Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

Azam, Marie-Hélène; Berger, Julien; Guernouti, Sihem; Poullain, Philippe; Musy, Marjorie

doi:10.1080/19401493.2020.1868577

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…With the computational gain, other studies of parametric problems using reduced-order methods are found in the literature. In this way, in [12] they have combined the POD and PGD approach to modeling the soil for application in the study of canyon streets and in [13] to assess efficiently the building's envelope thermal performance.…”

Section: Introductionmentioning

confidence: 99%

Solving parametric problems in building renovation with a spectral reduced-order method

Gasparin

Berger

Belarbi

et al. 2022

Journal of Building Performance Simulation

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In this paper, the spectral method is developed as a reduced-order model for the solution of parametric problems within the building refurbishment framework. We propose to use the spectral reduced-order method to solve parametric problems in an innovative way, integrating the unknown parameter as one of the coordinates of the decomposition. The residual is minimized combining the Tau-Galerkin method with the Collocation approach. The developed method is evaluated in terms of accuracy and reduction of the computational time in three different cases. The dynamic behavior of unidimensional moisture diffusion is investigated. The cases focus on solving parametric problems in which the solution depends on space, time, diffusivity, and material thickness. Results highlight that the parametric spectral reduced-order method provides accurate solutions and can reduce ten times the degree of freedom of the solution. It allows efficient computation of the physical phenomena with a lower error when compared to traditional approaches.

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Section: Introductionmentioning

confidence: 99%

Solving parametric problems in building renovation with a spectral reduced-order method

Gasparin

Berger

Belarbi

et al. 2022

Journal of Building Performance Simulation

Self Cite

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“…Image signals are subject to several processes such as transmission [1], enhancement [2], transformation [3], hiding [4], and compression [5,6]. Similarly to image processing, speech signals processing is also essential [7], and involves several stages such as transfer [8], acquisition [9], and coding [10]. Pattern recognition, which is considered an automated process, is widely used in various applications such as computer vision [11], statistical data analysis [12], information retrieval [13], shot boundary detection [14], and bio-informatics [15].…”

Section: Introductionmentioning

confidence: 99%

Reliable Recurrence Algorithm for High-Order Krawtchouk Polynomials

Al-Utaibi

Abdulhussain

Mahmmod

et al. 2021

Entropy

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Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the initial value of the KP parameter. In addition, a new diagonal recurrence relation is introduced and used in the proposed algorithm. The diagonal recurrence algorithm was derived from the existing n direction and x direction recurrence algorithms. The diagonal and existing recurrence algorithms were subsequently exploited to compute the KP coefficients. First, the KP coefficients were computed for one partition after dividing the KP plane into four. To compute the KP coefficients in the other partitions, the symmetry relations were exploited. The performance evaluation of the proposed recurrence algorithm was determined through different comparisons which were carried out in state-of-the-art works in terms of reconstruction error, polynomial size, and computation cost. The obtained results indicate that the proposed algorithm is reliable and computes lesser coefficients when compared to the existing algorithms across wide ranges of parameter values of p and polynomial sizes N. The results also show that the improvement ratio of the computed coefficients ranges from 18.64% to 81.55% in comparison to the existing algorithms. Besides this, the proposed algorithm can generate polynomials of an order ∼8.5 times larger than those generated using state-of-the-art algorithms.

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Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

Cited by 2 publications

References 26 publications

Solving parametric problems in building renovation with a spectral reduced-order method

Solving parametric problems in building renovation with a spectral reduced-order method

Reliable Recurrence Algorithm for High-Order Krawtchouk Polynomials

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