阅读说明：本技术 基于重构正则化矩阵的奇异值分解微振动振源定位方法 (Singular value decomposition micro-vibration source positioning method based on reconstruction regularization matrix ) 是由 孙长库 王柳丹 王鹏 付鲁华 于 2021-07-28 设计创作，主要内容包括：本发明公开了一种基于重构正则化矩阵的奇异值分解微振动振源定位方法,在空间中放置N个加速度传感器,根据空间位置关系得到定位模型,选取其中一个传感器作为参考传感器,通过作差将非线性方程组转换为线性方程组,写成矩阵形式得到矩阵方程；令迭代索引j＝0,设置迭代门限值ε,采用最小二乘法求解矩阵方程,将方程得到的解作为迭代初始值然后对矩阵方程的系数矩阵进行奇异值分解,求正则化参数,构造正则化矩阵,并结合正则化参数计算得到正则化估计值；计算正则化估计值的均方误差,计算出均方误差取最小值时所对应的新的正则化矩阵,进而计算新的正则化估计值若则此时的为优化结果,确定环境微振动振源位置。(The invention discloses a singular value decomposition micro-vibration source positioning method based on a reconstruction regularization matrix, which comprises the steps of placing N acceleration sensors in a space, obtaining a positioning model according to a space position relation, selecting one of the sensors as a reference sensor, converting a nonlinear equation set into a linear equation set by making a difference, and writing the linear equation set into a matrix form to obtain a matrix equation; setting the iteration index j to 0, setting an iteration threshold value epsilon, solving a matrix equation by adopting a least square method, and taking the solution obtained by the equation as an iteration initial value Then, performing singular value decomposition on a coefficient matrix of a matrix equation, solving regularization parameters, constructing a regularization matrix, and calculating by combining the regularization parameters to obtain a regularization estimated value; calculating the mean square error of the regularized estimation value, calculating a new regularization matrix corresponding to the minimum mean square error, and further calculating a new regularized estimation value If it is Then it is at this time And determining the position of the environmental micro-vibration source for optimizing the result.)

1. A singular value decomposition micro-vibration source positioning method based on a reconstruction regularization matrix is characterized by comprising the following steps:

s1: setting P as an environment micro-vibration source, placing N acceleration sensors in the space, establishing a three-dimensional rectangular coordinate system, setting the environment micro-vibration source coordinates as P (x, y, z), and setting the acceleration sensor coordinates as S_i(x_i，y_i，z_i) Obtaining a TDOA (time difference of arrival) positioning model according to the spatial position relation, selecting one sensor as a reference sensor, converting a nonlinear equation set into a linear equation set by making a difference, and writing the linear equation set into a matrix form to obtain a matrix equation;

s2: obtaining an acceleration time-course signal x of an environment micro-vibration source signal reaching N sensors in space_i(t) wherein the acceleration time course signal of the reference sensor is x₁(t) (i.e. the 1 st sensor is selected as the reference sensor) and the propagation time from the vibration source to the ith sensor is t_iPropagation time of vibration source to reference sensor is t₁The acceleration time-course signal x of the ith sensor_i(t) and acceleration time-course signal x of the reference sensor₁(t) carrying out generalized cross-correlation operation to obtain a time delay value tau between the vibration source and the ith sensor and between the vibration source and the reference sensor_i1＝t_i-t₁；

S3: setting the iteration index j to 0, setting an iteration threshold value epsilon, solving the matrix equation of the step S1 by adopting a least square method, and taking the solution obtained by the equation as an iteration initial value

S4: performing singular value decomposition on a coefficient matrix of a matrix equation;

s5: solving the regularization parameters of the matrix equation in the step S1 by using a generalized cross validation GCV method;

s6: constructing a regularization matrix based on singular value decomposition, and calculating by combining regularization parameters to obtain a regularization estimated value;

s7: calculating stepS6, calculating the mean square error of the regularized estimation value, calculating a new regularization matrix corresponding to the minimum mean square error, and further calculating a new regularized estimation value

S8: if it isTurning to the step S9, otherwise, updating the iteration index j, replacing the regularization estimated value obtained in the step S7 of the previous circulation with the new regularization estimated value obtained in the step S7, calculating the mean square error of the regularization estimated value and obtaining a new regularization estimated value, and executing the steps S7-S8 in a circulation manner;

s9: at this timeAnd determining the position of the environmental micro-vibration source for optimizing the result.

2. The singular value decomposition micro-vibration source positioning method based on the reconstruction regularization matrix as claimed in claim 1, wherein in step S1:

the TDOA location model is:

in the formula (d)_iDistance from the vibration source of the ambient micro-vibration to the i-th sensor, d_i＝vt_i，t_iThe time required from the vibration source of the environmental micro vibration to the ith sensor; v is the propagation speed of the environmental micro-vibration signal;

taking the first sensor as a reference sensor, taking the difference to convert the nonlinear equation system into a linear equation system, as shown in equation (2):

in the formula, x_i1＝x_i-x₁，y_i1＝y_i-y₁，z_i1＝z_i-z₁，d_i1＝d_i-d₁，i＝1，2，…，N；

S1-3: writing the formula (2) into a matrix form to obtain a matrix equation, as shown in the formula (3):

AX＝b(3)

in the formula (I), the compound is shown in the specification,

3. the singular value decomposition micro-vibration source positioning method based on the reconstruction regularization matrix as claimed in claim 2, wherein step S2 specifically includes:

s2-1: calculating acceleration time-course signal x of ith sensor_i(t) and acceleration time-course signal x of the reference sensor₁(t) cross correlation functionFor cross correlation functionPerforming windowing smoothing treatment, as shown in formula (4):

in the formula (I), the compound is shown in the specification,for the cross-correlation spectrum of the two sets of received signals, phi (f) is a window function,is a generalized correlation spectrum;

s2-2: the value of the time delay τ is obtained from the equation (4)_i1As shown in formula (5):

in this case, d in formula (2)_i1＝d_i-d₁＝vτ_i1。

4. The singular value decomposition micro-vibration source positioning method based on the reconstruction regularization matrix as claimed in claim 3, wherein step S3 specifically includes:

the solution of the matrix equation is calculated by using a least square method, as shown in formula (6):

the solution obtained by the formula (6) is used as an iteration initial valueAs shown in formula (7):

5. the singular value decomposition micro-vibration source positioning method based on the reconstruction regularization matrix as claimed in claim 4, wherein step S4 specifically includes:

s4-1: the matrix A is subjected to singular value decomposition to obtain

Wherein A is an m × n order matrix, and U ═ U₁，u₂，…，u_m]And V ═ V₁，v₂，…，v_n]Is an orthogonal matrix, u_iIs an m-dimensional column vector, v_iIs an n-dimensional column vector satisfyingAre the vectors of the left and right singular values of the matrix a,namely, it isλ₁≥λ₂≥…≥λ_n≥0，λ₁，λ₂，…，λ_nSingular values of the coefficient matrix;

s4-2: substituting formula (8) for formula (7) to obtain:

wherein W is the first n columns of U, i.e. W ═ U₁，u₂，…，u_n]；

S4-3: the observed value of the least squares estimator is corrected to:

6. the singular value decomposition micro-vibration source positioning method based on the reconstruction regularization matrix as claimed in claim 5, wherein step S5 specifically includes:

the generalized cross-validation GCV function is:

in the formula, trace represents the trace of the matrix, i.e. the sum of diagonal elements of the matrix, and α when the function takes the minimum value is the optimal regularization parameter.

7. The singular value decomposition micro-vibration source positioning method based on the reconstruction regularization matrix as claimed in claim 6, wherein step S6 specifically includes:

s6-1: structured regularization matrix R_tComprises the following steps:

in the formula, V_iColumn i of V;

s6-2: regularization estimateComprises the following steps:

8. the singular value decomposition micro-vibration source positioning method based on the reconstruction regularization matrix as claimed in claim 7, wherein step S7 specifically includes:

s7-1: regularization estimatorThe variance of (c) is:

in the formula (I), the compound is shown in the specification,

s7-2: regularization estimatorThe trace of the deviation of (1) is:

s7-3: regularization estimatorThe mean square error of (d) is:

s7-4: when t is 1, 2, …, n, calculating the mean square error corresponding to different t values, when the mean square error is minimum, let k be t, namely determining the boundary λ of small singular value_k＝λ_tAt this time, the matrix R is normalized_kComprises the following steps:

s7-5: computing regularization estimators

9. A computer-readable storage medium, characterized in that a computer program is stored which, when executed, implements the method of any one of claims 1 to 9.

Technical Field

The invention relates to the technical field of micro-vibration response analysis of electronic industry factory building environment, in particular to a singular value decomposition micro-vibration source positioning method based on a reconstruction regularization matrix.

Description of the background

With the continuous development of science and technology, various novel electronic industries are emerging continuously, semiconductor production test equipment such as a vertical pulling furnace, thin film equipment, photoetching equipment and process test equipment all put forward strict requirements on environmental micro-vibration, and the measurement and control of the environmental micro-vibration become important factors influencing the production detection links in the field of semiconductor manufacturing. The environmental micro-vibration belongs to random vibration and has the characteristics of long vibration duration, small vibration intensity and wide vibration frequency band, and in actual production life, the vibration source causing the environmental micro-vibration is very complex in composition and comprises external vibration sources such as natural conditions, traffic loads of adjacent roads and rails, construction loads, mechanical equipment vibration and blasting impact loads of adjacent factories and the like; and internal vibration sources such as production equipment, personnel walking and power equipment in the factory building. The environmental micro-vibration is transmitted to a building foundation or a terrace through a soil body and then transmitted to precision equipment and a plant body, so that the work of the equipment is influenced. Therefore, response analysis on the micro-vibration of the electronic industry plant environment is very important, the micro-vibration source of the environment is positioned, and the position and the distribution information of the micro-vibration source are mastered, so that the basis is provided for vibration isolation of the plant, the guarantee is provided for precision machining, and the economic loss is reduced.

At present, the vibration source positioning is applied to the fields of mine disaster emergency communication, cultural heritage protection, satellite communication and the like. The traditional method comprises the following steps: gauss-newton method, chan algorithm, particle swarm algorithm, etc. The TDOA positioning method is essentially used for solving a linear equation set, but when the linear equation set is solved, if the condition number of a coefficient matrix is larger, the linear equation set is a sick linear equation set, the sick condition is not considered in the traditional algorithm, the accuracy of numerical value solution is difficult to guarantee when the method is applied to solving the sick linear equation set, the practical problem cannot be solved, and the method cannot be well applied to the technical field of micro-vibration response analysis of the factory building environment in the electronic industry.

The high-precision solving problem of the ill-conditioned linear equation set is applied to the fields of electromagnetic inversion algorithms, remote sensing images, GNSS and the like, and is not applied to an environment micro-vibration source positioning algorithm. The most important method for solving the ill-conditioned problem is Tikhonov regularization, two key factors influencing regularization calculation are regularization parameters and a regularization matrix, but the structural method of the regularization matrix is rarely researched at present, small singular values can greatly influence the ill-conditioned state of the matrix, the method for selecting the boundaries of the small singular values is also rarely researched, and the estimation result of the conventional regularization method has larger deviation with the true value.

Because the existing vibration source positioning algorithm cannot be well applied to the field of environmental micro-vibration positioning, a vibration source positioning algorithm for solving a sick linear equation set with high precision is needed in the field.

The invention content is as follows:

the invention aims to provide a singular value decomposition micro-vibration source positioning method based on a reconstruction regularization matrix, which solves the technical problem that a traditional positioning algorithm cannot well solve a sick equation set, can convert a model into a benign problem to improve the solving precision and the stability of solution, and has strong applicability.

The invention is realized by the following technical scheme:

a singular value decomposition micro-vibration source positioning method based on a reconstruction regularization matrix comprises the following steps:

s1: setting P as an environment micro-vibration source, placing N acceleration sensors in the space, establishing a three-dimensional rectangular coordinate system, setting the environment micro-vibration source coordinates as P (x, y, z), and setting the acceleration sensor coordinates as S_i(x_i，y_i，z_i) Obtaining a TDOA (time difference of arrival) positioning model according to the spatial position relation, selecting one sensor as a reference sensor, converting a nonlinear equation set into a linear equation set by making a difference, and writing the linear equation set into a matrix form to obtain a matrix equation;

s2: obtaining environmental micro-vibration source signal arrival in spaceAcceleration time-course signal x of N sensors_i(t) wherein the acceleration time course signal of the reference sensor is x₁(t) (i.e. the 1 st sensor is selected as the reference sensor) and the propagation time from the vibration source to the ith sensor is t_iPropagation time of vibration source to reference sensor is t₁The acceleration time-course signal x of the ith sensor_i(t) and acceleration time-course signal x of the reference sensor₁(t) carrying out generalized cross-correlation operation to obtain a time delay value tau between the vibration source and the ith sensor and between the vibration source and the reference sensor_i1＝t_i-t₁；

S3: setting the iteration index j to 0, setting an iteration threshold value epsilon, solving the matrix equation of the step S1 by adopting a least square method, and taking the solution obtained by the equation as an iteration initial value

S4: performing singular value decomposition on a coefficient matrix of a matrix equation;

s5: solving the regularization parameters of the matrix equation in the step S1 by using a generalized cross validation GCV method;

s6: constructing a regularization matrix based on singular value decomposition, and calculating by combining regularization parameters to obtain a regularization estimated value;

s7: calculating the mean square error of the regularized estimation value in step S6, calculating a new regularization matrix corresponding to the minimum mean square error, and further calculating a new regularized estimation value

S8: if it isTurning to the step S9, otherwise, updating the iteration index j, replacing the regularization estimated value in the last circulation step S7 with the new regularization estimated value obtained in the step S7, calculating the mean square error of the regularization estimated value, calculating a new regularization matrix corresponding to the minimum mean square error, further calculating the new regularization estimated value, and circularly executing the step SS7-S8；

S9: at this timeAnd determining the position of the environmental micro-vibration source for optimizing the result.

In the above technical solution, in step S1:

the TDOA location model is:

in the formula (d)_iDistance from the vibration source of the ambient micro-vibration to the i-th sensor, d_i＝vt_i，t_iThe time required from the vibration source of the environmental micro vibration to the ith sensor; v is the propagation speed of the environmental micro-vibration signal;

taking the first sensor as a reference sensor, taking the difference to convert the nonlinear equation system into a linear equation system, as shown in equation (2):

in the formula, x_i1＝x_i-x₁，y_i1＝y_i-y₁，z_i1＝z_i-z₁，d_i1＝d_i-d₁，i＝1，2，…，N；

S1-3: writing the formula (2) into a matrix form to obtain a matrix equation, as shown in the formula (3):

AX＝b(3)

in the formula (I), the compound is shown in the specification,

in the above technical solution, step S2 specifically includes:

s2-1: calculating the ith sensorAcceleration time-course signal x_i(t) and acceleration time-course signal x of the reference sensor₁(t) cross correlation functionFor cross correlation functionPerforming windowing smoothing treatment, as shown in formula (4):

in the formula (I), the compound is shown in the specification,for the cross-correlation spectrum of the two sets of received signals, phi (f) is a window function,is a generalized correlation spectrum;

s2-2: the value of the time delay τ is obtained from the equation (4)_i1As shown in formula (5):

in this case, d in formula (2)_i1＝d_i-d₁＝vτ_i1。

In the above technical solution, step S3 specifically includes:

setting the iteration index j to be 0, setting an iteration threshold value epsilon, and calculating the solution of a matrix equation by adopting a least square method, wherein the formula (6) is as follows:

the solution obtained by the formula (6) is used as an iteration initial valueAs shown in formula (7):

in the above technical solution, step S4 specifically includes:

s4-1: the matrix A is subjected to singular value decomposition to obtain

Wherein A is an m × n order matrix, and U ═ U₁，u₂，…，u_m]And V ═ V₁，v₂，…，v_n]Is an orthogonal matrix, u_iIs an m-dimensional column vector, v_iIs an n-dimensional column vector satisfyingIs the vector of the left and right singular values of the matrix a, I is the identity matrix,namely, it isλ₁≥λ₂≥…≥λ_n≥0，λ₁，λ₂，…，λ_nSingular values of the coefficient matrix;

s4-2: substituting formula (8) for formula (7) to obtain:

wherein W is the first n columns of U, i.e. W ═ U₁，u₂，…，u_n]；

S4-3: the observed value of the least squares estimator is corrected to:

in the above technical solution, step S5 specifically includes:

the generalized cross-validation GCV function is:

in the formula, trace represents the trace of the matrix, i.e. the sum of diagonal elements of the matrix, and α when the function takes the minimum value is the optimal regularization parameter.

In the above technical solution, step S6 specifically includes:

s6-1: structured regularization matrix R_tComprises the following steps:

in the formula, V_iColumn i of V;

s6-2: regularization estimateComprises the following steps:

in the above technical solution, step S7 specifically includes:

s7-1: regularization estimatorThe variance of (c) is:

in the formula (I), the compound is shown in the specification,

s7-2: regularization estimatorThe trace of the deviation of (1) is:

s7-3: regularization estimatorThe mean square error of (d) is:

s7-4: when t is 1, 2, …, n, calculating the mean square error corresponding to different t values, when the mean square error is minimum, let k be t, namely determining the boundary λ of small singular value_k＝λ_tAt this time, the matrix R is normalized_kComprises the following steps:

s7-5: computing regularization estimators

In the above technical solution, the environmental micro-vibration source position determined in step S9:

the invention also provides a computer-readable storage medium, storing a computer program which, when executed, implements the method described above.

The invention has the advantages and beneficial effects that:

compared with the traditional positioning method, the TDOA positioning method of the environmental micro-vibration source considers the ill-conditioned problem of a linear equation set, and improves the solving precision and the resolving stability; meanwhile, compared with other singular value decomposition algorithms, the method for constructing the regularization matrix reduces the influence of small singular values on matrix ill-condition and improves the precision.

Drawings

FIG. 1 is a block flow diagram of the present invention.

FIG. 2 is a three-dimensional TDOA location model.

For a person skilled in the art, other relevant figures can be obtained from the above figures without inventive effort.

The specific implementation mode is as follows:

in order to make the technical solution of the present invention better understood, the technical solution of the present invention is further described below with reference to specific examples.

Example one

A singular value decomposition micro-vibration source positioning method based on a reconstruction regularization matrix specifically comprises the following steps:

s1: setting P as an environment micro-vibration source, placing N acceleration sensors in the space, establishing a three-dimensional rectangular coordinate system, setting the environment micro-vibration source coordinates as P (x, y, z), and setting the acceleration sensor coordinates as S_i(x_i，y_i，z_i) And wherein i is 1, 2, …, N, and the TDOA location model is obtained according to the spatial location relationship, and is:

in the formula (d)_iDistance from the vibration source of the ambient micro-vibration to the i-th sensor, d_i＝vt_i，t_iRequired for the vibration source of the environmental micro-vibration to the ith sensorThe time of (d); v is the propagation speed of the environmental micro-vibration signal;

taking the first sensor as a reference sensor, taking the difference to convert the nonlinear equation system into a linear equation system, as shown in equation (2):

in the formula, x_i1＝x_i-x₁，y_i1＝y_i-y₁，z_i1＝z_i-z₁，d_i1＝d_i-d₁，i＝1，2，…，N；

Writing the formula (2) into a matrix form to obtain a matrix equation, as shown in the formula (3):

AX＝b(3)

in the formula (I), the compound is shown in the specification,

s2: obtaining an acceleration time-course signal x of an environment micro-vibration source signal reaching N sensors in space_i(t) wherein the acceleration time course signal of the reference sensor is x₁(t) (i.e. the 1 st sensor is selected as the reference sensor) and the propagation time from the vibration source to the ith sensor is t_iPropagation time of vibration source to reference sensor is t₁The acceleration time-course signal x of the ith sensor_i(t) and acceleration time-course signal x of the reference sensor₁(t) carrying out generalized cross-correlation operation to obtain a time delay value tau between the vibration source and the ith sensor and between the vibration source and the reference sensor_i1＝t_i-t₁(ii) a Time delay value tau_i1The specific calculation steps are as follows:

calculating acceleration time-course signal x of ith sensor_i(t) and acceleration time-course signal x of the reference sensor₁(t) cross correlation functionFor cross correlation functionPerforming windowing smoothing treatment, as shown in formula (4):

in the formula (I), the compound is shown in the specification,for the cross-correlation spectrum of the two sets of received signals, phi (f) is a window function,is a generalized correlation spectrum;

the value of the time delay τ is obtained from the equation (4)_i1As shown in formula (5):

in this case, d in formula (2)_i1＝d_i-d₁＝vτ_i1。

S3: setting the iteration index j to 0, setting an iteration threshold value epsilon, solving the matrix equation of the step S1 by adopting a least square method, and taking the solution obtained by the equation as an iteration initial value

The solution of the matrix equation is calculated by using a least square method, as shown in formula (6):

the solution obtained by the formula (6) is used as an iteration initial valueAs shown in formula (7):

s4: performing singular value decomposition on a coefficient matrix of a matrix equation, and specifically:

the matrix A is subjected to singular value decomposition to obtain

Wherein A is an m × n order matrix, and U ═ U₁，u₂，…，u_m]And V ═ V₁，v₂，…，v_n]Is an orthogonal matrix, u_iIs an m-dimensional column vector, v_iIs an n-dimensional column vector satisfyingAre the vectors of the left and right singular values of the matrix a,namely, it isλ₁≥λ₂≥…≥λ_n≥0，λ₁，λ₂，…，λ_nSingular values of the coefficient matrix;

substituting formula (8) for formula (7) to obtain:

wherein W is the first n columns of U, i.e. W ═ U₁，u₂，…，u_n]；

The observed value of the least squares estimator is corrected to:

s5: solving the regularization parameters of the matrix equation in the step S1 by using a generalized cross validation GCV method; the generalized cross-validation GCV function is:

in the formula, trace represents the trace of the matrix, i.e. the sum of diagonal elements of the matrix, and α when the function takes the minimum value is the optimal regularization parameter.

S6: and constructing a regularization matrix based on singular value decomposition, and calculating by combining regularization parameters to obtain a regularization estimated value. Specifically speaking:

structured regularization matrix R_tComprises the following steps:

in the formula, V_iColumn i of V;

regularization estimateComprises the following steps:

s7: calculating the mean square error of the regularized estimation value in step S6, calculating a new regularization matrix corresponding to the minimum mean square error, and further calculating a new regularized estimation valueSpecifically speaking:

regularization estimatorThe variance of (c) is:

in the formula (I), the compound is shown in the specification,

regularization estimatorThe trace of the deviation of (1) is:

regularization estimatorThe mean square error of (d) is:

when t is 1, 2, …, n, calculating the mean square error corresponding to different t values, when the mean square error is minimum, let k be t, namely determining the boundary λ of small singular value_k＝λ_tAt this time, the new regularization matrix R_kComprises the following steps:

computing a new regularization estimator

S8: if it isAnd (4) turning to the step S9, otherwise, updating the iteration index j, replacing the regularization estimated value in the last circulation step S7 with the new regularization estimated value obtained in the step S7, calculating the mean square error of the regularization estimated value, calculating a new regularization matrix corresponding to the minimum mean square error, further calculating a new regularization estimated value, and circularly executing the steps S7-S8.

S9: at this timeDetermining the position of the environmental micro-vibration source for optimizing the result

Example two

The implementation adopts the method to verify the positioning accuracy of the environmental micro-vibration source:

in this embodiment, 5 sensors are placed on the ground surface, one of the sensors is selected as a reference sensor, the environmental micro-vibration source S transmits signals to the set reference sensor and the other sensors, and the time difference is solved according to the received signals.

In this embodiment, a two-dimensional rectangular coordinate system is established by obtaining a propagation velocity of the vibration wave through a test as v 275m/s, and obtaining sensor coordinates as: a (0, 0), B (4.225, 0.1306), C (2.3288, 1.2978), D (4.1684, 2.428), E (-0.0586, 2.4103), and the simulated vibration source coordinate is S (-4.1505, 0).

By using the method of the first embodiment, the vibration source position is calculated to be (-4.2973, -0.1511), and the actual vibration source position is S (-4.1505, 0). The invention effectively solves the ill-conditioned problem of the linear equation set in the traditional TDOA scheme, and improves the solving precision and the resolving stability; meanwhile, compared with other singular value decomposition algorithms, the method for constructing the regularization matrix reduces the influence of small singular values on matrix ill-condition and improves the precision.