A pipeline leakage positioning method based on tensor completion

Abstract

This invention provides a pipeline leak location method based on tensor completion, comprising: collecting leakage vibration data of a leaking pipeline using wireless accelerometers, wherein the leakage vibration data includes data sampled by N wireless accelerometers over M time periods; constructing a tensor completion model using a truncated tensor weighted norm algorithm, and constructing an optimal three-dimensional tensor structure using the firefly algorithm based on the leakage vibration data of the leaking pipeline and the tensor completion model; inputting the optimal three-dimensional tensor structure into the tensor completion model for completion; and calculating the leakage location of the leaking pipeline based on the completed three-dimensional tensor. This invention utilizes a truncated tensor weighted norm to construct a tensor completion model, which efficiently preserves effective information in the missing data, improves the tensor completion accuracy, ensures effective recovery of effective feature information from the pipeline leak data, and improves location accuracy.

Description

Technical Field

[0001] This invention belongs to the field of pipeline leak diagnosis, and in particular relates to a pipeline leak location method based on tensor completion. Background Technology

[0002] Pipeline monitoring is a crucial component of urban pipeline monitoring systems, responsible for transporting industrial and domestic liquids and directly impacting the daily lives of urban residents. However, various factors such as overuse, aging, corrosion, and external interference contribute to pipeline damage and frequent leaks. These leaks not only cause pollution and waste but also result in significant economic losses, potential environmental problems, and public health risks. Therefore, addressing pipeline leaks is of paramount importance.

[0003] With the development of Information and Communication Technology (ICT), the scale and dimensionality of sensor data are increasing. However, these datasets are also plagued by data loss problems, which weaken their utility and effectiveness in practical applications. In practice, data loss can be caused by sensor malfunctions, communication failures, and maintenance issues. Another key reason for data loss is insufficient sensor coverage in both spatial and temporal dimensions. For example, acoustic sensors in a pipe can provide excellent data between two sensors. However, this data may be lost during sampling. Therefore, interpolation of pipe data has become a crucial step for further applications.

[0004] In the field of data completion, most researchers predict missing data by analyzing partially observable data. Directly analyzing large-scale high-order data requires expensive computation and storage, especially as the data order increases and the number of parameters multiplies, leading to the curse of dimensionality. In reality, most high-order data is redundant; for example, adjacent elements in image data often exhibit high correlation. Therefore, we can analyze the low-rank structure of the data instead of directly separating high-order data, thus improving data processing efficiency. The paper "A nonconvex low-rank tensor completion model for spatiotemporal trafficdata imputation" proposes a low-rank tensor completion model based on tensor truncation kernel norm, which can effectively imput missing data. However, when constructing the tensor for the time series, the tensor dimension needs to be manually determined, which cannot guarantee the information structure of the tensor and reduces the final imputation accuracy. The truncation kernel norm provides a uniform threshold for truncating all singular values, which also causes the model to lose original data information, affecting the accuracy of pipeline leak prediction. Summary of the Invention

[0005] To address the problems existing in the background art, the present invention provides a pipeline leak location method based on tensor completion, comprising:

[0006] S1: Collect leakage vibration data of the leaking pipeline using wireless accelerometers. The leakage vibration data includes data sampled by N wireless accelerometers over M time periods.

[0007] S2: Construct a tensor completion model using the truncated tensor weighted nuclear norm algorithm, and construct the optimal three-dimensional tensor structure using the firefly algorithm based on the leakage vibration data of the leaking pipeline and the tensor completion model.

[0008] S3: Input the optimal three-dimensional tensor structure into the tensor completion model for completion; calculate the leakage location of the leaking pipeline based on the completed three-dimensional tensor.

[0009] Preferably, the step of constructing a three-dimensional tensor using the firefly algorithm based on the leakage vibration data and tensor completion model of the leaking pipeline includes:

[0010] S21: Define the data sampled by the wireless accelerometer in each time period as follows:

[0011]

[0012] in, Indicates the first The wireless accelerometer is in the first Data sampled over a time period, Indicates the first The wireless accelerometer is in the first The first time period sampled One data point; This indicates the number of data points sampled by the wireless accelerometer in each time period;

[0013] S22: Let the size of the three-dimensional tensor in the first dimension be... Define the size of the three-dimensional tensor in the second dimension as The size of a three-dimensional tensor in the third dimension is ,in, ;

[0014] S23: The parameters for initializing the firefly algorithm include the number of fireflies, the search space of the firefly population [1,2,3,…,L], the maximum number of iterations M, and the step size factor. The greatest attraction and light absorption coefficient ;

[0015] S24: Initialize a position for each firefly within the search space. The position of each firefly is related to the 3D tensor in the second dimension. The sizes correspond to each other;

[0016] S25: Calculate the fitness value of fireflies, and calculate the relative fluorescence intensity and attractiveness of the firefly with the highest fitness value and the remaining fireflies:

[0017]

[0018]

[0019]

[0020] in, This represents the fitness value of fireflies. This indicates that the leakage vibration data will be processed according to... The root mean square error between the result obtained from the constructed 3D tensor input tensor completion model and the complete tensor; Represents the natural base; define the firefly with the highest fitness value in a firefly population as a firefly. ,but Fireflies and fireflies The distance between them; Fireflies and fireflies The relative fluorescence brightness between them Fireflies fireflies The attractiveness;

[0021] S26: Update the location of fireflies:

[0022]

[0023] in, This indicates the firefly after the update. Location, This refers to the fireflies before the update. Location, This represents the firefly with the highest fitness value. Location; Represents a random number between [0, 1]; This means rounding to the nearest integer. When the value is less than 1 or greater than L, then let ;

[0024] S27: Repeat steps S24-S26 until the maximum number of iterations M is reached. Use the location of the firefly with the highest fitness value as the size of the three-dimensional tensor in the second dimension to construct the optimal three-dimensional tensor structure.

[0025] Preferably, the tensor completion model includes:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] in, Indicates the tensor to be completed; Tensor The truncated weighted nuclear norm; Represents the regularization parameter; Represents a copy matrix; This indicates leakage vibration data; This indicates retrieving known observation data; This represents the transformation from a matrix to a tensor. Tensor The mode-k expansion matrix; Tensor The degree of truncation across all modal expansion matrices; Tensor The truncated weighted nuclear norm of the mode-k expansion matrix; express Weighting coefficients; Indicates rounding up. Tensor The cutoff ratio across all modal expansion matrices. for The singular value matrix obtained by singular value decomposition; For regularization parameters, For copying the matrix, This is the autoregressive coefficient matrix. It is a lag set. Represents singular value matrix The middle diagonal One element, Represents the weight vector The One element, Tensor No. The size of each dimension.

[0034] Preferably, the completion of the optimal three-dimensional tensor structure input tensor completion model includes:

[0035] S31: The optimization problem of the tensor completion model is transformed into an augmented Lagrange function using the Lagrange multiplier method;

[0036] S32: The augmented Lagrangian function is solved using the ADMM optimization algorithm to obtain the completed three-dimensional tensor.

[0037] Preferably, the augmented Lagrangian function comprises:

[0038]

[0039] in, This represents the augmented Lagrange function. Indicates the penalty parameter. This represents the autoregression of matrix Z. Describing the Frobenius norm, Inner product and The inner product, This represents an auxiliary tensor.

[0040] Preferably, solving for the augmented Lagrangian function includes:

[0041]

[0042]

[0043]

[0044]

[0045] when When the value is less than the set threshold, the completed 3D tensor is obtained. ;

[0046] in, Indicates the first The three-dimensional tensor obtained in the next iteration; Indicates the singular value threshold; Indicates the first Auxiliary tensor during the next iteration; This indicates that data from unobserved locations will be retrieved; This represents the transformation from a tensor to a matrix. Indicates the first Copy tensor during the next iteration.

[0047] Preferably, the step of calculating the leakage location of the leaking pipe based on the completed three-dimensional tensor includes:

[0048] S31: Reshape the completed 3D tensor into a matrix, and extract the data x1 and x2 from the pair of wireless accelerometers that are closest to the current time after completion;

[0049] S32: Calculate the cross-correlation function from x1 to x2 using the Fast Fourier Transform based on the data completed by the two wireless accelerometers;

[0050] S33: Use a peak detection algorithm to find the peak of the cross-correlation function, and obtain the time delay based on the ratio of the peak position of the cross-correlation function to the signal sampling rate. ;

[0051] S34: Utilize the formula Calculate the distance between the leak point and sensor x1 to obtain the location of the leak point. This indicates the speed at which sound travels through a pipe.

[0052] The present invention has at least the following beneficial effects

[0053] This invention utilizes the principle of tensor completion. First, it employs the Firefly algorithm to find the optimal tensor representation structure for spatiotemporal data, highlighting a representation method that effectively showcases data features. Then, it constructs a tensor completion model using the weighted nuclear norm of truncated tensors, efficiently preserving valuable information from missing data and improving tensor completion accuracy. Finally, it expands the tensors into matrices and introduces a vector autoregression process to better utilize the global and local consistency of the data, ultimately ensuring the effective recovery of valuable feature information from pipeline leak data and improving location accuracy. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0055] Figure 2 This is a flowchart of the method of the present invention. Detailed Implementation

[0056] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0057] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0058] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0059] Please see Figure 1 This invention provides a pipeline leak location method based on tensor completion, comprising:

[0060] S1: Collect leakage vibration data of the leaking pipeline using wireless accelerometers. The leakage vibration data includes data sampled by N wireless accelerometers over M time periods.

[0061] In this embodiment, with N=2, two wireless accelerometers are respectively set on the left and right sides of the leaking pipe to collect leakage vibration data. By analyzing the collected leakage vibration data, some sampling points are randomly deleted as training data. The complete data corresponding to the training data is used as labels to construct sample pairs. Based on the sample pairs, the optimal three-dimensional tensor structure is constructed using the firefly algorithm. Using data sampled from multiple time periods can make full use of the correlation between data and improve the completion accuracy.

[0062] S2: Construct a tensor completion model using the truncated tensor weighted nuclear norm algorithm, and construct the optimal three-dimensional tensor structure using the firefly algorithm based on the leakage vibration data of the leaking pipeline and the tensor completion model.

[0063] S3: Input the optimal three-dimensional tensor structure into the tensor completion model for completion; calculate the leakage location of the leaking pipeline based on the completed three-dimensional tensor.

[0064] Preferably, the step of constructing a three-dimensional tensor using the firefly algorithm based on the leakage vibration data and tensor completion model of the leaking pipeline includes:

[0065] S21: Define the data sampled by the wireless accelerometer in each time period as follows:

[0066]

[0067] in, Indicates the first The wireless accelerometer is in the first Data sampled over a time period, Indicates the first The wireless accelerometer is in the first The first time period sampled One data point; This indicates the number of data points sampled by the wireless accelerometer in each time period;

[0068] S22: Let the size of the three-dimensional tensor in the first dimension be... Define the size of the second dimension of the three-dimensional tensor as The size of a three-dimensional tensor in the third dimension is ,in, ;

[0069] S23: The parameters for initializing the firefly algorithm include the number of fireflies, the search space of the firefly population [1,2,3,…,L], the maximum number of iterations M, and the step size factor. The greatest attraction and light absorption coefficient ;

[0070] S24: Initialize a position for each firefly within the search space. The position of each firefly is related to the 3D tensor in the second dimension. The sizes correspond to each other;

[0071] S25: Calculate the fitness value of fireflies, and calculate the relative fluorescence intensity and attractiveness of the firefly with the highest fitness value and the remaining fireflies:

[0072]

[0073]

[0074]

[0075] in, This represents the fitness value of fireflies. This indicates that the leakage vibration data will be processed according to... The root mean square error between the result obtained from the constructed 3D tensor input tensor completion model and the complete tensor; Represents the natural base; define the firefly with the highest fitness value in a firefly population as a firefly. ,but Fireflies and fireflies The distance between them; Fireflies and fireflies The relative fluorescence brightness between them Fireflies fireflies The attractiveness;

[0076] S26: Update the location of fireflies:

[0077]

[0078] in, This indicates the firefly after the update. Location, This refers to the fireflies before the update. Location, This represents the firefly with the highest fitness value. Location; Represents a random number between [0, 1]; This means rounding to the nearest integer. When the value is less than 1 or greater than L, then let ;

[0079] S27: Repeat steps S24-S26 until the maximum number of iterations M is reached. Use the location of the firefly with the highest fitness value as the size of the three-dimensional tensor in the second dimension to construct the optimal three-dimensional tensor structure.

[0080] Preferably, the tensor completion model includes:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] in, Indicates the tensor to be completed; Tensor The truncated weighted nuclear norm; Represents the regularization parameter; Represents a copy matrix; This indicates leakage vibration data; This indicates retrieving known observation data; This represents the transformation from a matrix to a tensor. Tensor The mode-k expansion matrix; Tensor The degree of truncation across all modal expansion matrices; Tensor The truncated weighted nuclear norm of the mode-k expansion matrix; express Weighting coefficients; Indicates rounding up. Tensor The cutoff ratio across all modal expansion matrices. for The singular value matrix obtained by singular value decomposition; For regularization parameters, For copying the matrix, This is the autoregressive coefficient matrix. It is a lag set. Represents singular value matrix The middle diagonal One element, Represents the weight vector The One element, Tensor No. The size of each dimension.

[0089] In this embodiment, a coefficient matrix is ​​defined. and a time lag set When the coefficient is Vector autoregression fitting time series vector hour, The total squared error is quantified to provide an estimate. Minimizing time variation will make time series data It exhibits stronger temporal consistency, meaning that the vector autoregressive model can better explain multivariate time series data. The mathematical model for vector autoregression is as follows:

[0090]

[0091] in, This represents the element in the m-th row and t-th column of matrix Z. This represents the m-th row of the matrix. express? Let represent the element in the m-th row and i-th column of the coefficient matrix A. Minimizing time variation through vector autoregression can better capture the local consistency of tensor data, making it possible to handle more challenging missing data scenarios.

[0092] Preferably, the completion of the optimal three-dimensional tensor structure input tensor completion model includes:

[0093] S31: The optimization problem of the tensor completion model is transformed into an augmented Lagrange function using the Lagrange multiplier method;

[0094] S32: The augmented Lagrangian function is solved using the ADMM optimization algorithm to obtain the completed three-dimensional tensor.

[0095] Preferably, the augmented Lagrangian function comprises:

[0096]

[0097] in, This represents the augmented Lagrange function. Indicates the penalty parameter. This represents the autoregression of matrix Z. Describing the Frobenius norm, Inner product and The inner product, This represents an auxiliary tensor.

[0098] Preferably, solving for the augmented Lagrangian function includes:

[0099]

[0100]

[0101]

[0102]

[0103] when When the value is less than the set threshold, the completed 3D tensor is obtained. ;

[0104] in, Indicates the first The three-dimensional tensor obtained in the next iteration; Indicates the singular value threshold; Indicates the first Auxiliary tensor during the next iteration; This indicates that data from unobserved locations will be retrieved; This represents the transformation from a tensor to a matrix. Indicates the first Copy tensor during the next iteration.

[0105] Preferably, the step of calculating the leakage location of the leaking pipe based on the completed three-dimensional tensor includes:

[0106] S31: Reshape the completed 3D tensor into a matrix, and extract the data x1 and x2 from the pair of wireless accelerometers that are closest to the current time after completion;

[0107] S32: Calculate the cross-correlation function from x1 to x2 using the Fast Fourier Transform based on the data completed by the two wireless accelerometers;

[0108] S33: Use a peak detection algorithm to find the peak of the cross-correlation function, and obtain the time delay based on the ratio of the peak position of the cross-correlation function to the signal sampling rate. ;

[0109] S34: Utilize the formula Calculate the distance between the leak point and sensor x1 to obtain the location of the leak point. This indicates the speed at which sound travels through a pipe.

[0110] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0111] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A pipeline leak location method based on tensor completion, characterized in that, Including the following steps: S1: Collect leakage vibration data of the leaking pipeline using wireless accelerometers. The leakage vibration data includes data sampled by N wireless accelerometers over M time periods. S2: Construct a tensor completion model using the truncated tensor weighted nuclear norm algorithm, and construct the optimal three-dimensional tensor structure using the firefly algorithm based on the leakage vibration data of the leaking pipeline and the tensor completion model. The construction of a three-dimensional tensor using the firefly algorithm based on the leakage vibration data and tensor completion model of the leaking pipeline includes: S21: Define the data sampled by the wireless accelerometer in each time period as follows: in, Indicates the first The wireless accelerometer is in the first Data sampled over a time period, Indicates the first The wireless accelerometer is in the first The first time period sampled One data point; This indicates the number of data points sampled by the wireless accelerometer in each time period; S22: Let the size of the three-dimensional tensor in the first dimension be... Define the size of the three-dimensional tensor in the second dimension as The size of a three-dimensional tensor in the third dimension is ,in, ; S23: The parameters for initializing the firefly algorithm include the number of fireflies, the search space of the firefly population [1,2,3,…,L], the maximum number of iterations M, and the step size factor. The greatest attraction and light absorption coefficient ; S24: Initialize a position for each firefly within the search space. The position of each firefly is related to the 3D tensor in the second dimension. The sizes correspond to each other; S25: Calculate the fitness value of fireflies, and calculate the relative fluorescence intensity and attractiveness of the firefly with the highest fitness value and the remaining fireflies: in, This represents the fitness value of fireflies. This indicates that the leakage vibration data will be processed according to... The root mean square error between the result obtained from the constructed 3D tensor input tensor completion model and the complete tensor; Represents the natural base; define the firefly with the highest fitness value in a firefly population as a firefly. ,but Fireflies and fireflies The distance between them; Fireflies and fireflies The relative fluorescence brightness between them Fireflies fireflies The attractiveness; S26: Update the location of fireflies: in, This indicates the firefly after the update. Location, This refers to the fireflies before the update. Location, This represents the firefly with the highest fitness value. Location; Represents a random number between [0, 1]; This means rounding to the nearest integer. When the value is less than 1 or greater than L, then let ; S27: Repeat steps S24-S26 until the maximum number of iterations M is reached. Use the location of the firefly with the highest fitness value as the size of the three-dimensional tensor in the second dimension to construct the optimal three-dimensional tensor structure. S3: Input the optimal three-dimensional tensor structure into the tensor completion model for completion; calculate the leakage location of the leaking pipeline based on the completed three-dimensional tensor.

2. The pipeline leak location method based on tensor completion according to claim 1, characterized in that... The tensor completion model includes: in, Indicates the tensor to be completed; Tensor The truncated weighted nuclear norm; Represents the regularization parameter; Represents a copy matrix; This indicates leakage vibration data; This indicates retrieving known observation data; This represents the transformation from a matrix to a tensor. Tensor The mode-k expansion matrix; Tensor The degree of truncation across all modal expansion matrices; Tensor The truncated weighted nuclear norm of the mode-k expansion matrix; express Weighting coefficients; Indicates rounding up. Tensor The cutoff ratio across all modal expansion matrices. for The singular value matrix obtained by singular value decomposition; For regularization parameters, For copying the matrix, This is the autoregressive coefficient matrix. It is a lag set. Represents singular value matrix The middle diagonal One element, Represents the weight vector The One element, Tensor No. The size of each dimension.

3. The pipeline leak location method based on tensor completion according to claim 2, characterized in that, The optimal three-dimensional tensor structure input tensor completion model is completed by including: S31: The optimization problem of the tensor completion model is transformed into an augmented Lagrange function using the Lagrange multiplier method; S32: The augmented Lagrangian function is solved using the ADMM optimization algorithm to obtain the completed three-dimensional tensor.

4. The pipeline leak location method based on tensor completion according to claim 3, characterized in that, The augmented Lagrange function includes: in, This represents the augmented Lagrange function. Indicates the penalty parameter. This represents the autoregression of matrix Z. Describing the Frobenius norm, Inner product and The inner product, This represents an auxiliary tensor.

5. The pipeline leak location method based on tensor completion according to claim 4, characterized in that, The solution to the augmented Lagrange function includes: when When the value is less than the set threshold, the completed 3D tensor is obtained. ; in, Indicates the first The three-dimensional tensor obtained in the next iteration; Indicates the singular value threshold; Indicates the first Auxiliary tensor during the next iteration; This indicates that data from unobserved locations will be retrieved; This represents the transformation from a tensor to a matrix. Indicates the first Copy tensor during the next iteration.

6. The pipeline leak location method based on tensor completion according to claim 1, characterized in that, The calculation of the leak location of the leaking pipe based on the completed three-dimensional tensor includes: S31: Reshape the completed 3D tensor into a matrix, and extract the data x1 and x2 from the pair of wireless accelerometers that are closest to the current time after completion; S32: Calculate the cross-correlation function from x1 to x2 using the Fast Fourier Transform based on the data completed by the two wireless accelerometers; S33: Use a peak detection algorithm to find the peak of the cross-correlation function, and obtain the time delay based on the ratio of the peak position of the cross-correlation function to the signal sampling rate. ; S34: Utilize the formula Calculate the distance between the leak point and sensor x1 to obtain the location of the leak point. This indicates the speed at which sound travels through a pipe.

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