A sensitivity-based structural damage identification method with unknown input excitation using transmissibility concept

Unknown input excitation and local damages universally coexist in a practical situation. Therefore, in this paper a structural damage identification method based on the transmissibility concept in state space domain is proposed without the need for input measurements. On the basis of the transformation matrix which is computed using the system Markov parameters in state space, the relationship between two different sets of acceleration response measurements can be formulated under the same input excitation. A sensitivity-based model updating approach is applied to identify the local damages by minimizing the difference between the measured response and the reconstructed response. The sensitivity of the dynamic acceleration response with respect to the elemental stiffness factors is derived analytically in the state space domain, which accelerates the process of damage identification. A numerical cantilever beam is employed to validate that the variation of structural parameters induced by the local damages can be accurately and effectively identified without the input excitation information by the proposed method even with measurement noise considered. A laboratory test is further carried out to verify the proposed structural damage identification method based on the response reconstruction technique.     

Structural damage identification for railway bridges based on train-induced bridge responses and sensitivity analysis

A damage identification approach using train-induced responses and sensitivity analysis is proposed for the nondestructive evaluation of railway bridges. The dynamic responses of railway bridges under moving trains composed of multiple vehicles are calculated by a train-bridge dynamic interaction analysis. Using the stiffness variation of the bridge element as an index for damage identification, the sensitivities of train-induced bridge responses to structural damage are analyzed and the sensitivity matrices are formed. By comparing the theoretical measurement responses of one measurement point in two different states, the damage indices of all elements are updated iteratively, and finally the absolute or relative damage is located and quantified. A three-span continuous bridge numerical example proves that the proposed dynamic response sensitivity-based FE model updating damage identification method is not only effective to detect local damage of railway bridges, but also insensitive to the track irregularity and the measurement noise.     

Singular spectrum analysis for enhancing the sensitivity in structural damage detection

Time domain structural condition assessment methods have been studied extensively in the last two decades due to their effectiveness in dealing with limited and short duration measurements from a structure under operational conditions. The sensitivity-based method is revisited in this paper with an enhancement in the sensitivity with respect to local damages via the singular spectrum analysis technique. The measured response of the structure is decomposed and the sensitivity vectors as well as the computed response vectors are projected into the corresponding decomposition subspace. The projected identification equations associate with components which contain the least measurement noise and the most damage information are then used to detect local damages in the structure. The enhanced sensitivity-based method is shown to be capable of yielding more accurate identified results with noisy measurement in a planar truss structure compared to conventional sensitivity-based method. A seven-storey steel frame test is performed in the laboratory, and the proposed method is checked to be able to identify the damage location and extend of this structure with an acceptable accuracy.     

On the tuning of variable piezoelectric transducer circuitry network for structural damage identification

The concept of using piezoelectric transducer circuitry with tunable inductance has been recently proposed to enhance the performance of frequency-shift-based damage identification method. While this approach has shown promising potential, a piezoelectric circuitry tuning methodology that can yield the optimal damage identification performance has not been synthesized. This research aims at advancing the state-of-the-art by exploring the characteristics of inductance tuning such that the enrichment of frequency measurements can be effectively realized to highlight the damage occurrence. Analysis shows that when the inductance is tuned to accomplish eigenvalue curve veering, the change of system eigenvalues induced by structural damage will vary significantly with respect to the change of inductance. Therefore, by tuning the inductance near the curve-veering range, one may obtain a family of frequency response functions that could effectively reflect the damage occurrence. When multiple tunable piezoelectric transducer circuitries are integrated to the mechanical structure, multiple eigenvalue curve veering can be simultaneously accomplished, and a series of inductance tunings can be formed by accomplishing curve veering between different pairs of system eigenvalues. It will then be shown that, to best characterize the damage occurrence, the favorable inductance tuning sequence should be selected as that leads to a “comprehensive” set of eigenvalue curve veering, i.e., all measurable natural frequencies undergo curve veering at least once. An iterative second-order perturbation-based algorithm is used to identify the locations and severities of the structural damages based on the frequency measurements before and after the damage occurrence. Numerical analyses on benchmark beam and plate structures have been carried out to examine the system performance. The effects of measurement noise on the effectiveness of the proposed damage identification method are also evaluated. It is demonstrated that the damage identification results can be significantly improved by using the variable piezoelectric transducer circuitry network with the favorable inductance-tuning scheme proposed in this research.     

A FREQUENCY-DOMAIN METHOD OF STRUCTURAL DAMAGE IDENTIFICATION FORMULATED FROM THE DYNAMIC STIFFNESS EQUATION OF MOTION

This paper introduces a frequency-domain method of structural damage identification. It is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a beam structure. Only the dynamic stiffness matrix for the intact state appears in the final form of the damage identification algorithm as the structure model. The appealing features of the present damage identification method are: (1) it requires only the frequency response functions experimentally measured from the damaged structure as the input data, and (2) it can locate and quantify many local damages at the same time. The feasibility of the present damage identification method is tested through some numerically simulated damage identification analyses and then experimental verification is conducted for a cantilevered beam with damage caused by introducing three slots.     

Structural damage evolution assessment using the regularised time step integration method

This paper presents an approach to identify both the location and severity evolution of damage in engineering structures directly from measured dynamic response data. A relationship between the change in structural parameters such as stiffness caused by structural damage development and the measured dynamic response data such as accelerations is proposed, on the basis of the governing equations of motion for the original and damaged structural systems. Structural damage parameters associated with time are properly chosen to reflect both the location and severity development over time of damage in a structure. Basic equations are provided to solve the chosen time-dependent damage parameters, which are constructed by using the Newmark time step integration method without requiring a modal analysis procedure. The Tikhonov regularisation method incorporating the L-curve criterion for determining the regularisation parameter is then employed to reduce the influence of measurement errors in dynamic response data and then to produce stable solutions for structural damage parameters. Results for two numerical examples with various simulated damage scenarios show that the proposed method can accurately identify the locations of structural damage and correctly assess the evolution of damage severity from information on vibration measurements with uncertainties.     

Substructure methods for structural condition assessment

It is commonly known that an accurate analysis of a large structure requires an accurate analytical model. This is also true for the inverse analysis of a structural system where measured structural responses are used as input to assess the structural conditions. However, an accurate model of the structure is always not available in practice. Two substructural identification methods are presented in this paper with the structure divided into substructures and with one substructure assessed at one time. In the first method, an accurate finite element model of the whole structure is assumed known. A state space method is applied to identify the external forces acting on the structure, and a damage identification method is then applied to identify the local damages using time domain information. Iterative model updating method based on the measured acceleration in the selected substructure is employed for the assessment. The second identification method requires only the finite element model of the substructure. The interface forces and the external forces acting on the target substructure are all taken as excitations and they are identified in state space. The substructure is then assessed similar to the first method. Since the target substructure for updating consists of a much reduced number of components and the identification problem is more efficient. The validation of the proposed methods is demonstrated by a truss structure with polluted measured accelerations with promising results.     

Damage localization in linear-form structures based on sensitivity investigation for principal component analysis

This paper addresses the problem of damage detection and localization in linear-form structures. Principal component analysis (PCA) is a popular technique for dynamic system investigation. The aim of the paper is to present a damage diagnosis method based on sensitivities of PCA results in the frequency domain. Starting from frequency response functions (FRFs) measured at different locations on the structure; PCA is performed to determine the main features of the signals. Sensitivities of principal directions obtained from PCA to structural parameters are then computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. It is worth noting that damage localization is performed without the need of modal identification. Influences of some features as noise, choice of parameter and number of sensors are discussed. The efficiency and limitations of the proposed method are illustrated using numerical and real-world examples.     

VIBRATION-BASED DAMAGE IDENTIFICATION USING RECONSTRUCTED FRFS IN COMPOSITE STRUCTURES

This work aims to establish a vibration-based damage identification method for fiber-reinforced laminated composites and their sandwich construction. This new on-line structural damage identification technique uses the structural dynamic system reconstruction method exploiting the frequency response functions (FRFs) of a damaged structure. To verify the effectiveness of this damage identification method, the frequency responses obtained by vibration testing of fatigue-damaged laminated composites and honeycomb sandwich beams with debonding are examined according to the extent of the damage via the fatigue-damage load cycle for laminated composites, and via the debonding extent for honeycomb sandwich beams. The changes of the peaks and valley of the FRFs according to the debonding extent and the fatigue load cycles are examined, and the area changes in the FRFs are also discussed as the damage index. The residual FRFs or the difference between intact and damaged FRFs are newly defined for application of the on-line damage identification method. Finally, the delamination extent for the sandwich beams and the fatigue damage level for the laminated composites can be easily identified in terms of the changes in natural frequencies and damping ratios of the reconstructed FRFs for these damaged composite structures.     

Identification of structural systems with full characteristic matrices under single point excitation

The aim of “System Identification” is to determine modal and system properties of structural systems. This is while in “Damage Detection”, the identification of system characteristic matrices is as important as or even more important than the identification of frequency characteristics. Because of various constraints – i.e. difficulties in force excitation of structures due to their large size, geometry, and location – in practice only single excitation and partial measurement, at selected degrees of freedom, is possible. In this paper, a single dynamic load was applied to identify a structural system only along one of the degrees of freedom of the structure. Further, responses corresponding to a few degrees of freedom were also measured. To identify a system with this sort of restricted information, a new approach was introduced enabling identification of the structure?s parameters of mass, damping and stiffness. Taking into account the significant effect of noise reduction in improving system identification accuracy levels, a noise reduction technique was also proposed. The accuracy of the method was also assessed against noise level and location of single excitation. It was shown that as noise level increases, identification errors will also increase (less than 3.5 percent). It was further observed that applying single force at the first storey of the flexural structure would yield the lowest error levels in the identification results. Later, the method?s efficiency and precision were examined through the application of a “closed loop solution” to a six-storey flexural structure, and a four-span Pratt truss. The obtained results showed that the proposed method could act as an effective model in identification of system properties.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

Identification of structural damage based on locally perturbed dynamic equilibrium with an application to beam component

In recognition of the obvious limitations of most global vibration-based and local guided-wave-based damage detection techniques, a novel inverse identification approach was developed by canvassing the local perturbance to equilibrium characteristics of the structural component under inspection. Characterized by high-order spatial derivatives, this approach has in particular proven sensitivity to structural damage. Most importantly, it requires neither benchmark structures nor baseline signals; neither global models nor additional excitation sources as long as the structure undergoes steady vibration under its normal operation. Independent of a global model, prior knowledge on structural boundary conditions is not compulsory. To minimize unavoidable influence of measurement noise on high-order spatial derivatives, various de-noising treatments, including wavenumber filtering, optimal selection of measurement configuration and hybrid information fusion were introduced independently. Using a simple beam as a representative structural component for illustration, relationships among vibration frequency, density of measurement points and size of detectable damage were explored, facilitating a judicious selection of measurement parameters. Proof-of-concept validation was numerically conducted, and then experimentally demonstrated using a scanning laser vibrometer. In principle, this proposed methodology is applicable to a complex system comprising various structural components, provided that the local equilibrium relationships of the components are known a priori.     

A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source

The problem of detecting local/distributed change of stiffness in bridge structures using ambient vibration data is considered. The vibration induced by a vehicle moving on the bridge is taken to be the excitation source. A validated finite element model for the bridge structure in its undamaged state is assumed to be available. Alterations to be made to this initial model, to reflect the changes in bridge behaviour due to occurrence of damage, are determined using a time-domain approach. The study takes into account complicating features arising out of dynamic interactions between vehicle and the bridge, bridge deck unevenness, spatial incompleteness of measured data and presence of measurement noise. The inclusion of vehicle inertia, stiffness and damping characteristics into the analysis makes the system time variant, which, in turn, necessitates treatment of the damage detection problem in time domain. The efficacy of the procedures developed is demonstrated by considering detection of localized/distributed damages in a beam-moving oscillator model using synthetically generated vibration data.     

STOCHASTIC DYNAMIC SENSITIVITY OF UNCERTAIN STRUCTURES SUBJECTED TO RANDOM EARTHQUAKE LOADING

The present study involves computation of stochastic sensitivity of structures with uncertain structural parameters subjected to random earthquake loading. The formulations are provided in frequency domain. A strong earthquake-induced ground motion is considered as a random process defined by respective power spectral density function. The uncertain structural parameters are modelled as homogeneous Gaussian stochastic field and discretized by the local averaging method. The discretized stochastic field is simulated by the Cholesky decomposition of respective co-variance matrix. By expanding the dynamic stiffness matrix about its reference value, the advantage of Neumann Expansion technique is explored within the framework of Monte Carlo simulation, to compute responses as well as sensitivity of response quantities. This approach involves only a single decomposition of the dynamic stiffness matrix for the entire simulated structure and the facility that several stochastic fields can be tackled simultaneously are basic advantages of the Neumann Expansion. The proposed algorithm is explained by an example problem.     

A novel sensitivity-based method for damage detection of structures under unknown periodic excitations

This paper presents a technique for damage detection in structures under unknown periodic excitations using the transient displacement response. The method is capable of identifying the damage parameters without finding the input excitations. We first define the concept of displacement space as a linear space in which each point represents displacements of structure under an excitation and initial condition. Roughly speaking, the method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering this novel geometrical viewpoint, an equation called kernel parallelization equation (KPE) is derived for damage detection under unknown periodic excitations and a sensitivity-based algorithm for solving KPE is proposed accordingly. The method is evaluated via three case studies under periodic excitations, which confirm the efficiency of the proposed method.     

Modal flexibility-based damage detection of cantilever beam-type structures using baseline modification

This paper presents a new damage detection approach for cantilever beam-type structures using the damage-induced inter-storey deflection (DIID) estimated by modal flexibility matrix. This approach can be utilized for damage detection of cantilever beam-type structures such as super high-rise buildings, high-rise apartment buildings, etc. Analytical studies on the DIID of cantilever beam-type structures have shown that the DIID abruptly occurs from damage location. Baseline modification concept was newly introduced to detect multiple damages in cantilever beam-type structures by changing the baseline to the prior damage location. This approach has a clear theoretical base and directly identifies damage location(s) without the use of a finite element (FE) model. For validating the applicability of the proposed approach to cantilever beam-type structures, a series of numerical and experimental studies on a 10-storey building model were carried out. From the tests, it was found that the damage locations can be successfully identified by the proposed approach for multiple damages as well as a single damage. In order to confirm the superiority of the proposed approach, a comparative study was carried out on two well-known damage metrics such as modal strain-based damage index approach and uniform load surface curvature approach.     

Damage detection in plates structures based on frequency shift surface curvature

This paper presents a novel damage detection method for plate structures based on the curvature of frequency shift surface (FSS). Unlike other commonly used vibration properties like mode shapes which have low accuracy in practice; this method uses the FSS curvature to improve the accuracy because the measurement of frequency gives better accuracy. Furthermore, it is found that the local damage will only cause local change on the FSS curvature which can be considered as abnormality because the FSS curvature of an intact plate is smooth according to the assumption that intact plate structures are often homogenous and smooth. To avoid the usage of prior knowledge of the health structure, the curve fitting technique based on local regression is adopted to simulate the FSS curvature for the intact state so that only the data from the damaged plate structure is required. Compared with traditional methods, this method is more sensitive and accurate.     

Damage identification in beam type structures based on statistical moment using a two step method

This paper defines a novel damage index-strain statistical moment, and formulates the fourth strain statistical moment (FSSM) of beam-type structures under white noise excitation. Based on this newly defined strain statistical moment index and the least square optimization algorithm, a two-step damage identification method is proposed. This two-step method is operated like this: first use the difference curves of FSSMs before and after damage to locate damage elements; then for those identified damage elements, employ the model updating method based on the least square algorithm to assess their damage severity. Numerical studies on a simply supported beam and a two-span continuous beam are performed and the study results show that the newly defined index is effective to locate damages, even when the noise intensity is as high as 15 percent. Integrating with the least square-based model updating technique, the damage severities of beam-type structures can also be determined quantitatively. In this way, the proposed two-step method is verified and found to be capable of identifying damage positions and severities of beam-type structures and insensitive to measurement noise.     

Impact load identification of composite structure using genetic algorithms

For structural health monitoring of composite structure, it is important to quickly and accurately identify the impact load whenever an impact event occurs. This paper proposes a genetic algorithms (GA)-based approach for impact load identification, which can identify the impact location and reconstruct the impact force history simultaneously. In this study, impact load is represented by a set of parameters, thus the impact load identification problem in both space (impact location) and time (impact force history) domains is transformed to a parameter identification problem. A forward model characterizes the dynamic response of the structure subject to a known impact force is incorporated in the identification procedure. By minimizing the difference between the analytical responses given by the forward model and the measured ones, GA adaptively identify the impact location and force history with its global search capability. This new impact identification approach is applied to a stiffened composite panel. The stiffened composite panel is modeled as an equivalent laminate with varying properties and the forward response is obtained by using an assumed modes approach. To improve the computational efficiency, micro-GA (μGA) is employed to perform the identification task. Numerical simulation studies are conducted to demonstrate the effectiveness and applicability of the proposed method.     

A damage identification technique based on embedded sensitivity analysis and optimization processes

A vibration based structural damage identification method, using embedded sensitivity functions and optimization algorithms, is discussed in this work. The embedded sensitivity technique requires only measured or calculated frequency response functions to obtain the sensitivity of system responses to each component parameter. Therefore, this sensitivity analysis technique can be effectively used for the damage identification process. Optimization techniques are used to minimize the difference between the measured frequency response functions of the damaged structure and those calculated from the baseline system using embedded sensitivity functions. The amount of damage can be quantified directly in engineering units as changes in stiffness, damping, or mass. Various factors in the optimization process and structural dynamics are studied to enhance the performance and robustness of the damage identification process. This study shows that the proposed technique can improve the accuracy of damage identification with less than 2 percent error of estimation.