An efficient method for structural damage detection using a differential evolution algorithm-based optimisation approach

An efficient method employing the differential evolution algorithm (DEA) as an optimisation solver is presented here to identify the multiple damage cases of structural systems. Natural frequency changes of a structure are considered as a criterion for damage occurrence. The structural damage detection problem is first transformed into a standard optimisation problem dealing with continuous variables, and then the DEA is utilised to solve the optimisation problem for finding the site and extent of structural damage. In order to assess the performance of the proposed method for structural damage identification, some illustrative examples are numerically tested, considering also measurement noise. All the numerical results demonstrate the effectiveness of the proposed method for accurately determining the site and extent of multiple-structural damage. Also, the performance of the DEA for damage detection compared to the standard particle swarm optimisation is confirmed by a test example.     

A Bayesian Probabilistic Approach for Crack Characterization in Plate Structures

Abstract: This article explores the possibility of using a Bayesian probabilistic approach for the detection of cracks in thin plate structures, utilizing measured dynamic responses at only a few points on the plate. Existing laser scanning or shearography based crack detection methods are applicable only when measurement at the region near the defect is possible. These types of techniques are important in providing information, in addition to that obtained through visual inspection, for the purpose of structural health monitoring. Because of the global nature of the vibration characteristics of structural systems, this article puts forward a crack detection approach that can be applicable with only a few sensors and when the sensor locations are not close to the crack. This kind of method is particularly valuable as it can be applied when visual inspection is not possible (e.g., part of the plate is obstructed and is not assessable by inspectors). Owing to the problems of measurement noise and incomplete measurement (i.e., only a limited number of measurement points are employed and high‐mode information is lost because of the digitization of the signal and measurement noise), the results of crack detection as an inverse problem contain uncertainties. To explicitly handle such uncertainty, the proposed crack detection method follows the Bayesian statistical system identification framework. Rather than pinpointing the crack parameters (i.e., the crack location, length, and depth), the posterior probability density function (PDF) of the crack parameters is calculated to quantify the confidence level of the identified results, which is extremely important for engineers when they make judgments about remedial works. This article reports the theoretical development of the modeling of a cracked plate and a crack detection method together with numerical verification of the proposed method. The case study results are very encouraging, and indicate that the proposed method is feasible.     

Response covariance-based sensor placement for structural damage detection

One important function of a structural health monitoring system is to detect structural damage in a structure. However, this is a very challenging task since the measurement is often incomplete in a civil structure due to a limited number of sensors. This paper presents a response covariance-based sensor placement method for structural damage detection with two objective functions for optimisation. The relationship between the covariance of acceleration responses and the covariance of unit impulse responses of a structure subjected to multiple white noise excitations is first derived. The response covariance-based damage detection method is then presented. Two objective functions based on the response covariance sensitivity and the response independence are, respectively, formulated and finally integrated into a single objective function for optimal sensor placement. Numerical studies are conducted to investigate the feasibility and effectiveness of the proposed method via a three-dimensional frame structure. Numerical results show that the proposed method with the backward sequential sensor placement algorithm is effective for damage detection.     

Dynamic reduction-based structural damage detection of transmission tower utilizing ambient vibration data

This paper reports a feasibility study of utilizing ambient vibration data measured from a limited number of sensors in the structural damage detection of transmission towers, which are large-scaled three-dimensional spatial structures. To develop a practical and efficient structural damage detection methodology, the characteristics of transmission towers are considered in the development stage, including the most common types of damage, accessible locations for installing sensors, the technique needed to identify a reliable set of modal parameters utilizing ambient vibration data, a method to divide the transmission tower into sub-structures for structural damage detection, a way to formulate the damage detection problem, and the corresponding solution method. The proposed methodology is numerically verified by simulated noisy data from a three-dimensional transmission tower sample under both single and multiple damage cases. Very encouraging results are obtained, showing that the proposed methodology can identify the damaged sub-structure by estimating the ‘equivalent’ stiffness reduction even in the presence of both measurement noise and modeling error.     

A simulation optimisation tool for planning of low-income housing projects

Construction of low-income housing projects is a recurring process and is associated with uncertainties that arise from the unavailability of resources. This paper presents a case study that discusses how computer simulation and optimisation are used to aid government agencies and/or contractors in planning of such projects. It illustrates the optimisation of project objectives, taking into consideration the interaction amongst involved resources. As such, total duration and the associated total costs, including direct and indirect costs, can be estimated and optimised. One Youth Habitation project that is executed in 6th of October City in Egypt is analysed in a step-by-step procedure to demonstrate the capability of proposed computer simulation and optimisation prototype (named LIHouse{_}Sim) in the modelling construction of low-income housing projects using bearing block walls with hollow core technique. The presented tool proves its practicality to contractors in estimating the time and costs of the recurring process of low-income housing construction, considering complex interdependencies between construction resources and the uncertainties associated with construction activities. The LIHouse{_}Sim prototype is used to perform a wide analysis for the alternative of the effective optimisation criteria in the bearing block walls/hollow core technique and for the genetic algorithm optimisation approach elements.     

Vibration based structural health monitoring: Wavelet packet transform based solution

One prominent problem for vibration-based structural health monitoring is to extract condition indices which are sensitive to damage and yet insensitive to measurement noise. In this paper, a condition index extraction method based on the wavelet packet transform (WPT) is proposed. This transform leads to the formulation of a novel condition index: wavelet packet signature (WPS). The sensitivity of the WPS to the change of structural parameters is derived and validated on a five-degrees-of-freedom spring-mass system. Results show that the WPS is significantly more sensitive to the stiffness change than the natural frequencies and the mode shapes. Its sensitivity is slightly better or comparable to that of the modal flexibility matrices depending on the location of damage. A variability analysis is also performed to study the effect of measurement noise on the proposed WPS. Results show that the WPS does not show any significant variation even under the presence of 10 dB noise. To illustrate the potential of the WPS, a damage indicator is formulated and used to monitor the health condition of the structural system. An experimental study on a three-storey frame shows that when incorporated with a statistical process control approach, the WPS-based damage indicator can distinctly identify the presence of damage in the system.     

Monitoring Structural Health Using a Probabilistic Measure

A Bayesian probabilistic methodology for structural health monitoring is presented. The method uses a sequence of identified modal parameter data sets to continually compute the probability of damage. In this approach, a high likelihood of a reduction in model stiffness at a location is taken as a proxy for damage at the corresponding structural location. The concept extends the idea of using as indicators of damage the changes in model parameters identified using a linear finite-element model and modal parameter data sets from the structure in undamaged and possibly damaged states. This extension is needed because of uncertainties in the updated model parameters that in practice obscure health assessment. These uncertainties arise due to effects such as variation in the identified modal parameters in the absence of damage, as well as unavoidable model error. The method is illustrated by simulating on-line monitoring, wherein specified modal parameters are identified on a regular basis and the probability of damage for each substructure is continually updated. Examples are given for abrupt onset of damage and progressive deterioration.     

Measurement-based support for post-earthquake assessment of buildings

After a damaging earthquake, assessment of the residual seismic capacity is required for large parts of the building stock. Increased vulnerability of structures together with the threat of immediate aftershocks call for rapid and objective decision making. Structural identification has the potential to reduce parameter-value uncertainties of physics-based models through interpreting measurement data. Significant amounts of uncertainty are associated with the non-linear behaviour of structures during extreme events such as earthquakes. Therefore, a structural identification methodology that accommodates multiple sources of systematic modelling uncertainties is used. Error-domain model falsification (EDMF) enables structural identification through combining damage grades observed by visual inspection with fundamental frequencies that are derived from ambient vibrations. Parametric uncertainties of a hysteretic model are reduced with the two information sources in order to extrapolate the vulnerability of the building regarding future earthquakes. The applicability of the methodology is shown using measurements made on a mixed reinforced-concrete unreinforced-masonry building tested on a shaking table. Based on nonlinear time-history analyses involving single-degree-of-freedom models, EDMF leads to more precise, yet robust, vulnerability predictions of earthquake-damaged buildings when compared with prediction ranges that are obtained without data interpretation.     

Structural damage assessment with incomplete and noisy modal data using model reduction technique and LAPO algorithm

Abstract

The present article proposes an efficient method for damage assessment of structures with incomplete and noisy modal data using model reduction method and Lightning Attachment Procedure Optimisation (LAPO) algorithm. The damage identification problem is formulated as an optimisation problem, in which the extent of damaged elements and a combination of both natural frequencies and modal flexibility changes are considered as the continuous design variables and a hybrid objective function, respectively. The LAPO algorithm, a recently developed algorithm, is for the first time extended to solve the formulated optimisation problem. In addition, due to incomplete modal data, an iterated improved reduction system (IIRS) technique is adopted to condense structural physical properties. The efficiency and robustness of the proposed method are investigated using three types of structures and the results are compared with those obtained by other well-known optimisation algorithms. It is shown that regardless of the effect of incomplete and noisy modal data, the proposed method not only successfully determines the location and extent of single and multiple damage cases in the structures, but also has lower computational cost than the other optimisers.     

Fuzzy-based optimised subset simulation for reliability analysis of engineering structures

This paper presents a numerical strategy for the efficient reliability assessment of engineering structures with random variables and fuzzy variables using fuzzy based optimised subset simulation (SS) approach. The proposed method relies on the performance function of the structure, which involves probability distribution functions and fuzzy variables for the modelling of the structural system. The values of the fuzzy variables for every alpha level are first obtained using the membership function. Therefore, the set values of the fuzzy variable bound the reliability of the structure, and this is evaluated using optimisation and efficient SS approach. The rationale behind the proposed strategy is to locate a failure domain or region where the objective function is minimised or maximised and compute the reliability using SS. The proposed algorithm in this study inherits the benefits of direct Monte Carlo approach in propagating the uncertainties associated with structural parameters but also demonstrate more robustness against the latter. The methodology can be applied to any engineering structures, and the applicability is demonstrated here, using a buried pipeline.     

Spectral element modeling based structure piezoelectric impedance computation and damage identification

This paper presents a numerical simulation study on electromechanical impedance technique for structural damage identification. The basic principle of impedance based damage detection is structural impedance will vary with the occurrence and development of structural damage, which can be measured from electromechanical admittance curves acquired from PZT patches. Therefore, structure damage can be identified from the electromechanical admittance measurements. In this study, a model based method that can identify both location and severity of structural damage through the minimization of the deviations between structural impedance curves and numerically computed response is developed. The numerical model is set up using the spectral element method, which is promised to be of high numerical efficiency and computational accuracy in the high frequency range. An optimization procedure is then formulated to estimate the property change of structural elements from the electric admittance measurement of PZT patches. A case study on a pin-pin bar is conducted to investigate the feasibility of the proposed method. The results show that the presented method can accurately identify bar damage location and severity even when the measurements are polluted by 5% noise.     

Fractal Dimension‐Based Damage Detection Method for Beams with a Uniform Cross‐Section

Abstract: For civil structures, damage usually occurs in localized areas. As fractal dimension (FD) analysis can provide insight to local complexity in geometry, a damage detection approach based on Katz's estimation of the FD measure of displacement mode shape for homogeneous, uniform cross‐sectional beam structures is proposed in this study. An FD‐based index for damage localization (FDIDL) is developed utilizing the difference of angles of sliding windows between two successive points, which is expressed in FD. To improve robustness against noise, FDIDL is calculated using multisliding windows. The influence of the spatial sampling interval length and the number of 2‐sampling sliding windows on sensitivity to damage and robustness against noise is investigated. The relationship between the angle expressed in FD and the modal strain energy is established and thereby an FD‐based index for the estimation of damage extent (FDIDE) is presented. The two damage indices are applied to a simply supported beam to detect the simulated damage in the beam. The results indicate that the proposed FDIDL can locate the single or multiple damages, and FDIDE can reliably quantify the damage extent. The optimal spatial sampling interval and the number of sliding windows are investigated. Furthermore, the simulation with measurement noise is carried out to demonstrate the effectiveness and robustness of the two defined FD‐based damage indices. Finally, experiments are conducted on simply supported steel beams damaged at different locations. It is demonstrated that the proposed approach can locate the damages to a satisfactory precision.     

A non-iterative structural damage identification methodology using state space eigenstructure assignment

In this article, a novel approach to damage identification (location as well as intensity) is presented using eigenstructure assignment (ESA)-based finite-element model (FEM) updating. ESA is a control-based approach that utilises state or output feedback of a system to alter its eigenstructure. The proposed method identifies the system’s state transition matrix and its eigenstructure from the response time history. The identified eigenstructure is first mapped onto the physical space and then reconstructed in state space in the preferred orientation and order which, in turn, is used as the target for the ESA algorithm to uniquely update the system matrices of the baseline FEM. Comparing the updated stiffness matrix with the baseline, the location and intensity of damage are estimated. Numerical validation of the method is performed on a shear frame, a Euler–Bernoulli beam, and an aluminium plate. A parametric study involving different levels of noise in the simulated response histories is undertaken. The algorithm is then tested with actual response histories from a damaged (notched) two span continuous steel beam and a damaged (indented) aluminium plate in the laboratory. The accuracy of the method in identifying the location and extent of damage is found satisfactory. Being eigenstructure based, the proposed methodology is restricted to linear time-invariant systems.     

Statistical analysis on results of optimal power sharing between linked microgrids

The future distribution network will be made of interconnected distribution systems, so-called microgrids (MGs). MGs provide an effective means of utilising energy from small-scale renewable resources. The probabilistic power generation behaviour renewable generations and load forecasting errors are the most important uncertainties in the MG operation. The proposed methodology of this paper applies these uncertainties into the operation problem in order to find the practical solutions. So, in this research the economic operation of multi-MGs is formulated as a cost-based objective function which is minimised using particle swarm optimisation algorithm. As a result, the problem outputs must be defined by probability distribution functions (PDFs) in order to achieve comprehensive analysis of the literature. Another contribution of the paper, which rises the accuracy of the analysis in operation discussion, is applying suitable fitting criteria to select the best PDF for each obtained result based on Akaike's information criterion.     

Modal Flexibility Analysis of Cable-Stayed Ting Kau Bridge for Damage Identification

Abstract:   The cable-stayed Ting Kau Bridge has been permanently instrumented with more than 230 sensors for long-term structural health monitoring. In this article, the feasibility of using the measured dynamic characteristics of the bridge for damage detection is studied. Making use of a validated three-dimensional (3D) finite element model (FEM), modal flexibility matrices of the bridge are constructed using a few truncated modes and incomplete modal vectors at the sensor locations. The relative flexibility change (RFC) between intact and damage states is then formulated as an index to locate damage. The applicability of this flexibility index for damage location in the cable-stayed bridge is examined by investigating various damage scenarios including those at stay cables, longitudinal stabilizing cables, bearings and supports, longitudinal girders and cross girders, and taking into account measurement noise in modal data. The influence of two ambient factors, that is, temperature change and traffic loading, on the damage detectability is also analyzed by approximately considering an equivalent alteration in the material and structural behaviors. It is revealed that in the absence of ambient effects the RFC index performs well for locating damage of different severities in single-damage cases. In multi-damage cases the RFC index may provide false-negative identification for damage at the members with low sensitivity. Eliminating ambient effects is requisite for reliable detection of damage at stay cables and cross girders. The capability of the RFC index for locating damage at cross girders is significantly dropped in the presence of measurement noise.     

Damage identification of a tunnel liner based on deformation data

A new system identification approach based on tunnel deformation data is proposed to find the damage in the tunnel liner. For this, an inverse problem in which deformation data and dead load of concrete lining are known a priori is introduced to estimate the degree and location of the damage. Models based on uniform reduction of stiffness and smeared crack concept are both employed and the efficiency and relative advantage are compared with each other. Numerical analyses are performed on the idealized tunnel structure and the effect of white noise, common in most measurement data, is also investigated to better understand the suitability of the proposed models. As a result, model 1 based on uniform stiffness reduction method is shown to be relatively insensitive to the noise, while model 2 with the smeared crack concept is proven to be easily applied to the field situation since the effect of stiffness reduction is rather small. Finally, real deformation data of a rail tunnel in which health monitoring system is in operation are introduced to find the possible damage and it is shown that the prediction shows quite satisfactory result.     

A multi-objective framework for energy resource scheduling in active distribution networks

Purpose: The purpose of this paper is to investigate the impacts of electric vehicles' (EVs) charging/discharging decisions in energy resources scheduling problem of active distribution networks. Design/methodology/approach: The problem under study is modelled as a two-stage optimisation problem in which the main requirements of EV owners are introduced as an objective function of the first stage. The total energy costs and the emission factor are considered as the main criteria of the second stage. The output generation schedules of distributed generation (DG) technologies together with the charging/discharging schedule of EVs are proposed as decision variables of the energy scheduling problem. Therefore, some effective methods are presented to model the uncertainties associated with these variables. Findings: The results proved that an efficient compromise can be reached between the emission factor and the energy cost of the system. In addition, it has been emphasised on the importance of such comprehensive energy scheduling frameworks. Originality/value: This paper contributes by: (a) providing a multi-objective framework for energy scheduling of active distribution networks, (b) extracting the mathematical model of this two-stage problem and (c) employing a linearised optimisation model to reach its global optimal solution.     

基于关联模态云推理算法的输电塔结构损伤识别

为了解决输电塔等工程结构在不确定因素干扰下的损伤识别问题,提出了一种基于关联模态的云推理算法。建立残余力基本方程,并分析了基于残余力向量的损伤识别原理;提出了基于残余力的云推理算法,给出了云模型的数字特征,分析了前件云发生器和后件云发生器,给出了基于灰云模型的定性规则库建立方法,并利用云规则组成了相应的云推理系统。考虑到残余力法易受测量噪声等不确定因素干扰的弱点,进一步提出了关联模态云推理算法,以提高损伤识别的精度和可靠性,并采用输电塔结构模型进行了损伤识别研究。数值计算结果表明,关联模态云推理算法可以较好地识别出结构损伤,其识别效果明显优于残余力向量法和残余力云推理算法。     

Vibration‐Based Damage Localization in Flexural Structures Using Normalized Modal Macrostrain Techniques from Limited Measurements

Abstract: This article presents damage locating indices based on normalized modal macrostrain (MMS) as improvement on the typical curvature‐dependent methods. Vulnerability to noise and the use of numerical differentiation procedures are the key factors for the poor performance of many curvature‐dependent methods using displacement mode shapes. Whereas dynamic distributed strain measurement data from long‐gauge FBG sensors have significantly improved the performance of many damage identification methods, the sensitivity to local damage diminishes as the gauge length increases. The proposed model‐free damage identification techniques based on normalized MMS vectors are successfully implemented to locate damage in beam‐like structures through numerical simulations and experimental verifications. The unique advantages of the techniques are their simplicity, robustness to noise, ability to precisely identify small damage extents, and localize single and multiple damage states using limited measurable modes from few sensors.     

Qualitative and quantitative assessment of interior moisture buffering by enclosures

The significance of interior humidity in attaining sustainable, durable, healthy and comfortable buildings is increasingly recognised. Given their significant interaction, any interior humidity appraisal requires a qualitative and/or quantitative assessment of interior moisture buffering. While the effective moisture penetration depth and effective capacitance models allow quantified assessment, their reliance on the ‘moisture penetration depth’ necessitates comprehensive material properties and hampers their application to multidimensional interior objects. On the other hand, while various recently suggested protocols for the simple and fast measurement of the moisture buffer potential of interior elements allow qualitative assessment, none of these are currently dependable for a wide range of moisture production regimes.In response to these flaws, this paper introduces the production-adaptive characterisation of the moisture buffer potential of interior elements and corroborates their superposition toward a room-enclosure moisture buffer potential. It is verified that this enables qualitative comparison of enclosures in relation to interior moisture buffering. It is moreover demonstrated that it forms an alternative basis for quantitative evaluation of interior moisture buffering by the effective moisture penetration depth and effective capacitance models. The presented methodology uses simple and fast measurements only and can also be applied to multimaterial and/or multidimensional interior elements.