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Minimal dynamical structure realisations with application to network reconstruction from data ; ; et al in The proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009) Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics, and engineering. Previous work introduced dynamical structure functions as a tool for ... [more ▼] Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics, and engineering. Previous work introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not measured, in many situations it is important to estimate the number of hidden states in order to understand the complexity of the network under investigation and help identify potential targets for measurements. Estimating the number of hidden states is also crucial to obtain the simplest state-space model that captures the network structure and is coherent with the measured data. This paper characterises minimal order state-space realisations that are consistent with a given dynamical structure function by exploring properties of dynamical structure functions and developing algorithms to explicitly obtain a minimal reconstruction. [less ▲] Detailed reference viewed: 66 (0 UL)Minimal-time network reconstruction for DTLTI systems ; Goncalves, Jorge in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010) This paper considers the problem of obtaining in minimal time the “dynamical network structure” (DNS) from partial state observations of a discrete-time linear time-invariant system. From the DNS, we can ... [more ▼] This paper considers the problem of obtaining in minimal time the “dynamical network structure” (DNS) from partial state observations of a discrete-time linear time-invariant system. From the DNS, we can not only obtain the network structure of the system at the measurement level, but also estimate the minimal number of hidden states which are not observed directly. First, we discuss when reconstruction of the DNS is and is not possible. Then, we give an algorithm to find the minimal number of successive outputs to find the DNS. Finally, we discuss extensions of the results to non-linear and noisy systems. These results can be directly applied to the decentralised network control problem of multi-agent systems to find network connections of the observed agents. [less ▲] Detailed reference viewed: 77 (0 UL)Minimal-time uncertain output final value of unknown DT-LTI systems with application to the decentralised network consensus problem ; ; et al Scientific Conference (2010) Detailed reference viewed: 27 (0 UL)Minimum energy multiple crack propagation Part I: Theory. Sutula, Danas ; Bordas, Stéphane in Engineering Fracture Mechanics (n.d.) The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and ... [more ▼] The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-I of this three-part paper are: (1) formulation of the total energy functional governing multiple crack behaviour, (2) three solution methods to the problem of competing crack growth for different fracture front stabilities (e.g. stable, unstable, or a partially stable configuration of crack tips), and (3) the minimum energy criterion for a set of crack tip extensions is posed as the criterion of vanishing rotational dissipation rates with respect to the rotations of the crack extensions. The formulation lends itself to a straightforward application within a discrete framework for determining the crack extension directions of multiple finite-length crack tip increments, which is tackled in Part-II, using the extended finite element method. In Part-III, we discuss various applications and benchmark problems. The open-source Matlab code, documentation, benchmark/example cases are included as supplementary material. [less ▲] Detailed reference viewed: 1720 (165 UL)Minimum energy multiple crack propagation. Part II: Discrete Solution with XFEM. Sutula, Danas ; Bordas, Stéphane in Engineering Fracture Mechanics (n.d.) The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and ... [more ▼] The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. This Part-II of our three-part paper examines three discrete solution methods for solving fracture mechanics problems based on the principle of minimum total energy. The discrete solution approach is chosen based on the stability property of the fracture configuration at hand. The first method is based on external load-control. It is suitable for stable crack growth and stable fracture configurations. The second method is based on fractured area-control. This method is applicable to stable or unstable fracture growth but it is required that the fracture front be stable. The third solution method is based on a gradient-descent approach. This approach can be applied to arbitrary crack growth problems; however, the gradient-descent formulation cannot be guaranteed to yield the optimal solution in the case of competing crack growth and an unstable fracture front configuration. The main focus is on the gradient-descent solution approach within the framework of the extended finite element discretisation. Although a viable solution method is finally proposed for resolving competing crack growth in the case of an unstable fracture front configuration, the method is not implemented within the present XFEM code but rather exists as a separate proof-of-concept algorithm that is tested against several fabricated benchmark problems. The open-source Matlab code, documentation and example cases are included as supplementary material. [less ▲] Detailed reference viewed: 787 (106 UL)Minimum energy multiple crack propagation. Part III: XFEM computer implementation and applications. Sutula, Danas ; Bordas, Stéphane in Engineering Fracture Mechanics (n.d.) The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and ... [more ▼] The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-III of the three-part paper are as follows: (1) implementation of XFEM in Matlab with emphasis on the design of the code to enable fast and efficient computational times of fracture problems involving multiple cracks and arbitrary crack intersections, (2) verification of the minimum energy criterion and comparison with the maximum tension criterion via multiple benchmark studies, and (3) we propose a numerical improvement to the crack growth direction criterion that gives significant improvements in accuracy and convergence rates of the fracture paths, especially on coarse meshes. The comparisons of the fracture paths obtained by the maximum tension (or maximum hoop-stress) criterion and the energy minimisation approach via a multitude of numerical case studies show that both criteria converge to virtually the same fracture solutions albeit from opposite directions. In other words, it is found that the converged fracture path lies in between those obtained by each criterion on coarser meshes. Thus, a modified crack growth direction criterion is proposed that assumes the average direction of the directions obtained by the maximum tension and the minimum energy criteria. The numerical results show significant improvements in accuracy (especially on coarse discretisations) and convergence rates of the fracture paths. Finally, the open-source Matlab code, documentation, benchmarks and example cases are included as supplementary material. [less ▲] Detailed reference viewed: 788 (100 UL)Mitarbeiterführung und Social-Media-Nutzung im Führungsalltag von Generation-Y-Führungskräften - Eine explorative Analyse mittels Mixed-Methods-Ansatz Feltes, Florian Doctoral thesis (2016) The topic of this thesis is the qualitative and quantitative evaluation of leadership behaviour and therefore the leadership style of Generation Y (GenY) considering the use of social media in day-to-day ... [more ▼] The topic of this thesis is the qualitative and quantitative evaluation of leadership behaviour and therefore the leadership style of Generation Y (GenY) considering the use of social media in day-to-day management. It examines the question of how GenY leaders lead and how they use social media in this context. It explores the topic based on a sequential mixed methods approach of qualitative interviews and a quantitative online questionnaire. Using the qualitative content analysis, it examines 25 qualitative interviews concerning the following aspects: leadership behaviour of generation Y, generation-based differences in the leadership and different strength of leadership styles, influence of contextual factors like hierarchies, sector and company size on the leadership style and use of social media, use of social media on day-to-day management, and, finally, connections between applied leadership styles and social media usage of GenY leaders. The findings and tendencies were then verified in an online questionnaire. The results of the online questionnaire [self-evaluation of leaders (N=406), bottom-up evaluation by employees (N=622)] show a significant discrepancy between the leaders’ statements and those of the employees. However, there are clear results and tendencies that confirm the findings of the qualitative study. It was established that GenY leaders show characteristics of task-oriented, person-oriented, transactional and transformational leadership. GenY leadership is characterised by clear outcome orientation, flat hierarchies and feedback. The use of social media varies considerably, depending for example on the context in which the leader works, e. g. sector and level of management. In summary, it can be stated that there is a connection between the strength of the leadership style and the usage of social media in day-to-day management. [less ▲] Detailed reference viewed: 226 (13 UL)Mixed hybrid and electric bus dynamic fleet management in urban networks: a model predictive control approach Rinaldi, Marco ; Picarelli, Erika ; et al Scientific Conference (2019, June) Abstract—Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport, are increasingly becoming key objectives for policymakers worldwide. In order to jointly ... [more ▼] Abstract—Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport, are increasingly becoming key objectives for policymakers worldwide. In order to jointly achieve these goals, careful consideration should be put on the operational cost and management of PT services, in order to promote the adoption of green mobility solutions and advanced management techniques by operators. In this work we develop a dynamic fleet management approach for next generation Public Transportation systems, considering the instance of mixed electric / hybrid fleet. Our objective is that of investigating to what extent electrification, coupled with optimal fleet management, can yield operational cost savings for PT operators, explicitly considering real-time disturbances, including delays, service disruptions etc. We propose a Mixed Integer Linear Program to address the problem of optimal scheduling of a mixed fleet of electric and hybrid / non-electric buses, and employ it as predictor in a Model Predictive Control approach. Test results based upon a real-life scenario showcase how the proposed approach is indeed capable of yielding a sizable reduction in operational costs, even when considerable disturbances arise from the underlying system. [less ▲] Detailed reference viewed: 53 (4 UL)Mixed hybrid and electric bus dynamic fleet management in urban networks: a model predictive control approach Rinaldi, Marco ; ; Laskaris, Georgios et al Scientific Conference (2019, January) Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport, are increasingly becoming key objectives for policymakers worldwide. In order to jointly achieve ... [more ▼] Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport, are increasingly becoming key objectives for policymakers worldwide. In order to jointly achieve these goals, careful consideration should be put on the operational cost and management of PT services, in order to promote the adoption of green mobility solutions and advanced management techniques by operators. In this work we develop a dynamic fleet management approach for next generation Public Transportation systems, considering the instance of mixed electric / hybrid fleet. Our objective is that of investigating to what extent electrification, coupled with optimal fleet management, can yield operational cost savings for PT operators, explicitly considering real-time disturbances, including delays, service disruptions etc. We propose a Mixed Integer Linear Program to address the problem of optimal scheduling of a mixed fleet of electric and hybrid / non-electric buses, and employ it as predictor in a Model Predictive Control approach. Test results based upon a real-life scenario showcase how the proposed approach is indeed capable of yielding a sizable reduction in operational costs, even when considerable disturbances arise from the underlying system. [less ▲] Detailed reference viewed: 179 (7 UL)A mixed integer linear programming approach to pursuit evasion problems with optional connectivity constraints Thunberg, Johan ; in Autonomous Robots (2011), 31(4), 333-343 In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. By discretizing the problem, and applying a Mixed Integer Linear Programming (MILP) framework ... [more ▼] In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. By discretizing the problem, and applying a Mixed Integer Linear Programming (MILP) framework, we are able to address problems requiring so-called recontamination and also impose additional constraints, such as connectivity between the pursuers. The proposed MILP formulation is less conservative than solutions based on graph discretizations of the environment, but still somewhat more conservative than the original underlying problem. It is well known that MILPs, as well as multi pursuer pursuit evasion problems, are NP-hard. Therefore we apply an iterative Receding Horizon Control (RHC) scheme where a number of smaller MILPs are solved over shorter planning horizons. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples. [less ▲] Detailed reference viewed: 93 (0 UL)A Mixed Similarity Measure for Data with Numeric, Symbolic and Ordinal Attributes ; ; Nguyen, Thanh-Phuong et al in The proceeding of Japan-Vietnam Joint Workshop on Active Mining (Artificial Intelligence I) (2004) Detailed reference viewed: 51 (1 UL)Mixed-fleet single-terminal bus scheduling problem: Modelling, solution scheme and potential applications Rinaldi, Marco ; Picarelli, Erika ; et al in Omega: the International Journal of Management Science (in press) Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport (PT), are increasingly becoming key objectives for policymakers worldwide. In this work we develop an ... [more ▼] Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport (PT), are increasingly becoming key objectives for policymakers worldwide. In this work we develop an optimal vehicle scheduling approach for next generation PT systems, considering the instance of mixed electric / hybrid fleet. Our objective is that of investigating to what extent electrification, coupled with optimal fleet management, can yield operational cost savings for PT operators. We propose a Mixed In- teger Linear Program (MILP) to address the problem of optimal scheduling of a mixed fleet of electric and hybrid / non-electric buses, coupled with an ad-hoc decomposition scheme aimed at enhancing the scalability of the proposed MILP. Two case studies arising from the PT network of the city of Luxem- bourg are employed in order to validate the model; sensitivity analysis to fleet design parameters is performed, specifically in terms of fleet size and fleet composition. Conclusions point to the fact that careful modelling and handling of mixed-fleet conditions are necessary to achieve operational savings, and that marginal savings gradually reduce as more conventional buses are replaced by their electric counterparts. We believe the methodology proposed may be a key part of advanced decision support systems for policymakers and operators that are dealing with the on-going transition from conventional bus fleets towards greener transport solutions. [less ▲] Detailed reference viewed: 93 (5 UL)Mobile Satellite Broadcast and Multichannel Communications Analysis and Design Martin, Cristoff Book published by KTH (2005) In this thesis, analytical analysis and design techniques for wireless communications with diversity are studied. The impact of impairments such as correlated fading is analyzed using statistical models ... [more ▼] In this thesis, analytical analysis and design techniques for wireless communications with diversity are studied. The impact of impairments such as correlated fading is analyzed using statistical models. Countermeasures designed to overcome, or even exploit, such effects are proposed and examined. In particular two applications are considered, satellite broadcast to vehicular terminals and communication using transmitters and receivers equipped with multiple antennas. Mobile satellite broadcast systems offer the possibility of high data rate services with reliability and ubiquitous coverage. The design of sys- tem architectures providing such services requires complex trade-offs involving technical, economical, and regulatory aspects. A satisfactory availability can be ensured using space, terrestrial, and time diversity techniques. The amount of applied diversity affects the spectral efficiency and system performance. Also, dedicated satellite and terrestrial networks represent significant investments and regulatory limitations may further complicate system design. The work presented in this thesis provides insights to the technical aspects of the trade-offs above. This is done by deriving an efficient method for estimating what resources in terms of spectrum and delay are required for a broadcast service to reach a satisfactory number of end users using a well designed system. The results are based on statistical models of the mobile satellite channel for which efficient analytical design and error rate estimation methods are derived. We also provide insight to the achievable spectral efficiency using different transmitter and receiver configurations. Multiple-element antenna communication is a promising technology for future high speed wireless infrastructures. By adding a spatial dimension, radio resources in terms of transmission power and spectrum can be used more efficiently. Much of the design and analysis work has focused on cases where the transmitter either has access to perfect channel state information or it is blind and the spatial channels are uncorrelated. Herein, systems where the fading of the spatial channels is correlated and/or the transmitter has access to partial channel state information are considered. While maintaining perfect channel knowledge at the transmitter may prove difficult, updating parameters that change on a slower time scale could be realistic. Here we formulate analysis and design techniques based on statistical models of the multichannel propagation. Fundamental properties of the multi-element antenna channel and limitations given by information theory are investigated under an asymptotic assumption on the number of antennas on either side of the system. For example, limiting normal distributions are derived for the squared singular values of the channel matrix and the mutual information. We also propose and examine a practical scheme capable of exploiting partial channel state information. In both applications outlined above, by using statistical models of the channel characteristics in the system design, performance can be improved. The main contribution of this thesis is the development of efficient techniques for estimating the system performance in different scenarios. Such techniques are vital to obtain insights to the impact of different impairments and how countermeasures against these should be designed. [less ▲] Detailed reference viewed: 40 (2 UL)Model and mesh-burden reduction for multiscale fracture: applications to polycrystals, delamination and surgical simulation Bordas, Stéphane ; ; Hale, Jack et al Presentation (2014, April 23) ABSTRACT We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a ... [more ▼] ABSTRACT We present recent results aiming at affording faster and error-controlled simulations of multi scale phenomena including fracture of heterogeneous materials and cutting of biological tissue. In a second part, we describe methodologies to isolate the user from the burden of mesh generation and regeneration as moving boundaries evolve. Results include advances in implicit boundary finite elements, (enriched) isogeometric extended boundary elements/finite element methods for multi-crack propagation and an asynchronous GPU/CPU method for contact and cutting of heterogeneous materials in real-time with applications to surgical simulation. ABOUT THE PRESENTER In 1999, Stéphane Bordas joined a joint graduate programme of the French Institute of Technology (Ecole Spéciale des Travaux Publics) and the American Northwestern University. In 2003, he graduated in Theoretical and Applied Mechanics with a PhD from Northwestern University. Between 2003 and 2006, he was at the Laboratory of Structural and Continuum Mechanics at the Swiss Federal Institute of Technology in Lausanne, Switzerland. In 2006, he became permanent lecturer at Glasgow University’s Civil Engineering Department. Stéphane joined the Computational Mechanics team at Cardiff University in September 2009, as a Professor in Computational Mechanics and directed the institute of Mechanics and Advanced Materials from October 2010 to November 2013. He is the Editor of the book series “Advances in Applied Mechanics” since July 2013. In November 2013, he joined the University of Luxembourg as a Professor in Computational Mechanics. The main axes of his research team include (1) free boundary problems and problems involving complex geometries, in particular moving boundaries and (2) ‘a posteriori’ discretisation and model error control, rationalisation of the computational expense. Stéphane’s keen interest is to actively participate in innovation, technological transfer as well as software tool generation. This has been done through a number of joint ventures with various industrial partners (Bosch GmbH, Cenaero, inuTech GmbH, Siemens-LMS, Soitec SA) and the release of open-source software. In 2012, Stéphane was awarded an ERC Starting Independent Research Grant (RealTcut), to address the need for surgical simulators with a computational mechanics angle with a focus on the multi-scale simulation of cutting of heterogeneous materials in real-time. [less ▲] Detailed reference viewed: 648 (17 UL)Model and parameter identification through Bayesian inference in solid mechanics Rappel, Hussein Doctoral thesis (2018) Predicting the behaviour of various engineering systems is commonly performed using mathematical models. These mathematical models include application-specific parameters that must be identified from ... [more ▼] Predicting the behaviour of various engineering systems is commonly performed using mathematical models. These mathematical models include application-specific parameters that must be identified from measured data. The identification of model parameters usually comes with uncertainties due to model simplifications and errors in the experimental measurements. Quantifying these uncertainties can effectively improve the predictions as well as the performance of the engineering systems. Bayesian inference provides a probabilistic framework for quantifying these uncertainties in parameter identification problems. In a Bayesian framework, the user's initial knowledge, which is represented by a probability distribution, is updated by measurement data through Bayes' theorem. In the first two chapters of this thesis, Bayesian inference is developed for the identification of material parameters in elastoplasticity and viscoelasticity. The effect of the user's prior knowledge is systematically studied with respect to the number of measurements available. In addition, the influence of different types of experiments on the uncertainty is studied. Since all mathematical models are simplifications of reality, uncertainties of the model itself may also be incorporated. The third chapter of this thesis presents a Bayesian framework for parameter identification in elastoplasticity in which not only the uncertainty of the experimental output is included (i.e. stress measurements), but also the uncertainty of the model and the uncertainty of the experimental input (i.e. strain). Three different formulations for describing the model uncertainty are considered: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. In the fourth chapter of this thesis, a Bayesian scheme is proposed to identify material parameter distributions, instead of material parameters. The application in this chapter are random fibre networks, in which the set of material parameters of each fibre is assumed to be a realisation from a material parameter distribution. The fibres behave either elastoplastically or in a perfectly brittle manner. The goal of the identification scheme is to avoid the experimentally demanding task of testing hundreds of constituents. Instead, only 20 fibres are considered. In addition to their material randomness, the macroscale behaviours of these fibre networks are also governed by their geometrical randomness. Another question aimed to be answered in this chapter is therefore is `how precise the material randomness needs to be identified, if the geometrical randomness will also influence the macroscale behaviour of these discrete networks'. [less ▲] Detailed reference viewed: 189 (32 UL)Model and Solution Methods for the Mixed-Fleet Multi-Terminal Bus Scheduling Problem ; Rinaldi, Marco ; et al in Transportation Research Procedia (2019, September) Detailed reference viewed: 13 (0 UL)Model I cohesive zone models of different rank coals ; Lian, Haojie ; et al in International Journal of Rock Mechanics and Mining Sciences (2019), 115 The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals ... [more ▼] The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals and anthracite, through disk-shaped compact tension tests. Firstly, the experiments show that with the coal rank rising, the critical crack separation displacements and the degrees of the nonlinearity of the softening function decline gradually. By fitting the experimental data with the four commonly used cohesive zone models including the power law, the exponential law, the bilinear law and the linear law, the best-fitted model for each rank of coals was identified and the corresponding parameters were found. Secondly, to arrive at a general CZM formulation for the different rank coals, Karihaloo’s polynomial law was employed, which also gave better fit to the experimental data compared with the aforementioned four CZMs. After obtaining the CZM for coals, fracture energy was evaluated which is equal to the area under the softening curve. With the increase of the coal rank, the fracture energy reduces but its coefficient of variation increases. Thirdly, the geometric characteristics of fractures in different rank coals are studied. The lower rank coals have more tortuous crack propagation paths and larger roughness coefficients, whereas the higher rank coals possess wider average fracture apertures. Lastly, in order to further test the applicability of the obtained cohesion-separation laws, we implemented the Karihaloo’s polynomial CZM and the bilinear CZM into the cohesive elements of ABAQUS® using the user-subroutine VUMAT, and thereby simulated the crack propagation in single-edge notched beams made of weakly caking coals, fat coals, and meager-lean coals, respectively. It is found that the numerical results based on Karihaloo’s polynomial CZM have a better agreement with the experimental data than the bilinear CZM [less ▲] Detailed reference viewed: 22 (0 UL)Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties Ding, Chensen ; ; et al in Computer Methods in Applied Mechanics and Engineering (2019), 349 Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially ... [more ▼] Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially uncorrelated material uncertainties. They are not representative of realistic and practical engineering situations. In particular, it is more serious for composite structures comprised of dissimilar materials. Therefore, we propose a novel model order reduction via proper orthogonal decomposition accelerated Monte Carlo stochastic isogeometric method (IGA-POD-MCS) for stochastic analysis of exactly represented (composite) structures. This approach particularly enables high-dimensional material uncertainties wherein the characteristics of each element are independent. And the novelties include: (1) the structural geometry is exactly modeled thanks to isogeometric analysis (IGA), as well as providing more accurate deterministic and stochastic solutions, (2) we innovatively consider high-dimensional and independent material uncertainties by separating the stochastic mesh from the IGA mesh, and modeling different stochastic elements to have different (independent) uncertainty behaviors, (3) the classical Monte Carlo simulation (MCS) is employed to universally solve the high-dimensional uncertainty problem. However, to circumvent its computational expense, we employ model order reduction via proper orthogonal decomposition (POD) into the IGA coupled MCS stochastic analysis. In particular, we observe that this work decouples all IGA elements and hence permits independent uncertainty models easily, thereby the engineering problem is modeled to be more realistic and authentic. Several illustrative numerical examples verify the proposed IGA-POD-MCS approach is effective and efficient; and the larger the scale of the problem is, the more advantageous the method will become. [less ▲] Detailed reference viewed: 10 (0 UL)Model order reduction applied to ALE‐fluid dynamics Baroli, Davide ; Zilian, Andreas in Proceedings in Applied Mathematics and Mechanics (2019) Detailed reference viewed: 51 (4 UL)A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation ; ; et al in Proceedings of the 17th U.S. National Congress on Theoretical and Applied Mechanics (2014, June 15) Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2 ... [more ▼] Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2]. Indeed, it relies on fewer assumptions than analytical or semi-analytical homogenisation approaches and can be used to coarse-grain a large range of micro-mechanical models. However, this accuracy comes at large computational costs, which prevents computational homogenisation from being used routinely in optimisation, even in the context of linear elastic materials. Indeed, a unit cell problem has to be solved for each microscopic distribution of interest in order to obtain the corresponding homogenised material constants. In the context of nonlinear, time-dependant problem, the computational effort becomes even greater as computational homogenisation requires solving for the time-evolution of the microstructure at every point of the macroscopic domain. In this paper, we propose to address these two issues within the unified framework of projection-based model order reduction (see for instance [3, 4, 5, 6]). The smoothness of the solution of the unit cell problem with respect to parameter or time variations is used to create a reduced order model with very few degrees of freedom, hence reducing the computational burden by orders of magnitude. [1] Tarek J. Zohdi and Peter Wriggers. Introduction to Computational Micromechanics, volume 20 of lecture notes in applied and computational mechanics. Springer, 2005. [2] M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans. Multi-scale computational homogenization: Trends and challenges. J. Computational Applied Mathematics, 234(7):2175–2182, 2010. [3] D.B.P. Huynh G. Rozza and A.T. Patera. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics. Archives of Computational Methods in Engineering, 15(3):229–275, 2008. [4] D. Amsallem and C. Farhat. An Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity. AIAA Journal, 46(7):1803–1813, 2008. [5] P. Kerfriden, P. Gosselet, S. Adhikari, and S.P.-A. Bordas. Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Computer Methods in Applied Mechanics and Engineering, 200(5- 8):850–866, 2011. [6] P. Kerfriden, J.-C. Passieux, and S.P.-A. Bordas. Local/global model order reduction strategy for the simulation of quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 89(2):154–179, 2011. [7] M. Barrault, Y. Maday, N.C. Nguyen, and A.T. Patera. An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de Math´ematiques, 339(9):667–672, 2004. [less ▲] Detailed reference viewed: 321 (6 UL) |
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