A data acquisition method for a fuel nozzle test bench

Abstract

The present application relates to the technical field of data processing, and particularly relates to a data acquisition method of a fuel nozzle test bench, which comprises the following steps: initializing a covariance matrix, recursively calculating the covariance matrix at the current time through rank two updating, and performing eigenvalue decomposition on the covariance matrix to obtain a singular value spectrum; traversing candidate segmentation points of the singular value spectrum, calculating a comprehensive feature contrast index of each candidate segmentation point according to the kurtosis and zero-crossing rate of the potential signal group and the potential noise group divided by each candidate segmentation point, and adaptively determining an optimal segmentation point based on the maximum criterion of the comprehensive feature contrast index; finally, determining all feature vectors of the real signal based on the optimal segmentation point, performing signal reconstruction, and obtaining the data acquisition result at the current time. The method realizes real-time and high-fidelity acquisition of the fuel nozzle test data through sequential updating and adaptive noise separation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing. Specifically, it relates to a data acquisition method for a fuel nozzle test bench. BACKGROUND

[0002] A fuel nozzle is a core component of high-end power systems such as aircraft engines, and its performance directly affects the efficiency, stability, and reliability of the engine. To accurately evaluate its performance, the fuel nozzle must undergo rigorous dynamic performance testing on a specially designed test bench. A fuel nozzle test bench is a complex device that can simulate harsh conditions such as high temperature and high pressure inside an engine. It monitors key parameters such as pressure and flow rate in real time through sensors during the nozzle's operation, aiming to accurately quantify core dynamic indicators such as opening time and response rate. Therefore, the ultimate goal of data acquisition is to obtain a pure and uncontaminated signal sequence that fully reflects the real physical behavior.

[0003] Existing data acquisition methods usually include a key data purification step, which typically uses singular spectrum analysis to process the collected data to eliminate noise data interference. The principle is to decompose complex time series into multiple independent components that can be sorted by energy size. In theory, abnormal values in the signal will be concentrated in a few specific components due to their suddenness and high energy. By identifying and removing these components, the data can be purified.

[0004] However, when this general purification logic is directly applied to dynamic testing of fuel nozzles, it cannot accurately distinguish data during the dynamic transition period. At the beginning of the test, the fuel supply system of the test bench starts to work, and the pressure and flow rate inside the nozzle will undergo a dramatic but completely normal physical change process to reach a stable working point. The signal generated by this normal physical process usually has a non-stationary mathematical form, which is highly similar to random noise or glitches that need to be removed. Standard singular spectrum analysis methods cannot distinguish between this information-rich normal dynamic process and abnormal values, and may mistakenly identify high-energy components during the transition phase as abnormalities and remove them. This misjudgment discards the entire dynamic process that contains key information such as opening time and response rate, reducing the accuracy and reliability of data acquisition. SUMMARY

[0005] To solve the problem in the prior art that standard singular spectrum analysis methods are prone to mistakenly removing data generated by key normal dynamic processes as abnormal interference, thereby reducing the accuracy and reliability of data acquisition, the present application proposes a data acquisition method for a fuel nozzle test bench, which comprises:

[0006] define a data window sliding with a step of one in data collection and containing a preset number of data points; slide and intercept the data points in the data window according to a preset intercept length to obtain a plurality of data vectors overlapping with each other, and form a trajectory matrix by taking each data vector as a column;

[0007] calculate a covariance matrix based on the trajectory matrix, perform a complete covariance matrix calculation for an initial data window, and recursively obtain a covariance matrix at a current time by performing rank-two updating on a covariance matrix at a previous time when the data window slides;

[0008] perform eigenvalue decomposition on the covariance matrix at the current time to obtain a singular value spectrum composed of a plurality of singular values, and for each candidate partition point for partitioning the singular value spectrum into a potential signal group and a potential noise group, calculate a comprehensive feature contrast index of the candidate partition point based on a comparison result of the potential signal group and the potential noise group in kurtosis and zero-crossing rate;

[0009] determine an optimal partition point according to a maximum criterion of the comprehensive feature contrast index, determine all feature vectors of a real signal according to the optimal partition point, and perform signal reconstruction based on the all feature vectors of the real signal to obtain a purified data point of a data collection result at the current time.

[0010] The technical scheme provides a data purification method integrating real-time processing and intelligent identification, which first maps a one-dimensional real-time data stream into a two-dimensional trajectory matrix capable of revealing the internal dynamic structure of the one-dimensional real-time data stream by using a sliding window, thereby providing a basis for deep analysis; then, efficiently recursively updates a covariance matrix representing signal structure information, and integrates a complex signal purification process into a real-time data collection process. A signal separation criterion based on physical insight is established, which no longer depends on only a single dimension of signal energy size which is easy to misjudge, but rather goes deep into the internal attributes of signal components, measures the distribution form of the signal components by using kurtosis, measures the structural complexity of the signal components by using a zero-crossing rate, quantifies a comprehensive feature contrast index by comprehensively quantifying the distribution form and the structural complexity, and automatically and objectively finds an optimal partition point capable of maximizing the distinction between a structured real signal and a noisy interference signal by maximizing the index. Finally, signal reconstruction is performed based on the real signal feature vectors defined by the optimal partition point, so that the output data points not only eliminate noise interference, but also truly retain key physical process information such as a dynamic transition stage, thereby improving the accuracy and reliability of data collection.

[0011] In a preferred scheme, the all eigenvectors of the real signal determined according to the optimal split point are the eigenvector corresponding to the optimal split point and all eigenvectors corresponding to all singular values before the optimal split point.

[0012] In a preferred scheme, the rank-two updating method for the covariance matrix of the previous moment is: according to the sliding of the data window, determining the new data vector entering the data window and the old data vector moving out of the data window; based on the covariance matrix of the previous moment, adding a rank-one matrix composed of the outer product of the new data vector, and subtracting a rank-one matrix composed of the outer product of the old data vector, to realize rank-two updating and obtain the covariance matrix of the current moment.

[0013] This technical scheme avoids repeated calculation of all data in the entire window when each new data point arrives by designing an efficient covariance matrix recursive updating algorithm. This rank-two updating mechanism of adding new and removing old optimizes the calculation complexity of matrix updating to only be related to the length of the interception, reduces the calculation complexity of data, and improves the efficiency and real-time performance of data processing.

[0014] In a preferred scheme, the eigenvalue decomposition of the covariance matrix of the current moment is realized by applying a long-term equation solution, including: splitting the rank-two updating into a first rank-one updating corresponding to the new data vector and a second rank-one updating corresponding to the old data vector; in each rank-one updating, a long-term equation is constructed and solved to update the eigenvalue, and the eigenvalue decomposition result of the covariance matrix of the current moment is obtained.

[0015] This technical scheme deeply optimizes the calculation complexity of the feature decomposition link with the largest performance bottleneck in the original scheme by introducing a long-term equation, so that the calculation complexity of each step in the entire process from the data point entering the data window to the final output of the purification result is strictly controlled, ensuring that the algorithm can still meet the strict real-time requirements when processing high sampling rate and long sequence data, and realizing true high efficiency and smoothness.

[0016] In a preferred scheme, the kurtosis and zero-crossing rate are determined based on the following manner: determining the kurtosis of the potential signal group / potential noise group through the fourth-order standard matrix of all singular values contained in the potential signal group / potential noise group; and taking the average zero-crossing rate of all eigenvectors corresponding to all singular values contained in the potential signal group / potential noise group as the zero-crossing rate of the potential signal group / potential noise group.

[0017] In a preferred scheme, the comprehensive feature contrast index of the candidate split point is determined based on the following manner: the kurtosis of the potential signal group is divided by the kurtosis of the potential noise group to obtain a kurtosis quotient; the zero-crossing rate of the potential noise group is divided by the zero-crossing rate of the potential signal group to obtain a zero-crossing rate quotient; the kurtosis quotient and the zero-crossing rate quotient are multiplied to obtain the comprehensive feature contrast index of the candidate split point.

[0018] The technical scheme can reflect the significant difference between normal data and abnormal noise by analyzing the signal distribution mode and signal structure complexity of the data points and comprehensively quantifying the same into an index. The significant difference can be used to automatically and objectively identify data representing a normal dynamic process and data generated by abnormal interference.

[0019] In a preferred scheme, the step of reconstructing the signal based on all feature vectors of the real signal comprises: projecting and transforming the trajectory matrix at the current moment by using all feature vectors of the real signal to obtain a purified trajectory matrix; performing diagonal averaging on the trajectory matrix to convert the purified trajectory matrix into a one-dimensional time sequence, and obtaining purified data points on the one-dimensional time sequence.

[0020] In a preferred scheme, the step of updating the feature values by constructing and solving a long-term equation comprises: step one, determining a correction vector: determining a new data vector entering the window and an old data vector moving out of the window according to the sliding of the data window, and the correction vector is the new data vector or the old data vector; step two, calculating a projection vector: projecting the correction vector determined in step one into the feature vector space at the previous update moment to obtain a projection vector; step three, constructing and solving a long-term equation: constructing and solving the long-term equation by using the projection vector obtained in step two and all known feature values at the previous update moment, and a scalar coefficient determined by rank-one update, to determine the updated feature values.

[0021] The technical scheme provides an efficient feature value decomposition update method, which decomposes the complex rank-two update into two simpler rank-one updates, and provides an accurate solution path based on a long-term equation for each update, thereby obtaining the updated feature values with lower time complexity, improving the calculation efficiency and real-time performance.

[0022] In a preferred scheme, the singular value spectrum is divided into a potential signal group and a potential noise group, comprising: arranging all singular values in the singular value spectrum in descending order, and sequentially taking the first to the th singular values as candidate split points; for the th candidate split point, the first singular values before the candidate split point are divided into the potential signal group, and the remaining singular values are divided into the potential noise group. singular values are divided into a potential noise group, is a total number of singular values, is a serial number of singular values.

[0023] In a preferred scheme, all eigenvectors corresponding to all singular values are determined based on the following manner: performing eigenvalue decomposition on the covariance matrix to obtain a plurality of eigenvalues and eigenvectors corresponding to the eigenvalues, taking square roots of the eigenvalues as the singular values, and then obtaining a corresponding relationship between the singular values and the eigenvectors, and determining all eigenvectors corresponding to all singular values based on the corresponding relationship.

[0024] The present application has the following effects:

[0025] The present application introduces a serialized recursive updating mechanism and an adaptive separation criterion based on a comprehensive feature contrast index, and constructs a brand-new online data purification and collection method, discards the logic of simply relying on energy size for judgment in the prior art, realizes intelligent differentiation of normal dynamic processes and abnormal noise interference by deeply analyzing the inherent distribution form and structural complexity of signal components represented by the zero-crossing rate, solves the defect of misjudging normal dynamic processes as noise interference, and can retain complete dynamic information while effectively filtering noise, thereby improving the fidelity and accuracy of data collection. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 is a method flowchart of the present application;

[0027] Figure 2 is a singular spectrum distribution diagram after eigenvalue decomposition of the covariance matrix at the current moment in the present application;

[0028] Figure 3 is a diagram of kurtosis, zero-crossing rate and comprehensive feature contrast index of all candidate segmentation points when determining the optimal segmentation point in the present application;

[0029] Figure 4 is a comparison diagram of signals before and after purification corresponding to the trajectory matrix at the current moment in the present application. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0031] This embodiment provides a data acquisition method for a fuel injector test bench. Within a continuously sliding data window, the method cyclically executes the following core steps: First, the one-dimensional raw signal is transformed into a high-dimensional mathematical model (trajectory matrix and covariance matrix) that reflects its inherent dynamic structure. Next, based on an evaluation system that integrates multiple physical features (comprehensive feature comparison index), the model is intelligently analyzed to automatically and objectively distinguish between real signals and random noise. Finally, the signal is reconstructed using only the identified real signal components, thereby outputting data points with both high fidelity and high signal-to-noise ratio.

[0032] Reference Figure 1 This includes the following steps:

[0033] S1: Set the initial data window and the initial covariance matrix.

[0034] This step is the cold start or initialization phase of the entire real-time processing flow, executed when a test task is started on the fuel injector test bench. When the pressure or flow sensor on the test bench begins to output the first frame of data points, this method does not process them immediately, but instead first acquires and buffers a specified length of data. The initial data sequence forms the initial data window.

[0035] Subsequently, based on the data within this initial data window Data points, and cut according to a preset length. By sequentially sliding and capturing data, starting from the first point in the data window, a data sequence of length 50 (a total of 50 data points) is captured to form a data vector, which serves as the first column of the trajectory matrix. Then, the window slides one point, and starting from the second data point, another data sequence of length 50 is captured to form a data vector, which serves as the second column of the trajectory matrix. This process continues until starting from the 51st data point, when a final data sequence of length 50 (from the 51st data point to the 100th data point) is captured to form the last data vector, which serves as the last column of the trajectory matrix.

[0036] In this way, a trajectory matrix of 50 rows and 51 columns is finally constructed. OK, (Columns). Each column of the trajectory matrix is ​​a... The dimensional state vector captures the historical information of each data point within the initial data window, mapping one-dimensional time-series-based data points to a high-dimensional space.

[0037] Finally, the initial covariance matrix is ​​calculated through a complete matrix multiplication operation:

[0038]

[0039] In the formula, the initial covariance matrix, is the trajectory matrix, denotes the transpose operation, is the transpose matrix of is the sum of the correlations between all data vectors (i.e., columns of the trajectory matrix), which is an unstandardized covariance matrix, is the total number of data points in the initial data window, is the truncation length, is the total number of columns of the trajectory matrix.

[0040] Therefore, the operation of dividing by is to average the unstandardized covariance matrix, which evenly distributes the total correlation to each data vector, thereby obtaining a standardized covariance matrix that can represent the average structural characteristics of the data vectors in the initial data window.

[0041] In summary, this step condenses the large trajectory matrix into a smaller covariance matrix that contains the core structural information. Subsequent analysis of this covariance matrix can obtain the same core feature information with much smaller computational cost.

[0042] S2: Recursion based on rank-two update to obtain the covariance matrix at the current time and perform eigenvalue decomposition to obtain the singular spectrum at the current time.

[0043] After obtaining the covariance matrix corresponding to the initial data window, this step introduces an efficient matrix update algorithm, so that when new data points arrive, only one low-cost fine-tuning is needed to obtain the new covariance matrix. The eigenvalue decomposition of the covariance matrix is performed to obtain the features between the data in real time and efficiently.

[0044] Using the sliding window mechanism, when the data window slides forward by one data point, the oldest data vector is removed and the newest data vector is added. This step first uses the rank-two update theory to efficiently recursively calculate the covariance matrix at the current time. By performing eigenvalue decomposition on the covariance matrix at the current time, the eigenvalues and corresponding eigenvectors of the covariance matrix are extracted for data analysis. Subsequently, in a preferred embodiment, the rank-two update of the covariance matrix is split into two rank-one updates executed sequentially. At each rank-one update, the eigenvalue decomposition process of the covariance matrix itself is optimized through a deeper design of the long-term equation, further improving the data processing efficiency and enhancing the real-time performance.

[0045] In one embodiment, the method for efficiently recursively calculating the covariance matrix at the current time step using the rank-2 update theory is as follows:

[0046] Based on the sliding of the data window, determine the new data vector entering the data window and the old data vector moving out of the data window; based on the covariance matrix of the previous time step, add a rank-one matrix composed of the outer product of the new data vectors and subtract a rank-one matrix composed of the outer product of the old data vectors to achieve rank-two update, and obtain the covariance matrix of the current time step.

[0047] For example, let the current time be time, The covariance matrix at time t is When the data window is from Slide to At time t, the old data vector Remove, new data vector Move in, then The covariance matrix at time t is determined based on the following recursive update formula:

[0048]

[0049] In this formula, for The covariance matrix at time t, for The covariance matrix at time t, The total number of data vectors within the data window. For the new data vector to be moved in, the symbol This represents the transpose operation. yes The transpose of the vector, this transpose operation will... This column vector is converted into a row vector. express The outer product of the two matrices produces a rank-1 matrix. For the old data vector that was moved out, yes The transpose of the vector, this transpose operation will... This column vector is converted into a row vector. express The outer product of the two matrices produces a rank-1 matrix.

[0050] The essence of the recursive update formula is adding new information and removing old information. It applies to the old matrix... Based on the existing data, plus new data The resulting correlation information, minus the old data The correlation information of the contribution, this operation of adding new and removing old is called rank-two update. The traditional matrix update is to update the entire covariance matrix every time the sliding window is updated, and the time complexity is , The time complexity of the rank-two update recursive operation of this step is , which is independent of the length of the time window . In the scene of fuel nozzle testing, this optimization improves the calculation efficiency and is suitable for online processing of real-time data.

[0051] After obtaining the updated covariance matrix , eigenvalue decomposition is performed on to obtain all eigenvalues and corresponding eigenvectors of the covariance matrix . The eigenvalue decomposition algorithm is a mathematical operation for matrices, which decomposes a complex matrix into its most basic components, i.e., eigenvalues and eigenvectors.

[0052] Eigenvalues represent the energy of each signal component contained in the covariance matrix, and eigenvectors represent the structural pattern or form of each signal component. This is because the covariance matrix to be decomposed itself is a mathematical embodiment of the structural characteristics of the original signal.

[0053] The complete logic chain is:

[0054] From signal to matrix: the starting point of the entire analysis is the one-dimensional time series signal from the test bench. By intercepting the data vector through the sliding window and constructing the trajectory matrix, this process has converted the dynamic information of the original signal into a high-dimensional matrix structure.

[0055] The trajectory matrix is the condensation of the signal: the subsequently calculated covariance matrix is a further condensation of the structural characteristics of the trajectory matrix, which quantifies the autocorrelation and patterns within the signal.

[0056] Decompose the matrix to decompose the signal: therefore, eigenvalue decomposition of the covariance matrix is essentially a decomposition of the structural information of the original signal. Therefore, the most basic components obtained by decomposition (i.e., eigenvalues and eigenvectors) naturally correspond to each basic signal component of the original signal.

[0057] In an embodiment, considering that the time complexity of the conventional eigenvalue decomposition algorithm is , will become a new performance bottleneck, and the embodiment optimizes it to further improve the calculation efficiency. Specifically: the rank-two update is split into two independent rank-one updates to process, and for each rank-one update, the eigenvalue of the covariance matrix at the current time is obtained by constructing and solving a long-term equation to update the eigenvalue.

[0058] For example, the eigenvalue of the covariance matrix at the current time obtained by the rank-two update is split into two independent rank-one updates, including:

[0059] The first rank-one update is a new operation, which is based on the following formula:

[0060]

[0061] In this formula, is the covariance matrix obtained after performing the new operation on , which is a temporary intermediate variable, is the covariance matrix at the current time, is the total number of data vectors in the data window, is the data vector moving in, symbol represents the transpose operation, is the transpose vector of , and represents the outer product of , which produces a rank-one matrix. The second rank-one update is an old operation, which is based on the following formula:

[0062]

[0063] In this formula,

[0064] is the covariance matrix at the current time, is the covariance matrix obtained after performing the new operation on , which is a temporary intermediate variable, is the total number of data vectors in the data window, is the data vector moving out, is the transpose vector of , and this transpose operation will convert the column vector into a row vector. represents the outer product of , which produces a rank-one matrix. In each rank-one update, a long-term equation is applied to directly solve the updated eigenvalue, and the steps of constructing and solving a long-term equation to update the eigenvalue include:

[0065] ​​​

[0066] Step one, determine the correction vector: according to the sliding of the data window, determine a new data vector entering the window and an old data vector moving out of the window, the correction vector is the new data vector or the old data vector.

[0067] For example, at the time of , is the new data vector moving in, is the old data vector moving out, at the first rank-one update, as the correction vector, at the second rank-one update, as the correction vector.

[0068] Step two, calculate the projection vector: project the correction vector determined in step one into the eigenvector space at the previous update time to obtain a projection vector.

[0069] For example, construct an eigenspace with all eigenvectors corresponding to the covariance matrix at the previous update time, project or into the eigenspace to obtain the projection vector .

[0070] Step three, construct and solve the long-term equation: use the projection vector obtained in step two, all known eigenvalues at the previous update time, and a scalar coefficient determined by the rank-one update to jointly construct and solve the long-term equation to determine the updated eigenvalues.

[0071] The formula of the long-term equation is:

[0072]

[0073] In the formula, is the unknown new eigenvalue to be solved, is the independent variable of the equation, is the long-term equation to be solved, is a scalar coefficient from the rank-one update. When the add-new operation is performed, is positive, and the value is equal to , when the remove-old operation is performed, is negative, and the value is equal to , is the th known old eigenvalue (i.e., the th eigenvalue corresponding to the covariance matrix at the previous update time), which is a known parameter of the equation, is the th component of the projection vector , and the projection vector is obtained by projecting or The projection onto the old eigenvector space is or the projection onto the eigenspace spanned by all eigenvectors corresponding to the covariance matrix at the previous update time.

[0074] The long-term equation establishes an exact mathematical relationship about the unknown new eigenvalue. By serially executing the solution of this equation twice, once for adding new and once for removing old, the decomposition result at time can be directly derived from the decomposition result at time within the time complexity of . This optimizes the eigenvalue decomposition algorithm with the worst performance in the original scheme, whose time complexity is , to , achieving true real-time performance and ensuring the high efficiency and smoothness of the algorithm in practical applications.

[0075] A complete example is as follows:

[0076] S21: Perform initial eigenvalue decomposition on the initial covariance matrix.

[0077] Perform eigenvalue decomposition on to obtain the initial eigenvalue diagonal matrix and the eigenvector matrix , satisfying . The eigenvalue diagonal matrix contains all eigenvalues of the initial covariance matrix, the eigenvector matrix contains all eigenvectors of the initial covariance matrix, and the eigenvalues and eigenvectors are one-to-one corresponding.

[0078] S22: When determining the covariance matrix at any subsequent time, perform the first rank-one update and the second rank-one update in series to obtain the final result by first obtaining the intermediate value through the first rank-one update and then performing the second rank-one update based on the intermediate value.

[0079] S221: First rank-one update.

[0080] For time, the diagonal matrix of all eigenvalues corresponding to the covariance matrix is , and the eigenvector matrix of all eigenvectors corresponding to the covariance matrix is . The goal of this process is to calculate the eigenvalue decomposition result of the intermediate covariance matrix .

[0081] Calculate the projection vector: project the new vector onto the eigenvector space at the known time to obtain the projection vector​ According to the mathematical principle of eigenvalue decomposition and vector space projection, combined with the theory of rank-one update, the updated eigenvector should be calculated by projecting the correction vector in the old eigenspace. is the correction vector, is the old eigenvector matrix, that is the eigenvector matrix composed of all eigenvectors corresponding to the covariance matrix at time is projected into the corresponding eigenspace, and the projection vector is obtained.

[0082] The long-term equation is constructed and solved: the equation about all eigenvalues corresponding to the intermediate covariance matrix is established:

[0083]

[0084] In this formula, is the long-term equation for solving the eigenvalue of the intermediate covariance matrix , is the unknown new eigenvalue to be solved, that is one of the eigenvalues of the intermediate covariance matrix obtained after the first rank-one update (i.e. the new operation) of the covariance matrix at time Since each covariance matrix is dimensional, there will be eigenvalues. Here represents the total number of eigenvalues corresponding to the covariance matrix at time The eigenvalues corresponding to the covariance matrix at time are all known. is the th eigenvalue corresponding to the covariance matrix at time is the projection of into the eigenvector matrix composed of all eigenvectors corresponding to the covariance matrix at time corresponding eigenspace, and the projection vector is obtained. is the th component of the projection vector is the index of the eigenvalue corresponding to the covariance matrix at time , which is also the index of the component of the projection vector (because the th component of the projection vector is exactly in The covariance matrix at time t corresponding to the th The projection results along the directions of each eigenvector, and since the eigenvalues ​​and eigenvectors of the covariance matrix are in one-to-one correspondence, therefore, a unified approach is taken... (to maintain the corresponding relationship) The scalar coefficient is equal to , It represents the total number of data vectors contained in the data window.

[0085] Next, using an efficient numerical root-finding algorithm, the solution that sets the long-term equation to zero is obtained. indivual As the intermediate covariance matrix All eigenvalues, these This constitutes the intermediate covariance matrix. diagonal matrix .

[0086] Use again and Calculate the intermediate covariance matrix eigenvector matrix:

[0087]

[0088] In this formula, yes The corresponding number There are 1 eigenvectors, which is a column vector. yes The eigenvector matrix at time step 1, each column of which is... A known eigenvector of the covariance matrix at time t. yes The diagonal matrix formed by all the eigenvalues ​​corresponding to the covariance matrix at time t is a matrix whose diagonal elements are known eigenvalues. It is the intermediate covariance matrix The corresponding number 1 eigenvalue, the one in the upper right corner This represents the matrix inversion operation. It is the projection vector. The identity matrix is ​​a very fundamental and crucial matrix. Its characteristics include: it is a square matrix (the number of rows and columns are the same); all elements on its main diagonal are 1; and all elements off-diagonal are 0. In the expression... middle, It is a matrix, and It is a scalar (a single number). Mathematically, matrices cannot be directly added or subtracted from scalars. For this subtraction to be valid, the scalar needs to be... into a matrix. By multiplying by the identity matrix I one gets a diagonal matrix with ones on the diagonal and zeros elsewhere. In this way, the operation becomes a subtraction between two matrices of the same dimension, which is a legitimate, well-defined operation, and this operation is the standard step in the computation of eigenvectors.

[0089] In summary, by this formula, the new eigenvectors are derived directly from the old eigenvectors / eigenvalues and the projection vectors at a lower computational cost. One gets a corresponding eigenvector by multiplying by the intermediate eigenvector matrix , which is obtained by executing the formula for all vectors from 1 to M, and then combining them column-wise. This will serve as the input for the next step of the old operation.

[0090] S222: Second rank-one update.

[0091] The goal of this procedure is to compute the eigendecomposition of the covariance matrix at time , the scalar coefficients , and the projection vectors : project the old vectors into the eigenvector matrix corresponding to the intermediate covariance matrix (the eigenspace spanned by ).

[0092] The equation for all eigenvalues of the covariance matrix at time is set up to build the equation for the eigenvalues :

[0093]

[0094] In this formula, is the long-term equation for solving the eigenvalues of , and is the unknown new eigenvalue of the covariance matrix at time , which is the eigenvalue obtained after the second rank-one update (i.e., the old operation) of the intermediate covariance matrix . Since each covariance matrix is -dimensional, there will be Each feature value. The scalar coefficient has a value equal to , It is the intermediate covariance matrix The corresponding number 1 eigenvalue (known) It is the projection vector The One portion, express The total number of eigenvalues ​​corresponding to the covariance matrix at any given time is constant. Regardless of the time of day, the number of eigenvalues ​​and eigenvectors corresponding to the decomposed covariance matrix is ​​always the same; therefore, it is used consistently. express.

[0095] Again, using a numerical root-finding algorithm, the solution that sets the long-term equation to zero is obtained. indivual , as the covariance matrix at the current moment All eigenvalues, these It constitutes diagonal matrix .

[0096] Similarly, use and calculate Covariance matrix at time step eigenvector matrix:

[0097]

[0098] In this formula, yes The corresponding number There are 1 eigenvectors, which is a column vector. It is the intermediate eigenvector matrix, and each column of it is the intermediate covariance matrix. A known eigenvector, It is the intermediate covariance matrix A diagonal matrix whose diagonal elements are known eigenvalues. yes Covariance matrix at time step The 1 eigenvalue, the one in the upper right corner This represents the matrix inversion operation. It is the projection vector. Represents the identity matrix, design logic and They are consistent.

[0099] In summary, this formula allows for the direct derivation of the current-time eigenvector from the eigenvectors / eigenvalues ​​and projection vectors corresponding to the intermediate covariance matrix with lower computational cost. This will result in a corresponding feature vector. ,Will From 1 to Execute the formula once for each case to obtain all the results. The vectors are then combined column-wise to form the complete eigenvector matrix. .

[0100] Thus far, the complete process, through two cascaded rank-one updates and the solution of the long-term equation, in Within the time complexity, from The decomposition results of the covariance matrix at time t are recursively derived Decomposition results of the covariance matrix at time t. and .

[0101] After the above calculations, this step finally obtains all the eigenvalues ​​and their corresponding eigenvectors at the current time. Subsequently, by taking the square root of each eigenvalue, a singular value can be obtained. Based on the one-to-one correspondence between eigenvalues ​​and eigenvectors, a correlation relationship is established between each singular value and each eigenvector. Finally, all eigenvalues ​​constitute the singular spectrum at the current time, which will serve as the direct input for step S3.

[0102] like Figure 2 As shown in the figure, this graph illustrates the result after arranging all singular values ​​in descending order. The horizontal axis represents the singular value index, from 1 to 50, which corresponds to the truncation length (i.e., feature vector dimension) set in the embodiment. Completely consistent. The singular values ​​on the vertical axis represent the energy levels of each signal component. Visually, the first few singular values ​​are very large and decrease rapidly, while subsequent singular values ​​are smaller and decrease more gradually, forming a "long tail." This reflects that the real signal with concentrated energy is mainly represented in a few large singular values, while the noise with dispersed energy is distributed in a large number of smaller singular values. This provides a direct and visual data basis for dividing the potential signal group and potential noise group in the subsequent step S3.

[0103] S3: Use candidate segmentation points to divide the singular spectrum, and calculate the comprehensive feature comparison index of the candidate segmentation points based on the segmentation results.

[0104] The purpose of this step is to perform intelligent analysis on the singular value spectrum obtained in the previous step based on an objective and computable criterion.

[0105] Arrange all singular values ​​in the singular value spectrum in descending order, and then select the first to the second singular values. The singular values are sequentially taken as candidate split points. For the candidate split point, the first singular values of the candidate split point are divided into a potential signal group, and the remaining singular values are divided into a potential noise group. Among them, is the total number of singular values, is the serial number of the singular value.

[0106] For example, there are 10 singular values in the singular value spectrum, which are sorted first. When the 3rd singular value is taken as the candidate split point (the 3rd candidate split point), the first 3 singular values (the 1st singular value, the 2nd singular value and the 3rd singular value) corresponding to all feature vectors of the 3rd candidate split point are taken as a potential signal group, and all feature vectors corresponding to the 4th to 10th singular values are taken as a potential noise group.

[0107] Then, for each division mode, a comprehensive feature comparison index is calculated based on the comparison results of the two groups in kurtosis and zero-crossing rate. The design logic of the index is based on a physical principle: the energy of the real signal component is concentrated (high kurtosis), and the structure is smooth (low zero-crossing rate); while the energy of the noise component is dispersed (low kurtosis), and the structure is chaotic (high zero-crossing rate), and the comprehensive feature comparison index aims to maximize the quantification of this difference.

[0108] In one embodiment, the kurtosis of the potential signal group and the potential noise group is determined based on the following method:

[0109] The singular value sets contained in the potential signal group and the potential noise group are extracted respectively; then, the fourth-order standard moment of the two singular value sets is calculated independently, and the calculation result is taken as the kurtosis of each group.

[0110] For example, the standard moment definition of kurtosis is adopted in this scheme, that is, the kurtosis of a group of data is given by its fourth-order standard moment. The potential signal group divided by the 1st candidate split point is denoted as , and the potential noise group divided by the 1st candidate split point is denoted as Both the potential signal group and the potential noise group contain multiple singular values.

[0111] The kurtosis of the potential signal group is determined based on the following method:

[0112] First, the mean and standard deviation of are calculated, and Each singular value in is subtracted by the mean and then divided by the standard deviation, achieving the standardization of each singular value. The purpose is to eliminate the influence of the position (determined by the mean) and the scale (determined by the standard deviation) of the data itself. Regardless of the size and range of the original singular values, after this step, a new dataset with a mean of 0 and a standard deviation of 1 will be obtained. This ensures that subsequent analysis only focuses on the pure shape of the data distribution, rather than being disturbed by the numerical size.

[0113] In the second step, the fourth power of each standardized singular value in is taken. Taking the fourth power greatly amplifies the influence of data points far from the mean (i.e. outliers or extreme values). A distribution with a prominent peak or heavy tail means it contains some values far from the center, which will become very large after taking the fourth power, thus dominating the final calculation result.

[0114] In the third step, the average of all results after the fourth power calculation in is taken. This step combines the influence of all data points and finally obtains a single value that can represent the degree of peak of the entire data set distribution, i.e. kurtosis. Kurtosis quantifies the sharpness or flatness of a group of data distribution. A highly concentrated peak distribution (such as the energy distribution of the real signal) will get a high kurtosis, while a dispersed flat distribution (such as the energy distribution of noise) will get a lower kurtosis.

[0115] According to this way, the kurtosis of the potential signal group is obtained, denoted as

[0116] , and by analogy, the kurtosis of the potential noise group is also obtained in this way, denoted as .

[0117] In an embodiment, the zero-crossing rate of the potential signal group and the potential noise group is determined based on the following way: first, find the feature vector set corresponding to each singular value in the potential signal group and the potential noise group respectively; then, for each feature vector, calculate the number of sign changes between adjacent elements and normalize it to obtain the zero-crossing rate of the vector; finally, average the zero-crossing rates of all feature vectors in a set to obtain the final zero-crossing rate of the signal group or noise group.

[0118] For example, for the th feature vector in all feature vectors corresponding to the potential signal group, the zero-crossing rate is:

[0119]

[0120] In this formula, is the​​ The rate of zero crossing of each eigenvector. It is a single character used to represent the zero-crossing rate. It is the total dimension of the feature vector (which is equal to the truncation length in step S1). It is the dimension number. It is the first The th eigenvector of the th feature vector The values ​​of each dimension It is the first The th eigenvector of the th feature vector The values ​​of each dimension It is the absolute value symbol. Let be a sign function. If the independent variable is greater than 0, the value of the sign function is 1; if the independent variable is equal to 0, the value of the sign function is 0; if the independent variable is less than 0, the value of the sign function is 0. .

[0121] Calculate the zero-crossing rates of all eigenvectors corresponding to the latent signal set according to this formula, and then calculate the average value as the zero-crossing rate of the latent signal set, denoted as . The zero-crossing rate of a latent noise group is calculated in the same way as that of a latent signal group, and is denoted as... .

[0122] In one embodiment, for each candidate segmentation point, the method for determining the comprehensive feature contrast index of the candidate segmentation point based on its divided potential signal group and potential noise group is as follows:

[0123] The kurtosis of the potential signal group is divided by the kurtosis of the potential noise group to obtain the kurtosis quotient; the zero-crossing rate of the potential noise group is divided by the zero-crossing rate of the potential signal group to obtain the zero-crossing rate quotient; the kurtosis quotient and the zero-crossing rate quotient are fused by multiplication to obtain the comprehensive feature contrast index of the candidate segmentation point.

[0124] For example, for the first 1 candidate split point Singular values ​​are divided into (The set of singular values ​​comprised of all singular values ​​contained in the potential signal set) and (The set of singular values ​​consisting of all singular values ​​contained in the potential noise group).

[0125] No. The comprehensive comparison index of each candidate split point is calculated based on the following formula:

[0126]

[0127] In this formula, For the first A comprehensive comparison index of candidate split points. It is a single character. It is the first Kurtosis of the potential signal group divided by candidate segmentation points It is the first Kurtosis of the potential noise group divided by the candidate segmentation points It is the first The zero-crossing rate of the potential signal group divided by the candidate segmentation points It is the first The zero-crossing rate of the potential noise group divided by the candidate segmentation points. To prevent abnormal calculations due to extreme cases, this is set here: if or When it is 0, it is set to a very small positive number with a value of 0. This prevents unreasonable calculations caused by a zero denominator. The formula can be divided into two parts according to the multiplication sign: the first part is the kurtosis quotient and the second part is the zero-crossing rate quotient.

[0128] For the first part, the kurtosis quotient is used to compare the differences in energy distribution patterns between the latent signal group and the latent noise group. The real signal energy tends to concentrate on a few singular values, forming a peak distribution. The larger the value, the more likely the noise energy is to be distributed across multiple singular values, forming a flat distribution. The smaller the value, the better. (At the dividing point) This ratio becomes very large when the concentrated signal singularities are correctly separated from the dispersed noise singularities. Therefore, the larger the value of this term, the more successful the separation is in terms of energy distribution.

[0129] For the second part, the zero-crossing rate quotient is used to compare the differences in component structural complexity between the latent signal group and the latent noise group. Real signal components (such as smooth dynamic transitions) have simple structures, and their corresponding eigenvectors oscillate slowly. The smaller the value, the more likely it is to be positively correlated with noise; however, noise components have a chaotic structure, and their corresponding eigenvectors oscillate at high frequencies. The larger it is. Therefore, when the first When a segmentation point can correctly distinguish between signal components with simple structures and noise components with complex structures, It will be very big, and The value of the first part will be very small, making the overall value of the second part very large. The larger the value of the second part, the more successful the partition is from the perspective of the complexity of the component structure.

[0130] In summary, the overall design of this formula establishes a multi-dimensional and comprehensive evaluation system through multiplicative fusion. It requires that an optimal segmentation point must simultaneously demonstrate excellent discriminative ability across multiple dimensions. This mechanism is more robust and reliable than methods relying on a single indicator, automatically and objectively finding the segmentation point that maximizes the distinction between structured real signals and random noise, thereby achieving high-fidelity data acquisition.

[0131] S4: Determine the optimal segmentation point by comparing comprehensive features with the index, and determine all feature vectors of the real signal based on the optimal segmentation point.

[0132] In step S3, the comprehensive comparison index of each candidate segmentation point has been obtained. Based on the maximization principle, the candidate segmentation point with the largest comprehensive comparison index is selected as the optimal segmentation point, which is the optimal segmentation point under the data window at the current moment.

[0133] The optimal split point physically represents an optimal boundary. Before this boundary, singular values ​​are mainly contributed by real signal components with concentrated energy and simple structure; while after this boundary, singular values ​​are mainly dominated by noise components with dispersed energy and complex structure. This point, found by maximizing the comprehensive feature contrast index, ensures that this division achieves optimal distinguishing effect in both kurtosis (energy distribution pattern) and zero-crossing rate (component structural complexity).

[0134] Then, the eigenvectors corresponding to the optimal segmentation point and all eigenvectors corresponding to all singular values ​​before the optimal segmentation point are determined as all eigenvectors of the true signal.

[0135] Once the optimal segmentation point is determined, the signal subspace and noise subspace can be accurately divided, and all feature vectors specific to the real signal can be identified. Specifically, the optimal segmentation point...

[0136] The corresponding eigenvectors, along with all eigenvectors corresponding to all singular values ​​before the optimal segmentation point, collectively determine all eigenvectors of the true signal. This set of eigenvectors forms a pure signal subspace. This subspace fully captures the key physical process information in the dynamic fuel injector test, including both steady-state and dynamic transition phases. Other eigenvectors are assigned to the noise subspace, and the random interference components they represent will be removed in the next signal reconstruction step.

[0137] This step completes the transition from evaluation to decision-making, and the final output of all feature vectors of the real signal will serve as the direct basis for signal reconstruction in step S5.

[0138] like Figure 3 As shown,Figure 3 is a quantitative and visual summary of the entire decision-making process of S3 and S4. Figure 3 The uppermost part of shows the kurtosis changes of potential signal group and potential noise group as the candidate split point k moves. It can be seen that the kurtosis of signal group tends to be stable or slowly increases as k increases, while the kurtosis of noise group is generally small, which verifies the judgment basis of “real signal component energy concentration (high kurtosis); while noise component energy dispersion (low kurtosis)”. Figure 3 The middle part of shows the zero-crossing rates of the two groups. The zero-crossing rate of signal group is significantly lower than that of noise group, reflecting the core principle that real signal structure is smooth (low zero-crossing rate), while noise component structure is chaotic (high zero-crossing rate). Figure 3 The lowermost part of is the key to the final decision, which combines the above two indicators according to the calculation formula of comprehensive feature contrast index, the trend of comprehensive feature contrast index CFCI with k shows a clear peak. At this peak, the kurtosis of signal group is large and the zero-crossing rate is small, and the calculated comprehensive feature contrast index reaches the maximum value. The maximum value position marked by the dashed arrow is a direct embodiment of “determining the optimal split point according to the maximum criterion of the comprehensive feature contrast index”. The comprehensive feature contrast index 42 of the 46th candidate split point is the maximum value, so the 46th candidate split point is taken as the optimal split point, and the final decision result of S4 step is obtained, which provides the basis for obtaining all feature vectors of real signal for signal reconstruction of S5.

[0139] S5: Signal reconstruction is performed on all feature vectors of real signal to obtain the data acquisition result at the current time.

[0140] This step is the final link of the data acquisition and purification process, responsible for restoring the pure signal component identified in step S4 from a high-dimensional mathematical model to a one-dimensional, directly applicable physical signal time series, thereby outputting the final data acquisition result.

[0141] Firstly, all feature vectors of real signal determined in step S4 are used to form a signal subspace. Then, the original trajectory matrix containing noise is projected onto this pure signal subspace to obtain a purified trajectory matrix. In this projection process, all noise components that do not match the real signal pattern will be filtered out. Finally, by performing diagonal averaging on the purified trajectory matrix, it is converted from a two-dimensional matrix form to a one-dimensional time series without loss, thereby obtaining the purified data points as the data acquisition result at the current time.

[0142] Specifically, a reconstruction method containing projection transformation and diagonal averaging is adopted, which includes:

[0143] S51: Projection transformation.

[0144] The essence of the projection transformation is to project a complex signal containing various components onto a signal subspace containing only pure signal patterns, thereby filtering out noise components that do not conform to the space pattern. In this process, the trajectory matrix at the current time is needed, which contains all the original information (including the true signal and noise) in the data window corresponding to the current time. The operation must be based on this complete information body to ensure that the final restored signal is not only pure, but also completely corresponds to the current physical process.

[0145] In theory, each time corresponds to a forward sliding data window. The trajectory matrix at the current time is obtained by sliding and intercepting all data points in the data window at the current time in the same way as the initial trajectory matrix is constructed, that is, according to the preset intercepting length.

[0146] After obtaining the trajectory matrix at the current time, a projection matrix is constructed using all the eigenvectors of the true signal. Then, the trajectory matrix at the current time is projected onto the signal subspace composed of the eigenvectors of the true signal. In this projection process, any component in the trajectory matrix at the current time that is orthogonal to the signal subspace (i.e., a component in the noise subspace) will be naturally filtered out because their projection on the signal subspace is zero. After this transformation, a purified trajectory matrix is obtained, which retains all the core dynamic information of the original signal while effectively eliminating the interference of random noise.

[0147] S52: Diagonal averaging.

[0148] The purified trajectory matrix is still a two-dimensional matrix, and in order to restore it to a one-dimensional time series, diagonal averaging operation needs to be performed. In the construction principle of the trajectory matrix, all elements on the anti-diagonal line of the matrix actually correspond to the same data point in the original one-dimensional time series. Therefore, diagonal averaging is to average the element values on each anti-diagonal line of the purified trajectory matrix, and the average value is taken as the value of the data point at the corresponding position in the reconstructed one-dimensional time series.

[0149] S53: Determine the data acquisition result.

[0150] By performing complete diagonal averaging operation on the purified trajectory matrix, it can be converted from two-dimensional matrix form to one-dimensional time series without loss, and finally a series of purified data points are obtained. These data points are the final data acquisition results at the current time, which not only maintain the dynamic process of the original signal (such as the opening time, response rate and other key information), but also have a high signal-to-noise ratio, thereby realizing real-time and high-fidelity acquisition of the test data of the fuel nozzle.

[0151] As shown in Figure 4 The horizontal coordinate is all the sampling points corresponding to the trajectory matrix at the current time, ranging from 0 to 100, which corresponds to the The one-dimensional time sequence corresponding to the trajectory matrix at the current time is equivalent to the original signal, representing the original one-dimensional time sequence containing noise in the current data window, which is the input of the entire purification process. The one-dimensional time sequence purified by the trajectory matrix at the current time is obtained by projecting the original trajectory matrix onto the pure signal subspace determined by the optimal segmentation point, and then reconstructing by diagonal averaging. Through the direct comparison of "before processing" and "after processing", it is reflected that the smooth dynamic trend reflecting the real physical process is extracted from the original noisy sampling by the technical solution, while the key dynamic information (such as S-shaped rising process) in the signal is preserved, the defect that such normal dynamic process is misjudged as noise in the background technology is solved, and the accuracy of data acquisition is improved.

[0152] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of data acquisition for a fuel injector test bench, characterized in that, The method comprises the following steps: defining a data window sliding in data collection with a step size of one and containing a preset number of data points; sliding and intercepting the data points in the data window according to a preset intercepting length to obtain a plurality of data vectors overlapping with each other, taking each data vector as a column to form a trajectory matrix; calculating a covariance matrix based on the trajectory matrix, performing a complete covariance matrix calculation for an initial data window, and recursively obtaining a covariance matrix at a current time by performing rank-two updating on a covariance matrix at a previous time when the data window slides; performing eigenvalue decomposition on the covariance matrix at the current time to obtain a singular value spectrum composed of a plurality of singular values, and calculating a comprehensive feature comparison index of each candidate segmentation point for dividing the singular value spectrum into a potential signal group and a potential noise group based on a comparison result of the potential signal group and the potential noise group in kurtosis and zero-crossing rate; determining an optimal segmentation point according to a maximum criterion of the comprehensive feature comparison index, and determining all eigenvectors of a real signal according to the optimal segmentation point, and performing signal reconstruction based on all eigenvectors of the real signal to obtain purified data points of the data collection result at the current time.

2. The data collection method of claim 1, wherein, The all eigenvectors of the real signal are determined according to the optimal segmentation point by determining the eigenvectors corresponding to the optimal segmentation point and all eigenvectors corresponding to all singular values before the optimal segmentation point as all eigenvectors of the real signal.

3. The data collection method of claim 1, wherein, The method for performing rank-two updating on the covariance matrix at the previous time comprises the following steps: determining a new data vector entering the data window and an old data vector moving out of the data window according to the sliding of the data window; adding a rank-one matrix composed of the outer product of the new data vector to the covariance matrix at the previous time, and subtracting a rank-one matrix composed of the outer product of the old data vector to realize rank-two updating, so as to obtain the covariance matrix at the current time.

4. The data collection method of claim 1, wherein, The eigenvalue decomposition on the covariance matrix at the current time is realized by applying a long-term equation, comprising the following steps: the rank-two updating is divided into a first rank-one updating corresponding to the new data vector and a second rank-one updating corresponding to the old data vector; in each rank-one updating, a long-term equation is constructed and solved to update the eigenvalue, so as to obtain the eigenvalue decomposition result of the covariance matrix at the current time.

5. The data collection method of claim 1, wherein, The kurtosis and the zero-crossing rate are determined based on the following method: the kurtosis of the potential signal group / potential noise group is determined by the fourth-order standard matrix of all singular values contained in the potential signal group / potential noise group; the average zero-crossing rate of all eigenvectors corresponding to all singular values contained in the potential signal group / potential noise group is taken as the zero-crossing rate of the potential signal group / potential noise group.

6. The data collection method of claim 5, wherein, The comprehensive feature comparison index of the candidate segmentation point is determined based on the following method: the kurtosis of the potential signal group is divided by the kurtosis of the potential noise group to obtain a kurtosis quotient; the zero-crossing rate of the potential noise group is divided by the zero-crossing rate of the potential signal group to obtain a zero-crossing rate quotient; the kurtosis quotient and the zero-crossing rate quotient are multiplied to obtain the comprehensive feature comparison index of the candidate segmentation point.

7. The data collection method of claim 1, wherein, The steps of performing signal reconstruction based on all eigenvectors of the real signal comprise: Projecting and transforming the track matrix at the current moment by using all eigenvectors of the real signal to obtain a purified track matrix; performing diagonal average on the track matrix to convert the purified track matrix into a one-dimensional time sequence, and obtaining multiple purified data points on the one-dimensional time sequence.

8. The data collection method of claim 4, wherein, The step of updating the eigenvalues by constructing and solving a long-term equation comprises: Step one, determining a correction vector: according to the sliding of the data window, determining a new data vector entering the window and an old data vector moving out of the window, and the correction vector is the new data vector or the old data vector; Step two, calculating a projection vector: projecting the correction vector determined in step one into the eigenvector space at the previous update moment to obtain a projection vector; Step three, constructing and solving a long-term equation: using the projection vector obtained in step two and all known eigenvalues at the previous update moment, and a scalar coefficient determined by rank-one update, to jointly construct and solve the long-term equation to determine the updated eigenvalues.

9. The data collection method of claim 1, wherein, The singular value spectrum is divided into a potential signal group and a potential noise group, comprising: All singular values in the singular value spectrum are arranged in descending order, and the first to the second singular values are taken as candidate segmentation points in turn; For the There are 10 candidate split points, and the first 10 of the 10 candidate split points are selected. The singular values ​​are divided into potential signal groups, and the remaining ones are... Each singular value is divided into a potential noise group. The total number of singular values. The index of the singular value.

10. The data acquisition method of claim 2 or 9, wherein, All eigenvectors corresponding to all singular values are determined based on the following manner: The eigenvalue decomposition of the covariance matrix obtains multiple eigenvalues and the eigenvectors corresponding to the eigenvalues, the square roots of the eigenvalues are taken as the singular values, and the correspondence between the singular values and the eigenvectors is obtained, and all eigenvectors corresponding to all singular values are determined based on the correspondence.

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