Samy Missoum
 Professor, AerospaceMechanical Engineering
 Professor, Applied Mathematics  GIDP
Contact
 (520) 6212235
 Aerospace & Mechanical Engr., Rm. N639
 Tucson, AZ 85721
 smissoum@email.arizona.edu
Awards
 Associate Fellow
 American Institute of Aeronautics and Astronautics, Spring 2017
 Article in Aerospace America
 CODES Laboratory Research on Multidisciplinary Design Optimization, Fall 2014
 Most Helpful to Their College EducationJunior Faculty Member
 AME Seniors, Spring 2014
Interests
No activities entered.
Courses
202021 Courses

Dissertation
AME 920 (Spring 2021) 
Finite Elem Anal Ansys
AME 463 (Spring 2021) 
Graduate Seminar
AME 696G (Spring 2021) 
Research
AME 900 (Spring 2021) 
Design Optimization
AME 565 (Fall 2020) 
Dissertation
AME 920 (Fall 2020) 
Research
AME 900 (Fall 2020)
201920 Courses

Dissertation
AME 920 (Spring 2020) 
Finite Elem Anal Ansys
AME 463 (Spring 2020) 
Research
AME 900 (Spring 2020) 
Adv Finite Elemnt Analys
AME 563 (Fall 2019) 
Finite Element Methods
AME 561 (Fall 2019) 
Research
AME 900 (Fall 2019)
201819 Courses

Independent Study
AME 599 (Summer I 2019) 
Research
AME 900 (Spring 2019) 
Thesis
AME 910 (Spring 2019) 
Design Optimization
AME 565 (Fall 2018) 
Finite Element Methods
AME 561 (Fall 2018) 
Research
AME 900 (Fall 2018)
201718 Courses

Thesis
AME 910 (Summer I 2018) 
Finite Elem Anal Ansys
AME 463 (Spring 2018) 
Independent Study
AME 499 (Spring 2018) 
Probabilistic Design
AME 568 (Spring 2018) 
Research
AME 900 (Spring 2018) 
Thesis
AME 910 (Spring 2018) 
Finite Element Methods
AME 561 (Fall 2017) 
Independent Study
AME 499 (Fall 2017) 
Research
AME 900 (Fall 2017)
201617 Courses

Adv Finite Elemnt Analys
AME 563 (Spring 2017) 
Finite Elem Anal Ansys
AME 463 (Spring 2017) 
Research
AME 900 (Spring 2017) 
Biomechanical Engr
AME 466 (Fall 2016) 
Biomechanical Engr
AME 566 (Fall 2016) 
Biomechanical Engr
BME 466 (Fall 2016) 
Biomechanical Engr
BME 566 (Fall 2016) 
Design Optimization
AME 565 (Fall 2016) 
Directed Research
AME 492 (Fall 2016) 
Finite Element Methods
AME 561 (Fall 2016) 
Independent Study
AME 199 (Fall 2016) 
Research
AME 900 (Fall 2016)
201516 Courses

Engr Component Design
AME 324B (Spring 2016) 
Finite Elem Anal Ansys
AME 463 (Spring 2016)
Scholarly Contributions
Journals/Publications
 Ahmadisoleymani, S. S., & Missoum, S. (2019). Construction of a risk model through the fusion of experimental data and finite element modeling: Application to car crashinduced TBI. Computer Methods in Biomechanics and Biomedical Engineering, 22, 605619.
 Panchal, J. H., Fuge, M., Liu, Y., Missoum, S., & Tucker, C. (2019). Machine Learning for Engineering Design. Journal of Mechanical Design, 141(11).
 Pidaparthi, B., & Missoum, S. (2019). Stochastic Optimization of Nonlinear Energy Sinks for the Mitigation of Limit Cycle Oscillations. AIAA Journal, 57, 21342144.
 Ahmadisoleymani, S. S., & Missoum, S. (2017). RISK PREDICTION OF TRAUMATIC BRAIN INJURY FROM CAR ACCIDENTS. PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2017, VOL 3.
 Boroson, E., & Missoum, S. (2017). Stochastic optimization of nonlinear energy sinks. STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, 55(2), 633646.
 Boroson, E., Missoum, S., Mattei, P., & Vergez, C. (2017). Optimization under uncertainty of parallel nonlinear energy sinks. JOURNAL OF SOUND AND VIBRATION, 394, 451464.
 Missoum, S., Lacaze, S., Amabili, M., & Alijani, F. (2017). Identification of material properties of composite sandwich panels under geometric uncertainty. Composite Structures, 179, 695  704.
 Doc, J., Vergez, C., & Missoum, S. (2014). A Minimal Model of a Singlereed Instrument Producing Quasiperiodif Sounds. Acta Acustica united with Acustica, 100(3), 543554.
 Jiang, P., Missoum, S., & Chen, Z. (2014). Optimal SVM Parameter Selection for Nonseparable and Unbalanced Data. Structural and Multidisciplinary Optimization, 50(4), 523535.
 Jiang, P., Missoum, S., & Chen, Z. (2014). Optimal SVM Parameter Selection for Nonseparable and Unbalanced Datasets.. Structural and Multidisciplinary Optimization, 50, 523535.More infoJiang, P., Missoum, S., and Chen, Z., Optimal SVM Parameter Selection for Nonseparable and Unbalanced Datasets. Structural and Multidisciplinary Optimization, vol. 50, 2014, pp. 523535.
 Lacaze, S., & Missoum, S. (2014). A generalized "maxmin" sample for surrogate update. Structural and Multidisciplinary Optimization, 49(4), 683687.More infoAbstract: This brief note describes the generalization of the "maxmin" sample that was originally used in the update of approximated feasible or failure domains. The generalization stems from the use of the random variables joint distribution in the sampling scheme. In addition, this note proposes a numerical improvement of the maxmin optimization problem through the use of the Chebychev norm. © 2013 SpringerVerlag Berlin Heidelberg.
 Lacaze, S., & Missoum, S. (2014). Parameter Estimation with Correlated Outputs Using Fidelity Maps. Probabilistic Engineering Mechanics, 38, 1321.
 Missoum, S., Vergez, C., & Doc, J. (2014). Explicit Mapping of Acoustic Regimes for Wind Instruments. Journal of Sound and Vibration, 333(20), 50185029.
 Basudhar, A., & Missoum, S. (2013). Reliability assessment using probabilistic support vector machines'. International Journal of Reliability and Safety, 7(2), 156173.More infoAbstract: 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 Carlobased 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 sigmoidbased PSVM model along with the identification of a region where the probability of misclassification is large. The PSVMbased probabilities of failure are, by construction, always more conservative than the deterministic SVMbased probability estimates. Copyright © 2013 Inderscience Enterprises Ltd.
 Jiang, P., & Missoum, S. (2013). Estimation of probability of failure with dependent variables using copulas and support vector machines. Proceedings of the ASME Design Engineering Technical Conference, 8.More infoAbstract: This paper presents an approach to estimate probabilities of failure in the case of dependent random variables. The approach is based on copulas and support vector machines (SVMs). A copula is used to generate dependent Monte Carlo samples and an SVM is used to construct the explicit boundary of the failure domain. It is shown that this construction of the failure boundary cannot be made in the original space due to the lack of "isotropy" of the probability densities. In this work the SVM is built in the uncorrelated standard normal space and refined using an adaptive sampling scheme. A transformation is used to map SVM training points and MonteCarlo samples between the original space and the uncorrelated standard normal space. Because SVM is a classificationbased approach, it can handle discontinuous responses and, more importantly, several limit states using one single SVM. Several analytical examples are used to demonstrate the methodology. Copyright © 2013 by ASME.
 Jiang, P., Missoum, S., Chengcheng, H. u., & Chen, Z. (2013). Optimal parameter selection of an SVM model: Application to hip fracture risk prediction. 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.More infoAbstract: This article presents a study of three (cross) validation metrics used for the selection of the optimal parameters of a support vector machine (SVM) classifier. The study focuses on problems for which the data is nonseparable and unbalanced as is often the case for experimental and clinical data. The three metrics selected in this work are the area under the ROC curve, accuracy, and balanced accuracy. As a test example, the study investigates the optimal parameters for an SVM classification model for hip fracture. The hip fracture data is obtained from a finite element model that is fully parameterized. Because the data is computational, fully separable sets of data (fracture and safe) can be obtained. By projection onto a lower dimensional subspace, the data becomes nonseparable and is used to construct the SVM. The knowledge of the separable case provides a comparison metric (the weighted likelihood) that would be unknown if only clinical data is used. The performance of the various metrics are compared for several levels of separability, unbalance and size of training samples. A probabilistic SVM is used to compute the probability of fracture. © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
 Jiang, P., Missoum, S., Chengcheng, H. u., & Chen, Z. (2013). Optimal parameter selection of an svm model: Application to hip fracture risk prediction. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: This article presents a study of three (cross) validation metrics used for the selection of the optimal parameters of a support vector machine (SVM) classifier. The study focuses on problems for which the data is nonseparable and unbalanced as is often the case for experimental and clinical data. The three metrics selected in this work are the area under the ROC curve, accuracy, and balanced accuracy. As a test example, the study investigates the optimal parameters for an SVM classification model for hip fracture. The hip fracture data is obtained from a finite element model that is fully parameterized. Because the data is computational, fully separable sets of data (fracture and safe) can be obtained. By projection onto a lower dimensional subspace, the data becomes nonseparable and is used to construct the SVM. The knowledge of the separable case provides a comparison metric (the weighted likelihood) that would be unknown if only clinical data is used. The performance of the various metrics are compared for several levels of separability, unbalance and size of training samples. A probabilistic SVM is used to compute the probability of fracture.© 2012 AIAA.
 Lacaze, S., & Missoum, S. (2013). Bayesian calibration using fidelity maps. Safety, Reliability, Risk and LifeCycle Performance of Structures and Infrastructures  Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013, 32893296.More infoAbstract: This paper introduces a new approach for model calibration based on fidelity maps. Fidelity maps refer to the regions of the parameter space within which the discrepancy between computational and experimental data is below a userdefined threshold. It is shown that fidelity maps, which are built explicilty in terms of the calibration parameters and aleatory variables, provide a rigourous approximation of the likelihood for maximum likelihood estimation or Bayesian update. Because the maps are constructed using a support vector machine classifier (SVM), the approach has the advantage of handling numerous correlated responses, possibly discontinuous, at a moderate computational cost.This is made possible by the use of a dedicated adaptive sampling scheme to refine the SVM classifier. A simply supported plate with uncertainties in the boundary conditions is used to demonstrate the methodology. In this example, the construction of the map and the Bayesian calibration is based on several natural frequencies and mode shapes to be matched simultaneously. © 2013 Taylor & Francis Group, London.
 Lacaze, S., & Missoum, S. (2013). Reliabilitybased design optimization using Kriging and support vector machines. Safety, Reliability, Risk and LifeCycle Performance of Structures and Infrastructures  Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013, 33053312.More infoAbstract: This article presents a novel approach for ReliabilityBased Design Optimization (RBDO) using Kriging and Support Vector Machines (SVMs). The proposed algorithm is based on a sequential two level scheme. The first stage consists of solving an approximated probabilistic optimization problem. The objective function and the failure domains are approximated by Kriging and SVMs respectively. The probability of failure and its sensitivity are estimated using subset simulation. The availability of the sensitivity allows one to solve the subproblem using a gradientbased method. The second level deals with the local refinement of the failure domains approximations around the first stage subproblem solution. In the second stage, a key contribution of this work is the use of a novel probabilistic "maxmin" sample that refines the failure boundary based on the random variable distributions as well as the locations of the samples. The proposed scheme is applied to three test cases including an analytical example featuring a failure domain defined by 100 dummy failure modes and a crashworthiness analysis featuring 11 dimensions and 10 failure domains. © 2013 Taylor & Francis Group, London.
 Lin, K., Basudhar, A., & Missoum, S. (2013). Parallel construction of explicit boundaries using support vector machines. Engineering Computations (Swansea, Wales), 30(1), 132148.More infoAbstract: Purpose  The purpose of this paper is to present a study of the parallelization of the construction of explicit constraints or limitstate functions using support vector machines. These explicit boundaries have proven to be beneficial for design optimization and reliability assessment, especially for problems with large computational times, discontinuities, or binary outputs. In addition to the study of the parallelization, the objective of this article is also to provide an approach to select the number of processors. Design/methodology/approach  This article investigates the parallelization in two ways. First, the efficiency of the parallelization is assessed by comparing, over several runs, the number of iterations needed to create an accurate boundary to the number of iterations associated with a theoretical linear speedup. Second, by studying these differences, an appropriate range of parallel processors can be inferred. Findings  The parallelization of the construction of explicit boundaries can lead to a markedly reduced computational burden. The study provides an approach to select the number of processors for an optimal use of computational resources. Originality/value  The construction of explicit boundaries for design optimization and reliability assessment is designed to alleviate many hurdles in these areas. The parallelization of the construction of the boundaries is a much needed study to reinforce the efficacy and efficiency of this approach. © Emerald Group Publishing Limited.
 Missoum, S., & Vergez, C. (2013). Explicit maps of acoustic regimes of a wind instrument. Proceedings of the ASME Design Engineering Technical Conference, 8.More infoAbstract: An approach to map the various acoustic regimes of a wind instument is presented. In this work, the regimes are first classified based on the occurence or the lack of sound. Physically, the production of a sound corresponds to the existence of selfsustained oscillations in the resonator of the instrument, whereas the lack of sound is associated with a stable static regime. Another classification based on the sound frequency is also investigated. The maps are created in a space consisting of design and control parameters. The boundaries of the maps are obtained explicitly in terms of the parameters using a support vector machine classifier as well as a dedicated adaptive sampling scheme. The approach is applied to a simplified clarinet model. Copyright © 2013 by ASME.
 Mokdad, F., & Missoum, S. (2013). A fully parameterized finite element model of a grand piano soundboard for sensitivity analysis of the dynamic behavior. Proceedings of the ASME Design Engineering Technical Conference, 8.More infoAbstract: This work in progress aims at investigating the influence of several parameters on the modal behavior of a grand piano soundboard. The sensitivity analysis is made possible by the development of a fully parameterized Finite Element model of the soundboard which allows the user to modify most geometric and material parameters involved in its dynamic behavior. In addition, crowning and downbearing are included in the model. This study also considers the influence of geometric nonlinearities due to downbearing. The sensitivity analysis is performed using Spearman rank correlation and Sobol indices. Copyright © 2013 by ASME.
 Basudhar, A., Dribusch, C., Lacaze, S., & Missoum, S. (2012). Constrained efficient global optimization with support vector machines. Structural and Multidisciplinary Optimization, 46(2), 201221.More infoAbstract: This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVMbased "probability of feasibility" using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the "expected improvement" of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binaryoutput are presented. Overall, the results indicate that the constrained formulation is more robust and efficient. © SpringerVerlag 2012.
 Dribusch, C., & Missoum, S. (2012). Construction of aeroelastic stability boundaries using a multifidelity approach. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012.More infoAbstract: Two of the challenges in the construction of aeroelastic stability boundaries are the high cost of simulations and the binary nature (stable/unstable) of the problem. This paper introduces a multifldelity approach for the construction of a stability boundary using a Support Vector Machine classifier. The boundary is refined using an adaptive sampling scheme which automatically selects the level of fldelity (low or high) needed for each sample. One of the key features of the approach stems from the iterative definition of the region of the space where highfldelity samples are needed. The proposed method brings a major improvement to a published work on the topic.1 The efficiency of the approach is tested on two analytical problems of several dimensions before it is applied to the construction of the stability boundary including both flutter and divergence of a simplified parameterized wing. © 2012 by Samy Missoum. Published by the American Institute of Aeronautics and Astronautics, Inc.
 Dribusch, C., & Missoum, S. (2012). Construction of aeroelastic stability boundaries using a multifidelity approach. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: Two of the challenges in the construction of aeroelastic stability boundaries are the high cost of simulations and the binary nature (stable/unstable) of the problem. This paper introduces a multifidelity approach for the construction of a stability boundary using a Support Vector Machine classifier. The boundary is refined using an adaptive sampling scheme which automatically selects the level of fidelity (low or high) needed for each sample. One of the key features of the approach stems from the iterative definition of the region of the space where highfidelity samples are needed. The proposed method brings a major improvement to a published work on the topic.1 The efficiency of the approach is tested on two analytical problems of several dimensions before it is applied to the construction of the stability boundary including both utter and divergence of a simplified parameterized wing. © 2012 AIAA.
 Lacaze, S., & Missoum, S. (2012). Fidelity maps for model update under uncertainty: Application to a piano soundboard. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012.More infoAbstract: This paper presents a new approach for model updating based on fidelity maps. Fidelity maps are used to explicitly define regions of the random variable space within which the discrepancy between computational and experimental data is below a threshold value. It is shown that fidelity maps, built as a function of epistemic and aleatory uncertainties, can be used to calculate the likelihood for maximum likelihood estimates or Bayesian update. The fidelity map approach has the advantage of handling numerous correlated responses at a moderate computational cost. This is made possible by the use of an adaptive sampling scheme to build accurate boundaries of the fidelity maps. Although the proposed technique is general, it is specialized to the case of model update for modal properties (natural frequencies and mode shapes). A simple plate and a piano soundboard finite element model with uncertainties on the boundary conditions are used to demonstrate the methodology. © 2012 by Samy Missoum and Sylvain Lacaze. Published by the American Institute of Aeronautics and Astronautics, Inc.
 Lacaze, S., & Missoum, S. (2012). Fidelity maps for model update under uncertainty: Application to a piano soundboard. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: This paper presents a new approach for model updating based on fidelity maps. Fidelity maps are used to explicitly define regions of the random variable space within which the discrepancy between computational and experimental data is below a threshold value. It is shown that fidelity maps, built as a function of epistemic and aleatory uncertainties, can be used to calculate the likelihood for maximum likelihood estimates or Bayesian update. The fidelity map approach has the advantage of handling numerous correlated responses at a moderate computational cost. This is made possible by the use of an adaptive sampling scheme to build accurate boundaries of the fidelity maps. Although the proposed technique is general, it is specialized to the case of model update for modal properties (natural frequencies and mode shapes). A simple plate and a piano soundboard finite element model with uncertainties on the boundary conditions are used to demonstrate the methodology. © 2012 AIAA.
 Jiang, P., Basudhar, A., & Missoum, S. (2011). Reliability assessment with correlated variables using support vector machines. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: This paper presents an approach to estimate probabilities of failure in cases where the random variables are correlated. An explicit limit state function is constructed in the uncorrelated standard normal space using the Nataf transformation and a support vector machine (SVM). An adaptive sampling strategy is used to build an accurate SVM approximation. Several analytical examples with various distributions and also multiple failure modes are presented. Copyright © 2011 by Peng Jiang, Anirban Basudhar and Samy Missoum.
 Basudhar, A., & Missoum, S. (2010). An improved adaptive sampling scheme for the construction of explicit boundaries. Structural and Multidisciplinary Optimization, 42(4), 517529.More infoAbstract: This article presents an improved adaptive sampling scheme for the construction of explicit decision functions (constraints or limit state functions) using Support Vector Machines (SVMs). The proposed work presents substantial modifications to an earlier version of the scheme (Basudhar and Missoum, Comput Struct 86(1920):19041917, 2008). The improvements consist of a different choice of samples, a more rigorous convergence criterion, and a new technique to select the SVM kernel parameters. Of particular interest is the choice of a new sample chosen to remove the "locking" of the SVM, a phenomenon that was not understood in the previous version of the algorithm. The new scheme is demonstrated on analytical problems of up to seven dimensions. © 2010 SpringerVerlag.
 Basudhar, A., & Missoum, S. (2010). Reliability assessment using probabilistic support vector machines (PSVMs). Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: This article presents a new probability of failure measure based on the notion of probabilistic support vector machines (PSVMs). A PSVM allows one to quantify the probability of having an error in the approximation of the failure boundary using a support vector machine (SVM). SVM can define explicitly the boundaries of disjoint and nonconvex failure domains. The approximation of the failure boundary can be refined using an adaptive sampling scheme with a limited number of samples. However, the calculation of the probability of failure might still be inaccurate despite the adaptive sampling. In order to refine the probability estimate, the "quality" of the approximated boundary is quantified through the probability of misclassification of a sample by the SVM. A new measure of probability is then calculated using MonteCarlo simulations that include the probability of misclassification. The proposed measure of probability of failure is such that it is always larger (i.e., more conservative) than the one obtained using a deterministic SVM. Several analytical examples are presented, including a case with two failure modes. Copyright © 2010 by Anirban Basudhar and Samy Missoum.
 Basudhar, A., Lacaze, S., & Missoum, S. (2010). Constrained effcient global optimization with probabilistic support vector machines. 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2010.More infoAbstract: This paper presents a methodology for constrained effcient global optimization (EGO) using support vector machines (SVMs). The proposed SVMbased method has several advantages. It is more general because it is applicable to a wider variety of problems compared to current techniques. These include problems with discontinuous and binary (pass/fail) states and multiple constraints. In this paper, the objective function is ap proximated using Kriging while the constraint boundary is approximated using an SVM classifier. The probability of misclassification by the SVM is calculated using a probabilistic support vector machine (PSVM). The existing PSVM models have certain limitations that make them unsuitable for application in the proposed methodology. Therefore, a modified PSVM model is also proposed to overcome these limitations. Several constrained EGO for mulations are implemented and compared in this paper. The results are also compared to EGO implementations with Krigingbased constraint approximations from the literature. © 2010 by Anirban Basudhar, Sylvain Lacaze and Samy Missoum. Published by the American Institute of Aeronautics and Astronautics, Inc.
 Dribusch, C., Missoum, S., & Beran, P. (2010). A multifidelity approach for the construction of explicit decision boundaries: Application to aeroelasticity. Structural and Multidisciplinary Optimization, 42(5), 693705.More infoAbstract: This paper presents a multifidelity approach for the construction of explicit decision boundaries (constraints or limitstate functions) using support vector machines. A lower fidelity model is used to select specific samples to construct the decision boundary corresponding to a higher fidelity model. This selection is based on two schemes. The first scheme selects samples within an envelope constructed from the lower fidelity model. The second technique is based on the detection of regions of inconsistencies between the lower and the higher fidelity decision boundaries. The approach is applied to analytical examples as well as an aeroelasticity problem for the construction of a nonlinear flutter boundary. © c SpringerVerlag 2010.
 Missoum, S., Dribusch, C., & Beran, P. (2010). Reliabilitybased design optimization of nonlinear aeroelasticity problems. Journal of Aircraft, 47(3), 992998.More infoAbstract: This paper introduces a methodology for the reliabilitybased design optimization of systems with nonlinear aeroelastic constraints. The approach is based on the construction of explicit flutter and subcritical limit cycle oscillation boundaries in terms of deterministic and random design variables. The boundaries are constructed using a support vector machine that provides a way to efficiently evaluate probabilities of failure and solve the reliabilitybased design optimization problem. Another major advantage of the approach is that it efficiently manages the discontinuities that might appear during subcritical limit cycle oscillations. The proposed approach is applied to the construction of flutter and subcritical limit cycle oscillation boundaries for a twodegreeoffreedom airfoil with nonlinear stiffnesses. The solution of a reliabilitybased design optimization problem with a constraint on the probability of subcritical limit cycle oscillation is also provided. Copyright © 2010 by Samy Missoum.
 Basudhar, A., & Missoum, S. (2009). A samplingbased approach for probabilistic design with random fields. Computer Methods in Applied Mechanics and Engineering, 198(4748), 36473655.More infoAbstract: An original technique to incorporate random fields nonintrusively in probabilistic design is presented. The approach is based on the extraction of the main features of a random field using a limited number of experimental observations (snapshots). An approximation of the random field is obtained using proper orthogonal decomposition (POD). For a given failure criterion, an explicit limit state function (LSF) in terms of the coefficients of the POD expansion is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated LSF. The coefficients of the orthogonal decomposition are considered as random variables with distributions determined from the snapshots. Based on these distributions and the explicit LSF, the approach allows for an efficient assessment of the probabilities of failure. In addition, the construction of explicit LSF has the advantage of handling discontinuous responses. Two testproblems are used to demonstrate the proposed methodology used for the calculation of probabilities of failure. The first example involves the linear buckling of an arch structure for which the thickness is a random field. The second problem concerns the impact of a tube on a rigid wall. The planarity of the walls of the tube is considered as a random field. © 2009 Elsevier B.V. All rights reserved.
 Basudhar, A., & Missoum, S. (2009). Local update of support vector machine decision boundaries. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: This paper presents a new adaptive sampling technique for the construction of locally refined explicit decision functions. The decision functions can be used for both deterministic and probabilistic optimization, and may represent a constraint or a limitstate function. In particular, the focus of this paper is on reliabilitybased 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 EDSDbased 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. © 2009 by Anirban Basudhar and Samy Missoum.
 Dribusch, C., Missoum, S., & Beran, P. (2009). A multifidelity approach for the construction of explicit decision boundaries: Application to aeroelasticity. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: This paper presents a multifidelity approach for the construction of explicit decision boundaries (constraints or limitstate functions) using a Support Vector Machine (SVMs). A lower fidelity model is used to select specific samples to construct the decision boundary corresponding to a higher fidelity model. This selection is based on two schemes. The first scheme selects samples within an envelope constructed from the lower fidelity model. The second technique is based on the detection of regions of inconsistencies between the lower and the higher fidelity decision boundaries. The approach is applied to analytical examples as well as an aeroelasticity problem for the construction of a nonlinear utter boundary.
 Basudhar, A., & Missoum, S. (2008). A samplingbased approach for probabilistic design with random fields. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.More infoAbstract: In this paper, a technique to efficiently include random fields in probabilistic design is presented. The approach is based on the extraction of the main features of a random field using a limited number of experimental observations (snapshots). An approximation of the random field is obtained using proper orthogonal decomposition (POD). For a given failure criterion, an explicit decision function in terms of the coefficients of the POD expansion, separating failure and safe regions, is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated decision function. The coefficients of the orthogonal decomposition are considered as random variables with distributions that are found from the snapshots. This allows an efficient calculation of probabilities of failure based on the explicit decision function. The methodology is demonstrated for the estimation of the probability of failure for two problems. The first example involves the linear buckling of an arch structure, for which the thickness is a random field. The second problem deals with a random field which modifies the planarity of the walls of a tube impacting a rigid wall.
 Basudhar, A., & Missoum, S. (2008). Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Computers and Structures, 86(1920), 19041917.More infoAbstract: This article presents a methodology to generate explicit decision functions using support vector machines (SVM). A decision function is defined as the boundary between two regions of a design space (e.g., an optimization constraint or a limitstate function in reliability). The SVMbased decision function, which is initially constructed based on a design of experiments, depends on the amount and quality of the training data used. For this reason, an adaptive sampling scheme that updates the decision function is proposed. An accurate approximated explicit decision functions is obtained with a reduced number of function evaluations. Three problems are presented to demonstrate the efficiency of the update scheme to explicitly reconstruct known analytical decision functions. The chosen functions are the boundaries of disjoint regions of the design space. A convergence criterion and error measure are proposed. The scheme is also applied to the definition of an explicit failure region boundary in the case of the buckling of a geometrically nonlinear arch. © 2008 Elsevier Ltd. All rights reserved.
 Basudhar, A., & Missoum, S. (2008). Two alternative schemes to update SVM approximations for the identification of explicit decision functions. 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, MAO.More infoAbstract: This paper presents a new adaptive sampling technique for the construction of explicit decision functions using support vector machine (SVM). Two approaches are used for the adaptive selection of the training samples. The first approach involves the construction of a single initial decision function using a limited number of samples, which is then up dated by adding subsequent samples on the decision function by maximizing the minimum distance. The second approach involves the generation of competing decision functions using di®erent SVM parameters. The difference between the competing approximations provides an idea about the regions of design space with possible need for improvement. Several examples are presented to show the construction of decision functions using the proposed methods. The update schemes are validated by comparing the predicted explicit functions to actual analytical decision functions. Also, the results obtained using the two methods are compared to each other. Copyright © 2008 by Anirban Basudhar and Samy Missoum.
 Basudhar, A., Missoum, S., & Sanchez, A. H. (2008). Limit state function identification using Support Vector Machines for discontinuous responses and disjoint failure domains. Probabilistic Engineering Mechanics, 23(1), 111.More infoAbstract: This article presents a method for the explicit construction of limit state functions using Support Vector Machines (SVM). Specifically, the approach aims at handling the difficulties associated with the reliability assessment of problems exhibiting discontinuous responses and disjoint failure domains. The SVMbased explicit construction of limit state functions allows for an easy calculation of a probability of failure and enables the association of a specific system behavior with a region of the design space. The explicit limit state function can then be used within a reliabilitybased design optimization (RBDO) problem. Two problems are presented to demonstrate the successful application of the developed method for explicit construction of limit state function and reliabilitybased optimum design. © 2007 Elsevier Ltd. All rights reserved.
 Missoum, S. (2008). Probabilistic optimal design in the presence of random fields. Structural and Multidisciplinary Optimization, 35(6), 523530.More infoAbstract: This article describes a methodology to incorporate a random field in a probabilistic optimization problem. The approach is based on the extraction of the features of a random field using a reduced number of experimental observations. This is achieved by proper orthogonal decomposition. Using Lagrange interpolation, a modified random field is obtained by changing the contribution of each feature. The contributions are controlled using scalar parameters, which can be considered as random variables. This allows one to perform a randomfieldbased probabilistic optimization with few random variables. The methodology is demonstrated on a tube impacting a rigid wall for which a random field modifies the planarity of the tube's wall. © 2007 SpringerVerlag Berlin Heidelberg.
 Basudhar, A., & Missoum, S. (2007). Update of explicit limit state functions constructed using support vector machines. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2, 20522068.More infoAbstract: This article presents a method for the explicit construction of limit state functions using Support Vector Machines (SVM). An algorithm is proposed for updating the SVM decision function by carefully selecting the training samples. This results in the construction of an accurate limit state function with a reduced number of function evaluations. Specifically, the SVMbased approach aims at handling the difficulties associated with the reliability assessment of problems exhibiting discontinuous responses and disjoint failure domains. The explicit construction of limit state functions allows for an easy calculation of a probability of failure and enables the association of a specific system behavior with a region of the design space. Three problems are presented to demonstrate the explicit construction of a limit state function. The proposed update scheme is validated by comparing the obtained explicit function to actual analytical limit state functions.
 Missoum, S. (2007). Controlling structural failure modes during an impact in the presence of uncertainties. Structural and Multidisciplinary Optimization, 34(6), 463472.More infoAbstract: A methodology to enforce a given structural dynamic behavior during an impact while accounting for uncertainty is presented. The approach is based on locating structural fuses that weaken the structure locally and help enforce a deformation mode. The problem of enforcing the crushing of a tube impacting a rigid wall is chosen. In order to find the positions of the fuses, the method identifies distinct structural dynamic behaviors using designs of experiments and clustering techniques. The changes in behavior are studied with respect to variations of the fuse positions and random parameters, such as the thickness. Based on the probabilistic distributions, a measure of the likelihood of occurrence of global buckling is defined. The positions of the fuses are defined using an optimization problem in terms of the likelihood of global buckling and the amount of absorbed energy in the tube. A first formulation of the problem considers variability in the tube's thickness only. A second formulation also accounts for uncertainties in the positions of the fuses. © 2007 SpringerVerlag Berlin Heidelberg.
 Missoum, S., Ramu, P., & Haftka, R. T. (2007). A convex hull approach for the reliabilitybased design optimization of nonlinear transient dynamic problems. Computer Methods in Applied Mechanics and Engineering, 196(2930), 28952906.More infoAbstract: Nonlinear transient dynamic problems exhibit structural responses that might be discontinuous due to numerous critical points. The discontinuous behavior hinders classical gradientbased or response surfacebased optimization. However, these discontinuities help to classify the system's responses and identify regions of the design space corresponding to distinct dynamic behaviors. In this paper, data mining techniques are employed to group the responses into clusters. The regions of the design space corresponding to the clusters of unwanted behaviors are delimited with convex hulls. This allows an explicit definition of the boundaries of the failure region in terms of the design variables. In addition, the identification of response clusters, within which the responses might be considered continuous, enables the use of traditional response surface approximation for optimization. The proposed approach is applied to the reliabilitybased design of a tube impacting a rigid wall, which is optimized for a prescribed dynamic behavior. © 2007 Elsevier B.V. All rights reserved.
 Missoum, S. (2006). Controlling structural failure modes during an impact in the presence of uncertainties. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2, 14521464.More infoAbstract: A methodology to enforce a given structural dynamic behavior during an impact is presented. The approach identifies distinct structural dynamic behaviors using designs of experiments and data mining techniques. The changes of behavior are studied with respect to variations of deterministic design variables and uncertainties. Based on the probabilistic distributions of random parameters, failure regions of unwanted behaviors can be identified. A measure of the likelihood of occurrence of unwanted deformation modes is defined and is minimized with respect to design variables. The methodology is specialized to the location of structural fuses on a tube impacting a rigid wall. The locations of fuses are found so that crushing of the tube is enforced while taking uncertainty on the wall thickness into account.
 Sanchez, A. H., Missouri, S., & Pablo, J. (2006). Design space decomposition using support vector machines for reliabilitybased design optimization. Collection of Technical Papers  11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 1, 339353.More infoAbstract: This article presents a method for the explicit decomposition of the design space using support vector machines (SVM). The decomposition identifies the explicit boundaries of a failure region (limit state function) in terms of deterministic and random design variables. This allows an easy calculation of a probability of failure and enables to associate a specific system behavior with a region of the design space. The explicit expression for a limit state function is then used in a reliabilitybased design optimization formulation. Two structural problems are presented to demonstrate the efficiency of the approach.
 Missoum, S., Gürdal, Z., & Setoodeh, S. (2005). Study of a new local update scheme for cellular automata in structural design. Structural and Multidisciplinary Optimization, 29(2), 103112.More infoAbstract: This paper investigates an improved local update scheme for cellular automata (CA) applied to structural design. Local analysis and design rules are derived for equilibrium and minimum compliance design. The new update scheme consists of repeating analysis and optimalitybased design rules locally. The benefits of this approach are demonstrated through a series of systematic experiments. Truss topology design problems of various sizes are used based on the GaussSeidel and the Jacobi iteration modes. Experiments show the robust convergence of the approach as compared to an earlier CA implementation. The approach is also extended to a plate problem. © SpringerVerlag 2004.
 Missoum, S., Chaabane, S. B., & Sudret, B. (2004). Handling bifurcations in the optimal design of transient dynamic problems. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 7, 54325441.More infoAbstract: 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 gradientbased 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, reliabilitybased optimization is considered. Copyright © 2004 by Samy Missoum.
 Ramu, P., Missoum, S., & Haftka, R. T. (2004). A convex hull approach for the reliabilitybased design optimization of transient dynamic problems. Collection of Technical Papers  10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 6, 35463558.More infoAbstract: Nonlinear problems such as transient dynamic problems exhibit structural responses that can be discontinuous due to numerous bifurcations. This hinders gradientbased or response surfacebased optimization. This paper proposes a novel approach to split the design space into regions where the response is continuous. This makes traditional optimization viable. A convex hull approach is adopted to isolate the points corresponding to unwanted bifurcations in the design space. The proposed approach is applied to a tube impacting a rigid wall representing a transient dynamic problem. Since nonlinear behavior is highly sensitive to small variations in design, reliabilitybased design optimization is performed. The proposed method provides the designer an optimal design with a prescribed dynamic behavior.
 Missoum, S., Abdalla, M., & Gürdal, Z. (2003). Nonlinear topology design of trusses using cellular automata. 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.More infoAbstract: 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 twodimensional nonlinear truss topology optimization problems. The optimization problem is stated as a minimization of complementary work (minimum compliance design). First order KuhnTucker 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. © 2003 by Samy Missoum, Mostafa Abdalla and Zafer Gürdal.
 Missoum, S., Abdalla, M., & Gürdal, Z. (2003). Nonlinear topology design of trusses using cellular automata. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 1, 422428.More infoAbstract: 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 twodimensional nonlinear truss topology optimization problems. The optimization problem is stated as a minimization of complementary work (minimum compliance design). First order KuhnTucker 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.
 Missoum, S., & Gürdal, Z. (2002). Displacementbased optimization for truss structures subjected to static and dynamic constraints. AIAA Journal, 40(1), 154161.More infoAbstract: The use of displacements as design variables for truss structure optimization is considered as an alternative to the conventional finiteelementanalysis based design approach. A twolevel nested optimization has been developed; in an inner level, crosssectional areas of truss members are designed for a given displacement field, and, at an outer level, optimal displacements corresponding to the minimum weight designs are searched through the use of sequential quadratic programming. The computational efficiency of the method is demonstrated through three examples, and the evolutions of the crosssectional areas and optimal weight as a function of the displacements are studied, Static, dynamic, and topology problems are considered. It is shown that the method is highly efficient compared to the conventional design approaches. It is also demonstrated that the weight is always continuous throughout the design history, although areas might exhibit large discontinuities.
 Missoum, S., & Gürdal, Z. (2002). Topology design using a twolevel displacementbased approach. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2, 11061114.More infoAbstract: A displacementbased optimization method is used to solve structural topology design problems. The method is a twolevel scheme that avoids the use of repeated finite element analysis often required in traditional structural optimization. The approach is based on an outer level that searches for the optimal displacements and an inner level which finds the optimal design for a given displacement field. For truss structures, the inner optimization problem is a linear programming problem and hence is efficiently solved. The method is applied to the topology design of trusses with linear and nonlinear behavior. The validity and efficiency of the approach for this class of problems is demonstrated through several test examples.
 Missoum, S., Gürdal, Z., & Gu, W. (2002). Optimization of nonlinear trusses using a displacementbased approach. Structural and Multidisciplinary Optimization, 23(3), 214221.More infoAbstract: A displacementbased optimization strategy is extended to the design of truss structures with geometric and material nonlinear responses. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal crosssectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples, which include material and geometric nonlinearities, for which it appears to be efficient and robust.
 Missoum, S., Gürdal, Z., & Watson, L. T. (2002). A displacement based optimization method for geometrically nonlinear frame structures. Structural and Multidisciplinary Optimization, 24(3), 195204.More infoAbstract: An extension of the displacement based optimization method to frames with geometrically nonlinear response is presented. This method, when applied to smallscale trusses with linear and nonlinear response, appeared to be efficient providing the same solutions as the classical optimization method. The efficiency of the method is due to the elimination of numerous finite element analyses that are required in using the traditional optimization approach. However, as opposed to trusses, frame problems have typically a larger number of degrees of freedom than cross sectional area design variables. This leads to difficulties in the implementation of the method compared to the truss implementation. A scheme that relaxes the nodal equilibrium equations is introduced, and the method is validated using test examples. The optimal designs obtained by using the displacement based optimization and the classical approaches are compared to validate the application to frame structures. The characteristics and limitations of the optimization in the displacement space for sizing problems, based on the current formulation, are discussed.
 Slotta, D. J., Tatting, B., Watson, L. T., Gürdal, Z., & Missoum, S. (2002). Convergence analysis for cellular automata applied to truss design. Engineering Computations (Swansea, Wales), 19(78), 953969.More infoAbstract: 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 structures 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 GaussSeidel 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 automation paradigm is tantamount to classical block Jacobi or block GaussSeidel iteration, and consequently the performance of a cellular automation can be rigorously analyzed and predicted.
 Wenjiong, G. u., Gürdal, Z., & Missoum, S. (2002). Elastoplastic truss design using a displacement based optimization. Computer Methods in Applied Mechanics and Engineering, 191(2728), 29072924.More infoAbstract: 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 pathindependent elastoplastic laws, including elastic perfectly plastic, linear strain hardening, and RambergOsgood 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 crosssectional areas equal to zero exactly. © 2002 Elsevier Science B.V. All rights reserved.
 Missoum, S., & Gürdal, Z. (2001). A Displacement based optimization for nonlinear frame structures. 19th AIAA Applied Aerodynamics Conference.More infoAbstract: An extension of the displacement based optimization method to frames with geometrically nonlinear response is presented. This method, when applied to trusses with linear and nonlinear response, provides a substantial reduction in computational time for design optimization. The efficiency of the method is due to the elimination of numerous finite element analyses that are required in using the traditional optimization approach. For frame problems, the number of degrees of freedom is typically larger than the number of cross sectional area design variables leading to difficulties in the implementation of the method compared to the truss implementation. A scheme that relaxes the nodal equilibrium equations is introduced, and the method is validated using test examples. The optimal designs obtained by using the displacement based optimization and the classical approaches are compared to demonstrate the computational efficiency of the method for frame structures. © 2001 by Samy Missoum.
 Missoum, S., & Gürdal, Z. (2001). A displacement based optimization for nonlinear frame structures. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 4, 27992805.More infoAbstract: An extension of the displacement based optimization method to frames with geometrically nonlinear response is presented. This method, when applied to trusses with linear and nonlinear response, provides a substantial reduction in computational time for design optimization. The efficiency of the method is due to the elimination of numerous finite element analyses that are required in using the traditional optimization approach. For frame problems, the number of degrees of freedom is typically larger than the number of cross sectional area design variables leading to difficulties in the implementation of the method compared to the truss implementation. A scheme that relaxes the nodal equilibrium equations is introduced, and the method is validated using test examples. The optimal designs obtained by using the displacement based optimization and the classical approaches are compared to demonstrate the computational efficiency of the method for frame structures.
 Missoum, S., & Gurdal, Z. (2000). Optimization of trusses with geometrically nonlinear response using a displacement based approach. Collection of Technical Papers  AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 1(I), 464469.More infoAbstract: A displacement based optimization strategy is extended to the design of truss structures with geometrically nonlinear response. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal crosssectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples for which it appears to be efficient and fast.
 Missoum, S., & Gürdal, Z. (2000). Optimization of trusses with geometrically nonlinear response using a displacement based approach. 41st Structures, Structural Dynamics, and Materials Conference and Exhibit.More infoAbstract: A displacement based optimization strategy is extended to the design of truss structures with geometrically nonlinear response. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal crosssectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples for which it appears to be efficient and fast. © 2000 by Samy Missoum. Published by the American Institute of Aeronautics and Astronautics, Inc.
 Missoum, S., Gürdal, Z., Hernandez, P., & Guillot, J. (2000). A genetic algorithm based topology tool for continuum structures. 8th Symposium on Multidisciplinary Analysis and Optimization.More infoAbstract: A new method for topology optimization of continuum structures modeled by finite elements is presented. The objective of the research presented in this paper is to build a flexible and meshindependent topology tool. This is accomplished by creating a GA implementation that defines functional components, referred to as masks that have standard geometric shapes such as circles, ellipses, or rectangles. When applied to a finite element model, all the elements that are covered by these masks are removed. The removal of elements can be performed without causing any singularities by using the birth and death capability available in the ANSYS software (SWANSON Ltd.). The method proved to be efficient, providing meaningful and easily manufacturable topologies for a variety of loadings and analysis options such as dynamic and static loads. Two different examples of structures are provided. © 2000 by Samy Missoum.
Proceedings Publications
 Ahmadisoleymani, S., & Missoum, S. (2018, June). Optimization of a chain of nonlinear resonators for vibra tion mitigation. In AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Aviation Forum (Paper AIAA20183105).
 Pidaparthi, B., & Missoum, S. (2018, June, 2018). Optimization of nonlinear energy sinks for the mitigation of limit cycle oscillations. In 2018 AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Aviation Forum (Paper AIAA20183569).
 Boroson, E., Missoum, S., Mattei, P., & Vergez, C. (2014, August 1720). Optimization Under Uncertainty of Nonlinear Energy Sinks. In ASME 2014 International Design & Engineering Technical Conferences and Computers & Information in Engineering Conference.
 Lacaze, A., & Missoum, S. (2014, August 1720). A Generalized "MaxMin" Sample for Reliability Assessment with Dependent Variables. In ASME 2014 International Design & Engineering Technical Conferences and Computers & Information in Engineering Conference.
 Lacaze, S., Missoum, S., Alijani, F., & Amabili, M. (2014, September 810). Identication Under Uncertainty of Material Properties of Composite Sandwich Panels. In American Society for Composites 29 Technical Conference/16th US Japan Conference on Composite Materials.
Presentations
 Ernoult, A., & Missoum, S. (2018, April). Comment l’optimisation peutelle ˆetre une aide `a la facture instrumentale ?. Congres Francais d’Acoustique. Le Havre, France: French Society of Acoustics.
 Gourc, E., Vergez, C., Mattei, P., & Missoum, S. (2018, April). Modele minimal de la note du loup (topic:Modeling of the dynamics of the Wolf tone on a cello). French Congress of Acoustics. Le Havre, France: French Society of Acoustics.
Poster Presentations
 Chen, Z., Jiang, P., & Missoum, S. (2014, July). Hip Fracture Prediction using Finite Element Modeling and Machine Learning. Proceedings of the 7th World Congress of Biomechanics, Boston, MA, Jul. 6  11, 2014..More infoJiang, P., Chen, Z., and Missoum, S. Hip Fracture Prediction using Finite Element Modeling and Machine Learning. Proceedings of the 7th World Congress of Biomechanics, Boston, MA, Jul. 6  11, 2014.
 Missoum, S. ., Jiang, P., Hu, C. ., Hsieh, P. S., Chen, Z. ., Missoum, S. ., Jiang, P., Hu, C. ., Hsieh, P. S., & Chen, Z. . (2013, Fall). Towards hip fracture prediction using finite element analysis and machine learning. The American Society for Bone and Mineral Research (ASBMR) 2013 Annual Meeting. Baltimore, MD.More infoSamy Missoum, Peng Jiang, Chengcheng Hu, Skye Nicholas, Zhao Chen. Towards Hip Fracture Prediction using Finite Element analysis and Machine Learning (poster presentation). The American Society for Bone and Mineral Research Annual Meeting, Oct 27, 2013. Baltimore, Maryland USA.
Other Teaching Materials
 Jiang, P., Chen, Z., & Missoum, S. (2014. Hip Fracture Prediction Using Finite Element Modeling and Machine Learning. World Congress of Biomechanics, Boston, MA.