Relevant bibliographies by topics / Stochastic Differential Inclusions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Stochastic Differential Inclusions'

Author: Grafiati
Published: 23 November 2024
Last updated: 7 July 2025

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Journal articles on the topic "Stochastic Differential Inclusions"

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Benaïm, Michel, Josef Hofbauer, and Sylvain Sorin. "Stochastic Approximations and Differential Inclusions." SIAM Journal on Control and Optimization 44, no. 1 (2005): 328–48. http://dx.doi.org/10.1137/s0363012904439301.

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Ekhaguere, G. O. S. "Lipschitzian quantum stochastic differential inclusions." International Journal of Theoretical Physics 31, no. 11 (1992): 2003–27. http://dx.doi.org/10.1007/bf00671969.

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Michta, Mariusz, and Kamil Łukasz Świa̧tek. "Stochastic inclusions and set-valued stochastic equations driven by a two-parameter Wiener process." Stochastics and Dynamics 18, no. 06 (2018): 1850047. http://dx.doi.org/10.1142/s0219493718500478.

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In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.
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Perkins, Steven, and David S. Leslie. "Asynchronous Stochastic Approximation with Differential Inclusions." Stochastic Systems 2, no. 2 (2012): 409–46. http://dx.doi.org/10.1287/11-ssy056.

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Michta, Mariusz. "Optimal solutions to stochastic differential inclusions." Applicationes Mathematicae 29, no. 4 (2002): 387–98. http://dx.doi.org/10.4064/am29-4-2.

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Kisielewicz, Michał. "Stochastic differential inclusions and diffusion processes." Journal of Mathematical Analysis and Applications 334, no. 2 (2007): 1039–54. http://dx.doi.org/10.1016/j.jmaa.2007.01.027.

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Kisielewicz, Michał. "Stochastic representation of partial differential inclusions." Journal of Mathematical Analysis and Applications 353, no. 2 (2009): 592–606. http://dx.doi.org/10.1016/j.jmaa.2008.12.022.

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Malinowski, Marek T., and Mariusz Michta. "The interrelation between stochastic differential inclusions and set-valued stochastic differential equations." Journal of Mathematical Analysis and Applications 408, no. 2 (2013): 733–43. http://dx.doi.org/10.1016/j.jmaa.2013.06.055.

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Papageorgiou, Nikolaos S. "Random fixed points and random differential inclusions." International Journal of Mathematics and Mathematical Sciences 11, no. 3 (1988): 551–59. http://dx.doi.org/10.1155/s0161171288000663.

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In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder-Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.
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Chaouche, Meryem, and Toufik Guendouzi. "Stochastic differential inclusions with Hilfer fractional derivative." Annals of the University of Craiova, Mathematics and Computer Science Series 49, no. 1 (2022): 158–73. http://dx.doi.org/10.52846/ami.v49i1.1524.

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In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
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Dissertations / Theses on the topic "Stochastic Differential Inclusions"

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Chen, Xiaoli. "Stochastic differential inclusions." Thesis, University of Edinburgh, 2006. http://hdl.handle.net/1842/13367.

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Stochastic differential inclusions (SDIs) on <i>R<sup>d </sup></i>have been investigated in this thesis, <i>dx</i>(<i>t</i>) Î <i>a</i>(<i>t, x(t)</i>)<i>dt </i>+   (<i>t, x (t)d</i> where <i>a</i> is a maximal monotone mapping, <i>b</i> is a Lipschitz continuous function, and <i>w</i> is a Wiener process. The principal aim of this work is to present some new results on solvability and approximations of SDIs. Two methods are adapted to obtain our results: the method of minimization and the method of implicit approximation. We interpret the method of monotonicity as a method of constructing minimizers to certain convex functions. Under the monotonicity condition and the usual linear growth condition, the solutions are characterized as the minimizers of convex functionals, and are constructed via implicit approximations. Implicit numerical scheme is given and the result on the rate of convergence is also presented. The ideas of our work are inspired by N.V. Krylov, where stochastic differential equations (SDEs0 in <i>R<sup>d</sup></i> are solved by minimizing convex functions via Euler approximations. Furthermore, since the linear growth condition is too strong, an approach is proposed for truncating maximal monotone functions to get bounded maximal monotone functions. It is a technical challenge in this thesis. Thus the existence of solutions to SDIs is proved under essentially weaker growth condition than the linear growth. For a special case of SDEs, a few of recent results from [5] are generalized. Some existing results of the convergence by implicit numerical schemes are proved under the locally Lipschitz condition. We will show that under certain weaker conditions, if the drift coefficient satisfies one-sided Lipschitz and the diffusion coefficient is Lipschitz continuous, implicit approximations applied to SDEs, converge almost surely to the solution of SDEs. The rate of convergence we get is ¼.
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Bauwe, Anne, and Wilfried Grecksch. "Finite dimensional stochastic differential inclusions." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800515.

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This paper offers an existence result for finite dimensional stochastic differential inclusions with maximal monotone drift and diffusion terms. Kravets studied only set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions in an infinite dimensional context. In the proof we make use of the Yosida approximation of maximal monotone operators to achieve stochastic differential equations which are solvable by a theorem of Krylov and Rozovskij [7]. The selection property is verified with certain properties of the considered set-valued maps. Concerning Lipschitz continuous set-valued diffusion terms, uniqueness holds. At last two examples for application are given.
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Bauwe, Anne, and Wilfried Grecksch. "A parabolic stochastic differential inclusion." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501221.

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Stochastic differential inclusions can be considered as a generalisation of stochastic differential equations. In particular a multivalued mapping describes the set of equations, in which a solution has to be found. This paper presents an existence result for a special parabolic stochastic inclusion. The proof is based on the method of upper and lower solutions. In the deterministic case this method was effectively introduced by S. Carl.
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Maulen, Soto Rodrigo. "A dynamical system perspective οn stοchastic and iΙnertial methοds fοr optimizatiοn". Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMC220.

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Motivé par l'omniprésence de l'optimisation dans de nombreux domaines de la science et de l'ingénierie, en particulier dans la science des données, ce manuscrit de thèse exploite le lien étroit entre les systèmes dynamiques dissipatifs à temps continu et les algorithmes d'optimisation pour fournir une analyse systématique du comportement global et local de plusieurs systèmes du premier et du second ordre, en se concentrant sur le cadre convexe, stochastique et en dimension infinie d'une part, et le cadre non convexe, déterministe et en dimension finie d'autre part. Pour les problèmes de minimisation convexe stochastique dans des espaces de Hilbert réels séparables de dimension infinie, notre proposition clé est de les analyser à travers le prisme des équations différentielles stochastiques (EDS) et des inclusions différentielles stochastiques (IDS), ainsi que de leurs variantes inertielles. Nous considérons d'abord les problèmes convexes différentiables lisses et les EDS du premier ordre, en démontrant une convergence faible presque sûre vers les minimiseurs sous hypothèse d'intégrabilité du bruit et en fournissant une analyse globale et locale complète de la complexité. Nous étudions également des problèmes convexes non lisses composites utilisant des IDS du premier ordre et montrons que, sous des conditions d'intégrabilité du bruit, la convergence faible presque sûre des trajectoires vers les minimiseurs, et avec la régularisation de Tikhonov la convergence forte presque sûre des trajectoires vers la solution de norme minimale. Nous développons ensuite un cadre mathématique unifié pour analyser la dynamique inertielle stochastique du second ordre via la reparamétrisation temporelle et le moyennage de la dynamique stochastique du premier ordre, ce qui permet d'obtenir une convergence faible presque sûre des trajectoires vers les minimiseurs et une convergence rapide des valeurs et des gradients. Ces résultats sont étendus à des EDS plus générales du second ordre avec un amortissement visqueux et Hessien, en utilisant une analyse de Lyapunov spécifique pour prouver la convergence et établir de nouveaux taux de convergence. Enfin, nous étudions des problèmes d'optimisation déterministes non convexes et proposons plusieurs algorithmes inertiels pour les résoudre, dérivés d'équations différentielles ordinaires (EDO) du second ordre combinant à la fois un amortissement visqueux sans vanité et un amortissement géométrique piloté par le Hessien, sous des formes explicites et implicites. Nous prouvons d'abord la convergence des trajectoires en temps continu des EDO vers un point critique pour des objectives vérifiant la propriété de Kurdyka-Lojasiewicz (KL) avec des taux explicites, et génériquement vers un minimum local si l'objective est Morse. De plus, nous proposons des schémas algorithmiques par une discrétisation appropriée de ces EDO et montrons que toutes les propriétés précédentes des trajectoires en temps continu sont toujours valables dans le cadre discret sous réserve d'un choix approprié de la taille du pas<br>Motivated by the ubiquity of optimization in many areas of science and engineering, particularly in data science, this thesis exploits the close link between continuous-time dissipative dynamical systems and optimization algorithms to provide a systematic analysis of the global and local behavior of several first- and second-order systems, focusing on convex, stochastic, and infinite-dimensional settings on the one hand, and non-convex, deterministic, and finite-dimensional settings on the other hand. For stochastic convex minimization problems in infinite-dimensional separable real Hilbert spaces, our key proposal is to analyze them through the lens of stochastic differential equations (SDEs) and inclusions (SDIs), as well as their inertial variants. We first consider smooth differentiable convex problems and first-order SDEs, demonstrating almost sure weak convergence towards minimizers under integrability of the noise and providing a comprehensive global and local complexity analysis. We also study composite non-smooth convex problems using first-order SDIs, and show under integrability conditions on the noise, almost sure weak convergence of the trajectory towards a minimizer, with Tikhonov regularization almost sure strong convergence of trajectory to the minimal norm solution. We then turn to developing a unified mathematical framework for analyzing second-order stochastic inertial dynamics via time scaling and averaging of stochastic first-order dynamics, achieving almost sure weak convergence of trajectories towards minimizers and fast convergence of values and gradients. These results are extended to more general second-order SDEs with viscous and Hessian-driven damping, utilizing a dedicated Lyapunov analysis to prove convergence and establish new convergence rates. Finally, we study deterministic non-convex optimization problems and propose several inertial algorithms to solve them derived from second-order ordinary differential equations (ODEs) combining both non-vanishing viscous damping and geometric Hessian-driven damping in explicit and implicit forms. We first prove convergence of the continuous-time trajectories of the ODEs to a critical point under the Kurdyka-Lojasiewicz (KL) property with explicit rates, and generically to a local minimum under a Morse condition. Moreover, we propose algorithmic schemes by appropriate discretization of these ODEs and show that all previous properties of the continuous-time trajectories still hold in the discrete setting under a proper choice of the stepsize
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Books on the topic "Stochastic Differential Inclusions"

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Kisielewicz, Michał. Stochastic Differential Inclusions and Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6756-4.

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Kisielewicz, Michal. Stochastic Differential Inclusions and Applications. Springer, 2013.

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Kisielewicz, Micha. Stochastic Differential Inclusions and Applications. Springer New York, 2015.

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Kisielewicz, Michał. Stochastic Differential Inclusions and Applications. Springer London, Limited, 2013.

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Stochastic Differential Inclusions And Applications. Springer-Verlag New York Inc., 2013.

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Book chapters on the topic "Stochastic Differential Inclusions"

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Kisielewicz, Michał. "Stochastic Differential Inclusions." In Springer Optimization and Its Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6756-4_4.

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Kisielewicz, Michał. "Stochastic Differential Inclusions." In Set-Valued Stochastic Integrals and Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40329-4_6.

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Dikko, Dauda Alani. "On Some Properties of Solution Sets of Discontinuous Quantum Stochastic Differential Inclusions." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-06170-7_15.

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Atangana, Abdon, and Seda İgret Araz. "Modeling the Spread of Covid-19 with a "Equation missing" Approach: Inclusion of Unreported Infected Class." In Fractional Stochastic Differential Equations. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0729-6_8.

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Ahmed, N. U. "Optimal Relaxed Controls for Nonlinear Infinite Dimensional Stochastic Differential Inclusions." In Optimal control of differential equations. CRC Press, 2020. http://dx.doi.org/10.1201/9781003072225-1.

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"Existence of solutions of nonlinear stochastic differential inclusions on Banach space." In World Congress of Nonlinear Analysts '92. De Gruyter, 1996. http://dx.doi.org/10.1515/9783110883237.1699.

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Epstein, Irving R., and John A. Pojman. "Delays and Differential Delay Equations." In An Introduction to Nonlinear Chemical Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195096705.003.0016.

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Mathematically speaking, the most important tools used by the chemical kineticist to study chemical reactions like the ones we have been considering are sets of coupled, first-order, ordinary differential equations that describe the changes in time of the concentrations of species in the system, that is, the rate laws derived from the Law of Mass Action. In order to obtain equations of this type, one must make a number of key assumptions, some of which are usually explicit, others more hidden. We have treated only isothermal systems, thereby obtaining polynomial rate laws instead of the transcendental expressions that would result if the temperature were taken as a variable, a step that would be necessary if we were to consider thermochemical oscillators (Gray and Scott, 1990), for example, combustion reactions at metal surfaces. What is perhaps less obvious is that our equations constitute an average over quantum mechanical microstates, allowing us to employ a relatively small number of bulk concentrations as our dependent variables, rather than having to keep track of the populations of different states that react at different rates. Our treatment ignores fluctuations, so that we may utilize deterministic equations rather than a stochastic or a master equation formulation (Gardiner, 1990). Whenever we employ ordinary differential equations, we are making the approximation that the medium is well mixed, with all species uniformly distributed; any spatial gradients (and we see in several other chapters that these can play a key role) require the inclusion of diffusion terms and the use of partial differential equations. All of these assumptions or approximations are well known, and in all cases chemists have more elaborate techniques at their disposal for treating these effects more exactly, should that be desirable. Another, less widely appreciated idealization in chemical kinetics is that phenomena take place instantaneously—that a change in [A] at time t generates a change in [B] time t and not at some later time t + τ. On a microscopic level, it is clear that this state of affairs cannot hold.
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Conference papers on the topic "Stochastic Differential Inclusions"

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Brenna, Andrea, Luciano Lazzari, and Marco Ormellese. "Probabilistic Model Based on Markov Chain for the Assessment of Localized Corrosion of Stainless Steels." In CORROSION 2014. NACE International, 2014. https://doi.org/10.5006/c2014-4091.

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Abstract Pitting, crevice and stress corrosion cracking are the most damaging corrosion forms of stainless steels in industrial applications. Generally, pitting and crevice susceptibility depends on a variety of factors related to the metal (chemical composition, differences in the metallurgical structure, inclusions), the environment (chloride content, pH, temperature, differential aeration) and the geometry of the system. Due to their unpredictable occurrence, localized corrosion events cannot be explained without using a proper statistical method. In this work a probabilistic approach based on Markov chains for the assessment of pitting and crevice corrosion initiation is proposed. A Markov chain is a stochastic process that undergoes transitions from one state to another through a finite number of possible states, until a so-called "absorbing state” from which the system has no tendency to evolve is attained. Formally, a Markov chain is characterized by a set of states and a transition probability matrix. The model calculates the probability to have pitting (and vice versa to maintain a stable passive condition) involving a large number of operating parameters related to both metal and environment. Experimental tests were carried out to validate the model which requires more accurate investigations.
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Yan Li and Junhao Hu. "Controllability of stochastic impulsive nondensely defined functional differential inclusions." In 2011 International Conference on Information Science and Technology (ICIST). IEEE, 2011. http://dx.doi.org/10.1109/icist.2011.5765146.

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Junhao Hu and Yan Li. "Controllability of stochastic impulsive evolution differential inclusions with infinite delay." In 2011 International Conference on Information Science and Technology (ICIST). IEEE, 2011. http://dx.doi.org/10.1109/icist.2011.5765145.

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Bernardin, F., C. H. Lamarque, and M. Schatzman. "Multivalued Stochastic Differential Equations and Its Applications in Dynamics." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48477.

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Using a maximal monotone graph we can deal with many nonlinear dynamical problems involving e.g. dry friction or impacts. When submitted to an external stochastic term, a class of differential inclusions is obtained. Existence and uniqueness results are recalled. An adapted numerical scheme is presented. Numerical results are presented for different examples of models.
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Huang, Jun, and Lei Yu. "Stabilization for stochastic one-sided Lipschitz nonlinear differential inclusion system." In 2017 36th Chinese Control Conference (CCC). IEEE, 2017. http://dx.doi.org/10.23919/chicc.2017.8027855.

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Huang, Jun, Lei Yu, and Lining Sun. "Stochastic observer design for Markovian jump Lur'e differential inclusion system." In 2014 26th Chinese Control And Decision Conference (CCDC). IEEE, 2014. http://dx.doi.org/10.1109/ccdc.2014.6852128.

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Liu, Leipo, Mengzeng Cheng, and Meiyu Xu. "H∞ guaranteed cost finite-time control for stochastic differential inclusion systems." In 2015 IEEE International Conference on Information and Automation (ICIA). IEEE, 2015. http://dx.doi.org/10.1109/icinfa.2015.7279514.

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Cuadrado, David G., Francisco Lozano, and Guillermo Paniagua. "Experimental Demonstration of Inverse Heat Transfer Methodologies for Turbine Applications." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-91105.

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Abstract Gas turbines operate at extreme temperatures and pressures, constraining the use of both optical measurement techniques as well as probes. A strategy to overcome this challenge consists of instrumenting the external part of the engine, with sensors located in a gentler environment, and use numerical inverse methodologies to retrieve the relevant quantities in the flowpath. An inverse heat transfer approach is a procedure used to retrieve the temperature, pressure or mass flow through the engine based on the external casing temperature data. This manuscript proposes an improved Digital Filter Inverse Heat Transfer Method, that consists of a linearization of the heat conduction equation using sensitivity coefficients. The sensitivity coefficient characterizes the change of temperature due to a change in the heat flux. The heat conduction equation contains a non-linearity due to the temperature-dependent thermal properties of the materials. In previous literature, this problem is solved via iterative procedures that however increase the computational effort. The novelty of the proposed strategy consists of the inclusion of a non-iterative procedure to solve the non-linearity features. This procedure consists of the computation of the sensitivity coefficients in function of temperature, together with an interpolation where the measured temperature is used to retrieve the sensitivity coefficients in each timestep. These temperature-dependent sensitivity coefficients, are then used to compute the heat flux by solving the linear system of equations of the Digital Filter Method. This methodology was validated in the Purdue Experimental Turbine Aerothermal Lab (PETAL) annular wind tunnel, a two minutes transient experiment with flow temperatures up to 450K. Infrared thermography is used to measure the temperature in the outer surface of the inlet casing of a high pressure turbine. Surface thermocouples measure the endwall metal temperature. The metal temperature maps from the IR thermography were used to retrieve the heat flux with the inverse method. The inverse heat transfer method results were validated against a direct computation of the heat flux obtained from temperature readings of surface thermocouples. The experimental validation was complemented with an uncertainty analysis of the inverse methodology: the Karhunen-Loeve Expansion. This technique allows the propagation of uncertainty through stochastic systems of differential equations. In this case, the uncertainty of the inner casing heat flux has been evaluated through the simulation of different samples of the uncertain temperature field of the outer casing.
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