Acoustic temperature field reconstruction method based on least square method and radial basis function

Abstract

The invention discloses an acoustic temperature field reconstruction method based on a least square method and a radial basis function, and the method comprises the steps: employing the least square method as a basis, and rapidly obtaining a temperature matrix in a to-be-measured region; according to the method, on the basis of a least square method in a direct method, a radial basis function is used as follow-up access, the temperature of each grid center is accurately calculated, finally global temperature field distribution is obtained, and temperature field reconstruction of a to-be-measured area is achieved. According to the provided new method for reconstructing the acoustic temperature field and solving the equation set, the two methods are combined, the respective limitation can be overcome, the three-dimensional temperature field can be analyzed from multiple angles, and therefore a more comprehensive view angle is obtained; the polynomial correction radial basis function can provide a solution thought for a boundary problem which cannot be solved by the least square method subsequently, and data are obtained through calculation.

Description

Technical Field

[0001] The invention relates to the technical field of acoustic temperature measurement, and in particular to an acoustic temperature field reconstruction method based on a least square method and a radial basis function. Background Art

[0002] Acoustic temperature measurement is a process of using the "result" (acoustic wave propagation time) to inversely find the "cause" (temperature distribution). It is essentially an inverse problem of temperature field solution. At present, domestic research on acoustic measurement of temperature field mainly focuses on the reconstruction of two-dimensional temperature field, while the actual temperature is often distributed in three dimensions. Therefore, the principle of acoustic temperature measurement technology is to solve the three-dimensional temperature field distribution process based on the acoustic wave flight time (TOF) on multiple paths. After obtaining the acoustic wave flight time measurement data on each path, the temperature field is discretized, and a set of algebraic equations for the relationship between the temperature values ​​of each discrete grid of the temperature field and the TOF value is established, thereby transforming the problem of reconstructing the temperature field into the problem of solving a set of equations.

[0003] Among the existing methods for solving the system of equations, the temperature field reconstruction method based on least squares is the most commonly used classical method for acoustic temperature field reconstruction. Its disadvantage is that due to the restriction between the number of block divisions in the area to be measured and the number of effective sound wave paths, the reconstruction results obtained by this method have limited accuracy and serious temperature information loss at the boundary of the area to be measured. Therefore, using a single least squares method to solve the system of equations will lead to the problem of poor stability of the solution of the equation. For example, when there are some slight changes in the observed values, due to some rounding errors and other errors, the obtained solution can be easily affected and deviate from the true value, or even fail to obtain a valid true value.

[0004] Radial basis function (RBF) is an effective method for dealing with multivariate problems. Its principle is to use a univariate function to act on the Euclidean distance, and then achieve the processing of the problem through translation operation. Introducing the concept of radial basis function on the basis of the original least squares method can solve the shortcomings of the single least squares method. The present invention combines the outstanding advantages of the least squares method and the radial basis function in data processing, and establishes a temperature field reconstruction method based on the least squares method and the polynomial corrected radial basis function (RBF-PR), which overcomes the limitation that the number of sound wave propagation paths in the traditional reconstruction model is less than the number of grid divisions, and can effectively capture the detailed information of the temperature distribution, and strives to solve the problem of missing boundary temperature information of the measured area while maintaining the advantages of simplicity and speed, and improving the reconstruction performance of the temperature field. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes an acoustic temperature field reconstruction method based on the least squares method and radial basis function.

[0006] The technical solution of the present invention is: a method for reconstructing an acoustic temperature field based on the least squares method and radial basis function, comprising the following steps:

[0007] Step 1: Using the least square method as a basis, quickly obtain the temperature matrix in the area to be measured, including the following steps: arranging sensors, demarcating the area to be measured, forming the sound wave path, measuring or calculating the sound wave flight time, and calculating the temperature matrix;

[0008] Step 2: Use the radial basis function as a subsequent access, and based on the obtained temperature matrix data, accurately calculate the temperature of each grid center, and finally obtain the global temperature field distribution, and realize the temperature field reconstruction of the measured area, including the following steps: reconstruct the interpolation model of the temperature field, and use the method based on least squares method and polynomial corrected radial basis function (RBF-PR) to calculate the temperature of the grid center to obtain the global temperature field distribution.

[0009] Furthermore, the detailed steps of obtaining the temperature matrix using the least square method in step 1 are as follows:

[0010] The area to be tested is divided into several small blocks. Assuming that the temperature inside each small block is uniform, acoustic wave transducers are arranged in the two-dimensional square area to be tested to form an effective acoustic wave propagation path;

[0011] Assume that the area to be tested is divided into N uniform small blocks, and M represents the number of effective sound wave propagation paths selected in the area to be tested, N≤M;

[0012] Since the internal temperature of each small block in the measured area is assumed to be uniform, the speed of the sound wave in each small block is also uniform. i represents the inverse of the acoustic wave velocity in the ith small block, expressed as ΔS ki It represents the length of the k-th sound wave propagation path passing through the i-th small block, through the formula The actual measured value of the sound wave flight time of this path can be measured. There must be a certain difference between the measured value and the theoretical value:

[0013] For all the sound wave propagation paths in the test area, the least square method is used to minimize the sum of square errors between the measured value and the theoretical value of the sound wave flight time of each path, that is, the following formula is established: From this formula, we can easily get the following canonical equation: S T SA=S T t; Solve the regular equation to get the matrix A, which is the inverse of the acoustic wave velocity of each small block in the area to be measured: A = (S T S) -1 S Tt; For a specific area to be measured, under a certain acoustic transducer layout and block division method, the distance matrix S is a constant matrix that can be calculated in advance. Therefore, when the acoustic wave flight time matrix t is obtained by actual measurement means, the acoustic wave spatial characteristic matrix A can be calculated, and then the temperature matrix can be solved according to the relationship between the acoustic wave propagation speed and temperature: The temperature matrix T = [T1, T2, ..., T N ] T In fact, it is the average temperature of N small blocks divided into the area to be measured, and this series of average temperatures is used as the temperature value of the corresponding geometric center point of each small block.

[0014] Furthermore, the step 2 uses radial basis function as a subsequent access to obtain the global temperature field distribution, and the detailed steps for reconstructing the temperature field of the measured area are as follows:

[0015] The measured area is evenly discretized into N sub-blocks, and the polynomial modified radial basis function is used to construct the interpolation model: (λ n is a parameter to be determined, is the basis function, (x n ,y n ) represents the coordinates of the center point of the nth sub-block, C is the shape parameter of the radial basis function, C = 60, and the radial basis function is modified using a linear polynomial), P (x, y) = c x x+c y y+c0, substituting it into the original formula, we get: At this time, the average temperature T of the N divided small blocks obtained by the least squares method is [T1, T2, ..., T N ] T As the temperature values ​​of the geometric center points of the N small blocks, then, for the constructed interpolation model, these N known temperature values ​​and their corresponding N pairs of coordinate values ​​can be regarded as N data collection points of the interpolation model, or N initial interpolation data. In other words, there will be N discrete initial data points {(x i ,y i ),T i}, i=1,2,…,N,;satisfy the following equations:

[0016]

[0017] Rewriting the above equations into matrix form yields: Where T is still the above average temperature matrix, C is a constant that can be calculated, and λ=[λ1,λ2,…λ n ] T is the unknown coefficient matrix, and its value is the key to solving the polynomial modified radial basis function interpolation model. The polynomial modified radial basis is the function value corresponding to the geometric center point of each divided small block, starting from the first block Arrange to the Nth block Then, solve the matrix equation Available

[0018] At this point, substitute the specific value of the coefficient matrix λ into the formula The temperature distribution interpolation model T(x,y) based on the polynomial modified radial basis function can be obtained.

[0019] Beneficial effects of the present invention:

[0020] The present invention is based on the least squares method in the direct method, combined with the ability of radial basis fitting scattered and sparse data, to provide a new method for reconstructing the acoustic temperature field and solving the system of equations. Combining these two methods can not only overcome their respective limitations, but also analyze the three-dimensional temperature field from multiple angles, thereby obtaining a more comprehensive perspective. The least squares method can provide basic temperature matrix data for the polynomial corrected radial basis function, which cannot be directly obtained by the polynomial corrected radial basis function alone. Conversely, the polynomial corrected radial basis function can provide solutions to boundary problems that cannot be solved by the least squares method later and calculate data, which helps to deepen the analysis of the least squares method.

[0021] Specifically, this method first obtains the average temperature of the small blocks divided into the area to be measured based on the least squares method, and then uses this group of average temperatures as the temperature value of the geometric center point of each small block, and estimates the temperature values ​​at other locations in the area to be measured by establishing a polynomial modified radial basis function reconstruction model T(x,y). The greatest value of this method is that it can obtain higher measurement accuracy compared with the classical reconstruction method, solves the problem of missing temperature information at the boundary of the area to be measured, and maintains the original advantages of simplicity and speed. Therefore, in application scenarios where the classical method is applicable, the improved method in this paper can well compensate for or improve the temperature field reconstruction effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a system flow chart of an acoustic temperature field reconstruction method based on the least squares method and radial basis function of the present invention.

[0023] Figure 2 This is a regional division diagram of an acoustic temperature field reconstruction method based on the least squares method and radial basis function of the present invention.

[0024] In the figure, the black solid dots are the acoustic wave transducers, N=16, M=24, the black solid lines between the black solid dots are the effective acoustic wave paths, and the dotted lines are the block dividing lines. DETAILED DESCRIPTION

[0025] The present invention will be further described in detail below with reference to the accompanying drawings.

[0026] like Figure 1 , Figure 2 As shown, the present invention discloses an acoustic temperature field reconstruction method based on the least squares method and radial basis function, comprising the following steps:

[0027] Step 1: Using the least square method as a basis, quickly obtain the temperature matrix in the area to be measured, including the following steps: arranging sensors, demarcating the area to be measured, forming the sound wave path, measuring or calculating the sound wave flight time, and calculating the temperature matrix;

[0028] Step 2: Use the radial basis function as a subsequent access, and based on the obtained temperature matrix data, accurately calculate the temperature of each grid center, and finally obtain the global temperature field distribution, and realize the temperature field reconstruction of the measured area, including the following steps: reconstruct the interpolation model of the temperature field, and use the method based on least squares method and polynomial corrected radial basis function (RBF-PR) to calculate the temperature of the grid center to obtain the global temperature field distribution.

[0029] The detailed steps of using the least square method to obtain the temperature matrix in step 1 are as follows:

[0030] The least square method requires that the area to be measured be divided into several small blocks, and it must be assumed that the temperature inside each small block is uniform. In the two-dimensional square area to be measured, the layout of the acoustic wave transducers commonly used in this reconstruction method, the effective acoustic wave propagation path formed, and the block division of the area to be measured are shown in the figure, where the black solid dots are the acoustic wave transducers;

[0031] Assume that the area to be tested is divided into N uniform small blocks, and M represents the number of effective sound wave propagation paths selected in the area to be tested. Limited by the characteristics of the least squares method for solving ill-conditioned matrices, the classical method requires N≤M (as shown in the figure, N=16, M=24, where the black solid line between the black solid dots is the effective sound wave path, and the red dotted line is the block division line);

[0032] Since the internal temperature of each small block in the measured area is assumed to be uniform, the speed of the sound wave in each small block is also uniform. i represents the inverse of the acoustic wave velocity in the ith small block, expressed as ΔS ki It represents the length of the k-th sound wave propagation path passing through the i-th small block, through the formula The actual measured value of the sound wave flight time of this path can be measured. There must be a certain difference between the measured value and the theoretical value:

[0033] For all the sound wave propagation paths in the test area, the least square method is used to minimize the sum of square errors between the measured value and the theoretical value of the sound wave flight time of each path, that is, the following formula is established: From this formula, we can easily get the following canonical equation: S T SA=S T t; Solve the regular equation to get the matrix A, which is the inverse of the acoustic wave velocity of each small block in the area to be measured: A = (S T S) -1 S T t; For a specific area to be measured, under a certain acoustic transducer layout and block division method, the distance matrix S is a constant matrix that can be calculated in advance. Therefore, when the acoustic wave flight time matrix t is obtained by actual measurement means, the acoustic wave spatial characteristic matrix A can be calculated, and then the temperature matrix can be solved according to the relationship between the acoustic wave propagation speed and temperature: The temperature matrix T = [T1, T2, ..., T N ] T In fact, it is the average temperature of N small blocks divided into the area to be measured, and this series of average temperatures is used as the temperature value of the corresponding geometric center point of each small block.

[0034] The step 2 uses radial basis function as a subsequent access to obtain the global temperature field distribution, and the detailed steps for reconstructing the temperature field of the measured area are as follows:

[0035] The measured area is evenly discretized into N sub-blocks, and the polynomial modified radial basis function is used to construct the interpolation model: (λ n is a parameter to be determined, is the basis function, (x n ,y n ) represents the coordinates of the center point of the nth sub-block, C is the shape parameter of the radial basis function, C = 60, and the radial basis function is modified using a linear polynomial), P (x, y) = c x x+c y y+c0, substituting it into the original formula, we get: At this time, the average temperature T of the N divided small blocks obtained by the least squares method is [T1, T2, ..., T N ] T As the temperature values ​​of the geometric center points of the N small blocks, then, for the constructed interpolation model, these N known temperature values ​​and their corresponding N pairs of coordinate values ​​can be regarded as N data collection points of the interpolation model, or N initial interpolation data. In other words, there will be N discrete initial data points {(x i ,y i ),T i}, i=1,2,…,N,;satisfy the following equations:

[0036]

[0037] Rewriting the above equations into matrix form yields: Where T is still the above average temperature matrix, C is a constant that can be calculated, and λ=[λ1,λ2,…λ n ] T is the unknown coefficient matrix, and its value is the key to solving the polynomial modified radial basis function interpolation model. The polynomial modified radial basis is the function value corresponding to the geometric center point of each divided small block, starting from the first block Arrange to the Nth block Then, solve the matrix equation We can get λ=φ -1 (TC);

[0038] At this point, substitute the specific value of the coefficient matrix λ into the formula The temperature distribution interpolation model T(x,y) based on the polynomial modified radial basis function can be obtained.

[0039] In contemporary academic research, the combined application of multiple research methods has become a key strategy to push the boundaries of knowledge and solve complex problems. This invention aims to explore the combined application of traditional methods and functional concepts in order to achieve a deeper understanding and wider application. In practical applications, this combined application can be reflected in application scenarios such as furnaces, pipelines, mines, etc. where a three-dimensional temperature field appears and needs to be inverted. By integrating the advantages of the two methods, researchers can more accurately obtain the required temperature data in the scene to achieve the ultimate research goal, while providing new insights and solutions for related fields of acoustic temperature measurement.

[0040] The present invention and its embodiments are described above, and such description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it, without departing from the purpose of the invention, they can design a structure and embodiment similar to the technical solution without creativity, which should belong to the protection scope of the present invention.

Claims

1. A method for reconstructing acoustic temperature fields based on least squares method and radial basis function, characterized in that: The following steps are involved: Step 1: Using the least square method as a basis, quickly obtain the temperature matrix in the area to be measured, including the following steps: arranging sensors, demarcating the area to be measured, forming the sound wave path, measuring or calculating the sound wave flight time, and calculating the temperature matrix; Step 2: Use the radial basis function as a subsequent access, and based on the obtained temperature matrix data, accurately calculate the temperature of each grid center, and finally obtain the global temperature field distribution, and realize the temperature field reconstruction of the measured area, including the following steps: reconstruct the interpolation model of the temperature field, and use the method based on least squares method and polynomial corrected radial basis function (RBF-PR) to calculate the temperature of the grid center to obtain the global temperature field distribution.

2. The acoustic temperature field reconstruction method based on least squares method and radial basis function according to claim 1, characterized in that: The detailed steps of using the least square method to obtain the temperature matrix in step 1 are as follows: The area to be tested is divided into several small blocks. Assuming that the temperature inside each small block is uniform, acoustic wave transducers are arranged in the two-dimensional square area to be tested to form an effective acoustic wave propagation path; Assume that the area to be tested is divided into N uniform small blocks, and M represents the number of effective sound wave propagation paths selected in the area to be tested, N≤M; Since the internal temperature of each small block in the measured area is assumed to be uniform, the speed of the sound wave in each small block is also uniform. i represents the inverse of the acoustic wave velocity in the ith small block, expressed as ΔS ki It represents the length of the k-th sound wave propagation path passing through the i-th small block, through the formula The actual measured value of the sound wave flight time of this path can be measured. There must be a certain difference between the measured value and the theoretical value: For all the sound wave propagation paths in the test area, the least square method is used to minimize the sum of square errors between the measured value and the theoretical value of the sound wave flight time of each path, that is, the following formula is established: From this formula, we can easily get the following canonical equation: S T SA=S T t; Solve the regular equation to get the matrix A, which is the inverse of the acoustic wave velocity of each small block in the area to be measured: A = (S T S) -1 S T t; For a specific area to be measured, under a certain acoustic transducer layout and block division method, the distance matrix S is a constant matrix that can be calculated in advance. Therefore, when the acoustic wave flight time matrix t is obtained by actual measurement means, the acoustic wave spatial characteristic matrix A can be calculated, and then the temperature matrix can be solved according to the relationship between the acoustic wave propagation speed and temperature: The temperature matrix T = [T1, T2, ..., T N ] T In fact, it is the average temperature of N small blocks divided into the area to be measured, and this series of average temperatures is used as the temperature value of the corresponding geometric center point of each small block.

3. The acoustic temperature field reconstruction method based on least squares method and radial basis function according to claim 1, characterized in that: The step 2 uses radial basis function as a subsequent access to obtain the global temperature field distribution, and the detailed steps for reconstructing the temperature field of the measured area are as follows: The measured area is evenly discretized into N sub-blocks, and the polynomial modified radial basis function is used to construct the interpolation model: (λ n is a parameter to be determined, is the basis function, (x n ,y n ) represents the coordinates of the center point of the nth sub-block, C is the shape parameter of the radial basis function, C = 60, and the radial basis function is modified using a linear polynomial), P (x, y) = c x x+c y y+c0, substituting it into the original formula, we get: At this time, the average temperature T of the N divided small blocks obtained by the least squares method is [T1, T2, ..., T N ] T As the temperature values ​​of the geometric center points of the N small blocks, then, for the constructed interpolation model, these N known temperature values ​​and their corresponding N pairs of coordinate values ​​can be regarded as N data collection points of the interpolation model, or N initial interpolation data. In other words, there will be N discrete initial data points {(x i ,y i ),T i }, i=1,2,…,N,;satisfy the following equations: Rewriting the above equations into matrix form yields: Where T is still the above average temperature matrix, C is a constant that can be calculated, and λ=[λ1,λ2,…λ n ] T is the unknown coefficient matrix, and its value is the key to solving the polynomial modified radial basis function interpolation model. The polynomial modified radial basis is the function value corresponding to the geometric center point of each divided small block, starting from the first block Arrange to the Nth block Then, solve the matrix equation Available At this point, substitute the specific value of the coefficient matrix λ into the formula The temperature distribution interpolation model T(x,y) based on the polynomial modified radial basis function can be obtained.

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