimization method

Sensor placement for time-domain modal parameter estimation

A new method of sensor placement for modal identification is presented. The sensor placement technique utilizes the variance of estimates derived from a perturbation analysis of a time-domain parameter estimation method to determine appropriate locations of sensors. An efficient scheme is developed to implement the backward elimination scheme for sensor placement. The performance of this method is compared with two alternatives: a process of maximizing the determinant of the Fisher information matrix corresponding to the target modal partitions and a process of minimizing the trace of the covariance matrix. The effect of finite element model error on this placement technique is investigated. Numerical examples demonstrate the efficiency and effectiveness of the new approach.