CN-116087267-B - Evaluation method for determining parameters capable of being measured simultaneously in transient heat reflection method based on sensitivity matrix

CN116087267BCN 116087267 BCN116087267 BCN 116087267BCN-116087267-B

Abstract

The invention discloses an evaluation method for determining parameters which can be measured simultaneously in a transient thermal reflection method based on a sensitivity matrix, which comprises the steps of determining known parameters and unknown parameters required in the fitting in the transient thermal reflection method experiment and experimental variables according to a multi-layer stacked sample structure, giving an unknown parameter pre-estimated value, calculating sensitivity parameters of all unknown parameters at all value points of the experimental variables to construct the sensitivity matrix, carrying out singular value decomposition on the sensitivity matrix S, and meeting the requirements in non-negative singular values The number m of non-negative singular values of (a) is the number of unknown parameters that can be measured simultaneously. The method is suitable for any transient heat reflection method experiment, can rapidly identify the physical quantity which can be measured simultaneously in the transient heat reflection method, can avoid incorrect fitting results and guide optimization of material measurement conditions, and is beneficial to simultaneous measurement of multiple unknown parameters of the novel material.

Inventors

WANG WEILIE
TU JING

Assignees

浙江大学

Dates

Publication Date: 20260512
Application Date: 20230128

Claims (4)

1. An evaluation method for determining parameters which can be measured simultaneously in a transient heat reflection method based on a sensitivity matrix, which is characterized in that the method comprises the following steps: step one, determining known parameters and unknown parameters required for fitting in transient heat reflection method experiments and experimental variables according to a multi-layer stacked sample structure, wherein the known parameters are expressed as The unknown parameters are expressed as The unknown parameters are kept unchanged in the range of the experimental variable values; Step two, giving an estimated value of the unknown parameters, calculating sensitivity parameters of all the unknown parameters at all the value points of the experimental variables, and constructing a sensitivity matrix S, wherein the calculation formula of the sensitivity parameters is as follows: ; Wherein, the Y is a response signal for fitting acquired in a transient thermal reflection method experiment, and F is a heat transfer model; for all the values of the experimental variables, ; As a result of the unknown parameters, ; The sensitivity matrix S is expressed as: ; step three, singular value decomposition is carried out on the sensitivity matrix S, Wherein And Respectively is And Is a unitary matrix of (a); Is that Matrix with diagonal elements of the first n rows of the matrix being non-negative singular values arranged in descending order ; Step four, from non-negative singular values Is selected to satisfy The number m of the non-negative singular values is the number of unknown parameters which can be measured simultaneously, wherein t is a threshold value with the value of 0-1.
2. The method for evaluating parameters which can be measured simultaneously in a transient heat reflection method based on a sensitivity matrix according to claim 1, wherein the value range of t is 0.02-0.1.
3. The method for evaluating parameters simultaneously measurable in a transient heat reflection method based on a sensitivity matrix according to claim 2, wherein the parameters are determined from the matrix Is at the back of (1) Zero space of column-derived sensitivity matrix S : ; Solving the following differential equation set to obtain the form of simultaneously measurable parameters in the unknown thermophysical parameters: ; Wherein, the ; Is in the form of a measurable parameter.
4. The method for evaluating parameters simultaneously measurable in a transient heat reflection method based on a sensitivity matrix according to claim 2, wherein the predicted values of unknown parameters are determined by: (1) By means of simulation; (2) Preliminary fitting of experimental data; (3) By reference.

Description

Evaluation method for determining parameters capable of being measured simultaneously in transient heat reflection method based on sensitivity matrix Technical Field The invention relates to the field of material thermophysical property measurement, in particular to an evaluation method for determining parameters which can be measured simultaneously in a transient heat reflection method based on a sensitivity matrix. Background The material thermophysical property measurement has obvious scientific significance and important engineering application value in the industrial fields of aerospace, energy utilization, microelectronics industry, new material development and the like, and is the basis of technical innovation, development and scientific research. Transient heat reflection methods based on material surface heat reflection, such as a frequency domain heat reflection method and a time domain heat reflection method, are the most advanced measuring methods of material thermophysical properties nowadays, and can measure bulk materials and micro-nano scale materials. Based on thermal reflection of the surface of the material, temperature response signals under different experimental variables are collected, and known heat conduction models are used for fitting experimental data to determine unknown parameters of the material. There is often more than one unknown parameter in this process. With the change of the physical property parameters of the measured sample and the change of the experimental conditions, the measurable parameters in one-time transient heat reflection method experiment can also be changed. Taking the measurement of bulk materials as an example, the thermal conductivity k and the specific heat by volume C can be measured simultaneously at low frequency measurement, but only at high frequency measurementCan be determined by fitting. The determination of measurable parameters in such transient thermography experiments can be used to exclude incorrect measurements and to guide optimization of experimental conditions. However, there is currently no universal, reliable method of measurable parameter determination. Disclosure of Invention Aiming at the defect of a measurable parameter determining method in the existing transient thermal reflection method experiment, the invention provides an evaluation method for determining parameters which can be measured simultaneously in the transient thermal reflection method based on a sensitivity matrix. The method is simple and convenient to operate, is reliable and widely used, and can be used for simultaneously measuring multiple unknown thermophysical parameters of the new material. The aim of the invention is achieved by the following technical scheme: An evaluation method for determining parameters which can be measured simultaneously in a transient heat reflection method based on a sensitivity matrix, the method comprising: Step one, determining known parameters and unknown parameters required for fitting in transient thermal reflection method experiments and experimental variables according to a multi-layer stacked sample structure, wherein the known parameters are represented as ζ= (B 1,B2,…,Bn), and the unknown parameters are represented as θ= (A 1,A2,…,An); Step two, giving an estimated value of the unknown parameters, calculating sensitivity parameters of all the unknown parameters at all the value points of the experimental variables, and constructing a sensitivity matrix S, wherein the calculation formula of the sensitivity parameters is as follows: Wherein y=f (x, θ, ζ), y is a response signal for fitting acquired in a transient thermal reflection method experiment, F is a heat transfer model, x j is all the value points of experimental variables, j=1, 2..p, a i is an unknown parameter, i=1, 2..n; The sensitivity matrix S is expressed as: Performing singular value decomposition on a sensitivity matrix S, wherein S=U sigma V T, U and V are unitary matrices of p multiplied by p and n multiplied by n respectively, sigma is a p multiplied by n matrix, and diagonal elements of the first n rows of the matrix are nonnegative singular values sigma 1,σ2,…,σn arranged in a descending order; Step four, selecting the non-negative singular value sigma 1,σ2,…,σn to meet the requirement The number m of the non-negative singular values is the number of unknown parameters which can be measured simultaneously, wherein t is a threshold value with the value of 0-1. Further, the value range of t is 0.02-0.1. Further, the null space V null of the sensitivity matrix S is derived from the next n-m columns of the matrix V: Solving the following differential equation set to obtain the form of simultaneously measurable parameters in the unknown thermophysical parameters: Where l=1, 2,..m, k=m+1,..n; g l(A1,…,An) is in the form of a measurable parameter. Further, the predicted value of the unknown parameter is determined by: (1) By means of simulation; (2) Prelimina