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 identification in plates using finite element model updating in time domain

A response sensitivity-based approach is presented for identifying the local damages in isotropic plate structures from the measured structural dynamic responses. The local damage is simulated by a reduction in the elemental Young's modulus of the plate. In the forward analysis, the forced vibration responses of the plate under external force are obtained from Newmark direct integration. In the inverse analysis, a response sensitivity-based finite element model updating approach is used to identify local damages of the plate in time domain. The damage identification results are obtained iteratively with the penalty function method with Tikhonov regularization using the measured structural dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Both single damage and multiple damages cases are studied. The effects of measurement noise and measurement point on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for both single and multiple damages for plate structures. Good identified results can be obtained from the short time histories of a few number of measurement points.     

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.     

EXTRACTION OF STRUCTURAL SYSTEM MATRICES FROM AN IDENTIFIED STATE-SPACE SYSTEM USING THE COMBINED MEASUREMENTS OF DVA

A time domain method for the extraction of the structural system matrices (mass, damping and stiffness matrices) from an identified state-space system is proposed in this paper using the combined measurements of displacement, velocity and acceleration (DVA) together with the input excitations. The method is based on the invariance of continuous-time Markov parameters. An explicit expression of the relationship between the continuous-time Markov parameters, the structural system matrices, and the influence matrices for output DVA as well as the input force has been derived. The determination of structural system matrices is also valid when only the displacement, velocity or acceleration responses are measured. In this paper, the equivalent state system matrices are obtained by an algorithm, which combines the eigensystem realization algorithm (ERA) and the autoregressive with exogeneous (ARX) model. The ARX model provides the necessary discrete-time Markov parameters from the measured input and output data, and then the equivalent state system matrices are identified from discrete-time Markov parameters by using the ERA. A lumped mass model with three degrees of freedom is employed to illustrate the accuracy and feasibility of the presented method.     

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.     

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.     

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.     

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.     

Structural damage detection of controlled building structures using frequency response functions

If a building structure requires both a vibration control system and a health monitoring system, the integration of the two systems will be cost-effective and beneficial. One of the key problems of this integrated system is how to use control devices to enhance system identification and damage detection. This paper presents a new method for system identification and damage detection of controlled building structures equipped with semi-active friction dampers through model updating based on frequency response functions. The two states of the building are first created by adding a known stiffness using semi-active friction dampers. A scheme based on the frequency response functions of the two states of the building is then presented to identify stiffness parameters of structural members in consideration of structural connectivity and transformation information. By applying the proposed model updating scheme to the damaged building, a damage detection scheme is proposed based on the identified stiffness parameters of structural members of both the original and damaged buildings. The feasibility of the proposed schemes is finally demonstrated through a detailed numerical investigation in terms of an example building, in which the effects of measurement noise and excitation conditions are discussed. The numerical results clearly show that the proposed method can locate and quantify damage satisfactorily even though measurement noise is taken into consideration.     

Structural damping identification based on an iterative regularization method

A time domain structural damping identification method is presented in this paper. The damping of a structure is assumed to be time-invariant Rayleigh damping, time-variant Rayleigh damping and modal damping, respectively, and an iterative regularization method is proposed to identify these three types of damping in turn. A sensitivity approach is adopted in the formulation of the ill-posed inverse problem. A new constraint is imposed on the identified iterative increment as well as on the unknown structural parameters to ensure their physical meaning in the identification process is not lost. The proposed method is verified in numerical studies with a space frame structure and laboratory measurements of accelerations with accurate results.     

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.     

Estimation of interfacial forces in time domain for linear systems

A structural path rank ordering process under transient excitations requires a good knowledge of the interfacial path forces, which are difficult to directly measure. Four time domain methods to estimate the interfacial forces are proposed and comparatively evaluated with application to linear time-invariant, proportionally damped discrete systems. First, the transient response is derived by modal analysis and a direct time domain technique to calculate the interfacial forces is outlined. Next, the frequency domain estimation methods, based on the sub-system concept are reviewed, and an inverse Fourier transform scheme is introduced. An indirect method of estimating interfacial force in transient state is then developed through an inverse procedure of modal analysis. The sub-system approach is employed to obtain the interfacial forces based on the forced vibration response of the original system and modal data of the sub-system. Finally, an approximate time domain scheme is suggested that could be used only if the system properties are known or precisely estimated. Although the proposed indirect methods are designed for eventual experimental applications, this article provides numerical feasibility studies via a simple source-path-receiver system (with parallel vibration paths) that has five translational degrees of freedom. The proposed methods are compared under ideal impulse force excitation input and a periodic sawtooth load (without and with Gaussian noise) to observe the starting transients as well as subsequent motions and interfacial forces. Preliminary comparisons with a laboratory experiment are very promising.     

HEALTH-MONITORING METHOD FOR BRIDGES UNDER ORDINARY TRAFFIC LOADINGS

A method for damage estimation of a bridge structure is presented using ambient vibration data caused by the traffic loadings. The procedure consists of identification of the operational modal properties and the assessment of damage locations and severities. An experimental study is carried out on a bridge model with a composite cross-section subjected to vehicle loadings. Vertical accelerations of the bridge deck are measured while vehicles are running. The modal parameters are identified from the free-decay signals extracted using the random decrement method. The damage assessment is carried out based on the estimated modal parameters using the neural networks technique. As input to the neural networks, the ratios of the resonant frequencies between before and after damages and the mode shapes after the damages are used to take into account the mass effect of the traffic on the bridge. The identified damage locations and severities agree reasonably well with the inflicted damages on the structure.     

Structural damage detection using cross correlation functions of vibration response

Structural damage detection methods based on vibration responses are appealing for a variety of reasons such as their potential to observe damage from sensors placed remote from an unknown damage site. Of particular interest to the authors is online damage detection in which changes in the structure can be flagged up in an automated fashion by permanently installed transducers. In a previous paper by the authors, the inner product vector (IPV) was proposed as a damage detection algorithm which uses cross correlation functions between response measurements. Implicitly assumed in the formulation is that the response quantity is that of displacement resulting from white noise excitation. In this paper, the IPV technique is first reviewed and then generalised to address velocity and acceleration response to band pass white noise excitation. It is shown that the IPV is a weighted summation of the mode shapes, and the effect of some particular measurement noise on the IPV can be adaptively eliminated in the calculation of IPV. Then, the damage detection method based on changes in the IPV is proposed. Finally, damage detection experiments of shear frame structure, honeycomb sandwich composite beam and aircraft stiffened panel are presented to illustrate the feasibility and effectiveness of the proposed method.     

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.     

Structural health monitoring of fixed offshore structures using the bicoherence function of ambient vibration measurements

This paper investigates the use of the bicoherence function of measured structural acceleration to provide automatic early detection of damage in an offshore structure. A detailed simulation model is developed, including realistic wave loading, and is used to assess the performance of the method. The method is shown through analytical and numerical analysis to be insensitive to typical operating parameter variations and to variations in wave excitation force. It is demonstrated that very small changes in stiffness of individual structural members are detectable from measurements of global structural motion.     

Vibration testing based on impulse response excited by pulsed-laser ablation: Measurement of frequency response function with detection-free input

We have developed a non-contact vibration-measurement system that is based on impulse excitation by laser ablation (i.e. laser excitation) to measure the high-frequency-vibration characteristics of objects. The proposed method makes it possible to analyse the frequency response function just by measuring the output (acceleration response) of a test object excited by pulsed-laser ablation. This technique does not require detection of the input force. Firstly, using a rigid block, the pulsed-laser-ablation force is calibrated via Newton's second law. Secondly, an experiment is conducted in which an object whose natural frequency lies in the high-frequency domain is excited by pulsed-laser ablation. The complex frequency spectrum obtained by Fourier transform of the measured response is then divided by the estimated pulsed-laser-ablation force. Finally, because of the error involved in the trigger position of the response with respect to the impulse arrival time, the phase of the complex Fourier transform is modified by accounting for the response dead time. The result is the frequency response function of the object. The effectiveness of the proposed method is demonstrated by a vibration test of an aluminium block.     

Nonlinear structural identification by the “Reverse Path” spectral method

When dealing with nonlinear dynamical systems, it is important to have efficient, accurate and reliable tools for estimating both the linear and nonlinear system parameters from measured data. An approach for nonlinear system identification widely studied in recent years is “Reverse Path”. This method is based on broad-band excitation and treats the nonlinear terms as feedback forces acting on an underlying linear system. Parameter estimation is performed in the frequency domain using conventional multiple-input–multiple-output or multiple-input–single-output techniques. This paper presents a generalized approach to apply the method of “Reverse Path” on continuous mechanical systems with multiple nonlinearities. The method requires few spectral calculations and is therefore suitable for use in iterative processes to locate and estimate structural nonlinearities. The proposed method is demonstrated in both simulations and experiments on continuous nonlinear mechanical structures. The results show that the method is effective on both simulated as well as experimental data.     

Structural damage evaluation using genetic algorithm

The detection and identification of structural damage is important in monitoring of structural systems during their lifetime. Many researchers have proposed a variety of damage evaluation methods based on structural monitoring. The stiffness matrix is used in some conventional damage detection methods; however, it leads to inevitable error due to the lack of data provided by structural monitoring. To overcome this problem, this study introduces a new damage evaluation method that identifies the structural damage in a shear building based on a genetic algorithm using the structural flexibility matrix with dynamic analyses. The proposed method enables the deduction of the extent and location of structural damage, even when there is insufficient data on the dynamic characteristics and insufficient accurate measurements of the structural stiffness and mass. The validity of the proposed damage evaluation method is demonstrated through numerical analyses using OpenSees.     

Level set based structural topology optimization for minimizing frequency response

For the purpose of structure vibration reduction, a structural topology optimization for minimizing frequency response is proposed based on the level set method. The objective of the present study is to minimize the frequency response at the specified points or surfaces on the structure with an excitation frequency or a frequency range, subject to the given amount of the material over the admissible design domain. The sensitivity analysis with respect to the structural boundaries is carried out, while the Extended finite element method (X-FEM) is employed for solving the state equation and the adjoint equation. The optimal structure with smooth boundaries is obtained by the level set evolution with advection velocity, derived from the sensitivity analysis and the optimization algorithm. A number of numerical examples, in the frameworks of two-dimension (2D) and three-dimension (3D), are presented to demonstrate the feasibility and effectiveness of the proposed approach.