【摘要】：熱物性參數(shù)反演具有重要的理論意義和工程應(yīng)用價(jià)值,可以通過迭代方法或優(yōu)化算法來數(shù)值求解。優(yōu)化算法主要包括梯度類算法和啟發(fā)式算法。共軛梯度法因其儲(chǔ)存空間和計(jì)算量小等優(yōu)點(diǎn)被廣泛使用。共軛梯度法屬于局部搜索算法,其對于迭代初始值敏感。作為一個(gè)新的啟發(fā)式算法,布谷鳥算法帶有全局搜索的天性,這為反問題的求解提供了一個(gè)強(qiáng)有力的工具。針對布谷鳥算法收斂速度慢的問題,將共軛梯度法法引入到布谷鳥算法中形成改進(jìn)布谷鳥算法,可以高效準(zhǔn)確地求解反問題。本文主要基于邊界元法和改進(jìn)布谷鳥算法反演二維熱傳導(dǎo)問題熱物性參數(shù)。針對非線性穩(wěn)態(tài)熱傳導(dǎo)問題,采用Kirchhoff變換將非線性熱傳導(dǎo)問題轉(zhuǎn)化為線性熱傳導(dǎo)問題,反演導(dǎo)熱系數(shù)。針對瞬態(tài)熱傳導(dǎo)問題,考慮不含熱源和含有熱源的情況,引入一個(gè)變換將帶熱源熱傳導(dǎo)問題轉(zhuǎn)換為無熱源熱傳導(dǎo)問題,反演熱擴(kuò)散系數(shù)。針對非線性瞬態(tài)熱傳導(dǎo)問題,也采用Kirchhoff變換將非線性熱傳導(dǎo)問題轉(zhuǎn)化為線性熱傳導(dǎo)問題,反演導(dǎo)熱系數(shù)。算例討論了單元數(shù)量、測點(diǎn)數(shù)量、鳥巢數(shù)量、測量誤差等對結(jié)果的影響。增加單元數(shù)量,迭代次數(shù)減少,計(jì)算結(jié)果更精確;增加測點(diǎn)數(shù)量,迭代次數(shù)增加;增加鳥巢數(shù)量,迭代次數(shù)減少;隨著測量誤差的增大,結(jié)果精度降低并且迭代次數(shù)增多。數(shù)值算例驗(yàn)證了改進(jìn)布谷鳥算法反演熱物性參數(shù)的準(zhǔn)確性和有效性。
[Abstract]:The inversion of thermal properties parameters has important theoretical significance and engineering application value. It can be solved numerically by iterative method or optimization algorithm. The optimization algorithm mainly includes gradient class algorithm and heuristic algorithm. Conjugate gradient method is widely used because of its advantages of less storage space and less computation. The conjugate gradient method belongs to the local search algorithm and is sensitive to the iterative initial value. As a new heuristic algorithm, Cuckoo algorithm has the nature of global search, which provides a powerful tool for solving inverse problems. In order to solve the problem of slow convergence of cuckoo algorithm, the conjugate gradient method is introduced to form an improved cuckoo algorithm, which can solve the inverse problem efficiently and accurately. In this paper, the boundary element method and the improved Cuckoo algorithm are used to retrieve the thermal properties of two-dimensional heat conduction problem. For the problem of nonlinear steady state heat conduction, the nonlinear heat conduction problem is transformed into a linear heat conduction problem by Kirchhoff transform, and the thermal conductivity is retrieved. For the transient heat conduction problem, a transformation is introduced to transform the heat conduction problem with a band heat source into a non-heat source heat conduction problem, and the thermal diffusion coefficient is retrieved. For the nonlinear transient heat conduction problem, the nonlinear heat conduction problem is transformed into a linear heat conduction problem by Kirchhoff transform, and the thermal conductivity is retrieved. The effects of the number of units, the number of measuring points, the number of bird's nests and the measurement errors on the results are discussed. With the increase of the number of units, the number of iterations is reduced, the calculation results are more accurate; the number of measured points is increased, the number of iterations is increased; the number of iterations is reduced by increasing the number of bird nests; with the increase of measurement error, the precision of the results decreases and the number of iterations increases. Numerical examples verify the accuracy and validity of the improved Cuckoo algorithm in inversion of thermal properties.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP18;O551.3

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