Structural Safety最新文献

Structural and multidisciplinary design under uncertainty for high reliability or equivalently small probability of failure is a challenging task owing to the high computational cost associated with generating the samples at the extreme (tail) of the underlying distribution. Among other approaches, statistics of extremes based techniques are usually suitable for small probability estimation. However, typically only 10% of the samples generated that correspond to the tail of the distribution are used for probability estimation. If apriori information about regions in the design space that corresponds to the tail is available, additional samples in the identified region permit better tail fit and hence better probability estimation. In the current work, we propose iSOM (interpretable Self-Organising Map) to identify region/s in the design space, that corresponds to the extremes. An initial sample is used to map (visualize) the limit state function and random/design variables using iSOM which permits the designer to identify the region(s) that corresponds to the tail of the response. Adaptive sampling is performed in the identified region of interest to obtain additional samples. Next, the cumulative distribution function (CDF) of the response using initial as well as adaptive samples is evaluated for probability estimation. The effectiveness of the proposed approach is evident from its successful implementation on benchmark examples, real-world engineering examples, and a multi-objective reliability-based design optimization (MORBDO) case. The proposed method showcases the capability of iSOM to perform adaptive sampling for limit-state functions characterized by non-linearity and multiple modes. iSOM-enabled sampling in conjunction with log-TPNT provides better estimates of small failure probabilities than log-TPNT alone. The results from the proposed approach is compared with results from state-of-the-art (SOTA) sampling and surrogate-based techniques. For a given number of limit state evaluations, the proposed approach estimates probabilities of the order 1e−4, with lesser variance, compared to other SOTA approaches. Hence, the proposed approach is likely to encourage further research into employing iSOM-assisted sampling for other reliability estimation methods as well.

Sparse polynomial chaos expansion (PCE) combined with the bootstrap resampling method is a viable alternative to obtain an active learning algorithm for reliability analysis. The existing learning functions in PCE-based active learning algorithms do not consider the joint probability density function (PDF) information. The present study explores a sparse PCE-based active learning algorithm based on a newly proposed learning function that maintains a balance between the misclassification probability and the joint PDF information of sample points. In doing so, the coefficients of the sparse PCE are estimated using a Bayesian compressive sensing regressor, as it is noted to be one of the best-performing regression solvers for PCE, irrespective of sampling schemes. The proposed learning function considers the weight of the joint PDF with the local accuracy measure of bootstrap PCE (bPCE) to add new samples iteratively in the existing training set. The convergence is achieved when the ten consecutive failure estimates are within a negligible discrepancy and also checks the confidence bounds of the bPCE estimates. The effectiveness of the proposed approach is demonstrated using two structural engineering examples and one well-known analytical test function and is found to be quite efficient and accurate in estimating reliability.

In this work, the Theory of Plastic Mechanism Control (TPMC) is combined with a probabilistic method to account for the influence of random material variability. Reference is made to steel Moment Resisting Frames (MRFs) equipped with FREEDAM connections. FREEDAM connections are beam-to-column connections equipped with friction dampers to dissipate the seismic input energy. TPMC is used to guarantee that in case of destructive seismic events the structural members such as beams and columns remain undamaged. To this scope, the structure is designed to assure a collapse mechanism characterized by the activation of all the friction dampers of the beam ends and the formation of plastic hinges at the base of the first storey columns only. From the probabilistic point of view, the random uncertainties are given by the static friction coefficient of the contact surfaces and the preloading of the bolts of the friction dampers as well as the yielding resistance of the steel members. The failure domain is related to all the possible failure events, where the term “failure” concerns the development of an undesired mechanism different from the global one. Generally, the design conditions to prevent undesired collapse mechanisms are stochastic events within the framework of the kinematic theorem of plastic collapse. The limit state function corresponding to each event can be represented by a hyperplane in the space of random variables. Consequently, the failure domain is a surface resulting from the intersection of the hyperplanes corresponding to the limit states of each single failure event. Since dissipative zones (member ends or friction dampers) in the frame members are common to many different mechanisms, the single limit state functions are correlated. Therefore, the probability of failure can be evaluated by means of the Bimodal or Ditlevsen bounds by assuming that the failure events are located in series. The output of the work is a simple relationship which provides the overstrength factor of FREEDAM connections to be considered in the column design phase to account for random material variability thus assuring a given level of reliability in the application of TPMC.

This paper contains decision analytical approaches, conditions and models for the quantification of decision values for built environment systems. Specifically, (1) delta formulations of objective functions for decision value quantification are introduced, (2) conditions for decision value are identified and (3) action value analysis formulations are further developed. The delta objective functions are formulated with differences in utility, cost, and probabilities for consistent decision identification by expected utility and value. The delta formulations facilitate the direct calculation of action and information values and the explication of conditions for a positive decision value. Action value objective functions are derived in delta formulation for the action types of utility and system state actions and with action implementation states and action uncertainty models. The delta formulations are exemplified for predicted information and predicted actions values. The paper closes with a synthesis and discussion of decision values and with findings encompassing a computational effort reduction and the identification of predicted information value mechanisms.

Kriging has gained significant attention for reliability analysis primarily because of the analytical form of its uncertainty information, which facilitates adaptive training and establishing stopping criteria for the training process. Learning functions play a significant role in both selection of training points and stoppage of the training. For these functions, most existing learning functions evaluate candidate training points individually. However, lack of consideration for the global effects can lead to suboptimal training. In addition, the subjectivity of these stopping criteria may result in over or undertraining of surrogate models. To overcome these gaps, we propose Global Error-based Learning Function (GELF) for optimal refinement of Kriging surrogate models for the specific purpose of reliability analysis. Instead of prioritizing training points based on their uncertainty and proximity to the limit state like the existing learning functions, GELF for the first time directly and analytically associates the maximum error in the failure probability estimate to the global effect of choosing a candidate training point. This development subsequently facilitates an adaptive training scheme that minimizes the error in adaptive reliability estimation to the highest degree. For this purpose, GELF uses hypothetical future uncertainty information by treating the current construction of the surrogate model as a generative model. The proposed method is tested on three classic benchmark problems and one practical engineering problem. Results indicate that the proposed method has significantly better computational efficiency than the state-of-the-art methods while achieving high accuracy in all the numerical examples.

Assessing the seismic capacity of pier columns is a crucial element in the performance-based seismic design of bridges. Such assessment necessitates a probabilistic approach to accurately determine the marginal probability distributions of seismic capacities and to characterize the dependencies among these variables. In response to this need, this paper employs Multi-Output Gaussian Process Regression (MO-GPR), a probabilistic machine learning method, to jointly model the multiple seismic capacities of pier columns. We initially introduce a probabilistic seismic capacity model that utilizes MO-GPR for pier columns and validate its predictive accuracy in comparison to Bayesian linear regression and existing empirical methods. Subsequently, the methodology is augmented by the integration of hierarchical modeling within the MO-GPR framework, resulting in a Multi-Output Hierarchical Gaussian Process Regression (MO-HGPR) model that effectively estimates intraclass correlation coefficients for specific types of datasets. It is postulated that these correlation coefficients also reflect correlations associated with multiple components of the real structure. This study employs MO-HGPR and MO-GPR separately to investigate the potential correlations of seismic capacities among pier columns and distinct limit states. The results demonstrate that the MO-GPR model exhibits superior prediction accuracy and more effectively portrays uncertainty compared to existing empirical models. Moreover, the correlations of seismic capacities among piers and limit states are both robust and significantly impact the seismic fragility of bridges. This finding highlights the essential nature of considering capacities correlations in seismic fragility or risk assessment processes.