Samy Missoum

Convergence analysis for cellular automata applied to truss design

Traditional parallel methods for structural design, as well as modern preconditioned iterative linear solvers, do not scale well. This paper discusses the application of massively scalable cellular automata (CA) techniques to structural design, specifically trusses. There are two sets of CA rules, one used to propagate stresses and strains, and one to perform design updates. These rules can be applied serially, periodically, or concurrently, and Jacobi or Gauss‐Seidel style updating can be done. These options are compared with respect to convergence, speed, and stability for an example, problem of combined sizing and topology design of truss domain structures. The central theme of the paper is that the cellular automaton paradigm is tantamount to classical block Jacobi or block Gauss‐Seidel iteration, and consequently the performance of a cellular automaton can be rigorously analyzed and predicted.

Reliability-based design optimization of nonlinear aeroelasticity problems

This paper introduces a methodology for the reliability-based design optimization (RBDO) of nonlinear aeroelastic problems. It is based on the construction of explicit flutter and subcritical limit cycle oscillations (LCO) boundaries in terms of the design variables. The boundaries, generated using a Support Vector Machine (SVM), can then be used to efficiently evaluate probabilities of failure and solve an RBDO problem. Test results are presented demonstrating the construction of flutter boundaries as well as LCO boundaries for problems with structural nonlinearities. The solution of an example of RBDO problem is also provided.

Reliability-Based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition

This paper introduces a new approach for the optimal geometric design and tolerancing of multibody systems. The approach optimizes both the nominal system dimensions and the associated tolerances by solving a reliability-based design optimization (RDBO) problem under the assumption of truncated normal distributions of the geometric properties. The solution is obtained by first constructing the explicit boundaries of the failure regions (limit state function) using a support vector machine, combined with adaptive sampling and uniform design of experiments. The use of explicit boundaries enables the treatment of systems with discontinuous or binary behaviors. The explicit boundaries also allow for an efficient calculation of the probability of failure using importance sampling. The probability of failure is subsequently approximated over the whole design space (the nominal system dimensions and the associated tolerances), thus making the solution of the RBDO problem straightforward. The proposed approach is applied to the optimization of a web cutter mechanism.

Simulation and probabilistic failure prediction of grafts for aortic aneurysm

Purpose – The use of stent‐grafts to canalize aortic blood flow for patients with aortic aneurysms is subject to serious failure mechanisms such as a leak between the stent‐graft and the aorta (Type I endoleak). The purpose of this paper is to describe a novel computational approach to understand the influence of relevant variables on the occurrence of stent‐graft failure and quantify the probability of failure for aneurysm patients.Design/methodology/approach – A parameterized fluid‐structure interaction finite element model of aortic aneurysm is built based on a multi‐material formulation available in LS‐DYNA. Probabilities of failure are assessed using an explicit construction of limit state functions with support vector machines (SVM) and uniform designs of experiments. The probabilistic approach is applied to two aneurysm geometries to provide a map of probabilities of failure for various design parameter values.Findings – Parametric studies conducted in the course of this research successfully ident...

Reliability assessment using probabilistic support vector machines

This paper presents a methodology to calculate probabilities of failure using Probabilistic Support Vector Machines (PSVMs). Support Vector Machines (SVMs) have recently gained attention for reliability assessment because of several inherent advantages. Specifically, SVMs allow one to construct explicitly the boundary of a failure domain. In addition, they provide a technical solution for problems with discontinuities, binary responses, and multiple failure modes. However, the basic SVM boundary might be inaccurate; therefore leading to erroneous probability of failure estimates. This paper proposes to account for the inaccuracies of the SVM boundary in the calculation of the Monte Carlo-based probability of failure. This is achieved using a PSVM which provides the probability of misclassification of Monte Carlo samples. The probability of failure estimate is based on a new sigmoid-based PSVM model along with the identification of a region where the probability of misclassification is large. The PSVM-based probabilities of failure are, by construction, always more conservative than the deterministic SVM-based probability estimates.

Three Dimensional Active Contours for the Reconstruction of Abdominal Aortic Aneurysms

An aneurysm is a gradual and progressive ballooning of a blood vessel due to wall degeneration. Rupture of abdominal aortic aneurysm (AAA) constitutes a significant portion of deaths in the US. In this study, we describe a technique to reconstruct AAA geometry from CT images in an inexpensive and streamlined fashion. A 3D reconstruction technique was implemented with a GUI interface in MATLAB using the active contours technique. The lumen and the thrombus of the AAA were segmented individually in two separate protocols and were then joined together into a hybrid surface. This surface was then used to obtain the aortic wall. This method can deal with very poor contrast images where the aortic wall is indistinguishable from the surrounding features. Data obtained from the segmentation of image sets were smoothed in 3D using a Support Vector Machine technique. The segmentation method presented in this paper is inexpensive and has minimal user-dependency in reconstructing AAA geometry (lumen and wall) from patient image sets. The AAA model generated using this segmentation algorithm can be used to study a variety of biomechanical issues remaining in AAA biomechanics including stress estimation, endovascular stent-graft performance, and local drug delivery studies.

Local update of support vector machine decision boundaries

This paper presents a new adaptive sampling technique for the construction of locally reflned explicit decision functions. The decision functions can be used for both deterministic and probabilistic optimization, and may represent a constraint or a limit-state function. In particular, the focus of this paper is on reliability-based design optimization (RBDO). Instead of approximating the responses, the method is based on explicit design space decomposition (EDSD), in which an explicit boundary separating distinct regions in the design space is constructed. A statistical learning tool known as support vector machine (SVM) is used to construct the boundaries. A major advantage of using an EDSD-based method lies in its ability to handle discontinuous responses. A separate adaptive sampling scheme for calculating the probability of failure is also developed, which is used within the RBDO process. The update methodology is validated through several test examples with analytical decision functions.

Handling bifurcations in the optimal design of transient dynamic problems

This paper presents a methodology to tackle some of the difficulties encountered in the optimal design of transient dynamic problems. For this class of problems, the structural responses can be discontinuous due to numerous bifurcations. This characteristic makes gradient-based or response surface optimization techniques difficult to implement. This work (in progress) proposes an approach to define regions of the design space where the dynamic behavior is homogeneous and hence does not produce discontinuities. This is done by isolating points that correspond to unwanted bifurcations within boundaries that are defined explicitly in terms of the design variables. Using this method, a designer can obtain an optimal design with a prescribed dynamic behavior. The approach is applied to the design of a tube impacting a rigid wall. In addition, as the transient dynamic behavior is very sensitive to small variations of the design, reliability-based optimization is considered.

Nonlinear topology design of trusses using cellular automata

Cellular Automata (CA) is an emerging paradigm for the combined analysis and design of complex systems using local update rules. An implementation of the paradigm has recently been demonstrated successfully for the design of truss and beam structures. In the present paper, CA is applied to two-dimensional nonlinear truss topology optimization problems. The optimization problem is stated as a minimization of complementary work (minimum compliance design). First order Kuhn-Tucker conditions are derived for the general case of geometric and material nonlinear behavior. The derived optimality criterion is equivalent to fully stressed design and is used as a design update rule. The analysis update rules are derived using an Updated Lagrangian Formulation. The CA combined analysis and design algorithm is applied to demonstrative problems.

Elastoplastic truss design using a displacement based optimization

Abstract A displacement based optimization (DBO) method is applied to truss design problems with material nonlinearities, to explore feasibility and verify efficiency of the method as compared to traditional structural optimization. Minimum-weight truss sizing problems with various path-independent elastoplastic laws, including elastic perfectly plastic, linear strain hardening, and Ramberg–Osgood models, are investigated. This type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the DBO setting to nonlinear problems. To implement the methodology a computer program that uses the commercially available optimizer DOT by VR&D and IMSL Linear Programming solver by Visual Numerics is developed. Several test problems are successfully solved using the DBO approach and solutions are compared to those available in the literature, demonstrating significant reduction of computational time in comparison to the traditional structural optimization method. In particular, the DBO approach is found to be suitable for truss topology design since the method allows member areas to have cross-sectional areas equal to zero exactly.