Method, apparatus and medium for multivariate dynamic non-stationary coupling analysis based on sliding window

Abstract

The application discloses a kind of multivariate dynamic non-stationary coupling analysis method, equipment and medium based on sliding window, method includes: for input time series variable and numerical variable, determine influence subject and influence target, and the upper and lower limits of the first influence time interval of influence subject to influence target;The upper and lower limits of the preset time interval are used as the upper and lower limits of the sliding window, with 1 as step, according to sliding window, the first influence time interval of each influence subject is searched, to determine the second influence time interval.The application is applicable to the dynamic time series correlation calculation of unequal length time series, and the correlation between time series variable and numerical variable and influence time interval can be dynamically identified.

Description

Technical Field

[0001] This invention relates to the field of industrial data detection and processing technology, and in particular to a multivariate dynamic nonstationary coupling analysis method, device and medium based on a sliding window. Background Technology

[0002] Current mainstream correlation methods, such as Pearson correlation and Spearman correlation, require that the two data points used for correlation calculation be of exactly the same length and aligned. However, this becomes impossible when dealing with time-series variables of unequal length. For example, in a factory producing parts, product quality is inspected hourly. It is known that product quality is correlated with the production data of the previous hour, but the hourly quality data is a numerical variable, while the production data is continuous time-series data. The inconsistency and misalignment of the data, along with differences in noise, prevent the direct application of conventional correlation analysis methods. Summary of the Invention

[0003] Technical objective: To address the deficiencies in existing technologies, this invention discloses a multivariate dynamic nonstationary coupling analysis method, device, and medium based on a sliding window. It is applicable to the dynamic time-series correlation calculation of time series with unequal time durations and can dynamically identify the correlation and influence time interval between time series variables and numerical variables.

[0004] Technical solution: To achieve the above technical objectives, the present invention adopts the following technical solution.

[0005] A coupled analysis method for multivariate dynamic nonstationary based on a sliding window, the method comprising: S1: For the input time-series variables and numerical variables, determine the influencing subject and the influencing target, as well as the upper and lower limits of the first time interval of the influencing subject's influence on the influencing target; S2: Using the preset upper and lower limits of the time interval as the upper and lower limits of the sliding window, with a step size of 1, the second influence time interval is determined by searching for parameters for the first influence time interval of each influencing subject according to the sliding window.

[0006] An electronic device includes a memory for storing a computer program and a processor for executing the computer program to implement the above-described multivariate dynamic nonstationary coupling analysis method based on a sliding window.

[0007] A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the above-described sliding window-based multivariate dynamic nonstationary coupling analysis method.

[0008] Beneficial effects: This invention is applicable to the dynamic time series correlation calculation of time series with unequal time durations. It can dynamically identify the correlation and influence time interval between time series variables and numerical variables, and obtain a precise second influence time interval. Compared with the first influence time range, the influence time interval is narrowed and further determined, which can be used for more precise control of industrial production processes. Attached Figure Description

[0009] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention. Detailed Implementation

[0010] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application. Example 1

[0011] As attached Figure 1 As shown, a coupled analysis method for multivariate dynamic nonstationary based on a sliding window includes the following steps: S1: For the input time-series variables and numerical variables, determine the influencing subject and the influencing target, as well as the upper and lower limits of the first time interval of the influencing subject's influence on the influencing target; In this invention, the numerical and time-series variables are derived from industrial production data, and the numerical and time-series variables have only a one-way influence relationship. Therefore, determining the influencing subject and the influencing target involves judging the causal relationship between the time-series and numerical variables based on industrial production experience, thereby identifying the influencing subject and the influencing target. If the time-series variable influences the numerical variable, then the time-series variable is the influencing subject, and the numerical variable is the influencing target; conversely, if the numerical variable influences the time-series variable, then the time-series variable is the influencing target, and the numerical variable is the influencing subject.

[0012] For example, production data (time series variable) only affects the product quality (numerical variable) following that production data segment; conversely, product quality does not affect production data, and subsequent production data cannot affect the current product quality. In other words, the numerical variable and the time series variable have only a one-way influence relationship. For this situation, we need to analyze the following: 1. For multiple time-series variables, the strength of the influence of different time-series variables on numerical variables, such as the strength of the influence of pressure, temperature, machine power, etc. (time-series variables) on product quality (numerical variable) in production data; 2. For a single time series variable, the time interval in which it affects the numerical variable, such as the pressure in the first half hour to the first ten minutes (time series variable), has the greatest impact on the quality data (numerical variable).

[0013] S2: Using the preset upper and lower limits of the time interval as the upper and lower limits of the sliding window, with a step size of 1, the second influence time interval is determined by searching for parameters for the first influence time interval of each influencing subject according to the sliding window.

[0014] S2 includes the following steps: S21. Calculate the mean of the data of the influencing subject within the sliding window; this operation ensures that the data lengths of the influencing subject and the influencing target are consistent and correspond one-to-one, and removes noise from the influencing subject by means of the mean.

[0015] S22. Calculate the maximum mutual information coefficient between the mean of the influencing subject data and the influencing target data. This coefficient serves as the correlation between the influencing subject and the influencing target within the current window. The formula for calculating the maximum mutual information coefficient is as follows: , in, Let x be the maximum mutual information coefficient between variables x and y, where x and y correspond to the mean of the data affecting the subject and the target respectively. for Under the given grid division, the mutual information coefficients of x and y when they belong to subgrids X and Y are given. P(x,y) is the joint probability distribution of variables x and y, P(x) and P(y) are the marginal probability distributions of variables x and y, respectively, n is the data length of the variables, which limits the maximum number of grids, a and b are the number of grids, X is the subgrid after dividing variable x, and Y is the subgrid after dividing variable y. The grid is divided by scatter plotting variables x and y, and then the joint probability distribution P(x,y) and the marginal probability distributions P(x) and P(y) of x and y are calculated by the number of points in different subgrids. The mutual information coefficients are calculated in this way. Then the grid division method is changed, and the maximum mutual information coefficient is calculated as the correlation between the time series variables and numerical variables in the current window. S23. After updating the sliding window using the Gaussian regression model, recalculate the maximum mutual information coefficient and its score; the process includes: S231. Initially, ten different sliding windows are randomly generated, and their maximum mutual information coefficients are calculated as scores. The windows that have been calculated are recorded as historical windows. S232. Using all historical windows and their scores, perform Gaussian regression to establish a Gaussian regression model. Taking a sliding window, i.e., a set of two-dimensional timeframes, as a sample point x, and its corresponding maximum information coefficient y; the Gaussian regression model first calculates the covariance matrix between each sample point, as follows: , in, Each represents the start and end time of a sample point. , This refers to the number of sample points, i.e., the number of historical windows. For kernel function, The average value of the data is 1 in this embodiment. The scaling factor is set to 10 in this embodiment. The formula for calculating the score of the new sample point is as follows: , in, For the prediction score of the new window, This represents the start and end times of a new sample point, i.e., the start and end times of a new sliding window. This is the covariance matrix between the new sample points and all historical sample points.

[0016] S233. Limit the parameter search interval to 1 to control the sliding window length to not be less than 1. Based on the Gaussian regression model in S232, search for the window with the highest score other than the historical window as the next sliding window. Calculate the maximum mutual information coefficient and record it as the historical window. The purpose is to use the data distribution of known points as the prior distribution to estimate the score of new points, then prioritize searching for the window most likely to have a high score to calculate its score, and then use the newly calculated window and its score as the historical window to re-perform Gaussian regression, and calculate the window with the highest possible score as the next search window.

[0017] S234. Repeat S232 to S233 until the number of parameter searches is reached, then return to the window with the highest score in the current historical data.

[0018] S24. After reaching the maximum number of parameter searches, the largest information coefficient in the historical data is taken as the correlation. At this time, the start and end times of the sliding window are taken as the second influence time interval of the influencing subject. The second influence time interval is narrowed compared to the first influence time range, and the influence time interval is further determined, which can be used for more precise control of industrial production processes. Example 2

[0019] Taking the production process data of triple-effect distillation as an example, given that the system data sampling frequency is 3 seconds and chemical detection is performed every 2 hours, there are 12 quality data points and 28,800 production data points per day. The goal is to calculate the impact of the top temperature difference, top temperature, top pressure, bottom temperature difference, bottom temperature, tray temperature difference, and packing layer temperature difference on product quality. It is known that the current quality data is only related to the production data from the previous 2 hours, i.e., the current quality data is related to the previous 2400 (2x60x60 / 3) production data points. Therefore, the upper and lower limits of the sliding window are limited to -2400 (2x60x60) to 0.

[0020] Using the preset upper and lower limits of the time interval as the upper and lower limits of the sliding window, with a step size of 1, the second influence time interval is determined by searching for parameters based on the first influence time interval of each influencing subject according to the sliding window. The process includes: First, a sliding window is randomly generated, for example, (-2400, -1200). The start and end times of this sliding window correspond to the previous 2 hours to the previous 1 hour. Using the time corresponding to the quality data as a baseline, the mean of the time-series data from the previous 2 hours to the previous 1 hour is calculated. Taking the temperature difference at the top of the tower as an example, the following one-to-one numerical pairs are obtained:

[0021] Then, the maximum mutual information coefficient (MIC) is calculated as the score within that window, resulting in x1 being (-2400, -1200) and y1 being 0.5834. This process is repeated 10 times to obtain 10 different windows and their corresponding scores. A Gaussian regression model is then built using these 10 points, and the covariance matrix is ​​calculated. ,

[0022] in, For kernel functions, in this embodiment Take 1, Taking 10 as an example, with x1(-2400, -1200) and x2(-1800, -1420): , Then, the kernel functions between different windows are calculated to form the covariance matrix K.

[0023] For a new window, its score can be estimated. Then calculate the scores for the remaining windows. , in, For the prediction score of the new window, This represents the start and end times of a new sample point, i.e., the start and end times of a new sliding window. For the covariance matrix between the new sample points and all historical sample points, the window with the highest score among the remaining windows is selected as the next search window, and its maximum information coefficient is calculated as its score. This window and its score are then added to the historical data, which now contains 11 data points. Gaussian regression is performed again, and the next search window is calculated once more. This process is repeated until the maximum number of parameter searches is reached. The maximum mutual information coefficient in the current historical data is then output as the correlation between the time-series variable and the numerical variable. The start and end times of the window represent the time interval of the time-series variable's influence on the numerical variable. This scheme can reduce the number of parameter searches and accelerate the optimization process.

[0024] The results of the second influence time interval calculation are as follows: Based on the current time, the correlation between product quality and its influence time interval is as follows: the influence interval of the top temperature difference is from the first 90 minutes to the first 60 minutes, with a correlation of 0.6692; the top temperature is from the first 90 minutes to the first 60 minutes, with a correlation of 0.5962; the top pressure is from the first 30 minutes to the first 20 minutes, with a correlation of 0.5523; the bottom temperature difference is from the first 85 minutes to the first 55 minutes, with a correlation of 0.5578; the bottom temperature is from the first 85 minutes to the first 55 minutes, with a correlation of 0.5962; the packing temperature is from the first 40 minutes to the first 30 minutes, with a correlation of 0.6131; and the tray temperature difference is from the first 100 minutes to the first 90 minutes, with a correlation of 0.5342.

[0025] The above are merely examples and do not limit the application areas provided by this invention.

[0026] In the embodiments of this application, the terms "first" and "second" (if they exist) are used only as name identifiers and do not represent the order of first and second.

[0027] The present invention also discloses an electronic device, including a memory for storing a computer program and a processor for executing the computer program to implement the above-described multivariate dynamic nonstationary coupling analysis method based on a sliding window.

[0028] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that all or part of the steps in the methods of the above embodiments can be implemented by means of software plus a general-purpose hardware platform. Based on this understanding, the technical solution of this application can be embodied in the form of a software product. This computer software product can be stored in a storage medium. The memory can be various types of memory, such as random access memory, read-only memory, flash memory, etc., such as read-only memory (ROM) / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which can be a personal computer, server, or network communication device such as a router) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0029] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A coupled analysis method for multivariate dynamic nonstationary systems based on a sliding window, characterized in that, The methods include: S1: For the input time-series and numerical variables, determine the influencing subject and the influencing target, as well as the upper and lower limits of the first time interval of the influencing subject's influence on the influencing target; the numerical and time-series variables are derived from industrial production data, and there is only a one-way influence relationship between the numerical and time-series variables. In this case, determining the influencing subject and the influencing target means: judging the causal relationship between the time-series and numerical variables based on industrial production process experience, and then determining the influencing subject and the influencing target; the numerical variables include product quality, and the time-series variables include the temperature difference at the top of the tower, the temperature at the top of the tower, the pressure at the top of the tower, the temperature difference at the bottom of the tower, the temperature at the bottom of the tower, the temperature difference of the tray, and the temperature difference of the packing layer; S2: Use the preset upper and lower limits of the time interval as the upper and lower limits of the sliding window. With a step size of 1, search for parameters in the first influence time interval of each influencing subject according to the sliding window to determine the second influence time interval, and control the industrial process according to the second influence time interval. S2 includes the following steps: S21. Calculate the mean of the main data affecting the sliding window; S22. Calculate the maximum mutual information coefficient between the mean of the data of the influencing subject and the influencing target, and use it as the correlation between the influencing subject and the influencing target under the current window; S23. After updating the sliding window using the Gaussian regression model, recalculate the maximum mutual information coefficient and its score. S24. After reaching the maximum number of parameter searches, the largest information coefficient in the historical data is taken as the correlation. At this time, the start and end times of the sliding window are taken as the second influence time interval of the subject.

2. The multivariate dynamic nonstationary coupling analysis method based on a sliding window according to claim 1, characterized in that: The formula for calculating the maximum mutual information coefficient includes: ， in, Let x be the maximum mutual information coefficient between variables x and y, where x and y correspond to the mean of the data affecting the subject and the target, respectively. for Under the given grid division, the mutual information coefficients of x and y when they belong to subgrids X and Y, P(x,y) is the joint probability distribution of variables x and y, P(x) and P(y) are the marginal probability distributions of variables x and y respectively, n is the data length of the variables, a and b are the number of grid divisions, X is the subgrid after dividing variable x, and Y is the subgrid after dividing variable y.

3. The multivariate dynamic nonstationary coupling analysis method based on a sliding window according to claim 1, characterized in that: S23 includes the following steps: S231. Initially, ten different sliding windows are randomly generated, and their maximum mutual information coefficients are calculated as scores. The windows that have been calculated are recorded as historical windows. S232. Using all historical windows and their scores, perform Gaussian regression to establish a Gaussian regression model. S233. Limit the parameter search interval to 1 to control the sliding window length to not be less than 1. Based on the Gaussian regression model in S232, search for the window with the highest score other than the historical window as the next sliding window. Calculate the maximum mutual information coefficient and record it as the historical window. S234. Repeat S232 to S233 until the number of parameter searches is reached, then return to the window with the highest score in the current historical data.

4. The multivariable dynamic nonstationary coupling analysis method based on a sliding window according to claim 3, characterized in that: A sliding window, i.e., a set of sample points x with start and end times, has a corresponding maximum information coefficient y; The calculation formula for the Gaussian regression model includes: ， in, Each represents the start and end time of a sample point. ，n The number of sample points, i.e., the number of historical windows. For kernel function, The mean of the data. If the scaling factor is used, the formula for calculating the score of the new sample point is as follows: ， in, For the prediction score of the new window, This represents the start and end times of a new sample point, i.e., the start and end times of a new sliding window. This is the covariance matrix between the new sample points and all historical sample points.

5. An electronic device, characterized in that, Includes memory used to store computer programs; A processor for executing the computer program to implement a multivariate dynamic nonstationary coupling analysis method based on a sliding window as described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, wherein when the computer program is executed by a processor, it implements the steps of the sliding window-based multivariable dynamic nonstationary coupling analysis method as described in any one of claims 1 to 4.

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