Stochastic simulation methods for structural reliability under mixed uncertainties

Uncertainty quantification (UQ) has been widely recognized as one of the most important, yet challenging task in both structural engineering and system engineering, and the current researches are mainly on the proper treatment of different types of uncertainties, resulting from either natural randomness or lack of information, in all related sub-problems of UQ such as uncertainty characterization, uncertainty propagation, sensitivity analysis, model updating, model validation, risk and reliability analysis, etc. It has been widely accepted that those uncertainties can be grouped as either aleatory uncertainty or epistemic uncertainty, depending on whether they are reducible or not. For dealing with the above challenge, many non-traditional uncertainty characterization models have been developed, and those models can be grouped as either imprecise probability models (e.g., probability-box model, evidence theory, second-order probability model and fuzzy probability model) or non-probabilistic models (e.g., interval/convex model and fuzzy set theory). This thesis concerns the efficient numerical propagation of the three kinds of uncertainty characterization models, and for simplicity, the precise probability model, the distribution probability-box model, and the interval model are taken as examples. The target is to develop efficient numerical algorithms for learning the functional behavior of the probabilistic responses (e.g., response moments and failure probability) with respect to the epistemic parameters of model inputs, which is especially useful for making reliable decisions even when the available information on model inputs is imperfect. To achieve the above target, my thesis presents three main developments for improving the Non-intrusive Imprecise Stochastic Simulation (NISS), which is a general methodology framework for propagating the imprecise probability models with only one stochastic simulation. The first development is on generalizing the NISS methods to the problems with inputs including both imprecise probability models and non-probability models. The algorithm is established by combining Bayes rule and kernel density estimation. The sensitivity indices of the epistemic parameters are produced as by-products. The NASA Langley UQ challenge is then successfully solved by using the generalized NISS method. The second development is to inject the classical line sampling to the NISS framework so as to substantially improve the efficiency of the algorithm for rare failure event analysis, and two strategies, based on different interpretations of line sampling, are developed. The first strategy is based on the hyperplane approximations, while the second-strategy is derived based on the one-dimensional integrals. Both strategies can be regarded as post-processing of the classical line sampling, while the results show that their resultant NISS estimators have different performance. The third development aims at further substantially improving the efficiency and suitability to highly nonlinear problems of line sampling, for complex structures and systems where one deterministic simulation may take hours. For doing this, the active learning strategy based on Gaussian process regression is embedded into the line sampling procedure for accurately estimating the interaction point for each sample line, with only a small number of deterministic simulations. The above three developments have largely improved the suitability and efficiency of the NISS methods, especially for real-world engineering applications. The efficiency and effectiveness of those developments are clearly interpreted with toy examples and sufficiently demonstrated by real-world test examples in system engineering, civil engineering, and mechanical engineering

Distribution-free stochastic simulation methodology for model updating under hybrid uncertainties

In the real world, a significant challenge faced in the safe operation and maintenance of infrastructures is the lack of available information or data. This results in a large degree of uncertainty and the requirement for robust and efficient uncertainty quantification (UQ) tools in order to derive the most realistic estimates of the behavior of structures. While the probabilistic approach has long been utilized as an essential tool for the quantitative mathematical representation of uncertainty, a common criticism is that the approach often involves insubstantiated subjective assumptions because of the scarcity or imprecision of available information. To avoid the inclusion of subjectivity, the concepts of imprecise probabilities have been developed, and the distributional probability-box (p-box) has gained the most attention among various types of imprecise probability models since it can straightforwardly provide a clear separation between aleatory and epistemic uncertainty. This thesis concerns the realistic consideration and numerically efficient calibraiton and propagation of aleatory and epistemic uncertainties (hybrid uncertainties) based on the distributional p-box. The recent developments including the Bhattacharyya distance-based approximate Bayesian computation (ABC) and non-intrusive imprecise stochastic simulation (NISS) methods have strengthened the subjective assumption-free approach for uncertainty calibration and propagation. However, these methods based on the distributional p-box stand on the availability of the prior knowledge determining a specific distribution family for the p-box. The target of this thesis is hence to develop a distribution-free approach for the calibraiton and propagation of hybrid uncertainties, strengthening the subjective assumption-free UQ approach. To achieve the above target, this thesis presents five main developments to improve the Bhattacharyya distance-based ABC and NISS frameworks. The first development is on improving the scope of application and efficiency of the Bhattacharyya distance-based ABC. The dimension reduction procedure is proposed to evaluate the Bhattacharyya distance when the system under investigation is described by time-domain sequences. Moreover, the efficient Bayesian inference method within the Bayesian updating with structural reliability methods (BUS) framework is developed by combining BUS with the adaptive Kriging-based reliability method, namely AK-MCMC. The second development of the distribution-free stochastic model updating framework is based on the combined application of the staircase density functions and the Bhattacharyya distance. The staircase density functions can approximate a wide range of distributions arbitrarily close; hence the development achieved to perform the Bhattacharyya distance-based ABC without limiting hypotheses on the distribution families of the parameters having to be updated. The aforementioned two developments are then integrated in the third development to provide a solution to the latest edition (2019) of the NASA UQ challenge problem. The model updating tasks under very challenging condition, where prior information of aleatory parameters are extremely limited other than a common boundary, are successfully addressed based on the above distribution-free stochastic model updating framework. Moreover, the NISS approach that simplifies the high-dimensional optimization to a set of one-dimensional searching by a first-order high-dimensional model representation (HDMR) decomposition with respect to each design parameter is developed to efficiently solve the reliability-based design optimization tasks. This challenge, at the same time, elucidates the limitations of the current developments, hence the fourth development aims at addressing the limitation that the staircase density functions are designed for univariate random variables and cannot acount for the parameter dependencies. In order to calibrate the joint distribution of correlated parameters, the distribution-free stochastic model updating framework is extended by characterizing the aleatory parameters using the Gaussian copula functions having marginal distributions as the staircase density functions. This further strengthens the assumption-free approach for uncertainty calibration in which no prior information of the parameter dependencies is required. Finally, the fifth development of the distribution-free uncertainty propagation framework is based on another application of the staircase density functions to the NISS class of methods, and it is applied for efficiently solving the reliability analysis subproblem of the NASA UQ challenge 2019. The above five developments have successfully strengthened the assumption-free approach for both uncertainty calibration and propagation thanks to the nature of the staircase density functions approximating arbitrary distributions. The efficiency and effectiveness of those developments are sufficiently demonstrated upon the real-world applications including the NASA UQ challenge 2019

Uncertainty management in multidisciplinary design of critical safety systems

Managing the uncertainty in multidisciplinary design of safety-critical systems requires not only the availability of a single approach or methodology to deal with uncertainty but a set of different strategies and scalable computational tools (that is, by making use of the computational power of a cluster and grid computing). The availability of multiple tools and approaches for dealing with uncertainties allows cross validation of the results and increases the confidence in the performed analysis. This paper presents a unified theory and an integrated and open general-purpose computational framework to deal with scarce data, and aleatory and epistemic uncertainties. It allows solving of the different tasks necessary to manage the uncertainty, such as uncertainty characterization, sensitivity analysis, uncertainty quantification, and robust design. The proposed computational framework is generally applicable to solve different problems in different fields and be numerically efficient and scalable, allowing for a significant reduction of the computational time required for uncertainty management and robust design. The applicability of the proposed approach is demonstrated by solving a multidisciplinary design of a critical system proposed by NASA Langley Research Center in the multidisciplinary uncertainty quantification challenge problem

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Intelligent flight control systems

The capabilities of flight control systems can be enhanced by designing them to emulate functions of natural intelligence. Intelligent control functions fall in three categories. Declarative actions involve decision-making, providing models for system monitoring, goal planning, and system/scenario identification. Procedural actions concern skilled behavior and have parallels in guidance, navigation, and adaptation. Reflexive actions are spontaneous, inner-loop responses for control and estimation. Intelligent flight control systems learn knowledge of the aircraft and its mission and adapt to changes in the flight environment. Cognitive models form an efficient basis for integrating 'outer-loop/inner-loop' control functions and for developing robust parallel-processing algorithms

Highly redundant and fault tolerant actuator system: control, condition monitoring and experimental validation

This thesis is concerned with developing a control and condition monitoring system for a class of fault tolerant actuators with high levels of redundancy. The High Redundancy Actuator (HRA) is a concept inspired by biomimetics that aims to provide fault tolerance using relatively large numbers of actuation elements which are assembled in parallel and series configurations to form a single actuator. Each actuation element provides a small contribution to the overall force and displacement of the system. Since the capability of each actuation element is small, the effect of faults within the individual element of the overall system is also small. Hence, the HRA will gracefully degrade instead of going from fully functional to total failure in the presence of faults. Previous research on HRA using electromechanical technology has focused on a relatively low number of actuation elements (i.e. 4 elements), which were controlled with multiple loop control methods. The objective of this thesis is to expand upon this, by considering an HRA with a larger number of actuation elements (i.e. 12 elements). First, a mathematical model of a general n-by-m HRA is derived from first principles. This method can be used to represent any size of electromechanical HRA with actuation elements arranged in a matrix form. Then, a mathematical model of a 4-by-3 HRA is obtained from the general n-by-m model and verified experimentally using the HRA test rig. This actuator model is then used as a foundation for the controller design and condition monitoring development. For control design, two classical and control method-based controllers are compared with an H_infinity approach. The objective for the control design is to make the HRA track a position demand signal in both health and faulty conditions. For the classical PI controller design, the first approach uses twelve local controllers (1 per actuator) and the second uses only a single global controller. For the H_infinity control design, a mixed sensitivity functions is used to obtain good tracking performance and robustness to modelling uncertainties. Both of these methods demonstrate good tracking performance, with a slower response in the presence of faults. As expected, the H_infinity control method's robustness to modelling uncertainties, results in a smaller performance degradation in the presence of faults, compared with the classical designs. Unlike previous work, the thesis also makes a novel contribution to the condition monitoring of HRA. The proposed algorithm does not require the use of multiple sensors. The condition monitoring scheme is based on least-squares parameter estimation and fuzzy logic inference. The least-squares parameter estimation estimates the physical parameters of the electromechanical actuator based on input-output data collected from real-time experiments, while the fuzzy logic inference determines the health condition of the actuator based on the estimated physical parameters. Hence, overall, a new approach to both control and monitoring of an HRA is proposed and demonstrated on a twelve elements HRA test rig