Random orthogonal expansion method for solving uncertain heat conduction problem

Abstract

The invention discloses a random orthogonal expansion method for solving the uncertain heat conduction problem. The method comprises the following steps of performing quantification representation on uncertain parameters in the heat conduction problem by introducing random variables; building a random differential control equation of the heat conduction problem by combining the random variables; selecting an orthogonal polynomials substrate function according to the random variable distribution type; performing orthogonal expansion on the random temperature response; giving the collocation point number of each random variable; building a collocation point set of the whole uncertain space by using a tensor product law; calculating the temperature response in positions of all collocation points; solving each coefficient in the temperature response orthogonal expansion formula by using the generalized inverse of a matrix; and calculating the average value and the standard deviation of the random temperature response according to the orthogonal relationship of the substrate function. The method has the advantages that the heat conduction problem containing random uncertain parameters can be systematically solved; the calculation precision of a random uncertain analysis method is further improved; and the effect cannot be achieved by general commercial software.

Description

technical field [0001] The invention belongs to the field of mechanical engineering, and in particular relates to a random orthogonal expansion method for solving uncertain heat conduction problems. Background technique [0002] When analyzing and designing an engineering system, it is required to calculate the system response correctly in order to ensure that the engineering system meets the requirements of certain indicators. However, due to the limitations of people's understanding of the level and means of the objective world, there are often uncertainties related to material properties, external force loads, initial conditions, boundary constraints, and processing and assembly in actual engineering. For complex systems, even small uncertainties may cause significant disturbances to the final response output through propagation and diffusion among subsystems. Therefore, studying the influence of these uncertainties on the system response has a wide engineering backgroun...

AI Technical Summary

Problems solved by technology

At present, the stochastic finite element method derived from the combination of stochastic analysis theory and finite element calculation method has achieved many research results in the analysis of static and dynamic characteristics of uncertain structures, but its application in the field of heat transfer is still very limited.

In addition, the traditional stochastic simulation method uses digital simulation and statistical analysis to obtain the probability characteristics of the system response

Although the operation is simple, its calculation accuracy depends on a large number of sampling experiments, so it is difficult to apply to complex engineering systems

The random perturbation method has a small amount of calculation, but due to the neglect of some high-order terms, the calculation accuracy is difficult to meet the engineering requirements

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