Bayesian probabilistic damage detection of a reinforced‐concrete bridge column

A Bayesian probabilistic approach for damage detection has been proposed for the continuous monitoring of civil structures (Sohn H, Law KH. Bayesian probabilistic approach for structure damage detection. Earthquake Engineering and Structural Dynamics 1997; 26 :1259–1281). This paper describes the application of the Bayesian approach to predict the location of plastic hinge deformation using the experimental data obtained from the vibration tests of a reinforced‐concrete bridge column. The column was statically pushed incrementally with lateral displacements until a plastic hinge is fully formed at the bottom portion of the column. Vibration tests were performed at different damage stages. The proposed damage detection method was able to locate the damaged region using a simplified analytical model and the modal parameters estimated from the vibration tests, although (1) only the first bending and first torsional modes were estimated from the experimental test data, (2) the locations where the accelerations were measured did not coincide with the degrees of freedom of the analytical model, and (3) there existed discrepancies between the undamaged test structure and the analytical model. The Bayesian framework was able to systematically update the damage probabilities when new test data became available. Better diagnosis was obtained by employing multiple data sets than just by using each test data set separately. Copyright © 2000 John Wiley & Sons, Ltd.     

Seismic resilience of concrete structures under corrosion

A probabilistic approach to lifetime assessment of seismic resilience of deteriorating concrete structures is presented. The effects of environmental damage on the seismic performance are evaluated by means of a methodology for lifetime assessment of concrete structures in aggressive environment under uncertainty. The time‐variant seismic capacity associated with different limit states, from damage limitation up to collapse, is assumed as functionality indicator. The role of the deterioration process on seismic resilience is then investigated over the structural lifetime by evaluating the post‐event residual functionality and recovery of the deteriorating system as a function of the time of occurrence of the seismic event. The proposed approach is applied to a three‐story concrete frame building and a four‐span continuous concrete bridge under corrosion. The results show the combined effects of structural deterioration and seismic damage on the time‐variant system functionality and resilience and indicate the importance of a multi‐hazard life‐cycle‐oriented approach to seismic design of resilient structure and infrastructure systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability of elastic frames subjected to earthquake excitations

Dynamic stability of elastic multistorey frame structures subjected to vertical earthquake ground accelerations is studied. Different stationary, non-stationary, white and non-white random models for earthquake strong motion are considered. The concepts of mean-square and almost-sure stability are reviewed and the corresponding stability theorems are presented. Several general criteria regarding the dynamic stability of the equilibrium state of multistorey frames subjected to random excitations are developed. A few examples concerning the stability of single and multi-degree-of-freedom structures under earthquake excitations are presented. The stability of motion of frames under combined horizontal–vertical acceleration is also briefly discussed.     

Development of fragility functions as a damage classification/prediction method for steel moment‐resisting frames using a wavelet‐based damage sensitive feature

Fragility functions are commonly used in performance‐based earthquake engineering for predicting the damage state of a structure subjected to an earthquake. This process often involves estimating the structural damage as a function of structural response, such as the story drift ratio and the peak floor absolute acceleration. In this paper, a new framework is proposed to develop fragility functions to be used as a damage classification/prediction method for steel structures based on a wavelet‐based damage sensitive feature (DSF). DSFs are often used in structural health monitoring as an indicator of the damage state of the structure, and they are easily estimated from recorded structural responses. The proposed framework for damage classification of steel structures subjected to earthquakes is demonstrated and validated with a set of numerically simulated data for a four‐story steel moment‐resisting frame designed based on current seismic provisions. It is shown that the damage state of the frame is predicted with less variance using the fragility functions derived from the wavelet‐based DSF than it is with fragility functions derived from an alternate acceleration‐based measure, the spectral acceleration at the first mode period of the structure. Therefore, the fragility functions derived from the wavelet‐based DSF can be used as a probabilistic damage classification model in the field of structural health monitoring and an alternative damage prediction model in the field of performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Understanding acquisition and processing error in microseismic data: An example from Pouce Coupe Field,Canada

A challenge in microseismic monitoring is quantification of survey acquisition and processing errors, and how these errors jointly affect estimated locations. Quantifying acquisition and processing errors and uncertainty has multiple benefits, such as more accurate and precise estimation of locations, anisotropy, moment tensor inversion and, potentially, allowing for detection of 4D reservoir changes. Here, we quantify uncertainty due to acquisition, receiver orientation error, and hodogram analysis. Additionally, we illustrate the effects of signal to noise ratio variances upon event detection. We apply processing steps to a downhole microseismic dataset from Pouce Coupe, Alberta, Canada. We use a probabilistic location approach to identify the optimal bottom well location based upon known source locations. Probability density functions are utilized to quantify uncertainty and propagate it through processing, including in source location inversion to describe the three-dimensional event location likelihood. Event locations are calculated and an amplitude stacking approach is used to reduce the error associated with first break picking and the minimization with modelled travel times. Changes in the early processing steps have allowed for understanding of location uncertainty of the mapped microseismic events.     

Active control of MDOF structures with supplemental electrorheological fluid dampers

A method for design of an active control system for multistorey structures using Electrorheological (ER) dampers is presented. Incorporated at various levels of a structural frame, ER dampers are used to improve the response of the structure during earthquakes. Optimal control theory was used to design the ER devices. The aim of the design is to find the most suitable combination of the minimum required forces produced by the ER dampers to obtain the optimal structural response. The mechanical response of ER fluid dampers is regulated by an electric field, depending on the displacements and velocities of the frame. Numerical analysis of an ER damped seven-storey structure is represented as an example. Significant improvement of the structural response was obtained using optimal active controlled ER dampers compared to passive controlled and uncontrolled structures. Copyright © 1999 John Wiley & Sons, Ltd.     

基于时变地震损伤模型的多龄期钢框架结构易损性分析

基于时变地震损伤模型提出酸性大气环境作用下多龄期钢框架结构概率地震易损性分析的方法及步骤;考虑服役龄期对钢框架结构抗震性能的影响,分别建立时变概率地震需求模型、时变概率抗震能力模型及时变易损性模型;在概率地震需求分析及概率抗震能力分析的基础上,得到多龄期(20年、30年、40年、50年)钢框架结构的易损性模型及易损性曲线。     

Comparison of Bayesian estimates of peak ground acceleration (<Emphasis Type="Italic">A</Emphasis>max) with PSHA in Iran

Bayesian probability theory is an appropriate and useful method for estimating parameters in seismic hazard analysis. The analysis in Bayesian approaches is based on a posterior belief, also their special ability is to take into account the uncertainty of parameters in probabilistic relations and a priori knowledge. In this study, we benefited the Bayesian approach in order to estimate maximum values of peak ground acceleration (A_max) also quantiles of the relevant probabilistic distributions are figured out in a desired future interval time in Iran. The main assumptions are Poissonian character of the seismic events flow and properties of the Gutenberg-Richter distribution law. The map of maximum possible values of A_max and also map of 90% quantile of distribution of maximum values of A_max on a future interval time 100 years is presented. According to the results, the maximum value of the A_max is estimated for Bandar Abbas as 0.3g and the minimum one is attributed to Esfahan as 0.03g. Finally, the estimated values in Bayesian approach are compared with what was presented applying probabilistic seismic hazard (PSH) methods based on the conventional Cornel (1968) method. The distribution function of A_max for future time intervals of 100 and 475 years are calculated for confidence limit of probability level of 90%.     

A probabilistic framework for correlated seismic downtime and repair cost estimation of geo‐structures

An important component of probabilistic risk assessment methods is the development of models to quantify the direct consequences of damage to geo‐structural components for a given intensity of the hazard. This paper presents a general probabilistic framework for correlated repair cost and downtime estimation of geo‐structures exposed to seismic hazards. The framework uses as input the results of nonlinear time‐history analysis of geo‐structures for the set of earthquake records that are representative of the seismic hazard models for the region of interest. The repair cost and downtime are estimated for individual earthquakes probabilistically considering the uncertainties associated with damage states. In addition, the formulation of the repair cost and downtime accounts for the reduction in the repair requirements as the number of damaged components in the given damage state increases. An analytical linear and two bilinear regression models are proposed for conditional correlated seismic repair cost and downtime estimation of geo‐structures given the intensity measure. The proposed framework is demonstrated by developing seismic repair models of a typical pile‐supported wharf structure on the west coast of the United States. The presented framework is general and can be applied to other types of geo‐structures and hazards and can include other decision variables such as loss of life as well. Copyright © 2013 John Wiley & Sons, Ltd.     

Bayesian data fusion in a spatial prediction context: a general formulation

In spite of the exponential growth in the amount of data that one may expect to provide greater modeling and predictions opportunities, the number and diversity of sources over which this information is fragmented is growing at an even faster rate. As a consequence, there is real need for methods that aim at reconciling them inside an epistemically sound theoretical framework. In a statistical spatial prediction framework, classical methods are based on a multivariate approach of the problem, at the price of strong modeling hypotheses. Though new avenues have been recently opened by focusing on the integration of uncertain data sources, to the best of our knowledges there have been no systematic attemps to explicitly account for information redundancy through a data fusion procedure. Starting from the simple concept of measurement errors, this paper proposes an approach for integrating multiple information processing as a part of the prediction process itself through a Bayesian approach. A general formulation is first proposed for deriving the prediction distribution of a continuous variable of interest at unsampled locations using on more or less uncertain (soft) information at neighboring locations. The case of multiple information is then considered, with a Bayesian solution to the problem of fusing multiple information that are provided as separate conditional probability distributions. Well-known methods and results are derived as limit cases. The convenient hypothesis of conditional independence is discussed by the light of information theory and maximum entropy principle, and a methodology is suggested for the optimal selection of the most informative subset of information, if needed. Based on a synthetic case study, an application of the methodology is presented and discussed.     

Structural damage detection using empirical-mode decomposition and vector autoregressive moving average model

A method based on empirical-mode decomposition (EMD) and vector autoregressive moving average (VARMA) model is proposed for structural damage detection. The basic idea of the method is that the structural damages can be identified as the abrupt changes in energy distribution of structural responses at high frequencies. Using the time-varying VARMA model to represent the intrinsic mode functions (IMFs) obtained from the EMD of vibration signal, we define a damage index according to the VARMA coefficients. In the two examples given, the Imperial County Services Building and the Van Nuys hotel are used as the benchmark structures to verify the effectiveness and sensitivity of the damage index in real environments with the presence of actual noise. The analysis results show that the damage index can indicate the occurrence and relative severity of structural damages at multiple locations in an efficient manner. The damage index can also be potentially used for structural health monitoring, since it is based on the time-varying VARMA coefficients. Finally, some recommendations for future research are provided.     

Selection of noise parameters for Kalman filter

The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter. With state vectors and covariance matrices estimated by the Kalman filter, the likehood of the measurements can be constructed as a function of the process noise and measurement noise parameters. By maximizing the likelihood function with respect to these noise parameters, the optimal values can be obtained. Furthermore, the Bayesian probabilistic approach allows the associated uncertainty to be quantified. Examples using a single-degree-of-freedom system and a ten-story building illustrate the proposed method. The effect on the performance of the Kalman filter due to the selection of the process noise and measurement noise parameters was demonstrated. The optimal values of the noise parameters were found to be close to the actual values in the sense that the actual parameters were in the region with significant probability density. Through these examples, the Bayesian approach was shown to have the capability to provide accurate estimates of the noise parameters of the Kalman filter, and hence for state estimation.     

A deformation-based seismic design method for 3D R/C irregular buildings using inelastic dynamic analysis

A new deformation-based design method concerning 3D reinforced concrete (R/C) buildings is presented, which involves the use of advanced analysis tools, i.e. response-history analysis for appropriately scaled input motions, for multiple levels of earthquake action. The critical issues concerning the inelastic response-history analysis used for the design, namely the definition of the appropriate input, the set up of the analytical model that should account for post-yield behaviour of plastic hinge zones, and the direction of loading, are discussed. The proposed method is based on a partially inelastic model, while the design of structural members is carried out for different performance levels related to their inelastic behaviour. The aforementioned method builds on previous proposals by the first author and his co-workers, nevertheless a new procedure for the design of members that are expected to develop inelastic behaviour for the serviceability earthquake is proposed; its aim is the reduction of member design forces and the a-priori definition of their inelastic performance, by exploiting the deformation limits for the specific performance level, which are related to the damage level of the structural members. The proposed method was applied to irregular multistorey R/C 3D frame buildings with setbacks, and their performance for several levels of earthquake action was assessed using a fully inelastic model and additional ground motions not used at the design phase. The same buildings were designed according to the provisions of Eurocode 8. Comparison of the two methods of seismic design, revealed the advantages of the proposed design method, in particular the more economic detailing of transverse reinforcement in the members that develop very little inelastic behaviour even for very strong earthquakes.     

基于第四代地震区划的跨越发震断层永久位移概率分析方法

本文主要借鉴了Lee(2007)和Youngs(2003)提出的地表永久位移估计方法,联合中国第四代地震区划图的潜在震源区参数,给出了适合中国跨越发震断层永久位移概率分析方法。震害调查表明,近场的结构破坏不仅是地震动引起的,地震地表的破裂或永久位移引起的破坏也占很大比重。应用与概率估计地震动相似的方法,给出不同概率水准的地震地表永久位移,使之服务于穿越地震发震断层管线、桥梁工程的抗震设防,采取有效的抗御永久地表位移措施,减小地震灾害带来的损失。     

Seismic fragility functions for code compliant and non-compliant RC SMRF structures in Pakistan

Fragility functions are derived for low-rise code compliant & non-compliant special moment resisting frames (SMRFs). Non-compliant SMRFs those built in low strength concrete and lacking confining ties in joint panel zones, commonly found in developing countries. Shake table tests were performed on single-storey and two-storey 1:3 reduced scale representative frames to understand the damage mechanism and develop deformation-based damage scale. The non-compliant SMRF experienced column flexure cracking, longitudinal bar-slip in beam and observed with cover concrete spalling from the joint panels. The code compliant SMRF experienced flexure cracks in beam/column, and experienced joint cracking under extreme shaking. Numerical modeling technique is developed for inelastic modeling of reinforced concrete frame with beam bar-slip and joint damageability using SeismoStruct. Natural accelerograms were used to analyze the considered frames through incremental dynamic analyses in SeismoStruct. A probabilistic based approach was used to derive fragility functions for the considered frames. An example case study is presented for damageability evaluation of structures for earthquakes of various return periods (43, 72, 475, 2475 years).     

Probabilistic data integration for characterization of spatial distribution of residual LNAPL

The spatial distribution of residual light non-aqueous phase liquid (LNAPL) is an important factor in reactive solute transport modeling studies. There is great uncertainty associated with both the areal limits of LNAPL source zones and smaller scale variability within the areal limits. A statistical approach is proposed to construct a probabilistic model for the spatial distribution of residual NAPL and it is applied to a site characterized by ultra-violet-induced-cone-penetration testing (CPT–UVIF). The uncertainty in areal limits is explicitly addressed by a novel distance function (DF) approach. In modeling the small-scale variability within the areal limits, the CPT–UVIF data are used as primary source of information, while soil texture and distance to water table are treated as secondary data. Two widely used geostatistical techniques are applied for the data integration, namely sequential indicator simulation with locally varying means (SIS–LVM) and Bayesian updating (BU). A close match between the calibrated uncertainty band (UB) and the target probabilities shows the performance of the proposed DF technique in characterization of uncertainty in the areal limits. A cross-validation study also shows that the integration of the secondary data sources substantially improves the prediction of contaminated and uncontaminated locations and that the SIS–LVM algorithm gives a more accurate prediction of residual NAPL contamination. The proposed DF approach is useful in modeling the areal limits of the non-stationary continuous or categorical random variables, and in providing a prior probability map for source zone sizes to be used in Monte Carlo simulations of contaminant transport or Monte Carlo type inverse modeling studies.     

Estimation of inelastic deformation demands in multistorey RC frame buildings

Estimation of peak inelastic deformation demands is a key component of any displacement-based procedure for earthquake-resistant design of new structures or for seismic evaluation of existing structures. On the basis of the results of over a thousand non-linear dynamic analyses, rules are developed for the estimation of mean and upper-characteristic peak inelastic interstorey drifts and member chord rotations in multistorey RC frame buildings, either bare or infilled in all storeys but the first. For bare frame structures, mean inelastic deformation demands can be estimated from a linear, equivalent static, or preferably multimodal response spectrum analysis with 5 per cent damping and with the RC members considered with their secant stiffness at yielding. 95 per cent characteristic values can be estimated as multiples of the mean deformations. For open-first-storey buildings, the linear analysis can be equivalent static, with the infills modelled as rigid bidiagonal struts and all RC members considered with their secant stiffness to yielding. Copyright © 1999 John Wiley & Sons, Ltd.     

Effects of stiffness degradation on ductility requirements for multistorey buildings

The effect of stiffness degradation in reinforced concrete structural members on the inelastic response of multistorey buildings to earthquakes is investigated. In particular, the following question is examined. How do the ductility requirements for multistorey systems with degrading stiffness behaviour compare with those for structures with ordinary bilinear hysteretic property? Inelastic dynamic responses of two idealized multistorey buildings, one having a long and the other a relatively short fundamental period, to an ensemble of twenty simulated earthquakes representative of moderately intense ground motions in California at moderate epicentral distances on firm ground, are analysed for ordinary bilinear hysteretic behaviour and for bilinear hysteretic behaviour with stiffness degradation property. The conclusions deduced from the results of this investigation include the following (1) It is, in general, not possible to predict the maximum response of a degrading stiffness system from results for the corresponding ordinary bilinear system (2) The differences in ductility requirements due to stiffness degradation are generally smaller than those associated with probabilistic variability from one ground motion to another (3) Stiffness degradation has little influence on the ductility requirements for flexible buildings, but it leads to increased ductility requirements for stiff buildings.