@article {TERRIEN2025119241, title = {Basins of attraction in a dynamical system with a time-varying control parameter: The case of attack transients in a simple model of reed musical instrument}, journal = {Journal of Sound and Vibration}, volume = {618}, year = {2025}, pages = {119241}, abstract = {

Multistability, a common phenomenon in dynamical systems in general and in musical instruments in particular, corresponds to the coexistence of several stable regimes for a given set of parameters. When a system is multistable, which regime is observed depends on the initial conditions on the state variables, and therefore relates to the basins of attraction. Here we consider a simple model of reed musical instrument. A bifurcation analysis shows that the system is bistable on a range of the blowing pressure, which is one of the main control parameters for the musician. In the bistability region, the boundary between basins of attraction is computed for the classical case of constant control parameters in the one hand, and for saturating ramps of the blowing pressure on the other hand. These profiles of the blowing pressure are chosen as prototypical representations of the so-called attack transients of the blowing pressure, during which the musician starts to blow in the instrument to create a musical note from silence. Attack transients are known to be of crucial importance in a musical context, yet mostly overlooked in physical models of the musician{\textendash}instrument system. The separatrix between basins of attraction is computed numerically by combining time-domain simulations with a machine learning technique relying on support vector machine. Our results demonstrate that attack transients of the blowing pressure significantly affect the practical observability of the different stable regimes, suggesting that they might be used by musicians to navigate between basins. From a more general point of view, these results relate to rate-induced tipping phenomena and might therefore be of interest beyond the particular case of musical instruments.

}, keywords = {Attack transients, Basins of attraction, Bifurcation analysis, Musical acoustics, Nonlinear dynamical systems, Physical modeling, Rate-induced tipping}, issn = {0022-460X}, doi = {https://doi.org/10.1016/j.jsv.2025.119241}, url = {https://www.sciencedirect.com/science/article/pii/S0022460X25003153}, author = {Soizic Terrien and Baptiste Bergeot and Christophe Vergez and Samy Missoum} } @article {, title = {Stochastic Optimization of a Mass-in-Mass Cell with Piecewise Hybrid Nonlinear{\textendash}Linear Restoring Force}, journal = {Journal of Sound and Vibration}, volume = {595}, year = {2025}, month = {Jan-01-2025}, pages = {118755}, issn = {0022460X}, doi = {10.1016/j.jsv.2024.118755}, author = {da Silveira Zanin, C. and Missoum, S. and Ture Savadkoohi, A. and Baguet, S. and Gourdon, E. and Dufour, R.} } @proceedings {doi:10.2514/6.2025-1957, title = {Stochastic Optimization With Multiple Failure Modes of Systems Subjected to Random Vibrations}, year = {2025}, doi = {10.2514/6.2025-1957}, url = {https://arc.aiaa.org/doi/abs/10.2514/6.2025-1957}, author = {Luis Ballesteros and Samy Missoum and Christopher D. Noble} } @conference {dasilveirazanin:hal-04233773, title = {Towards the Robust Optimal Design of Nonlinear Metamaterials}, booktitle = {NODYCON 2023 Third International Nonlinear Dynamics Conference}, year = {2023}, address = {Rome, Italy}, url = {https://hal.science/hal-04233773}, author = {da Silveira Zanin, Camila and Missoum, Samy and Ture Savadkoohi, Alireza and Baguet, S{\'e}bastien and Dufour, R{\'e}gis} } @article {boroson2017optimization, title = {Optimization Under Uncertainty of Parallel Nonlinear Energy Sinks}, journal = {Journal of Sound and Vibration}, volume = {394}, year = {2017}, month = {04/2017}, pages = {451-464}, abstract = {

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy over a wider range of frequencies. Nevertheless, they are still only efficient over a limited range of excitations. In order to mitigate this limitation and maximize the efficiency range, this work investigates the optimization of multiple NESs configured in parallel. It is well known that the efficiency of a NES is extremely sensitive to small perturbations in loading conditions or design parameters. In fact, the efficiency of a NES has been shown to be nearly discontinuous in the neighborhood of its activation threshold. For this reason, uncertainties must be taken into account in the design optimization of NESs. In addition, the discontinuities require a specific treatment during the optimization process. In this work, the objective of the optimization is to maximize the expected value of the efficiency of NESs in parallel. The optimization algorithm is able to tackle design variables with uncertainty (e.g., nonlinear stiffness coefficients) as well as aleatory variables such as the initial velocity of the main system. The optimal design of several parallel NES configurations for maximum mean efficiency is investigated. Specifically, NES nonlinear stiffness properties, considered random design variables, are optimized for cases with 1, 2, 3, 4, 5, and 10 NESs in parallel. The distributions of efficiency for the optimal parallel configurations are compared to distributions of efficiencies of non-optimized NESs. It is observed that the optimization enables a sharp increase in the mean value of efficiency while reducing the corresponding variance, thus leading to more robust NES designs.

}, keywords = {Parallel nonlinear energy sinks; Optimization under uncertainty; Activation threshold}, doi = {http://dx.doi.org/10.1016/j.jsv.2016.12.043}, url = {http://www.sciencedirect.com/science/article/pii/S0022460X16308045}, author = {Ethan Boroson and Samy Missoum and Pierre-Olivier Mattei and Christophe Vergez} } @article {boroson2017stochastic, title = {Stochastic Optimization of Nonlinear Energy Sinks}, journal = {Structural and Multidisciplinary Optimization}, volume = {55}, year = {2017}, month = {02/2017}, pages = {633-646}, abstract = {

Nonlinear energy sinks (NES) are a promising technique to achieve vibration mitigation. Through nonlinear stiffness properties, NES are able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NES absorb energy from a wide range of frequencies. Many studies have focused on NES behavior and dynamics, but few have addressed the optimal design of NES. Design considerations of NES are of prime importance as it has been shown that NES dynamics exhibit an acute sensitivity to uncertainties. In fact, the sensitivity is so marked that NES efficiency is near-discontinuous and can switch from a high to a low value for a small perturbation in design parameters or loading conditions. This article presents an approach for the probabilistic design of NES which accounts for random design and aleatory variables as well as response discontinuities. In order to maximize the mean efficiency, the algorithm is based on the identification of regions of the design and aleatory space corresponding to markedly different NES efficiencies. This is done through a sequence of approximated sub-problems constructed from clustering, Kriging approximations, a support vector machine, and Monte-Carlo simulations. The refinement of the surrogates is performed locally using a generalized max-min sampling scheme which accounts for the distributions of random variables. The sampling scheme also makes use of the predicted variance of the Kriging surrogates for the selection of aleatory variables values. The proposed algorithm is applied to three example problems of varying dimensionality, all including an aleatory excitation applied to the main system. The stochastic optima are compared to NES optimized deterministically.

}, keywords = {Discontinuities, Generalized max-min, Kriging, Nonlinear energy sinks, Stochastic optimization, Support vector machine}, doi = { 10.1007/s00158-016-1526-y}, author = {Boroson, Ethan and Missoum, Samy} } @conference {boroson2016optimization, title = {Optimization Under Uncertainty of Parallel Nonlinear Energy Sinks}, booktitle = {57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference}, year = {2016}, address = {San Diego, CA}, doi = {10.2514/6.2016-1421 }, author = {Boroson, Ethan and Missoum, Samy} } @article {brevault2016reliability, title = {Reliability Analysis in the Presence of Aleatory and Epistemic Uncertainties, Application to the Prediction of a Launch Vehicle Fallout Zone}, journal = {Journal of Mechanical Design}, volume = {138}, year = {2016}, month = {09/2016}, pages = {111401}, doi = {10.1115/1.4034106}, author = {Brevault, Lo{\"\i}c and Lacaze, Sylvain and Balesdent, Mathieu and Missoum, Samy} } @proceedings {boroson2016stochastic, title = {Stochastic Optimization of Nonlinear Energy Sinks Using Resonance-based Clustering}, year = {2016}, publisher = {American Society of Mechanical Engineers}, address = {Phoenix, AZ}, doi = {10.1115/IMECE2016-67115}, url = {https://doi.org/10.1115/IMECE2016-67115}, author = {Ethan Boroson and Samy Missoum} } @inbook {balesdent2015methods, title = {Methods for High Dimensional and Computationally Intensive Models}, booktitle = { In Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems, A Practical Approach. }, year = {2015}, publisher = {Elsevier}, organization = {Elsevier}, chapter = {8}, author = {Balesdent, Mathieu and Brevault, Lo{\"\i}c and Lacaze, Sylvain and Missoum, Samy and Morio, Jerome} } @article {lacaze2015probability, title = {Probability of Failure Sensitivity with Respect to Decision Variables}, journal = {Structural and Multidisciplinary Optimization}, year = {2015}, month = {04/2015}, doi = {10.1007/s00158-015-1232-1}, url = {http://codes.arizona.edu/sites/default/files/pdf/Sylvain2015a.pdf}, author = {Lacaze, Sylvain and Brevault, Lo{\"\i}c and Missoum, Samy and Balesdent, Mathieu} } @conference {boroson2015reliability, title = {Reliability-based Design Optimization of Nonlinear Energy Sinks}, booktitle = {Proceedings of the 11th World Congress of Structural and Multidisciplinary Optimisation (WCSMO-11)}, year = {2015}, month = {06/2015}, address = {Sydney, Australia}, doi = {10.2514/6.2016-1421 }, url = {http://codes.arizona.edu/sites/default/files/pdf/Boroson2015.pdf}, author = {Boroson, Ethan and Missoum, Samy} } @conference {lacaze2015sampling, title = {A Sampling-based RBDO Algorithm with Local Refinement and Efficient Gradient Estimation}, booktitle = {12th International Conference on Applications of Statistics Probability in Civil Engineering, Vancouver, Canada}, year = {2015}, author = {Lacaze, Sylvain and Missoum, Samy and Brevault, Lo{\"\i}c and Balesdent, Mathieu} } @conference {boroson2014optimization, title = {Optimization Under Uncertainty of Nonlinear Energy Sinks}, booktitle = {Proceedings of the ASME International Design and Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 26th Conference on Mechanical Vibration and Noise}, year = {2014}, publisher = {American Society of Mechanical Engineers}, organization = {American Society of Mechanical Engineers}, address = {Buffalo, NY}, doi = {10.1115/DETC2014-34238}, url = {http://codes.arizona.edu/sites/default/files/pdf/Boroson2014.pdf}, author = {Boroson, Ethan and Missoum, Samy and Mattei, Pierre-Olivier and Vergez, Christophe} } @conference {basudhar2013classification, title = {Classification-based Violation Measurement for Constrained Efficient Global Optimization}, booktitle = {Paper 5577. Proceedings of the 10th ISSMO World Congress of Structural and Multidisciplinary Optimization}, year = {2013}, address = {Orlando, FL}, author = {Basudhar, Anirban and Missoum, Samy} } @article {lin2013parallel, title = {Parallel Construction of Explicit Boundaries Using Support Vector Machines}, journal = {Engineering Computations}, volume = {30}, number = {1}, year = {2013}, pages = {132-148}, publisher = {Emerald Group Publishing Limited}, doi = {10.1108/02644401311286099}, url = {http://codes.arizona.edu/sites/default/files/pdf/Lin2013.pdf}, author = {Lin, Ke and Basudhar, Anirban and Missoum, Samy} } @article {basudhar2013reliability, title = {Reliability Assessment Using Probabilistic Support Vector Machines}, journal = {Int. J. of Reliability and Safety}, volume = {7}, number = {2}, year = {2013}, pages = {156-173}, doi = {10.1504/IJRS.2013.056378}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2013a.pdf}, author = {Basudhar, Anirban and Missoum, Samy} } @article {basudhar2012constrained, title = {Constrained Efficient Global Optimization with Support Vector Machines}, journal = {Structural and Multidisciplinary Optimization}, volume = {46}, number = {2}, year = {2012}, pages = {201-221}, publisher = {Springer-Verlag}, issn = {1615-147X}, doi = {10.1007/s00158-011-0745-5}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2012.pdf}, author = {Basudhar, Anirban and Dribusch, Christoph and Lacaze, Sylvain and Missoum, Samy} } @mastersthesis {basudhar2011computational, title = {Computational Optimal Design and Uncertainty Quantification of Complex Systems Using Explicit Decision Boundaries}, year = {2011}, school = {University of Arizona}, type = {phd}, doi = {10150/201491}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2011a.pdf}, author = {Basudhar, Anirban} } @conference {basudhar2011reliability, title = {Reliability Assessment with Correlated Variables Using Support Vector Machines}, booktitle = {Proceedings of the 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference}, year = {2011}, doi = {10.2514/6.2011-1905}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2011.pdf}, author = {Jiang, Peng and Basudhar, Anirban and Missoum, Samy} } @conference {basudhar2010constrained, title = {Constrained Efficient Global Optimization with Probabilistic Support Vector Machines}, booktitle = {Proceedings of the 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference}, year = {2010}, doi = {10.2514/6.2010-9230}, author = {Basudhar, Anirban and Lacaze, Sylvain and Missoum, Samy} } @article {basudhar2010improved, title = {An Improved Adaptive Sampling Scheme for the Construction of Explicit Boundaries}, journal = {Structural and Multidisciplinary Optimization}, volume = {42}, number = {4}, year = {2010}, pages = {517-529}, publisher = {Springer-Verlag}, issn = {1615-147X}, doi = {10.1007/s00158-010-0511-0}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2010a.pdf}, author = {Basudhar, Anirban and Missoum, Samy} } @article {dribusch2010multifidelity, title = {A Multifidelity Approach for the Construction of Explicit Decision Boundaries: Application to Aeroelasticity}, journal = {Structural and Multidisciplinary Optimization}, volume = {42}, number = {5}, year = {2010}, pages = {693-705}, publisher = {Springer-Verlag}, issn = {1615-147X}, doi = {10.1007/s00158-010-0516-8}, url = {http://codes.arizona.edu/sites/default/files/pdf/Dribusch2010.pdf}, author = {Dribusch, Christoph and Missoum, Samy and Beran, Philip} } @conference {basudhar2010reliability, title = {Reliability Assessment Using Probabilistic Support Vector Machines (PSVMs)}, booktitle = {Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference}, year = {2010}, doi = {10.2514/6.2010-9230}, author = {Basudhar, Anirban and Missoum, Samy} } @article {missoum2010reliability, title = {Reliability-based Design Optimization of Nonlinear Aeroelasticity Problems}, journal = {Journal of Aircraft}, volume = {47}, number = {3}, year = {2010}, pages = {992 - 998}, doi = {10.2514/1.46665}, url = {http://codes.arizona.edu/sites/default/files/pdf/Missoum2010.pdf}, author = {Missoum, Samy and Dribusch, Christoph and Beran, Philip} } @article {arenbeck2010reliability, title = {Reliability-based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition}, journal = {Journal of Mechanical Design}, volume = {132}, number = {132}, year = {2010}, month = {02}, pages = {021010}, doi = {10.1115/1.4000760}, url = {http://codes.arizona.edu/sites/default/files/pdf/Arenbeck2010.pdf}, author = {Arenbeck, Henry and Missoum, Samy and Basudhar, Anirban and Nikravesh, Parviz} } @conference {basudhar2009local, title = {Local Update of Support Vector Machine Decision Boundaries}, booktitle = {Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference}, year = {2009}, doi = {10.2514/6.2009-2189}, author = {Basudhar, Anirban and Missoum, Samy} } @article {basudhar2009sampling, title = {A Sampling-Based Approach for Probabilistic Design with Random Fields}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {198}, number = {47-48}, year = {2009}, pages = {3647 - 3655}, issn = {0045-7825}, doi = {10.1016/j.cma.2009.07.003}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2009.pdf}, author = {Basudhar, Anirban and Missoum, Samy} } @article {basudhar2008adaptive, title = {Adaptive Explicit Decision Functions for Probabilistic Design and Optimization Using Support Vector Machines}, journal = {Computers \& Structures}, volume = {86}, number = {19-20}, year = {2008}, pages = {1904 - 1917}, issn = {0045-7949}, doi = {10.1016/j.compstruc.2008.02.008}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2008a.pdf}, author = {Basudhar, Anirban and Missoum, Samy} } @article {basudhar2008limit, title = {Limit State Function Identification Using Support Vector Machines for Discontinuous Responses and Disjoint Failure Domains}, journal = {Probabilistic Engineering Mechanics}, volume = {23}, number = {1}, year = {2008}, pages = {1 - 11}, issn = {0266-8920}, doi = {10.1016/j.probengmech.2007.08.004}, url = {http://codes.arizona.edu/sites/default/files/pdf/Basudhar2008.pdf}, author = {Basudhar, Anirban and Missoum, Samy and Sanchez, Antonio Harrison} } @conference {basudhar2008sampling, title = {A Sampling-Based Approach for Probabilistic Design with Random Fields}, booktitle = {Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference}, year = {2008}, doi = {10.2514/6.2008-2064}, author = {Basudhar, Anirban and Missoum, Samy} } @conference {basudhar2008two, title = {Two Alternative Schemes to Update SVM Approximations for the Identification of Explicit Decision Functions}, booktitle = {Proceedings of the 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference}, year = {2008}, doi = {10.2514/6.2008-5963}, author = {Basudhar, Anirban and Missoum, Samy} } @conference {arenbeck2007simulation, title = {Simulation Based Optimal Tolerancing for Multibody Systems}, booktitle = {Proceedings of the 19th ASME Reliability, Stress Analysis, and Failure Prevention Conference}, year = {2007}, doi = {10.1115/DETC2007-35706}, author = {Arenbeck, Henry and Missoum, Samy and Basudhar, Anirban and Nikravesh, Parviz} } @conference {basudhar2007update, title = {Update of Explicit Limit State Functions Constructed Using Support Vector Machines}, booktitle = {Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference}, year = {2007}, doi = {10.2514/6.2007-1872}, author = {Basudhar, Anirban and Missoum, Samy} }