Industrial predictive control adaptive filtering method and device based on time sequence decomposition
By using time series decomposition methods, industrial process data is decomposed into trend, periodic, and noise components, and feature extraction and filtering parameter matching are performed separately. This solves the problem of insufficient filtering accuracy and improves the adaptability and accuracy of predictive control.
Patent Information
- Application Number
- CN202511884564.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-15
- Publication Date
- 2026-01-13
- Estimated Expiration
- 2045-12-15
AI Technical Summary
In existing technologies, filtering parameters rely on manual setting, which is difficult to adapt to the complex characteristics of industrial process data, resulting in insufficient filtering accuracy and affecting the prediction accuracy and control effect of predictive control models.
A time series decomposition method is adopted to decompose industrial process data into trend components, periodic components, and residual components. Feature extraction is performed on each component, and the target filtering parameters are determined based on the feature extraction results using a matching filtering algorithm. The dataset is decomposed using a time series decomposition algorithm to obtain three independent components, and the data features are analyzed from three dimensions: trend, periodic fluctuation, and noise intensity.
It improves filtering accuracy, enhances the adaptability of industrial predictive control, avoids the problem of traditional filter parameter adjustment relying on experience without clear rules, and achieves higher data processing quality.
Smart Images

Figure CN121325628A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of industrial predictive control, and particularly relates to an industrial predictive control adaptive filtering method and device based on time series decomposition. BACKGROUND
[0002] Industrial predictive control refers to, in the field of industrial production and the like, processing complex fluctuation industrial process data in an application scene by applying a predictive control software, and then improving the efficiency of industrial production, and can be widely applied to a control system of an industrial production process such as chemical industry and petroleum.
[0003] In industrial predictive control, a filtering module is used to suppress noise of collected industrial process data, while effective process information needs to be retained to provide high-quality data guarantee for subsequent data input to a predictive model. The filtering effect depends on the rationality of the value of a filtering parameter. In a current filtering parameter calculation method, the filtering parameter depends on experience setting of a staff, and an actual production process is relatively complex, so that the manual parameter setting mode is difficult to adapt to the complex characteristics of the industrial process data, resulting in insufficient filtering precision, and then affecting the prediction precision and control effect of the predictive control model.
[0004] Therefore, there is an urgent need for a filtering method capable of adapting to and analyzing the complex characteristics of the industrial process data, so as to improve the filtering precision. SUMMARY
[0005] In view of the above-mentioned defects and deficiencies of the prior art, the present application provides an industrial predictive control adaptive filtering method and device based on time series decomposition, and the main purpose is to solve the problem that the current manual parameter setting mode is difficult to adapt to the complex characteristics of the industrial process data, resulting in insufficient filtering precision.
[0006] In order to achieve the above-mentioned purpose, the main technical scheme adopted by the present application includes: In a first aspect, the present application provides an industrial predictive control adaptive filtering method based on time series decomposition, comprising: collecting historical data of a controlled variable in an industrial process in a preset time period to obtain a time series data set; decomposing the time series data set by a time series decomposition algorithm to obtain three types of independent components; wherein the three types of independent components include a trend component representing trend change, a periodic component representing fluctuation frequency in a period, and a residual component representing noise intensity, and the trend component, the periodic component and the residual component are independent of each other; performing feature extraction on the three types of independent components respectively, and matching a filtering algorithm based on the feature extraction result and determining a target filtering parameter of the filtering algorithm.
[0007] In a second aspect, the embodiments of the present application provide an industrial predictive control adaptive filtering device based on time series decomposition, comprising: a collection unit configured to collect historical data of a controlled variable in an industrial process in a preset time period to obtain a time series data set; a calculation unit configured to decompose the time series data set by a time series decomposition algorithm to obtain three types of independent components; wherein the three types of independent components include a trend component representing a trend change, a periodic component representing fluctuation frequency within a period, and a residual component representing noise intensity, and the trend component, the periodic component, and the residual component are independent of each other; a processing unit configured to respectively extract features from the three types of independent components, and match a filtering algorithm based on the feature extraction results and determine target filtering parameters of the filtering algorithm.
[0008] By the above technical solution, the present application provides an industrial predictive control adaptive filtering method and device based on time series decomposition. First, historical data of a controlled variable in an industrial process in a preset time period is collected to obtain a time series data set. Then, the time series data set is decomposed by a time series decomposition algorithm to obtain three types of independent components; wherein the three types of independent components include a trend component representing a trend change, a periodic component representing fluctuation frequency within a period, and a residual component representing noise intensity, and the trend component, the periodic component, and the residual component are independent of each other. Then, features are respectively extracted from the three types of independent components, and a filtering algorithm is matched based on the feature extraction results and target filtering parameters of the filtering algorithm are determined. Compared with related technologies, the present application first arranges historical data in an industrial process in chronological order to form a time series data set, and then decomposes the time series data set into three types of independent components by a time series decomposition algorithm. The complex characteristics of industrial process data are analyzed from three different dimensions of change trend, fluctuation within a period, and specific residual data, solving the problem of "no clear rules for parameter adjustment and relying on experience" in traditional filtering. Finally, features are extracted based on the three types of independent components, and a filtering algorithm is matched based on the feature extraction results and target filtering parameters of the filtering algorithm are determined, thereby improving filtering precision and enhancing the adaptability of industrial predictive control. BRIEF DESCRIPTION OF DRAWINGS
[0009] Figure 1 A flowchart of an industrial predictive control adaptive filtering method based on time series decomposition provided by the embodiments of the present application is shown; Figure 2 A flowchart of a time series decomposition algorithm provided by the embodiments of the present application is shown; Figure 3 A flowchart of a target filtering parameter calculation method provided by the embodiments of the present application is shown; Figure 4A module schematic diagram of an implementation of an industrial predictive control adaptive filtering method based on time series decomposition is provided for an embodiment of the present application. Figure 5 A schematic diagram of an industrial predictive control adaptive filtering device based on time series decomposition is provided for an embodiment of the present application. DETAILED DESCRIPTION
[0010] In order to better understand the above technical solutions, exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a clearer, more thorough understanding of the present application and to convey the full scope of the present application to those skilled in the art.
[0011] As previously described in the background, industrial predictive control can improve the efficiency of industrial production through some industrial control software. In industrial predictive control, the filtering module is one of the core links: it needs to suppress noise on the collected industrial process data (such as temperature, pressure, hardness, flow, concentration, purity, etc.) while retaining effective process information to provide high-quality input data for subsequent prediction models. Filtering is a key technology in signal processing, which refers to the process of suppressing interference or extracting useful information by selecting specific frequency components, and its core role is to separate noise and effective information from the original data to improve data usability and accuracy. The effectiveness of the filtering effect directly depends on the rationality of the filtering parameter values.
[0012] Currently, the filtering parameters of existing industrial predictive control are usually manually adjusted by engineers according to field experience. However, it is obvious that the feedback industrial process data is a complex result, for example, the poor purity in the data is composed of multiple factors and is not caused by only one single factor. Therefore, the method of manually setting filtering parameters is difficult to adapt to the complex characteristics of industrial process data, resulting in insufficient filtering precision, which further affects the prediction precision and control effect of the prediction control model.
[0013] In order to improve the problem that the current manual parameter setting method is difficult to adapt to the complex characteristics of industrial process data, resulting in insufficient filtering precision, an industrial predictive control adaptive filtering method based on time series decomposition is proposed in an embodiment of the present application. The method can be applied to an adaptive filtering system of industrial predictive control, and can execute any one of the industrial predictive control adaptive filtering methods based on time series decomposition mentioned below during runtime. As shown in the figure, the method comprises: Figure 1 S101, collecting historical data of the controlled variable in the industrial process within a preset time period to obtain a time series data set.
[0014] First, the controlled variable (CV) in the industrial process refers to the industrial process data that needs to be analyzed, such as temperature, pressure, hardness, flow, concentration, purity, etc. can be used as one of the controlled variables. Further, time series is a set of observation data arranged in chronological order, the core feature is that the data change is strongly related to time, mainly used for analyzing historical rules, identifying fluctuation reasons and predicting future trends. The collection method can directly call the historical data in the preset time period through the control software used in the specific industrial field.
[0015] As a feasible implementation manner, S101 can collect the historical data of the controlled variable in the recent period through the data source interface of the industrial prediction software to obtain the time series data set.
[0016] S102, decompose the time series data set through a time series decomposition algorithm to obtain three types of independent components.
[0017] The time series decomposition algorithm (Seasonal-Trend decomposition using Loess, STL) is an analysis method that decomposes time series data into multiple components (such as long-term trend, seasonal / periodic fluctuation and residual). The core goal is to reveal the pattern relationship behind the data and support prediction. Among them, the three types of independent components include trend components representing trend changes, periodic components representing fluctuation frequencies within periods, and residual components representing noise intensities, and the trend components, periodic components and residual components are independent of each other.
[0018] Further, the trend component is also called a trend term, which reflects the change trend of the industrial process data in the preset time period, such as the slow decline of pressure data caused by equipment aging. The periodic component is also called a periodic term, which reflects the periodic fluctuation of the industrial process data, such as the periodic change of flow data caused by raw material replenishment every few hours; the residual component is also called a residual term, which is a direct reflection from the data level, reflecting the random noise in the industrial process data, such as sensor measurement error. The independent components mean that the components in the three dimensions have no influence relationship with each other.
[0019] S103, respectively extracting features of the three types of independent components, and matching a filtering algorithm based on the feature extraction result and determining target filtering parameters of the filtering algorithm.
[0020] In S103, the trend item, the periodic item and the residual item are respectively extracted to obtain feature parameters. The feature parameters can specifically include the average value and the change rate of the trend item, the main period (i.e. the period with the highest fluctuation frequency) and the period amplitude (the difference between the maximum value and the minimum value of the periodic item) of the periodic item, and the standard deviation of the residual item. These features can better reflect the changes of the respective components. For example, the greater the change rate of the trend item, the steeper the trend, and the greater the standard deviation of the residual item, the more serious the noise. After feature extraction, the corresponding filtering algorithm is calculated and matched according to the feature extraction result, and the target filtering parameter corresponding to the filtering algorithm is determined, so that the industrial prediction software performs filtering processing based on the target filtering parameter.
[0021] In the embodiment, first, the historical data of the controlled variable in the industrial process in a preset time period is collected to obtain a time series data set. Then, the time series data set is decomposed by a time series decomposition algorithm to obtain three types of independent components. The three types of independent components include a trend component representing trend change, a periodic component representing fluctuation frequency in a period, and a residual component representing noise intensity, and the trend component, the periodic component and the residual component are independent of each other. Then, the three types of independent components are respectively extracted, and the filtering algorithm is matched and the target filtering parameter of the filtering algorithm is determined based on the feature extraction result.
[0022] Compared with the related art, the embodiment first constructs a time series data set from the historical data in the industrial process in chronological order, and then decomposes the time series data set into three types of independent components by a time series decomposition algorithm. The complex characteristics of the industrial process data are analyzed from three different dimensions of change trend, fluctuation in a period and specific residual data, solving the problem of "no clear rules for parameter adjustment and relying on experience" in traditional filtering. Finally, the feature extraction is performed based on the three types of independent components, and the filtering algorithm is matched and the target filtering parameter of the filtering algorithm is determined based on the feature extraction result, thereby improving the filtering precision and enhancing the adaptability of the industrial prediction control.
[0023] Optionally, the feature extraction is performed on the three types of independent components respectively, and the filtering algorithm is matched and the target filtering parameter of the filtering algorithm is determined based on the feature extraction result, including: the feature extraction is performed on the three types of independent components respectively to obtain a feature vector corresponding to the time series data set; a noise coefficient is calculated based on the feature vector; the noise coefficient is compared with a first preset threshold, and in a case where the noise coefficient is greater than the first preset threshold, the filtering algorithm is determined as a moving average filtering algorithm; and the target filtering parameter of the moving average filtering algorithm is calculated based on the three types of independent components.
[0024] In the embodiment, firstly, feature extraction is performed on the three types of independent components to form a feature vector, and a noise-containing coefficient is calculated based on the feature vector. Then, in the case that the noise-containing coefficient is greater than a first preset threshold, it is determined that the filtering algorithm is a sliding average filtering algorithm, and a target filtering parameter of the sliding average filtering algorithm is calculated.
[0025] Firstly, the industrial predictive control algorithm itself has certain robustness and anti-interference ability. When the noise intensity of the controlled variable is not large, any filtering strategy does not need to be adopted, and good control effect can be achieved. In order to judge whether the data needs to be filtered, the noise-containing coefficient is used as a filtering necessity judgment index for the first time in the embodiment, and a critical threshold (a first preset threshold) is set to avoid data distortion caused by "forced filtering regardless of noise intensity" in some related technologies or control precision reduction caused by "missing necessary filtering", and the filtering necessity and the robustness of the control algorithm are considered.
[0026] Optionally, based on the three types of independent components, a target filtering parameter of the sliding average filtering algorithm is calculated, including: based on the three types of independent components, an initial sliding average filtering parameter is calculated; the time series data set is filtered by using the initial sliding average filtering parameter to obtain a first filtering result; a filtering evaluation index is calculated according to the first filtering result, and whether the filtering evaluation index meets a preset requirement is judged; in the case that the filtering evaluation index does not meet the preset requirement, the initial sliding average filtering parameter is iterated according to a first preset iteration formula; the time series data set is filtered by using the iterated sliding average filtering parameter, and a corresponding filtering evaluation index is calculated, until the filtering evaluation index meets the preset requirement, and the iterated sliding average filtering parameter is taken as the target filtering parameter of the sliding average filtering algorithm.
[0027] In the embodiment, the process of how to calculate the target filtering parameter of the sliding average filtering algorithm is described. Firstly, based on the three types of independent components, an initial sliding average filtering parameter is calculated, which is also the initial sliding window length in specific actual application. Then, the time series data set is filtered by using the initial sliding window length to obtain a first filtering result. The filtering result is essentially industrial process data, and the first filtering result is the result filtered by the sliding average filtering algorithm, which is used to distinguish from a second filtering result filtered by other filtering algorithms.
[0028] After filtering, a filtering evaluation index is calculated according to the first filtering result, and whether the filtering evaluation index meets a preset requirement is judged. The filtering evaluation index specifically includes information retention degree and noise suppression degree. The information retention degree is used to judge whether there is excessive filtering, which leads to excessive noise reduction of the original data and causes distortion. The noise suppression degree is used to judge the noise suppression effect.
[0029] Further, if the information retention degree and the noise suppression degree do not meet the preset requirements, the initial sliding window length is iterated according to a preset first iteration formula. The time series data set is re-processed by the moving average filtering based on the iterated sliding window length, and the corresponding filtering evaluation index is calculated until the filtering evaluation index meets the preset requirements. The sliding window length obtained by this iteration is taken as the target filtering parameter of the moving average filtering algorithm, and thus the target filtering parameter for the industrial prediction software to control is obtained. The specific formula will be explained in subsequent embodiments.
[0030] In this embodiment, the information retention degree and the noise suppression degree are constructed to quantify the filtering effect, avoiding the defects of the prior art that a single index evaluation is one-sided, such as only paying attention to noise suppression and ignoring the loss of original data information, so as to ensure that the filtered data neither has excessive noise remaining nor loses key industrial information.
[0031] Optionally, in the case that the number of iterations reaches the maximum and the filtering evaluation index corresponding to the first filtering result after iteration still does not meet the preset requirements, the method further comprises: clearing the number of iterations, determining the filtering algorithm as a first-order exponential filtering algorithm, and calculating the target filtering parameter of the first-order exponential filtering algorithm based on the three types of independent components. The target filtering parameter of the first-order exponential filtering algorithm based on the three types of independent components comprises: calculating an initial first-order exponential filtering parameter based on the three types of independent components; performing filtering processing on the time series data set by using the initial first-order exponential filtering parameter to obtain a second filtering result; calculating a filtering evaluation index according to the second filtering result and determining whether the filtering evaluation meets the preset requirements; in the case that the filtering evaluation does not meet the preset requirements, iterating the initial first-order exponential filtering parameter according to a preset second iteration formula; performing first-order exponential filtering processing on the time series data set based on the first-order exponential filtering parameter after iteration, and calculating the corresponding filtering evaluation index until the filtering evaluation index meets the preset requirements, and taking the first-order exponential filtering parameter after this iteration as the target filtering parameter of the first-order exponential filtering algorithm.
[0032] In the embodiment, in the case that the iteration number of the moving average filtering algorithm reaches the maximum and the filtering evaluation index corresponding to the first filtering result still does not meet the preset requirement, a subsequent filtering scheme is further proposed. The specific steps are similar to the steps of calculating the target filtering parameter according to the moving average filtering algorithm, which will not be described here again. It should be noted that the embodiment is not for all filtering algorithms, but for two specific filtering algorithms. A more comprehensive and more general adaptive filtering method based on time series decomposition for industrial predictive control is proposed. The moving average filtering algorithm is preferentially selected in the embodiment due to its low distortion advantage. Only when the maximum iteration number is reached and the result still does not meet the requirement, the first-order exponential filtering algorithm is switched to, forming a strategy of "low distortion priority and high adaptability backup". Further, the "parameter adjustment formula based on information retention degree and noise suppression degree" is designed for the two types of filtering, realizing dynamic and directional optimization of the parameters, thereby solving the problem of "no clear rule for parameter adjustment and relying on experience" in traditional filtering, and improving the applicability and generality.
[0033] Optionally, the filtering evaluation index includes an information retention degree and a noise suppression degree. According to the filtering result, a filtering evaluation index is calculated, and it is judged whether the filtering evaluation index meets a preset requirement, including: a correlation coefficient of the filtering result relative to a trend component and a periodic component is calculated to obtain an information retention degree; a residual term of the filtering result and a standard deviation of the residual term are calculated, and a noise suppression degree is calculated based on the standard deviation of the residual term of the filtering result and a standard deviation of a residual component; in the case that the information retention degree is greater than or equal to a second preset threshold and the noise suppression degree is less than or equal to a third preset threshold, it is determined that the preset requirement is met; wherein the filtering result includes a first filtering result or a second filtering result.
[0034] In the embodiment, how to calculate the filtering evaluation index, that is, how to calculate the information retention degree and the noise suppression degree, is described. Whether the filtering algorithm selects the moving average filtering algorithm or the first-order exponential filtering algorithm, the way of calculating the filtering evaluation index is the same, that is, the information retention degree and the noise suppression degree are determined based on three independent components. It is limited that in the case that the information retention degree is greater than or equal to the second preset threshold and the noise suppression degree is less than or equal to the third preset threshold, it is determined that the preset requirement is met, so that the filtering parameter is more accurate, and the effect of avoiding "excessive filtering leading to information loss" and "insufficient filtering leading to noise residue" is realized.
[0035] Optionally, the time series dataset is decomposed by a time series decomposition algorithm to obtain three types of independent components, including: initializing a period window parameter, a trend window parameter, and an inner loop iteration number; initializing the period component to zero, and calculating an initial residual based on the initialized period component and the time series dataset; performing inner loop processing on the initial residual to output an inner loop residual after the inner loop processing; performing outer loop processing on the inner loop residual after the inner loop processing to obtain an outer loop residual; determining whether the outer loop residual converges; if not, repeatedly performing the outer loop processing; if yes, outputting a final trend component and a final period component, and calculating a residual component based on the time series dataset, the final trend component, and the final period component.
[0036] Further, the inner loop processing includes: performing smoothing processing on the initial residual by using a Loess algorithm and the trend window parameter to obtain an initial trend term; updating the inner loop residual according to the initial trend term and the initial residual until the inner loop iteration number is reached, and outputting a current trend component as the inner loop residual; and the outer loop processing includes: performing smoothing processing on the inner loop residual output by the inner loop processing by using the Loess algorithm and the period window parameter, and updating the period component; and calculating the outer loop residual according to the inner loop residual after the smoothing processing and the updated period component.
[0037] In this embodiment, how to decompose the time series dataset by the STL algorithm to obtain three types of independent components is described, which can be combined with the process shown in FIG. 2. Figure 2 The process includes three steps of initial setting, inner loop, and outer loop. The initial setting includes initializing the period window parameter, the trend window parameter, and the inner loop iteration number, initializing the period component to zero, and calculating the initial residual based on the initialized period component and the time series dataset. Further, the initial residual is subjected to the inner loop and the outer loop to calculate the three types of independent components. By using the STL algorithm, the analysis and decoupling of the industrial process data are realized, and the problem that the related method directly calculates the filtering parameter based on the original data without distinguishing the filtering requirements of different components (such as retaining the trend term, strongly suppressing the noise term, and matching the period characteristic of the period term) is solved, so that the problem of distorted data (too strong filtering effect) or noise residue (too weak filtering effect) after filtering is solved.
[0038] Optionally, before the time series dataset is decomposed by the time series decomposition algorithm to obtain the three types of independent components, the process further includes: preprocessing the time series dataset; and the preprocessing of the time series dataset includes: removing outliers in the time series dataset by using a 3-sigma criterion; and supplementing missing elements in the time series dataset by using a linear interpolation method.
[0039] This embodiment also proposes a preprocessing step for the time series dataset. Specifically, it includes using the 3-sigma criterion to remove obvious outliers (such as extreme values outside the normal distribution range) from the time series dataset, and using linear interpolation to fill in missing values caused by communication interruptions, thereby obtaining a preprocessed time series to improve data quality.
[0040] Next, referring to S201-S206, a specific implementation method is proposed, providing a unified explanation of the formulas, preset requirements, thresholds, etc., mentioned in the time series decomposition-based adaptive filtering method for industrial predictive control in the above technical solution. S201-S206 are not shown separately in the accompanying drawings, but specifically include: S201: Obtaining Time Series Datasets By using the data source interface (such as OPCUA, OCDA, Modbus protocol) of industrial predictive control software, historical data of the desired controlled variable over a recent period are collected to obtain the original time series dataset. D= { d 1 ,d 2 ,......, d k ,.....,d n},in k Sampling time, n The total number of samples, d k for k Real-time industrial process data (such as temperature, liquid level, pressure, etc.).
[0041] Then, the dataset D Preprocessing was performed: The 3-sigma criterion was used to remove obvious outliers (such as extreme values exceeding the normal distribution range), and linear interpolation was used to complete missing values caused by communication interruptions, thus obtaining the preprocessed time series. X= { x 1 ,x 2 ,......,x k ,.....,x n}
[0042] S202: Decompose the time series dataset The STL algorithm is used to process the preprocessed time series. X The decomposition yielded three independent components, specifically including: Trend Item T= { t 1 ,t 2 ,......,t k ,.....,tn}: Reflects the long-term changing trend of industrial process data; Periodic terms S= { s 1 ,s 2 ,......,s k ,.....,s n}: Reflects the periodic fluctuations in industrial process data; residuals R= { r 1 ,r 2 ,......,r k ,.....,r n}: Reflects random noise in industrial data; Among them, three types of components meet the requirements. X = T + S + R And they are independent of each other.
[0043] The specific steps of the STL algorithm are as follows: First, STL parameters need to be initialized, which requires setting three core parameters: seasonal window (also known as periodic window). S For example, 12 sampling points, trend window T For example, 25 sampling points, and the number of iterations. L For example, 15 times. After completing the parameter settings, initialize the periodicity item. S 0 is 0. The initial periodic term here is also the initial periodic component, and the initial residual is calculated based on the initial periodic term. R 0, the calculation formula is R 0 = X - S 0.
[0044] Then, the inner loop (trend smoothing) phase begins: the Loess algorithm is first used to smooth the initial residuals. R Smoothing is performed on 0 to obtain the initial trend term. T 0; then through R 1 =R 0 -T 0 Calculate the inner loop residual R 1; Then check if the number of iterations in the inner loop has reached the preset number of iterations. L =15 times. If the target is not met, return to the starting point of the inner loop to continue smoothing and residual calculation. If the target is met, end the inner loop and enter the outer loop.
[0045] The outer loop phase focuses on optimizing the periodic terms: first, the Loess algorithm is used to optimize the newly obtained inner loop residuals. R 1. Perform smoothing, update the periodic item as follows S 1; then according to R 2 = T - S 1 -T0Compute outer loop residual R 2. Then determine whether the outer loop converges: the way to determine convergence can be by setting a predetermined convergence threshold, for example, if the residual fluctuation is greater than the predetermined convergence threshold, it means that it has not converged, and it needs to return to the starting point of the outer loop to continue updating the periodic term and the residual; if the residual fluctuation is less than or equal to the predetermined convergence threshold, it means that it has converged, and the outer loop is ended. The predetermined convergence threshold here can be determined according to the actual application and the specific values of each independent component.
[0046] After the outer loop is ended, the final trend term T , the periodic term S , and the residual term are outputted. R = X - T - S R According to the residual term calculation formula , the residual term is obtained and outputted
[0047] , thus completing the execution process of the entire STL algorithm. T S203: Feature extraction S According to the trend term R , the periodic term F , and the residual term obtained in S202, the feature parameters are extracted respectively and combined to form a feature vector . The feature parameters specifically include: F T : The average value T T and the change rate μ T of the trend term data δ characterize it. The average value can be obtained by simply taking the average value, δ T according to formula one: (Formula one) In formula one, t k is the trend term of the industrial process data at time k , which is taken from the trend term T= { t 1 , t 2 ,......,t k ,.....,t n}, n is the total number of samples. The change rate reflects the speed of trend change, δ T the greater the change rate, the steeper the trend; δ T the smaller the change rate, the flatter the trend.
[0048] Periodic term featuresF S Calculate the periodic term using Fast Fourier Transform S The main cycle P S (i.e., the period with the highest fluctuation frequency), and the period amplitude. A S (The difference between the maximum and minimum values of the periodic term).
[0049] Residual term characteristics F R Calculate the residual term R Standard deviation σ R The standard deviation reflects the noise intensity. σ R The larger the size, the more severe the noise. σ R The smaller the value, the quieter the noise.
[0050] Constructing feature vectors from time series data F= [ μ T , δ T , P S , A S , σ R ].
[0051] S204: Determining the Necessity of Data Filtering The noise coefficient is calculated using Formula 2. Y : (Formula 2) In this embodiment, the first preset threshold is 0. If Y If the value is ≤0, it means that the residual term accounts for a very small proportion of the data, and its noise intensity can be accepted by the predictive control algorithm. It will not significantly affect the performance of the controller, so no filtering strategy is required.
[0052] At this point, the output will show: Filtering method = "No filtering required", sliding window length. N =0, first-order exponential filter coefficient α =0, the algorithm process ends directly. If Y A value greater than 0 indicates that the residual term is not negligible and data filtering is required, proceeding to step S205. Simultaneously, the process of calculating the target filter parameters can be combined with... Figure 3 As shown, refer to the following processes S205 and S206.
[0053] S205: For a specific filtering algorithm, calculate the initial values of the filtering parameters using analytical formulas. The initial moving average filter parameters are given below. N 初始 (In practical applications, this is also called the initial value of the sliding window length for moving average filtering) and the initial first-order exponential filter parameters. α 初始 (In practical applications, the initial first-order exponential filter coefficients are also called the initial values of the first-order exponential filter.) The calculation formulas are Formula 3 and Formula 4, respectively: (Formula 3) In Formula 3, max The function is the function that takes the maximum of the two. ceil The function is a floor function. The specific logic is: the stronger the noise, the more... σ R The larger the sliding window length N The larger the value, the stronger the filtering effect; the weaker the noise, the better. σ R The smaller the sliding window length N The smaller the value, the weaker the filtering effect.
[0054] (Formula 4) The specific logic of Formula 4 is: the stronger the noise, σ R The larger the first-order exponential filter coefficient, the higher the first-order exponential filter coefficient. α The larger the value, the stronger the filtering effect; the more obvious the long-term trend or cyclical trend, the better. δ T or A S The larger the first-order exponential filter coefficient, the higher the first-order exponential filter coefficient. α The smaller the value, the weaker the filtering effect, thus preserving the data information.
[0055] S206: Evaluation of Filtering Performance and Iterative Optimization of Parameters S2061: Application of Moving Average Filtering Strategy In industrial predictive control software, the moving average filtering strategy is preferred because it introduces less data distortion. The initial moving window length is set... N 初始 Substitute the filter module of the industrial predictive control software to process the original time series after removing outliers. X Filtering is performed to obtain filtered data. X 滤波 .
[0056] S2062: Evaluating the filtering effect using two metrics Information retention I Calculated by weighted average X 滤波 With trend itemsT Periodic terms S The correlation coefficient. See Formula 5 for details: (Formula 5) In Formula 5, corr The function is a statistical measure of the strength and direction of a linear relationship between two variables. Its return value is a numerical value between 0 and 1. I The closer to 1, the better the information retention. Weighting coefficient. w The initial value is 0.7, which can be dynamically adjusted. It is recommended that the value range be 0.6-0.8.
[0057] Noise suppression V First calculate X 滤波 residuals R 滤波 Then calculate its standard deviation and the residual term of the original data. R The ratio of standard deviations, as shown in Formula Six: (Formula 6) In Formula Six, V The closer it is to 0, the better the noise suppression.
[0058] The threshold for filtered data to meet the standard is: I ≥0.875 and V ≤0.25, that is, in this embodiment, the second preset threshold is 0.875 and the third preset threshold is 0.25.
[0059] S2063: Iterative Optimization like X 滤波 Meets the qualification standards. N 初始 These are the final filter parameters, also known as the target filter parameters. N 最终 If the conditions are not met, the filter parameters need to be adjusted according to the following criteria: like I <0.875 (Excessive data distortion): The sliding window length needs to be reduced. N The iterative formula is N 新 =N -1; like V >0.25 (Too much residual noise): The sliding window length needs to be increased. N The iterative formula is N 新 =N +1; Then use the new parameters N新 Repeat steps S2061 and S2062 until the threshold is met. If the maximum number of iterations has not been reached when the condition is met... C max Then output the length of the sliding window after this iteration. N = N 最终 First-order exponential filter coefficients α =0, the algorithm process ends.
[0060] S2064: Application of First-Order Exponential Filtering Strategy If a moving average filtering strategy is used, the maximum number of iterations will be reached. C max If the threshold still cannot be met, a first-order exponential filtering strategy must be adopted. In this case, the current iteration number is reset to zero, and the initial first-order exponential filter coefficients are adjusted. α 初始 Substitute the filter module of the industrial predictive control software to process the original time series after removing outliers. X Filtering is performed to obtain filtered data. X 滤波 .
[0061] S2065: Iterative Optimization Calculate the evaluation index after applying the filter using S2062. If... X 滤波 Meets the qualification standards. α 初始 That is, the final filter parameters α 最终 If the conditions are not met, the filter parameters need to be adjusted according to the following criteria: like I <0.875 (Excessive data distortion): Reduce the filter coefficient. α The iterative formula is ; like V >0.25 (Too much residual noise): Increase the filter coefficient α The iterative formula is ; Then use the new parameters α 新 Calculate the filtering evaluation index until the target threshold is met or the maximum number of iterations is reached. C max The output at this point is: Filtering method = "First-order exponential filter", sliding window length. N =0, first-order exponential filter coefficient α=α 最终 The algorithm process ends.
[0062] Furthermore, based on the above embodiments, and in conjunction with a specific application scenario, a more specific implementation method is given. Specifically, Figure 4 The document also provides examples of specific execution modules to facilitate understanding of the overall processing flow. Taking the application scenario of "distillation column reboiler temperature data filtering" as an example, the normal fluctuation range of the distillation column reboiler temperature is 237±4℃. The historical data sampling frequency is 30 seconds, the data coverage period is 2 hours, and a total of 240 data points are collected. The goal is to determine a suitable filtering method (no filtering / moving average filtering / first-order exponential filtering) and to provide the corresponding filtering parameters (sliding window length). N Or first-order exponential filter coefficients α ).
[0063] S301: Data Acquisition and Preprocessing The raw dataset was obtained by collecting the column bottom temperature data using the OPC UA protocol. D Subsequently, the three sigma criterion was used to remove 12 outliers, and linear interpolation was used to fill in the 4 missing values, resulting in the preprocessed time series. X .
[0064] S302: Time Series Decomposition right X After STL decomposition, we get: Trend Item T The temperature slowly rose from 235℃ to 241℃ (average). μ T =237.6, rate of change δ T =0.05 / min); Periodic terms S A small fluctuation occurs every 30 minutes (main cycle) P S =30min, amplitude A S =2℃); residuals R Standard deviation σ R =1.4℃.
[0065] S303: Extract feature vectors F= [ μ T =237.6, δ T =0.05, P S =30, A S =2, σ R =1.4] S304: Determining the Necessity of Data Filtering Calculate the noise factor of the column bottom temperature data: Y= 3 + log (1.4 / 237.6) ≈ 0.77>0 This indicates that the noise in the data is not negligible, therefore subsequent filtering steps are required.
[0066] S305: Calculation of initial values for filter parameters Calculate the initial value of the sliding window length for the moving average filter: ; Calculate the initial values of the filter coefficients for a first-order exponential filter:
[0067] S306: Filtering Performance Evaluation and Parameter Iterative Optimization First, a moving average filtering strategy is selected, and the maximum number of iterations C is set. max 5: Use the initial value of the sliding window length N 初始 = 6. Information retention rate after filtering I =0.815 (does not meet the threshold), noise suppression score V =0.231 (satisfies the threshold); In the second iteration, due to lower information retention, the sliding window length needs to be reduced. N =5, the obtained information retention rate I= 0.843 (not meeting the threshold), noise suppression score V =0.235 (meets the threshold); In the third iteration, the sliding window length is further reduced. N =4, resulting in information retention rate I =0.882 (meets the threshold), noise suppression degree V =0.242 (meets the threshold). At this point, the maximum number of iterations has not been exceeded, so the final algorithm result is output as: Filtering method = "Moving average filter", sliding window length... N 最终 =4, first-order exponential filter coefficient α= 0.
[0068] The industrial predictive control adaptive filtering method based on time series decomposition provided by any of the above embodiments has at least the following technical effects: (1) Industrial data preprocessing technology: The combination of “three sigma criteria to remove outliers + linear interpolation to fill missing values” is adopted to address the common extreme values and data missing problems in industrial scenarios, ensuring the integrity and reliability of the time series after preprocessing, and providing a high-quality data foundation for subsequent decomposition.
[0069] (2) Time series decomposition based on STL algorithm: The time series is accurately decomposed into three independent components: trend (long-term change), periodic (periodic fluctuation) and residual (random noise) by using STL algorithm. The core parameters of STL algorithm (seasonal window, trend window, number of iterations) and the execution logic of "inner loop trend smoothing (Loess algorithm) - outer loop periodic optimization (residual fluctuation convergence judgment)" are clearly defined to achieve effective separation of data components.
[0070] (3) Feature extraction method of decomposed components: Differentiated feature indicators are designed for the three types of decomposed components: the trend component is characterized by "average value + rate of change" to represent the long-term change characteristics, the periodic component is characterized by "the main period calculated by fast Fourier transform + amplitude" to represent the fluctuation pattern, and the residual component is characterized by "standard deviation" to represent the noise intensity. Finally, the feature vector is formed by combining them to provide an accurate basis for the calculation of filter parameters.
[0071] (4) Quantitative judgment of the necessity of filtering: Define "noise coefficient" as the judgment index. By setting a critical threshold, avoid data distortion caused by "forced filtering regardless of noise intensity" or control accuracy reduction caused by "omission of necessary filtering" in the existing technology, and take into account both the necessity of filtering and the robustness of the control algorithm.
[0072] (5) A dual-filter priority strategy and iterative optimization logic of "moving average priority and first-order exponential backup" is proposed: the moving average filter (low distortion advantage) is selected first, and the first-order exponential filter is switched only when the maximum number of iterations is still not met, forming a strategy of "low distortion priority and high adaptability backup"; for the two types of filters, "parameter adjustment formula based on information retention and noise suppression" is designed respectively to realize the dynamic and directional optimization of parameters and solve the problem of "no clear rules for parameter adjustment and reliance on experience" in traditional filtering.
[0073] Furthermore, as Figures 1 to 4 The specific implementation of the method shown in this embodiment provides an industrial predictive control adaptive filtering device based on time series decomposition, such as... Figure 5 As shown, the device includes: a data acquisition unit 501, a computing unit 502, and a processing unit 503.
[0074] The acquisition unit 501 is configured to acquire historical data of the controlled variable in the industrial process within a preset time period to obtain a time series dataset. The computing unit 502 is configured to decompose the time series dataset using a time series decomposition algorithm to obtain three independent components. The three independent components include a trend component that represents the trend change, a periodic component that represents the fluctuation frequency within the period, and a residual component that represents the noise intensity. The trend component, periodic component, and residual component are independent of each other. The processing unit 503 is configured to extract features from the three independent components respectively, and to match a filtering algorithm based on the feature extraction results and determine the target filtering parameters of the filtering algorithm.
[0075] In specific application scenarios, the processing unit 503 is further configured to extract features from the three independent components to obtain feature vectors corresponding to the time series dataset; calculate the noise coefficient based on the feature vectors; compare the noise coefficient with a first preset threshold, and if the noise coefficient is greater than the first preset threshold, determine that the filtering algorithm is a moving average filtering algorithm; and calculate the target filtering parameters of the moving average filtering algorithm based on the three independent components.
[0076] In a specific application scenario, the processing unit 503 is further configured to: calculate initial moving average filter parameters based on three independent components; perform filtering processing on the time series dataset using the initial moving average filter parameters to obtain a first filtering result; calculate a filtering evaluation index based on the first filtering result and determine whether the filtering evaluation index meets preset requirements; if the filtering evaluation index does not meet the preset requirements, iterate the initial moving average filter parameters according to a preset first iteration formula; perform moving average filtering processing on the time series dataset based on the iterated moving average filter parameters and calculate the corresponding filtering evaluation index until the filtering evaluation index meets the preset requirements, and use the moving average filter parameters after this iteration as the target filtering parameters of the moving average filtering algorithm.
[0077] In a specific application scenario, the processing unit 503 is further configured to reset the iteration count to zero, determine that the filtering algorithm is a first-order exponential filtering algorithm, and calculate the target filtering parameters of the first-order exponential filtering algorithm based on three independent components. Specifically, calculating the target filtering parameters of the first-order exponential filtering algorithm based on the three independent components includes: calculating initial first-order exponential filtering parameters based on the three independent components; filtering the time series dataset using the initial first-order exponential filtering parameters to obtain a second filtering result; calculating a filtering evaluation index based on the second filtering result and determining whether the filtering evaluation meets the preset requirements; if the filtering evaluation does not meet the preset requirements, iterating the initial first-order exponential filtering parameters according to a pre-set second iteration formula; performing first-order exponential filtering on the time series dataset based on the iterated first-order exponential filtering parameters and calculating the corresponding filtering evaluation index until the filtering evaluation index meets the preset requirements, and using the first-order exponential filtering parameters after this iteration as the target filtering parameters of the first-order exponential filtering algorithm.
[0078] In specific application scenarios, the processing unit 503 is further configured to calculate the correlation coefficient of the filtering result relative to the trend component and the periodic component to obtain the information retention degree; calculate the residual term and the standard deviation of the residual term of the filtering result, and calculate the noise suppression degree based on the standard deviation of the residual term and the standard deviation of the residual component of the filtering result; and determine that the preset requirements are met when the information retention degree is greater than or equal to the second preset threshold and the noise suppression degree is less than or equal to the third preset threshold; wherein, the filtering result includes the first filtering result or the second filtering result.
[0079] In specific application scenarios, the calculation unit 502 is further configured to initialize the periodic window parameters, trend window parameters, and the number of inner loop iterations; initialize the periodic component to zero, and calculate the initial residual based on the initialized periodic component and the time series dataset; perform inner loop processing on the initial residual and output the inner loop residual after inner loop processing; perform outer loop processing on the inner loop residual after inner loop processing to obtain the outer loop residual; determine whether the outer loop residual has converged; if it has not converged, repeat the outer loop processing; if it has converged, output the final trend component and periodic component, and calculate the residual component based on the time series dataset, the final trend component, and the periodic component.
[0080] The inner loop process includes smoothing the initial residual using the Loess algorithm and trend window parameters to obtain the initial trend term; updating the inner loop residual based on the initial trend term and initial residual until the inner loop iteration count is reached, and outputting the current trend component and inner loop residual; the outer loop process includes smoothing the inner loop residual output by the inner loop process using the Loess algorithm and period window parameters, and updating the periodic component; calculating the outer loop residual based on the smoothed inner loop residual and the updated periodic component.
[0081] In specific application scenarios, computing unit 502 is further configured to preprocess time series datasets; preprocessing time series datasets includes: removing outliers from time series datasets using the 3-sigma criterion; and completing missing elements in time series datasets using linear interpolation.
[0082] It should be noted that other corresponding descriptions of the functional units involved in the industrial predictive control adaptive filtering device based on time series decomposition provided in this embodiment can be found in [reference needed]. Figures 1 to 4 The corresponding descriptions in [the document] will not be repeated here.
[0083] Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause a computer device (such as personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of this application.
[0084] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented using software plus necessary general-purpose hardware platforms, or it can be implemented in hardware. By applying the scheme of this embodiment, compared with related technologies, historical data from industrial processes are first arranged in chronological order to form a time-series dataset. Then, a time-series decomposition algorithm is used to decompose the time-series dataset into three independent components. These components are analyzed from three different dimensions: changing trends, fluctuations within periods, and specific residual data, respectively, addressing the problem of traditional filtering where "parameter adjustment lacks clear rules and relies on experience." Finally, feature extraction is performed based on the three independent components, and a filtering algorithm is matched and the target filtering parameters are determined based on the feature extraction results, thereby improving filtering accuracy and enhancing the adaptability of industrial predictive control.
[0085] In the description of this application, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.
[0086] In the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0087] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make modifications, alterations, substitutions and variations to the above embodiments within the scope of this application.
Claims
1. An adaptive filtering method for industrial predictive control based on time series decomposition, characterized in that, include: Historical data of the controlled variables in the industrial process within a preset time period are collected to obtain a time series dataset; The time series dataset is decomposed using a time series decomposition algorithm to obtain three independent components. These three independent components include a trend component representing trend changes, a periodic component representing the frequency of fluctuations within a period, and a residual component representing noise intensity. The trend component, the periodic component, and the residual component are independent of each other. Feature extraction is performed on three independent components respectively, and a matching filtering algorithm is used based on the feature extraction results to determine the target filtering parameters of the filtering algorithm.
2. The method according to claim 1, characterized in that, The step of extracting features from three independent components, matching a filtering algorithm based on the feature extraction results, and determining the target filtering parameters of the filtering algorithm includes: Feature extraction is performed on the three independent components respectively to obtain the feature vector corresponding to the time series dataset; Calculate the noise coefficient based on the feature vector; The noise coefficient is compared with a first preset threshold. If the noise coefficient is greater than the first preset threshold, the filtering algorithm is determined to be a moving average filtering algorithm. Based on the three independent components, the target filtering parameters of the moving average filtering algorithm are calculated.
3. The method according to claim 2, characterized in that, The calculation of the target filtering parameters of the moving average filtering algorithm based on the three independent components includes: Based on the three independent components, calculate the initial moving average filter parameters; The time series dataset is filtered using the initial moving average filter parameters to obtain a first filtering result. Based on the first filtering result, calculate the filtering evaluation index and determine whether the filtering evaluation index meets the preset requirements; If the filter evaluation index does not meet the preset requirements, the initial moving average filter parameters are iterated according to the preset first iteration formula. The time series dataset is subjected to moving average filtering based on the iterative moving average filtering parameters, and the corresponding filtering evaluation index is calculated until the filtering evaluation index meets the preset requirements. The moving average filtering parameters after this iteration are then used as the target filtering parameters of the moving average filtering algorithm.
4. The method according to claim 3, characterized in that, If the number of iterations reaches its maximum, and the filtering evaluation index corresponding to the first filtering result still does not meet the preset requirements after iteration, the method further includes: The iteration count is reset to zero, the filtering algorithm is determined to be a first-order exponential filtering algorithm, and the target filtering parameters of the first-order exponential filtering algorithm are calculated based on the three independent components. The target filtering parameters of the first-order exponential filtering algorithm are calculated based on the three independent components, including: Based on the three independent components, calculate the initial first-order exponential filter parameters; The time series dataset is filtered using the initial first-order exponential filter parameters to obtain a second filtering result. Based on the second filtering result, calculate the filtering evaluation index and determine whether the filtering evaluation meets the preset requirements; If the filter evaluation does not meet the preset requirements, the initial first-order exponential filter parameters are iterated according to the preset second iteration formula; The time series dataset is subjected to first-order exponential filtering based on the iterated first-order exponential filtering parameters, and the corresponding filtering evaluation index is calculated until the filtering evaluation index meets the preset requirements. The first-order exponential filtering parameters after this iteration are used as the target filtering parameters of the first-order exponential filtering algorithm.
5. The method according to claim 3 or 4, characterized in that, The filtering evaluation metrics include information retention and noise suppression. Based on the filtering results, a filtering evaluation index is calculated, and it is determined whether the filtering evaluation index meets preset requirements, including: The information retention rate is obtained by calculating the correlation coefficient of the filtering result relative to the trend component and the periodic component. Calculate the residual term and the standard deviation of the residual term of the filtering result, and calculate the noise suppression degree based on the standard deviation of the residual term and the standard deviation of the residual component of the filtering result; If the information retention is greater than or equal to the second preset threshold and the noise suppression is less than or equal to the third preset threshold, it is determined that the preset requirement is met; wherein, the filtering result includes the first filtering result or the second filtering result.
6. The method according to claim 1, characterized in that, The time series dataset is decomposed using a time series decomposition algorithm to obtain three independent components, including: Initialize the period window parameters, trend window parameters, and inner loop iteration count; The periodic components are initialized to zero, and the initial residuals are calculated based on the initialized periodic components and the time series dataset. The initial residual is processed by an inner loop, and the inner loop residual after the inner loop processing is output. The inner loop residual after the inner loop processing is processed by the outer loop to obtain the outer loop residual; Determine whether the outer loop residual has converged; If convergence is not achieved, the outer loop process is repeated. If convergence has been achieved, the final trend component and periodic component are output, and the residual component is calculated based on the time series dataset, the final trend component and periodic component.
7. The method according to claim 6, characterized in that, The inner loop processing includes: Based on the initial residual, the Loess algorithm is used to smooth the trend window parameters to obtain the initial trend term. Based on the initial trend term and the initial residual, update the inner loop residual until the inner loop iteration number is reached, and output the current trend component and inner loop residual. The external loop processing includes: Using the Loess algorithm and the periodic window parameters, the inner loop residuals output by the inner loop processing are smoothed, and the periodic components are updated. The outer loop residual is calculated based on the smoothed inner loop residual and the updated periodic component.
8. The method according to claim 1, characterized in that, Before decomposing the time series dataset into three independent components using a time series decomposition algorithm, the following steps are also included: The time series dataset is preprocessed; The preprocessing of the time series dataset includes: Outliers in the time series dataset were removed using the 3-sigma criterion. Missing elements in the time series dataset are filled in using linear interpolation.
9. An adaptive filtering device for industrial predictive control based on time series decomposition, characterized in that, include: The data acquisition unit is configured to collect historical data of the controlled variables in the industrial process within a preset time period to obtain a time series dataset. The computing unit is configured to decompose the time series dataset using a time series decomposition algorithm to obtain three independent components; wherein the three independent components include a trend component representing trend change, a periodic component representing fluctuation frequency within a period, and a residual component representing noise intensity, and the trend component, the periodic component, and the residual component are independent of each other. The processing unit is configured to extract features from three independent components, match a filtering algorithm based on the feature extraction results, and determine the target filtering parameters of the filtering algorithm.
Citation Information
Patent Citations
Multi-cycle time series data decomposition method and device, equipment and storage medium
CN114944831A
Medium and long term prediction method and device for power grid load and computer equipment
CN118249341A
Gas leakage monitoring method and system for intelligent pipe gallery
CN118570098A
Big data platform BI analysis method and system and computer equipment
CN119359093A
Settlement process automatic identification method based on adaptive iteration seasonal decomposition and trend analysis
CN119881891A
Cited By
Electric energy meter harmonic metering method and system based on adaptive filtering
CN122084970A