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Academic literature on the topic 'Non-attractive set of initial approximations'
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Journal articles on the topic "Non-attractive set of initial approximations"
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Anna, Malinova Angel Golev Anton Iliev* Nikolay Kyurkchiev. "SOME NOTES ON THE FAST ADAPTIVE NEURAL NETWORK SOLVERS." Global Journal of Engineering Science and Research Management 4, no. 10 (2017): 121–31. https://doi.org/10.5281/zenodo.1034497.
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With this paper, we discuss some important aspects related to the iterative solution of two classes of polynomials, nonlinear systems of equations, and the adapted to them – "FAST adaptive neural solver" (FANS). The crucial issue of choosing initial approximations (separation of unattractive networks of initial data) and the possibility of minimizing CPU–time with the use of existing FANS is discussed.
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Pelekh, Ya M., A. V. Kunynets, and R. Ya Pelekh. "TWO-SIDED METHODS FOR SOLVING INITIAL VALUE PROBLEM FOR NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS." Journal of Numerical and Applied Mathematics, no. 2 (2022): 116–21. http://dx.doi.org/10.17721/2706-9699.2022.2.13.
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Using the continued fractions and the method of constructing Runge-Kutta methods, numerical methods for solving the Cauchy problem for nonlinear Volterra non-linear integrodifferential equations are proposed. With appropriate values of the parameters, one can obtain an approximation to the exact solution of the first and second order of accuracy. We found a set of parameters for which we obtain two-sided calculation formulas, which at each step of integration allow to obtain the upper and lower approximations of the exact solution.
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Wang, Jinghua, and Hui Zhang. "Existence and decay rates of smooth solutions for a non-uniformly parabolic equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 6 (2002): 1477–91. http://dx.doi.org/10.1017/s0308210500002213.
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We obtain the existence and decay rates of the classical solution to the initial-value problem of a non-uniformly parabolic equation. Our method is to set up two equivalent sequences of the successive approximations. One converges to a weak solution of the initial-value problem; the other shows that the weak solution is the classical solution for t > 0. Moreover, we show how bounds of the derivatives to the classical solution depend explicitly on the interval with compact support in (0, ∞). Then we study decay rates of this classical solution.
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Hayes, Brian, and Michael Shearer. "Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 4 (1999): 733–54. http://dx.doi.org/10.1017/s0308210500013111.
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The Riemann initial value problem is studied for scalar conservation laws whose fluxes have a single inflection point. For a regularization consisting of balanced diffusive and dispersive terms, the travelling wave criterion is used to select admissible shocks. In some cases, the Riemann problem solution contains an undercompressive shock. The analysis is illustrated by exploring parameter space for the Buckley–Leverett flux. The boundary of the set of parameters for which there is a physical solution of the Riemann problem for all data is computed. Within the region of acceptable parameters, the solution hasseveral different forms, depending on the initial data; the different forms are illustrated by numerical computations. Qualitatively similar behaviour is observed in Lax–Wendroff approximations of solutions of the Buckley–Leverett equation with no dissipation or dispersion.
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Guseva, S. R., and D. N. Ibragimov. "A priori estimation of the minimal stabilization time for linear discrete-time systems with bounded control based on the apparatus of eigensets." Modelling and Data Analysis 15, no. 1 (2025): 110–32. https://doi.org/10.17759/mda.2025150106.
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<p>A linear system with discrete time and bounded control is considered. It is assumed that the system matrix is non-singular and diagonalizable, and the set of admissible control values is convex and compact. For a given system, the time-optimization problem is studied. In particular, it is required to construct a priori estimates of the optimal value of the minimal time as a function of the initial state and system parameters that do not require an exact construction of the class of null-controllable sets. To solve the problem, an apparatus of eigensets of a linear transformation is developed, and basic properties of non-trivial eigensets are formulated and proven. For the simplest case, when the set of admissible control values is a non-trivial eigenset of the system matrix, the response time function for a given initial state is constructed explicitly. For an arbitrary control system, a method is proposed for reducing to the simplest case by constructing internal and external approximations of a set of constraints on control values. Numerical calculations are presented demonstrating the efficiency and accuracy of the developed technique.</p>
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Trębicki, Grzegorz. "Merits of Fantastic Literature: A Proposal for Theoretical Framework." Literatura i Kultura Popularna 28 (October 6, 2022): 107–16. http://dx.doi.org/10.19195/0867-7441.28.8.
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The paper attempts to set ground for a comprehensive debate on the merits of non-mimetic (fantastic) literature, tentatively proposing a system of four basic merits — the entertaining/fabulative, the emotional-cognitive, the speculative/extrapolative, and the aesthetic. These merits can also be alternatively viewed as narrative functions, precisely defined presuppositions, agreements between the implied reader and writer as to what literary gratifications are to be expected by the reader from the reading experience. They constitute structural dominants which are well manifested in the texts themselves. The author’s proposals should be read merely as certain initial approximations, albeit hopefully useful ones, capable of inspiring further debate.
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Shevchenko, I. I. "Using sequential particle methods and non-parametric distributions in bayesian evaluations of abundance and catch at age time series." Problems of Fisheries 24, no. 1 (2023): 99–116. http://dx.doi.org/10.36038/0234-2774-2023-24-1-99-116.
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We describe an approach to analyzing time series for two variables connected through the state model with abundance and catch data sets and cohort and catch equations as an example. First, we create a deterministic model with parameters that maximizes the closeness of given data and data generated by a model. Then, we obtain cohort stochastic models using the difference between initial and modeled data. They are represented as hidden Bayesian models with abundances as states and catches as observations. Using these models, one can evaluate posterior densities and calculate averages, deviations, etc. As a general matter, the recursive equations met by posterior densities have no analytic solutions. We describe several particle methods that may be used for density approximations and following calculations of their statistical quantities. All generated sample densities are smoothed with non-parametric kernel density estimation. The Fishmetica package was extended with functions for generating samples and weights for filtering, predicting and smoothing densities. Numerical simulations were conducted for a test data set. Several extensions of the approach are proposed including an additional option for comparing the basic models with the use of a likelihood function.
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Almgren, A., R. Camassa, and R. Tiron. "Shear instability of internal solitary waves in Euler fluids with thin pycnoclines." Journal of Fluid Mechanics 710 (August 29, 2012): 324–61. http://dx.doi.org/10.1017/jfm.2012.366.
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AbstractThe stability with respect to initial condition perturbations of solitary travelling-wave solutions of the Euler equations for continuously, stably stratified, near two-layer fluids is examined numerically and analytically for a set of parameters of relevance for laboratory experiments. Numerical travelling-wave solutions of the Dubreil–Jacotin–Long equation are first obtained with a variant of Turkington, Eyland and Wang’s iterative code by testing convergence on the equation’s residual. In this way, stationary solutions with very thin pycnoclines (and small Richardson numbers) approaching the near two-layer configurations used in experiments can be obtained, allowing for a stability study free of non-stationary effects, introduced by lack of numerical resolution, which develop when these solutions are used as initial conditions in a time-dependent evolution code. The thin pycnoclines in this study permit analytical results to be derived from strongly nonlinear models and their predictions compared with carefully controlled numerical simulations. This brings forth shortcomings of simple criteria for shear instability manifestations based on parallel shear approximations due to subtle higher-order effects. In particular, evidence is provided that the fore–aft asymmetric growth observed in all simulations requires non-parallel shear analysis. Collectively, the results of this study reveal that while the wave-induced shear can locally reach unstable configurations and give rise to local convective instability, the global wave/self-generated shear system is in fact stable, even for extreme cases of thin pycnoclines and near-maximum-amplitude waves.
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Verykokou, Styliani, and Charalabos Ioannidis. "EXTERIOR ORIENTATION ESTIMATION OF OBLIQUE AERIAL IMAGERY USING VANISHING POINTS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B3 (June 9, 2016): 123–30. http://dx.doi.org/10.5194/isprs-archives-xli-b3-123-2016.
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In this paper, a methodology for the calculation of rough exterior orientation (EO) parameters of multiple large-scale overlapping oblique aerial images, in the case that GPS/INS information is not available (e.g., for old datasets), is presented. It consists of five main steps; (a) the determination of the overlapping image pairs and the single image in which four ground control points have to be measured; (b) the computation of the transformation parameters from every image to the coordinate reference system; (c) the rough estimation of the camera interior orientation parameters; (d) the estimation of the true horizon line and the nadir point of each image; (e) the calculation of the rough EO parameters of each image. A developed software suite implementing the proposed methodology is tested using a set of UAV multi-perspective oblique aerial images. Several tests are performed for the assessment of the errors and show that the estimated EO parameters can be used either as initial approximations for a bundle adjustment procedure or as rough georeferencing information for several applications, like 3D modelling, even by non-photogrammetrists, because of the minimal user intervention needed. Finally, comparisons with a commercial software are made, in terms of automation and correctness of the computed EO parameters.
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Verykokou, Styliani, and Charalabos Ioannidis. "EXTERIOR ORIENTATION ESTIMATION OF OBLIQUE AERIAL IMAGERY USING VANISHING POINTS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B3 (June 9, 2016): 123–30. http://dx.doi.org/10.5194/isprsarchives-xli-b3-123-2016.
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In this paper, a methodology for the calculation of rough exterior orientation (EO) parameters of multiple large-scale overlapping oblique aerial images, in the case that GPS/INS information is not available (e.g., for old datasets), is presented. It consists of five main steps; (a) the determination of the overlapping image pairs and the single image in which four ground control points have to be measured; (b) the computation of the transformation parameters from every image to the coordinate reference system; (c) the rough estimation of the camera interior orientation parameters; (d) the estimation of the true horizon line and the nadir point of each image; (e) the calculation of the rough EO parameters of each image. A developed software suite implementing the proposed methodology is tested using a set of UAV multi-perspective oblique aerial images. Several tests are performed for the assessment of the errors and show that the estimated EO parameters can be used either as initial approximations for a bundle adjustment procedure or as rough georeferencing information for several applications, like 3D modelling, even by non-photogrammetrists, because of the minimal user intervention needed. Finally, comparisons with a commercial software are made, in terms of automation and correctness of the computed EO parameters.
Conference papers on the topic "Non-attractive set of initial approximations"
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Grigore, Ionel, Cristina Miron, and Daniela Stoica. "THE STUDY OF THE SIMPLE GRAVITATIONAL PENDULUM WITH EXCEL SPREADSHEETS." In eLSE 2018. ADL Romania, 2018. http://dx.doi.org/10.12753/2066-026x-18-058.
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This paper presents a didactic tool designed with the help of Excel spreadsheets for the study of the simple gravitational pendulum in oscillation regime. The period of the pendulum is calculated for a certain value of the initial angular amplitude and it is compared with the zero, one and two-order approximations from the expansion series of the period. Moreover, the velocity and tension force of the thread are calculated according to the angular displacement from the input data. It is shown how the complete elliptic integral of the first kind can be evaluated in the spreadsheet, through the numerical algorithm of the trapezium, from the formula of the oscillation period. The tool charts are placed in the same spreadsheet with the input data and the numeric results to rapidly trace the graphical feedback to data change. The oscillation period was graphically rendered based on the initial angular amplitude and the value of the period for the amplitude fixed in the input data has been highlighted on the graph. Another graph overlaps the period-initial angular amplitude one with the graphs of zero and one-order approximations of the period. The other graph shows, at a set value of the amplitude in the input data, the pendulum velocity and the tension force of the thread according to the initial angular displacement. In the tension force-angle graph, the weight force is highlighted and also the maximum range of values for the tension force is highlighted according to the initial angular amplitude. With the help of this graph, it can be observed that, at small oscillations, the tension in the thread varies slowly with the angular displacement around certain values close to the value of the weight force. This justifies the approximations made when establishing the calculation formula for the period of small oscillations. It is thus demonstrated that the spreadsheet allows to both solve the non-linear equation of the simple pendulum and to graphically analyze some measures characteristic for the oscillatory motion. By using the tool in the classroom, students can simulate the simple pendulum oscillatory motion at any value of the initial angular amplitude and can more easily clarify under which conditions the oscillations of the pendulum can be considered as isocrone.
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Zou, Rui, and Sourabh Bhattacharya. "Approximation of Capture Sets in Visibility-Based Target-Tracking Games for Non-Holonomic Players." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5379.
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In this work, we analyze approximations of capture sets [1] for a visibility based pursuit-evasion game. In contrast to the capture problem, the pursuer tries to maintain a line-of-sight with the evader in free space in our problem. We extend the concept of U set initially proposed in [2] for holonomic players to the scenario in which the pursuer is holonomic. The problem of computing the U set is reduced to that of computing time-optimal paths for the non-holonomic vehicles to an arbitrary line. We characterize the primitives for time-optimal paths for the Dubin’s vehicle, Reed-shepps car and a Differential Drive robot. Based on these primitives, we construct the optimal paths and provide an algorithm to compute the U set.
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Buryachenko, Valeriy A. "Method of Fundamental Solution in Thermoelasticity of Random Structure Matrix Composites." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86515.
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One considers linear thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non-canonical (i.e. non-ellipsoidal) shape. The representations of the effective properties (effective moduli, thermal expansion, and stored energy) are expressed through the statistical averages of the interface polarization tensors (generalizing the initial concepts, see e.g. [1] and [2]) introduced apparently for the first time. The new general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities. The method is based on a recently developed centering procedure where the notion of a perturbator is introduced in terms of boundary interface integrals estimated by the method of fundamental solution for a single inclusion inside the infinite matrix. This enables one to reconsider basic concepts of micromechanics such as effective field hypothesis, quasi-crystalline approximation, and the hypothesis of ellipsoidal symmetry. The results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of non canonical shape. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.
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Gao, Guohua, Jeroen Vink, Fredrik Saaf, and Terence Wells. "Strategies to Enhance the Performance of Gaussian Mixture Model Fitting for Uncertainty Quantification by Conditioning to Production Data." In SPE Reservoir Simulation Conference. SPE, 2021. http://dx.doi.org/10.2118/204008-ms.
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Abstract When formulating history matching within the Bayesian framework, we may quantify the uncertainty of model parameters and production forecasts using conditional realizations sampled from the posterior probability density function (PDF). It is quite challenging to sample such a posterior PDF. Some methods e.g., Markov chain Monte Carlo (MCMC), are very expensive (e.g., MCMC) while others are cheaper but may generate biased samples. In this paper, we propose an unconstrained Gaussian Mixture Model (GMM) fitting method to approximate the posterior PDF and investigate new strategies to further enhance its performance. To reduce the CPU time of handling bound constraints, we reformulate the GMM fitting formulation such that an unconstrained optimization algorithm can be applied to find the optimal solution of unknown GMM parameters. To obtain a sufficiently accurate GMM approximation with the lowest number of Gaussian components, we generate random initial guesses, remove components with very small or very large mixture weights after each GMM fitting iteration and prevent their reappearance using a dedicated filter. To prevent overfitting, we only add a new Gaussian component if the quality of the GMM approximation on a (large) set of blind-test data sufficiently improves. The unconstrained GMM fitting method with the new strategies proposed in this paper is validated using nonlinear toy problems and then applied to a synthetic history matching example. It can construct a GMM approximation of the posterior PDF that is comparable to the MCMC method, and it is significantly more efficient than the constrained GMM fitting formulation, e.g., reducing the CPU time by a factor of 800 to 7300 for problems we tested, which makes it quite attractive for large scale history matching problems.
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Kamboukos, Philippos, and Kostas Mathioudakis. "Multipoint Non-Linear Method for Enhanced Component and Sensor Malfunction Diagnosis." In ASME Turbo Expo 2006: Power for Land, Sea, and Air. ASMEDC, 2006. http://dx.doi.org/10.1115/gt2006-90451.
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Operating gas turbine engines are usually equipped with a limited number of sensors. This situation is the common issue of gas turbine diagnostics where the absence of sufficient measurements from the engine gas path reduces the effectiveness of the applied methods. In addition the installed sensors of the engine deteriorate with time or present abrupt malfunctions which are not always detectable. One way to overcome this problem is the exploitation of information from a number of different operating points by constructing a multipoint diagnostic procedure. Information from different operating points is combined in order to increase the number of measurements and thus to form a well determined diagnostic system for the estimation of engine component health parameters. The paper presents the extension of the method in order to be able to assess both engine and sensors state. Initially the ability of the method to estimate the condition of a high bypass turbofan engine, exploiting information from different instances of its flight envelop is depicted. The problem of selecting the appropriate operating points is analyzed on the basis of the numerical condition of the formed diagnostic system. The method is also applied to a single shaft turbojet, for estimation of engine component health parameters and sensors state. Finally a number of aspects related to the formulation of the method are examined. These are the comparison between full method and its linear approximation, the effect of measurement noise on the derived estimation and the computational cost.
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Lindberg, Ole, Harry B. Bingham, and Allan Peter Engsig Karup. "A Coupled Finite Difference and Weighted Least Squares Simulation of Violent Breaking Wave Impact." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83823.
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Two model for simulation of free surface flow are presented. The first model is a finite difference based potential flow model with non-linear kinematic and dynamic free surface boundary conditions. The second model is a weighted least squares based incompressible and inviscid flow model. A special feature of this model is a generalized finite point set method which is applied to the solution of the Poisson equation on an unstructured point distribution. The presented finite point set method is generalized to arbitrary order of approximation. The two models are applied to simulation of steep and overturning wave impacts on a vertical breakwater. Wave groups with five different wave heights are propagated from offshore to the vicinity of the breakwater, where the waves are steep, but still smooth and non-overturning. These waves are used as initial condition for the weighted least squares based incompressible and inviscid model and the wave impacts on the vertical breakwater are simulated in this model. The resulting maximum pressures and forces on the breakwater are relatively high when compared with other studies and this is due to the incompressible nature of the present model.
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Zhong, Liang, Changgang Lu, and Jian Wu. "Spatio-Temporal Trajectory Planning Using Search And Optimizing Method for Autonomous Driving." In WCX SAE World Congress Experience. SAE International, 2024. http://dx.doi.org/10.4271/2024-01-2563.
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<div class="section abstract"><div class="htmlview paragraph">In the field of autonomous driving trajectory planning, it’s virtual to ensure real-time planning while guaranteeing feasibility and robustness. Current widely adopted approaches include decoupling path planning and velocity planning based on optimization method, which can’t always yield optimal solutions, especially in complex dynamic scenarios. Furthermore, search-based and sampling-based solutions encounter limitations due to their low resolution and high computational costs. This paper presents a novel spatio-temporal trajectory planning approach that integrates both search-based planning and optimization-based planning method. This approach retains the advantages of search-based method, allowing for the identification of a global optimal solution through search. To address the challenge posed by the non-convex nature of the original solution space, we introduce a spatio-temporal semantic corridor structure, which constructs a convex feasible set for the problem. Trajectory optimization is then performed through numerical optimization methods, resulting in real-time and robust spatio-temporal trajectory planning. The proposed approach initiates by constructing a 3D spatio- temporal map that incorporates information such as dynamic obstacles. Improved A* algorithm is used to search for a preliminary spatio- temporal trajectory, serving as an initial approximation for the trajectory. Based on this initial approximation, a spatio-temporal corridor is constructed as locally convex feasible driving area, then a quintic monomial polynomial is employed to represent a trajectory, considering vehicle kinematics, continuity, and other constraints, this formulation transforms the problem into a general quadratic programming problem. Ultimately, the generated trajectories are rigorously tested through simulations in scenarios involving overtaking and side car cut-in. The results indicate that the generated trajectories are feasible, reasonable, and exhibit good real-time performance<b>.</b></div></div>
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Colac¸o, Marcelo J., Helcio R. B. Orlande, Wellington B. da Silva, and George S. Dulikravich. "Application of a Bayesian Filter to Estimate Unknown Heat Fluxes in a Natural Convection Problem." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47652.
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Sequential Monte Carlo (SMC) or Particle Filter Methods, which have been originally introduced in the beginning of the 50’s, became very popular in the last few years in the statistical and engineering communities. Such methods have been widely used to deal with sequential Bayesian inference problems in fields like economics, signal processing, and robotics, among others. SMC Methods are an approximation of sequences of probability distributions of interest, using a large set of random samples, named particles. These particles are propagated along time with a simple Sampling Importance distribution. Two advantages of this method are: they do not require the restrictive hypotheses of the Kalman filter, and can be applied to nonlinear models with non-Gaussian errors. This papers uses a SMC filter, namely the ASIR (Auxiliary Sampling Importance Resampling Filter) to estimate a heat flux in the wall of a square cavity undergoing a natural convection. Measurements, which contain errors, taken at the boundaries of the cavity are used in the estimation process. The mathematical model, as well as the initial condition, are supposed to have some error, which are taken into account in the probabilistic evolution model used for the filter.
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Melli, Roberto, Enrico Sciubba, Claudia Toro, and Alessandro Zoli-Porroni. "An Example of Thermo-Economic Optimization of a CCGT by Means of the Proper Orthogonal Decomposition Method." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87317.
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This paper presents an application of the Proper Orthogonal Decomposition (POD) technique (also called Karhunen-Loève Decomposition, Principal Component Analysis, or Singular Value Decomposition) to the thermo-economic optimization of a realistic Combined-Cycle Gas Turbine (CCGT) process. The novel inverse-design approach proposed here employs the thermo-economic cost of the two products as objective function. The proposed procedure does not require the generation of a complete simulated set of results at each iteration step of the optimization, because POD constructs a very accurate approximation to the function described by a certain number of initial simulations, and thus “new” points in design space can be extrapolated without recurring to repeated process simulations. Thus, the often taxing computational effort needed to iteratively generate numerical process simulations of incrementally different configurations is substantially reduced by replacing much of it by easy-to-perform matrix operations: a non-negligible but quite small number N of initial process simulations is used to calculate the basis of the POD interpolation and to validate (i.e., extend) the results. Since the accuracy of a POD expansion depends of course on the number N of initial simulations (the “snapshots”), the computational intensity of the method is certainly not negligible: but, as successfully demonstrated in the paper for a realistic CCGT inverse process design problem, the idea that additional full simulations are performed only in the “right direction” indicated by the gradient of the objective function in the solution space leads to a successful strategy at a substantially reduced computational intensity. This “economy” with respect to other classical “optimization” methods is basically due to the capability of the POD procedure to identify the most important “modes” in the functional expansion of the vector basis consisting of a subset of the design parameters used in the evaluation of the objective function.
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Tsai, Ying-Kuan, and Richard J. Malak. "Control Co-Design With Approximate Explicit Model Predictive Controllers." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-109551.
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Abstract This paper presents a novel methodology for control co-design (CCD) with approximate explicit model predictive controllers. This paper also investigates how approximation errors impact the decision-making for design of dynamic systems. The explicit nonlinear control policies are approximated and represented as surrogate models by a function of states and plant parameters, which allows for offline solving control problems and reducing the computational time required for CCD optimization. Set invariance theory and Lyapunov stability theory are employed to ensure the stability of designed systems. To facilitate design exploration, a multi-objective optimization problem is formulated to trade-off between performance and probability of state-constraint satisfaction. A probability assessment for system stability with the sampled initial states and multiple pre-computed controllers is included in the optimization constraints. The approach is benchmarked using a numerical example and an engineering case study of a satellite attitude control system. Some of the non-dominated designs are selected to visualize their state and control trajectories for comparison. The visualization shows the successful implementation of explicit model predictive controllers in CCD problems while ensuring stability. The results of this study highlight the importance of including plant design and performing CCD to achieve system-optimal solutions and better understand dynamic characteristics.