Orthogonal-Array based Design Methodology for Complex, Coupled Space Systems

The process of designing a complex system, formed by many elements and sub-elements interacting between each other, is usually completed at a system level and in the preliminary phases in two major steps: design-space exploration and optimization. In a classical approach, especially in a company environment, the two steps are usually performed together, by experts of the field inferring on major phenomena, making assumptions and doing some trial-and-error runs on the available mathematical models. To support designers and decision makers during the design phases of this kind of complex systems, and to enable early discovery of emergent behaviours arising from interactions between the various elements being designed, the authors implemented a parametric methodology for the design-space exploration and optimization. The parametric technique is based on the utilization of a particular type of matrix design of experiments, the orthogonal arrays. Through successive design iterations with orthogonal arrays, the optimal solution is reached with a reduced effort if compared to more computationally-intense techniques, providing sensitivity and robustness information. The paper describes the design methodology in detail providing an application example that is the design of a human mission to support a lunar base

The MaxEnt method for probabilistic structural fire engineering : performance for multi-modal outputs

Probabilistic Risk Assessment (PRA) methodologies are gaining traction in fire engineering practice as a (necessary) means to demonstrate adequate safety for uncommon buildings. Further, an increasing number of applications of PRA based methodologies in structural fire engineering can be found in the contemporary literature. However, to date, the combination of probabilistic methods and advanced numerical fire engineering tools has been limited due to the absence of a methodology which is both efficient (i.e. requires a limited number of model evaluations) and unbiased (i.e. without prior assumptions regarding the output distribution type). An uncertainty quantification methodology (termed herein as MaxEnt) has recently been presented targeted at an unbiased assessment of the model output probability density function (PDF), using only a limited number of model evaluations. The MaxEnt method has been applied to structural fire engineering problems, with some applications benchmarked against Monte Carlo Simulations (MCS) which showed excellent agreement for single-modal distributions. However, the power of the method is in application for those cases where ‘validation’ is not computationally practical, e.g. uncertainty quantification for problems reliant upon complex modes (such as FEA or CFD). A recent study by Gernay, et al., applied the MaxEnt method to determine the PDF of maximum permissible applied load supportable by a steel-composite slab panel undergoing tensile membrane action (TMA) when subject to realistic (parametric) fire exposures. The study incorporated uncertainties in both the manifestation of the fire and the mechanical material parameters. The output PDF of maximum permissible load was found to be bi-modal, highlighting different failure modes depending upon the combinations of stochastic parameters. Whilst this outcome highlighted the importance of an un-biased approximation of the output PDF, in the absence of a MCS benchmark the study concluded that some additional studies are warranted to give users confidence and guidelines in such situations when applying the MaxEnt method. This paper summarises one further study, building upon Case C as presented in Gernay, et al

Quantile-based optimization under uncertainties using adaptive Kriging surrogate models

Uncertainties are inherent to real-world systems. Taking them into account is crucial in industrial design problems and this might be achieved through reliability-based design optimization (RBDO) techniques. In this paper, we propose a quantile-based approach to solve RBDO problems. We first transform the safety constraints usually formulated as admissible probabilities of failure into constraints on quantiles of the performance criteria. In this formulation, the quantile level controls the degree of conservatism of the design. Starting with the premise that industrial applications often involve high-fidelity and time-consuming computational models, the proposed approach makes use of Kriging surrogate models (a.k.a. Gaussian process modeling). Thanks to the Kriging variance (a measure of the local accuracy of the surrogate), we derive a procedure with two stages of enrichment of the design of computer experiments (DoE) used to construct the surrogate model. The first stage globally reduces the Kriging epistemic uncertainty and adds points in the vicinity of the limit-state surfaces describing the system performance to be attained. The second stage locally checks, and if necessary, improves the accuracy of the quantiles estimated along the optimization iterations. Applications to three analytical examples and to the optimal design of a car body subsystem (minimal mass under mechanical safety constraints) show the accuracy and the remarkable efficiency brought by the proposed procedure

Structural Reliability Assessment under Fire.

Structural safety under fire has received significant attention in recent years. Current approaches to structural fire design are based on prescriptive codes that emphasize insulation of steel members to achieve adequate fire resistance. The prescriptive approach fails to give a measure of the true performance of structural systems in fire and gives no indication of the level of reliability provided by the structure in the face of uncertainty. The performance-based design methodology overcomes many of the limitations of the prescriptive approach. The quantification of the structural reliability is a key component of performance-based design as it provides an objective manner of comparing alternative design solutions. In this study, a probabilistic framework is established to evaluate the structural reliability under fire considering uncertainties that exist in the system. The structural performance subjected to realistic fires is estimated by numerical simulations of sequentially coupled fire, thermal, and structural analyses. In this dissertation, multiple reliability methods (i.e., Latin hypercube simulation, subset simulation, and the first/second order reliability methods) are extended to investigate the structural safety under fire. The reliability analysis of structures in fire involves (i) the identification and characterization of uncertain parameters in the system, (ii) a probabilistic analysis of the thermo-mechanical response of the structure, and (iii) the evaluation of structural reliability based on a suitable limit state function. Several applications are considered involving the response of steel and steel-concrete composite structures subjected to natural fires. Parameters in the fire, thermal, and structural models are characterized, and an improved fire hazard model is proposed that accounts for fire spread to adjacent rooms. The importance of various parameters is determined by considering the response sensitivity, which is determined by finite difference and direct differentiation methods. The accuracy and efficiency of the various reliability methods, as applied to structures in fire, are compared, and the strengths and weaknesses of each approach are identified.PhDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111381/1/qianru_1.pd

Robust Estimation of Reliability in the Presence of Multiple Failure Modes

In structural design, every component or system needs to be tested to ascertain that it satisfies the desired safety levels. Due to the uncertainties associated with the operating conditions, design parameters, and material systems, this task becomes complex and expensive. Typically these uncertainties are defined using random, interval or fuzzy variables, depending on the information available. Analyzing components or systems in the presence of these different forms of uncertainty increases the computational cost considerably due to the iterative nature of these algorithms. Therefore, one of the objectives of this research was to develop methodologies that can efficiently handle multiple forms of uncertainty. Most of the work available in the literature about uncertainty analysis deals with the estimation of the safety of a structural component based on a particular performance criterion. Often an engineering system has multiple failure criteria, all of which are to be taken into consideration for estimating its safety. These failure criteria are often correlated, because they depend on the same uncertain variables and the accuracy of the estimations highly depend on the ability to model the joint failure surface. The evaluation of the failure criteria often requires computationally expensive finite element analysis or computational fluid dynamics simulations. Therefore, this work also focuses on using high fidelity models to efficiently estimate the safety levels based on multiple failure criteria. The use of high fidelity models to represent the limit-state functions (failure criteria) and the joint failure surface facilitates reduction in the computational cost involved, without significant loss of accuracy. The methodologies developed in this work can be used to propagate various types of uncertainties through systems with multiple nonlinear failure modes and can be used to reduce prototype testing during the early design process. In this research, fast Fourier transforms-based reliability estimation technique has been developed to estimate system reliability. The algorithm developed solves the convolution integral in parts over several disjoint regions spanning the entire design space to estimate the system reliability accurately. Moreover, transformation techniques for non-probabilistic variables are introduced and used to efficiently deal with mixed variable problems. The methodologies, developed in this research, to estimate the bounds of reliability are the first of their kind for a system subject to multiple forms of uncertainty

Modeling and synthesis of multicomputer interconnection networks

The type of interconnection network employed has a profound effect on the performance of a multicomputer and multiprocessor design. Adequate models are needed to aid in the design and development of interconnection networks. A novel modeling approach using statistical and optimization techniques is described. This method represents an attempt to compare diverse interconnection network designs in a way that allows not only the best of existing designs to be identified but to suggest other, perhaps hybrid, networks that may offer better performance. Stepwise linear regression is used to develop a polynomial surface representation of performance in a (k+1) space with a total of k quantitative and qualitative independent variables describing graph-theoretic characteristics such as size, average degree, diameter, radius, girth, node-connectivity, edge-connectivity, minimum dominating set size, and maximum number of prime node and edge cutsets. Dependent variables used to measure performance are average message delay and the ratio of message completion rate to network connection cost. Response Surface Methodology (RSM) optimizes a response variable from a polynomial function of several independent variables. Steepest ascent path may also be used to approach optimum points

Fragility curves for corrugated structural panel subjected to windborne debris impact

With the climate change, more and more extreme wind events such as cyclone take place around Australia and the world, which cause tremendous loss and damage. The wind speed has been reported constantly increasing with the climate change, which imposes more threats to building environments. The building envelopes are vulnerable to the windborne debris impact in a form of creating an opening in wall, roof, door, windows and screens, which leads to internal pressure increase and results in roof lifting up. The capacity requirements of wall or roof panels to resist windborne debris impact in cyclonic regions has been substantially increased in the 2011 Australian Wind Loading Code (AS/NZS 1170.2:2011) as compared to its previous version. The performance of commonly used structural panels in Australian Building Industry under the increased design wind speed needs be evaluated. Intensive laboratory tests and intensive numerical simulations on performances of typical structural panels subjected to windborne debris impacts have been carried out. This paper presents the results of one panel type, i.e., corrugated panel. The vulnerability curves of the corrugated panel with respect to the debris mass and impact speed are simulated. These results can be used in probabilistic loss estimations of structural panels in extreme wind events