A temperature field reconstruction method suitable for ultrasonic temperature measurement

Abstract

This invention belongs to the field of ultrasonic temperature measurement, specifically relating to a temperature field reconstruction method suitable for ultrasonic temperature measurement, comprising the following steps: Step 1, dividing the temperature measurement area into n sub-regions, with the center coordinates of the sub-regions being , such that there are m ultrasonic paths within the temperature measurement area; Step 2, measuring the ultrasonic fly-through time on each ultrasonic path to obtain K ultrasonic fly-through times; Step 3, using a linear combination of radial basis functions of a thin plate spline (TPS) for global approximation; Step 4, substituting the results from Step 3 into the formula in Step 2; Step 5, reorganizing the fly-through times of the m ultrasonic paths into a matrix equation form; Step 6, solving the matrix equation using the singular value decomposition method, and finally obtaining the result; Step 7, substituting the calculated result into Step 3 to finally obtain the temperature data.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic temperature measurement, and specifically relates to a method for reconstructing the temperature field suitable for ultrasonic temperature measurement. Background Technology

[0002] Accurate temperature field sensing is a key technology in industrial process control, materials processing, and additive manufacturing. Especially in processes such as microwave curing and laser sintering, the uniformity of temperature distribution directly determines the molding quality and performance of the finished product. However, achieving high-precision temperature field measurement in these applications still faces many challenges.

[0003] Existing temperature measurement technologies are mainly divided into two categories: invasive and non-invasive.

[0004] Invasive temperature measurement methods, such as thermocouples, resistance temperature detectors (RTDs), and fiber optic thermometers, acquire temperature information by directly contacting or inserting sensors into the object being measured. These methods are simple in principle and have a fast response time. However, in strong electromagnetic fields such as microwave curing, metal thermocouples can cause interference or even malfunction. While fiber optic thermometers are unaffected by electromagnetic interference, their insertion process can damage the structural integrity of the object being measured, and they can only measure temperature at a single point, making them unsuitable for scenarios with extremely high precision requirements, such as 3D printing. Furthermore, invasive temperature measurement cannot obtain information about the overall temperature field distribution.

[0005] Non-invasive temperature measurement methods, such as infrared thermography and optical thermometry, avoid direct contact with the object being measured and do not disrupt the temperature distribution in the measured area. However, these methods can only measure the surface temperature of an object and cannot perceive the internal temperature field distribution of the material. In bulk heating processes such as microwave curing, the internal temperature of the material often differs significantly from the surface temperature. Relying solely on surface temperature is insufficient to reflect the true heating state and cannot provide a comprehensive basis for process control.

[0006] Ultrasonic thermometry, a typical non-invasive temperature measurement method, utilizes the functional relationship between the propagation speed of ultrasonic waves in a medium and temperature. It inverts the temperature distribution of the measured area by measuring the time of flight (TOF) of multipath ultrasonic waves. This method has advantages such as real-time measurement, strong environmental adaptability, media penetration, and immunity to electromagnetic interference, and has achieved good application results in the field of gas temperature measurement. In recent years, researchers have attempted to extend ultrasonic thermometry to sensing the internal temperature field of solid materials, demonstrating enormous application potential.

[0007] However, the application of ultrasonic temperature measurement technology in solid media still faces key bottlenecks. The main problem lies in the fact that the calculation methods used in the existing technology are flawed, which makes it difficult to obtain a complete temperature field distribution. Summary of the Invention

[0008] This invention provides a temperature field reconstruction method suitable for ultrasonic temperature measurement, which aims to overcome the shortcomings of existing ultrasonic temperature measurement methods and obtain a more complete temperature field distribution.

[0009] To achieve the above objectives, the present invention provides a temperature field reconstruction method suitable for ultrasonic thermometry, comprising the following steps. Step 1, Set the coordinates of any point in the temperature measurement area to... ; The temperature measurement area is divided into n sub-regions, and the center coordinates of each sub-region are set as follows: ; Multiple pairs of ultrasonic transmitters and ultrasonic receivers are set up in the temperature measurement area, so that there are m ultrasonic paths in the temperature measurement area; Step two, The ultrasonic fly-through time was measured along each ultrasonic path to obtain K ultrasonic fly-through times. ; Among them, V Any point within the temperature measurement area The speed of sound at that location The path differential of the k-th ultrasound path; Step 3, Set helper functions And using a linear combination of radial basis functions to Perform a global approximation to obtain ,in, For the first The weighted coefficients of each sub-region For the first Radial basis functions of the center points of each subregion; Using the TPS radial basis function, we obtain ,in, Its value represents any point within the temperature measurement area. To the The center coordinates of each sub-region The distance; Introducing shape cardinality This is used to balance the global smoothness of the temperature field with the local fitting accuracy, resulting in... ;in, Determined through numerical experimental calibration; Step four, In step three Substituting into the formula in step two, we get ; in, Its value represents the value of the Kth ultrasound pathway. The path integral values ​​of the basis functions corresponding to each subregion; Step 5, The flight times of the m ultrasound pathways are rearranged into matrix equation form to obtain... ,in, , where is the flight time column vector of m ultrasonic paths; , which is the column vector of weighted coefficients corresponding to the n sub-blocks; , is an m×n dimensional coefficient matrix, whose matrix elements are those calculated in step four. ; Step Six, The matrix equation is solved using Singular Value Decomposition (SVD). Singular value decomposition is performed on the coefficient matrix H to obtain... Where U is an m×m left singular vector matrix, V is an n×n right singular vector matrix, and S is an m×n diagonal singular value matrix; Based on the singular value decomposition results, calculate pseudo-inverse of a matrix ,get ; Step 7, The calculated Substitute this into step three, based on the formula This yields the temperature measurement area at each point. of value; Then, according to the definition of the auxiliary function The ultrasonic velocity field within the temperature measurement area is obtained. ; Finally, based on the correspondence between ultrasonic velocity and temperature within the region... , will sound speed field Converted into a temperature field, this yields the temperature measurement result for any point within the temperature measurement area. The temperature value, of which It is a mapping function between sound speed and temperature, which is specifically determined based on the characteristics of the medium being measured.

[0010] Preferably, the temperature measurement area is divided into: n There are m ultrasound paths within each sub-region and the temperature measurement area. n > m.

[0011] The beneficial effects of this invention are as follows: 1. This invention uses the radial basis function of thin plate spline to fit the reciprocal field of sound velocity, which can ensure the global smoothness and second-order continuity of the temperature field and avoid unreasonable jumps in the temperature field. At the same time, the shape parameter δ is used to balance the global smoothness and local fitting accuracy.

[0012] 2. This invention uses the singular value decomposition method to solve the ill-conditioned matrix equation, which can effectively suppress the interference of measurement noise on the inversion results, solve the problem of result distortion caused by insufficient measurement data in traditional methods, and improve the stability of the inversion results.

[0013] 3. This method transforms the continuous integral problem into solving linear matrix equations, reducing computational complexity and enabling real-time online reconstruction of temperature fields in large spaces. It is suitable for non-contact temperature measurement needs in industrial settings. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating a temperature field reconstruction method suitable for ultrasonic thermometry. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0016] The basic implementation examples are as follows: Figure 1 As shown, a temperature field reconstruction method suitable for ultrasonic thermometry includes the following steps: Step 1, Set the coordinates of any point in the temperature measurement area to... The origin of the coordinate system can be any location within the temperature measurement area. The temperature measurement area is divided into n sub-regions, and the center coordinates of each sub-region are set as follows: ; Multiple pairs of ultrasonic transmitters and ultrasonic receivers are set up in the temperature measurement area, so that there are m ultrasonic paths in the temperature measurement area; The number of sub-regions n is much greater than the number of ultrasonic paths m within the temperature measurement region.

[0017] The ultrasonic transmitter and ultrasonic receiver can be conventional ultrasonic transmitters and ultrasonic receivers in the prior art, and this method is not limited thereto.

[0018] Step two, The ultrasonic fly-through time was measured along each ultrasonic path to obtain K ultrasonic fly-through times. ; ; Among them, V Any point within the temperature measurement area The speed of sound at that location Let be the path differential of the k-th ultrasound path.

[0019] The purpose of this step is to establish the relationship between path length and flight time for different sound speed regions under the same path.

[0020] Step 3, Set helper functions And using a linear combination of radial basis functions to Perform a global approximation to obtain , in, For the first The weighted coefficients of each sub-region For the first Radial basis functions of the center points of each subregion; Using the TPS radial basis function, we obtain , in, Its value represents any point within the temperature measurement area. To the The center coordinates of each sub-region The distance; Introducing shape cardinality This is used to balance the global smoothness of the temperature field with the local fitting accuracy, resulting in... ; in, Determined through numerical experiment calibration.

[0021] Step four, In step three Substituting into the formula in step two, we get ; in, Its value represents the value of the Kth ultrasound pathway. The path integral values ​​of the basis functions corresponding to each subregion are determined once the basis functions and paths are defined. The value can then be calculated.

[0022] Step 5, m The flight time of the ultrasound pathway and n The weighting coefficients of each sub-region are obtained through Connect the equations and rearrange them into matrix equation form to obtain... ,in, , where is the flight time column vector of m ultrasonic paths; , which is the column vector of weighted coefficients corresponding to the n sub-blocks; ,for The coefficient matrix is ​​a multidimensional matrix whose elements are those calculated in step four. .

[0023] H A matrix is ​​a The matrix, that is m Solve the equations n There are several unknowns, and typically, the number of sub-temperature zones in a grid is... n Far more than the number of ultrasound pathways m ,then H In most cases, it is an ill-conditioned matrix, which will cause significant errors in the output results even with small errors in the input data.

[0024] Step Six, Singular value decomposition (SVD) can be used to process and analyze ill-conditioned matrices. matrix H In other words, rank is r It can be subjected to singular value decomposition to obtain ,

[0025]

[0026] in and They are respectively and The square array represents and The eigenvectors are respectively called... The left and right singular vectors; represent of r There are singular values, and satisfy Based on this, we obtain The pseudo-inverse matrix after Singular Value Decomposition (SVD) ,get ; T and H The matrix is ​​known, and the calculation is obtained. .

[0027] Step 7, The calculated Substitute this into step three, based on the formula , Get the temperature measurement area at each point of value.

[0028] Then, according to the definition of the auxiliary function The ultrasonic velocity field within the temperature measurement area is obtained. .

[0029] Finally, based on the correspondence between ultrasonic velocity and temperature within the region... ,in, It is a mapping function between sound speed and temperature, which is specifically determined based on the characteristics of the medium being measured.

[0030] sound speed field Converted into a temperature field, this yields the temperature measurement result for any point within the temperature measurement area. Temperature value.

[0031] The above descriptions are merely embodiments of the present invention, and common knowledge regarding specific structures and characteristics is not elaborated upon here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the structure of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for reconstructing a temperature field suitable for ultrasonic thermometry, characterized in that: Includes the following steps, Step 1, Set the coordinates of any point in the temperature measurement area to... ; The temperature measurement area is divided into n sub-regions, and the center coordinates of each sub-region are set as follows: ; Multiple pairs of ultrasonic transmitters and ultrasonic receivers are set up in the temperature measurement area, so that there are m ultrasonic paths in the temperature measurement area; Step two, The ultrasonic fly-through time was measured along each ultrasonic path to obtain K ultrasonic fly-through times. ; ； Among them, V Any point within the temperature measurement area The speed of sound at that location The path differential of the k-th ultrasound path; Step 3, Set helper functions And using a linear combination of radial basis functions to By performing a global approximation, we obtain ,in, For the first The weighted coefficients of each sub-region For the first Radial basis functions of the center points of each subregion; Using the TPS radial basis function, we obtain ,in, Its value represents any point within the temperature measurement area. To the The center coordinates of each sub-region The distance; Introducing shape cardinality This is used to balance the global smoothness of the temperature field with the local fitting accuracy, resulting in... ;in, Determined through numerical experimental calibration; Step four, In step three Substituting into the formula in step two, we get ； in, Its value represents the value of the Kth ultrasound pathway. The path integral values ​​of the basis functions corresponding to each subregion; Step 5, The flight times of the m ultrasound pathways are rearranged into matrix equation form to obtain... ,in, , where is the flight time column vector of m ultrasonic paths; , which is the column vector of weighted coefficients corresponding to the n sub-blocks; , is an m×n dimensional coefficient matrix, whose matrix elements are those calculated in step four. ; Step Six, The matrix equation is solved using Singular Value Decomposition (SVD). Singular value decomposition is performed on the coefficient matrix H to obtain... Where U is an m×m left singular vector matrix, V is an n×n right singular vector matrix, and S is an m×n diagonal singular value matrix; Based on the singular value decomposition results, calculate pseudo-inverse of a matrix ,get ； Step 7, The calculated Substitute this into step three, based on the formula This yields the temperature measurement area at each point. of value; Then, according to the definition of auxiliary functions The ultrasonic velocity field within the temperature measurement area is obtained. ; Finally, based on the correspondence between ultrasonic velocity and temperature within the region... The sound speed field Converted into a temperature field, this yields the temperature measurement result for any point within the temperature measurement area. The temperature value, of which It is a mapping function between sound speed and temperature, which is specifically determined based on the characteristics of the medium being measured.

2. The temperature field reconstruction method for ultrasonic thermometry according to claim 1, characterized in that: Temperature measurement area is divided into n There are m ultrasound paths within each sub-region and the temperature measurement area. n > m.

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