Reliability Based Design Optimization of Concrete Mix Proportions Using Generalized Ridge Regression Model

This paper presents Reliability Based Design Optimization (RBDO) model to deal with uncertainties involved in concrete mix design process. The optimization problem is formulated in such a way that probabilistic concrete mix input parameters showing random characteristics are determined by minimizing the cost of concrete subjected to concrete compressive strength constraint for a given target reliability. Linear and quadratic models based on Ordinary Least Square Regression (OLSR), Traditional Ridge Regression (TRR) and Generalized Ridge Regression (GRR) techniques have been explored to select the best model to explicitly represent compressive strength of concrete. The RBDO model is solved by Sequential Optimization and Reliability Assessment (SORA) method using fully quadratic GRR model. Optimization results for a wide range of target compressive strength and reliability levels of 0.90, 0.95 and 0.99 have been reported. Also, safety factor based Deterministic Design Optimization (DDO) designs for each case are obtained. It has been observed that deterministic optimal designs are cost effective but proposed RBDO model gives improved design performance

Reliability-based design optimization using kriging surrogates and subset simulation

The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate. Starting with the premise that simulation-based approaches are not affordable for such problems, and that the most-probable-failure-point-based approaches do not permit to quantify the error on the estimation of the failure probability, an approach based on both metamodels and advanced simulation techniques is explored. The kriging metamodeling technique is chosen in order to surrogate the performance functions because it allows one to genuinely quantify the surrogate error. The surrogate error onto the limit-state surfaces is propagated to the failure probabilities estimates in order to provide an empirical error measure. This error is then sequentially reduced by means of a population-based adaptive refinement technique until the kriging surrogates are accurate enough for reliability analysis. This original refinement strategy makes it possible to add several observations in the design of experiments at the same time. Reliability and reliability sensitivity analyses are performed by means of the subset simulation technique for the sake of numerical efficiency. The adaptive surrogate-based strategy for reliability estimation is finally involved into a classical gradient-based optimization algorithm in order to solve the RBDO problem. The kriging surrogates are built in a so-called augmented reliability space thus making them reusable from one nested RBDO iteration to the other. The strategy is compared to other approaches available in the literature on three academic examples in the field of structural mechanics.Comment: 20 pages, 6 figures, 5 tables. Preprint submitted to Springer-Verla

Challenges in Geotechnical Reliability Based Design

Hazard

Reliability-Based Design of Thermal Protection Systems with Support Vector Machines

The primary objective of this work was to develop a computationally efficient and accurate approach to reliability analysis of thermal protection systems using support vector machines. An adaptive sampling approach was introduced informs a iterative support vector machine approximation of the limit state function used for measuring reliability. The proposed sampling approach efficient adds samples along the limit state function until the reliability approximation is converged. This methodology is applied to two samples, mathematical functions to test and demonstrate the applicability. Then, the adaptive sampling-based support vector machine approach is applied to the reliability analysis of a thermal protection system. The results of all three problems highlight the potential capability of the new approach in terms of accuracy and computational saving in determining thermal protection system reliability

Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels

Optimal design under uncertainty has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible failure probabilities for a set of performance functions. In order to address real-world engineering problems in which the performance is assessed through computational models (e.g., finite element models in structural mechanics) metamodeling techniques have been developed in the past decade. This paper introduces adaptive Kriging surrogate models to solve the RBDO problem. The latter is cast in an augmented space that "sums up" the range of the design space and the aleatory uncertainty in the design parameters and the environmental conditions. The surrogate model is used (i) for evaluating robust estimates of the failure probabilities (and for enhancing the computational experimental design by adaptive sampling) in order to achieve the requested accuracy and (ii) for applying a gradient-based optimization algorithm to get optimal values of the design parameters. The approach is applied to the optimal design of ring-stiffened cylindrical shells used in submarine engineering under uncertain geometric imperfections. For this application the performance of the structure is related to buckling which is addressed here by means of a finite element solution based on the asymptotic numerical method

Reliability-based design for debris flow barriers

In the European Union since 2010, the design of any type of structures must comply with EN-1997 Geotechnical Design (CEN 2004) (EC7) referring to engineering projects in the rock mechanics field. However, the design of debris flow countermeasures in compliance with EC7 requirements is not feasible: EC7 uses partial safety factors for design calculations, but safety factors are not provided for phenomena such as debris flows and rock falls. Consequently, how EC7 can be applied to the design of debris flow barriers is not clear, although the basic philosophy of reliability-based design (RBD), as defined in EN1990 (CEN 2002) and applicable to geotechnical applications, may be a suitable approach. However, there is insufficient understanding of interactions between debris flows and structures to support RBD application to debris flow barrier design, as full-scale experimental data are very limited and difficult to obtain. Laboratory data are available but they are governed by scale effects that limit their usefulness for full-scale problems. The article describes an analysis, using the first-order reliability method (FORM), of two different datasets, one obtained through laboratory experiments and the other reflecting historical debris flow events in the Jiangjia Ravine (China). Statistical analysis of laboratory data enabled a definition of the statistical distributions of the parameters that primarily influence debris flow and barrier interactions. These statistical distributions were then compared to the field data to explore the links between flume experiments and full-scale problems. This paper reports a first attempt to apply RBD to debris flow countermeasures, showing how the choice of the target probability of failure influences the barrier design resistance value. An analysis of the factors governing debris flows highlights the applicability and limitations of EN1990 and EN1997 in the design of these rock engineering structures

Reliability based design optimisation for system-in-package

This paper discusses a reliability based optimisation modelling approach demonstrated for the design of a SiP structure integrated by stacking dies one upon the other. In this investigation the focus is on the strategy for handling the uncertainties in the package design inputs and their implementation into the design optimisation modelling framework. The analysis of fhermo-mechanical behaviour of the package is utilised to predict the fatigue life-time of the lead-free board level solder interconnects and warpage of the package under thermal cycling. The SiP characterisation is obtained through the exploitation of Reduced Order Models (ROM) constructed using high fidelity analysis and Design of Experiments (DoE) methods. The design task is to identify the optimal SiP design specification by varying several package input parameters so that a specified target reliability of the solder joints is achieved and in the same time design requirements and package performance criteria are me

Reliability-based design of interventions in deteriorated timber structures

When accommodating new uses or mitigating the consequences of deterioration, the strength increase of existing structures is significantly more onerous than a similar increase at the design stage of new structures. The safety methods prescribed in current standards were defined for the design of new structures and are frequently conservative for the assessment and repair of existing structures. This work will introduce the fundamental aspects of structural reliability and their application in the context of existing timber structures regarding the use of target reliability indices. First, the fundamental methods of structural reliability are introduced. The use of reliability methods requires the use of more detailed information in respect with material properties, loads, and model uncertainty. The main sources of such information are described. After overviewing the fundamental methods of structural reliability, methods to introduce additional information, namely results of non-destructive tests in the structural assessment are discussed. Finally, the intervention on a timber structure will be analyzed, within a case study, by considering different repair scenarios that lead to discussions on different suitable safety thresholds for existing and repaired structures