Efficient joint reconstruction method for temperature field and thickness of solid based on quasi-newton method
By employing an alternating iterative method combining the quasi-Newtonian method L-BFGS and the steepest descent method DG, the problem of synchronous and efficient reconstruction of temperature field and thickness under high-temperature conditions was solved, achieving high-precision and high-efficiency online monitoring. This method is suitable for health monitoring of high-temperature equipment such as aero-engines and nuclear reactors.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-12
- Publication Date
- 2026-03-24
AI Technical Summary
Existing technologies struggle to achieve high-precision and high-efficiency synchronous reconstruction of temperature field and thickness in high-temperature environments, especially in the health monitoring of high-temperature equipment such as aero-engines and nuclear reactors, where there are problems of low computational efficiency and difficulty in balancing real-time performance and accuracy.
An alternating iterative method combining the quasi-Newton method L-BFGS and the steepest descent method DG is adopted. By constructing a multi-parameter inversion problem, the boundary heat flux is inverted using the L-BFGS algorithm and the thickness is inverted using the DG algorithm, so as to realize the synchronous reconstruction of temperature field and thickness. The advantages of the quasi-Newton method are used to accelerate convergence and the Wolfe-Powell line search strategy is combined to ensure stability.
It achieves high-precision and high-efficiency reconstruction of the internal temperature field and thickness of high-temperature structures, improving computational efficiency by 30%-80%. It is suitable for homogeneous and composite materials, has online real-time monitoring capabilities, and is suitable for non-invasive measurement of closed structures.
Smart Images
Figure CN121302729B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of ultrasonic nondestructive detection, and more particularly to a solid internal temperature field and thickness efficient joint reconstruction method based on quasi-Newton method. BACKGROUND
[0002] At present, the online nondestructive monitoring technology of high-temperature structure internal temperature field and thickness size mainly relies on the separated measurement of contact type temperature measurement means (such as thermocouple) and ultrasonic thickness measurement technology. Although the thermocouple can directly measure the temperature, it has inherent limitations such as low spatial resolution, invasive interference, response lag, etc., and cannot realize the global temperature field distribution perception; although the ultrasonic thickness measurement technology can non-invasively measure the thickness, it is significantly affected by the sound speed change caused by the temperature gradient, and it is difficult to realize the synchronous high-precision inversion of temperature and thickness in high-temperature environment.
[0003] The inversion method based on ultrasonic propagation time has been developed in recent years, especially the research on the inversion of temperature field distribution by establishing the relationship between sound speed and temperature has been relatively mature. For example, the sensitivity method, conjugate gradient method (CG) and steepest descent method (DG) are used to inverse one-dimensional and two-dimensional temperature field, and the inversion of heat flow boundary and thickness parameters is preliminarily explored.
[0004] However, the existing technology still has the following outstanding problems:
[0005] 1) Poor multi-parameter coupling inversion capability: most of the researches focus on single parameter (such as temperature field) inversion, and there are few systematic researches on temperature field and thickness double parameter strong coupling inversion problem;
[0006] 2) Low calculation efficiency: traditional optimization algorithms (such as conjugate gradient method and steepest descent method) need to frequently solve the positive problem and gradient calculation when dealing with nonlinear and multivariable inversion problems, resulting in heavy calculation burden and slow convergence speed, and the inversion process often takes more than a few minutes, which is difficult to meet the online real-time monitoring demand;
[0007] 3) Limited engineering applicability: the real-time performance and accuracy of the existing method in high-temperature and strong coupling environment are difficult to be considered, which limits its application in high-temperature equipment health monitoring such as aircraft engine and nuclear reactor. SUMMARY
[0008] The present application aims to overcome the deficiencies of the prior art and provide a solid internal temperature field and thickness efficient joint reconstruction method based on quasi-Newton method, which can realize the synchronous high-precision and high-efficiency reconstruction of solid structure internal temperature field and thickness size.
[0009] The purpose of the present application is achieved by the following scheme:
[0010] An efficient joint reconstruction method for the internal temperature field and thickness of a solid based on the quasi-Newtonian method includes the following steps:
[0011] A multi-parameter inversion problem with boundary heat flux and thickness as decision variables is constructed, and an objective function including a regularization term is defined to transform the inversion problem into a nonlinear optimization problem.
[0012] To address the aforementioned nonlinear optimization problem, the internal temperature and dimensions of the high-temperature structure are reconstructed by combining the quasi-Newton method L-BFGS inversion of heat flux with the steepest descent method DG inversion of thickness.
[0013] Furthermore, in constructing the inversion model, the construction of a multi-parameter inversion problem with boundary heat flow and thickness as decision variables specifically includes the following sub-steps: establishing a one-dimensional heat conduction equation and an ultrasonic propagation time model, and combining the relationship between sound speed and temperature to construct a multi-parameter inversion problem with boundary heat flow q(t) and thickness L as decision variables.
[0014] Furthermore, the relationship between sound speed and temperature includes a linear or quadratic fitting relationship.
[0015] Furthermore, the method of combining the L-BFGS inversion of heat flux using the quasi-Newton method with the DG inversion of thickness using the steepest descent method to reconstruct the internal temperature and dimensional thickness of the high-temperature structure specifically includes the following sub-steps:
[0016] The L-BFGS algorithm is used to invert the boundary heat flux, taking advantage of its quasi-Newton method to approximate the Hessian matrix to accelerate convergence; and the DG algorithm is used to invert the thickness parameters, combined with the Wolfe-Powell line search strategy to ensure convergence stability.
[0017] The strategy is then updated by iteratively alternating between heat flow and thickness, gradually approaching the optimal solution until the convergence condition is met.
[0018] Furthermore, before using the L-BFGS algorithm to invert the boundary heat flux, the following steps are also included:
[0019] Step (1): Given the initial values of material properties, heat flow, and thickness;
[0020] Step (2): Calculate the forward problem of heat conduction based on the given material properties, heat flow and initial thickness. Based on the temperature field calculation results and the correlation between ultrasonic propagation speed and temperature, calculate the propagation time of ultrasonic waves.
[0021] Furthermore, the strategy is updated by iteratively alternating between heat flow and thickness to gradually approach the optimal solution until the convergence condition is met. This process specifically includes the following sub-steps:
[0022] Step (3): Determine whether the objective function is less than the preset threshold based on the actual measured ultrasonic propagation time and the ultrasonic propagation time calculated in step (2). If so, end the process; otherwise, update the heat flow and thickness.
[0023] Step (4): Iterate steps (2) to (3) alternately until the objective function value is lower than the preset threshold, and output the inversion result.
[0024] Furthermore, the updating of heat flux and thickness specifically includes: fixing the thickness and updating the heat flux using the L-BFGS algorithm; and fixing the heat flux and updating the thickness using the DG algorithm.
[0025] Furthermore, the high-temperature structure includes a homogeneous material high-temperature structure and a composite material high-temperature structure.
[0026] The beneficial effects of this invention include:
[0027] This invention combines the L-BFGS method for inverting heat flux with the steepest descent method (DG) for inverting thickness to reconstruct the internal temperature and thickness of high-temperature structures. Compared with traditional methods that use the conjugate gradient method (CG) and the steepest descent method (DG) for inverting heat flux, this invention improves computational efficiency by 30%-80% while maintaining reconstruction accuracy. It provides reliable technical support for online, real-time health monitoring and safety assessment of high-temperature structures and is applicable to ultrasonic temperature measurement inside homogeneous materials and composite materials. Attached Figure Description
[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0029] Figure 1 This is a flowchart illustrating the reconstruction process of the method in an embodiment of the present invention.
[0030] Figure 2 This is a diagram showing the heat flow inversion results of the method in an embodiment of the present invention;
[0031] Figure 3 This is a convergence rate diagram of the method in an embodiment of the present invention. Detailed Implementation
[0032] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.
[0033] The specific implementation process of this invention is as follows:
[0034] To address the shortcomings of existing technologies, this invention proposes a highly efficient joint inversion method based on alternating iterations of the finite memory BFGS method (quasi-Newton method, hereinafter referred to as L-BFGS) and the steepest descent method (DG) (hereinafter referred to as L-BFGS-DG method), which is used to achieve synchronous, high-precision, and high-efficiency reconstruction of the internal temperature field and thickness dimensions of solid structures.
[0035] More specifically, the technical solution of the present invention mainly includes the following steps:
[0036] Step 1, Inversion Model Construction: (1) Establish a one-dimensional heat conduction equation and ultrasonic propagation time model, and combine the sound speed-temperature relationship (linear or quadratic fitting) to construct a multi-parameter inversion problem with boundary heat flow q(t) and thickness L as decision variables; (2) Define an objective function containing regularization terms to transform the inversion problem into a nonlinear optimization problem.
[0037] Step 2, Alternating Iterative Optimization Algorithm: (1) Use the L-BFGS algorithm to invert the boundary heat flow, take advantage of its quasi-Newton method, approximate the Hessian matrix to accelerate convergence and reduce memory consumption; (2) Use the steepest descent method (DG) to invert the thickness parameters, and combine the Wolfe-Powell line search strategy to ensure convergence stability; (3) Use the alternating iterative update strategy of heat flow and thickness to gradually approach the optimal solution until the convergence condition is met.
[0038] In other specific implementation steps, a method for efficient joint reconstruction of the internal temperature field and thickness of a solid based on the quasi-Newtonian method is provided, such as... Figure 1 As shown, perform the following steps:
[0039] Step (1): Given the initial values of material properties, heat flow, and thickness;
[0040] Step (2): Calculate the forward problem of heat conduction based on the given material properties, heat flow and initial thickness. Based on the temperature field calculation results and the correlation between ultrasonic propagation speed and temperature, calculate the propagation time of ultrasonic waves.
[0041] Step (3): Based on the actual measured ultrasonic propagation time and the ultrasonic propagation time calculated in step (2), determine whether the objective function is less than the preset threshold. If so, end the process; otherwise, update the heat flux and thickness. Specifically, for a fixed thickness, use L-BFGS to update the heat flux; for a fixed heat flux, use DG to update the thickness.
[0042] Step (4): Iterate steps (2) to (3) alternately until the objective function value is lower than the preset threshold, and output the inversion result.
[0043] The method of this invention has the following technical advantages:
[0044] (1) High precision: relative error of temperature field <5%, thickness deviation <0.1 mm;
[0045] (2) High efficiency: Compared with the traditional CG-DG and DG-DG methods, the computational efficiency is improved by more than 60%;
[0046] (3) Strong robustness: It is suitable for high temperature and strong coupling environments and has the potential for online real-time monitoring;
[0047] (4) Non-invasive: Based on ultrasonic measurement, no sensor needs to be implanted, suitable for closed structures.
[0048] In summary, the L-BFGS-DG method proposed in this invention effectively solves the efficiency and accuracy bottlenecks in multi-parameter coupled inversion through innovative algorithm structure design and optimization strategies, providing reliable technical support for online and real-time health monitoring and safety assessment of high-temperature structures.
[0049] The technical effects of the method in the embodiments of the present invention are verified as follows:
[0050] Numerical experiments were conducted: for actual thicknesses of... L A heat flow boundary condition is given at one end of a solid medium with a diameter of 50 mm. q (t), the other end is insulated, and the properties of the solid medium are as follows: thermal conductivity k = 50 W / (m °C), specific heat c = 400 J / (kg°C), material density p =7800 kg / m 3 Given an initial temperature distribution: T 0 = 26°C. The propagation speed of ultrasound in a medium is linearly related to the temperature field.
[0051] ;
[0052] The ultrasonic probe excites / receives an ultrasonic pulse echo signal once per second, with a total detection time of 500 seconds.
[0053] When the actual heat flow is constant ( q ( t ) = 10 5 Under the condition of J / s, the heat flow and thickness are inverted. Figure 2The heat flow inversion results were compared. It can be seen that, compared with the alternating iterative methods (CG-DG, DG-DG) that combine the conjugate gradient method and the steepest descent method to invert heat flow and the steepest descent method to invert thickness, the heat flow value obtained by the L-BFGS-DG method is closest to the true value, with an average relative error of 1.69%.
[0054] Table 1 shows the thickness inversion results obtained by the alternating iterative method based on L-BFGS-DG. The thickness inversion deviations are all less than 0.02 mm, indicating high accuracy.
[0055] Table 1 Thickness Inversion Results
[0056]
[0057] Figure 3 The convergence rate of the alternating iterative method based on L-BFGS-DG is presented and compared with that of two traditional classical optimization methods. The results show that the alternating iterative method based on L-BFGS-DG has the highest computational efficiency: under the condition of first-order approximate exact line search, its inversion rate is improved by 78.3% and 60.9% compared with DG-DG and CG-DG, respectively.
[0058] In summary, the alternating iterative method based on L-BFGS-DG can effectively invert boundary heat flux and solid thickness. Compared with the two traditional optimization methods, the L-BFGS-DG optimization method significantly improves computational efficiency while ensuring high inversion accuracy.
[0059] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.
[0060] According to one aspect of the present invention, a computer program product or computer program is provided, the computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and executes the computer instructions, causing the computer device to perform the methods provided in the various optional implementations described above.
[0061] In another aspect, embodiments of the present invention also provide a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods described in the above embodiments.
Claims
1. A method for efficient joint reconstruction of the internal temperature field and thickness of a solid based on the quasi-Newtonian method, characterized in that, Includes the following steps: A multi-parameter inversion problem with boundary heat flux and thickness as decision variables is constructed. A one-dimensional heat conduction equation and an ultrasonic propagation time model are established. Combining the relationship between sound speed and temperature, a multi-parameter inversion problem with boundary heat flux q(t) and thickness L as decision variables is constructed. An objective function including a regularization term is defined to transform the inversion problem into a nonlinear optimization problem. For the aforementioned nonlinear optimization problem, the heat flux inversion method L-BFGS (quasi-Newton method) and the thickness inversion method DG (steepest descent method) are combined to reconstruct the internal temperature and thickness of the high-temperature structure. The boundary heat flux is inverted using the L-BFGS algorithm, and its quasi-Newton method advantage is utilized to approximate the Hessian matrix to accelerate convergence. Furthermore, the DG algorithm is used to invert thickness parameters, and the Wolfe-Powell line search strategy is combined to ensure convergence stability. The strategy is then updated by iteratively alternating between heat flow and thickness, gradually approaching the optimal solution until the convergence condition is met.
2. The efficient joint reconstruction method for the internal temperature field and thickness of a solid based on the quasi-Newtonian method according to claim 1, characterized in that, The relationship between sound speed and temperature includes linear or quadratic fitting relationships.
3. The efficient joint reconstruction method for the internal temperature field and thickness of a solid based on the quasi-Newtonian method according to claim 1, characterized in that, Before using the L-BFGS algorithm to invert the boundary heat flux, the following steps are also included: Step (1): Given the initial values of material properties, heat flow, and thickness; Step (2): Calculate the forward problem of heat conduction based on the given material properties, heat flow and initial thickness. Based on the temperature field calculation results and the correlation between ultrasonic propagation speed and temperature, calculate the propagation time of ultrasonic waves.
4. The efficient joint reconstruction method of solid internal temperature field and thickness based on quasi-Newtonian method according to claim 3, characterized in that, The strategy is updated by iteratively alternating between heat flow and thickness to gradually approach the optimal solution until the convergence condition is met. This process includes the following sub-steps: Step (3): Determine whether the objective function is less than the preset threshold based on the actual measured ultrasonic propagation time and the ultrasonic propagation time calculated in step (2). If so, end the process; otherwise, update the heat flow and thickness. Step (4): Iterate steps (2) to (3) alternately until the objective function value is lower than the preset threshold, and output the inversion result.
5. The efficient joint reconstruction method for the internal temperature field and thickness of a solid based on the quasi-Newtonian method according to claim 4, characterized in that, The updating of heat flux and thickness specifically includes: fixing the thickness and updating the heat flux using the L-BFGS algorithm; and fixing the heat flux and updating the thickness using the DG algorithm.
6. The efficient joint reconstruction method of solid internal temperature field and thickness based on quasi-Newtonian method according to claim 1, characterized in that, The high-temperature structures include high-temperature structures made of homogeneous materials and high-temperature structures made of composite materials.