Methods for constructing pressure prediction models for water supply networks, pressure prediction methods and devices

Abstract

This application provides a method for constructing a pressure prediction model for a water supply network, a pressure prediction method, and an apparatus, comprising: determining a target time window including the time of pressure wave generation; acquiring pressure time-series data of the target node and the water supply end within the target time window, and offsetting the time corresponding to the non-reference data according to different time offsets, calculating the similarity between the offset non-reference data and the reference data, and determining a first target similarity greater than a preset similarity threshold; determining the propagation delay time of the pressure wave from the water supply end to the target node according to the time offset corresponding to the first target similarity; determining the attenuation degree of the pressure wave from the water supply end to the target node according to the propagation delay time; and constructing a pressure prediction model for the target node based on the propagation delay time and attenuation degree. The model constructed by this method can accurately depict the dynamic propagation process of the pressure wave from the water supply end to the target node, with low modeling cost and interpretability.

Description

Technical Field

[0001] This application relates to the field of water supply network technology, and in particular to a method for constructing a pressure prediction model for a water supply network, a pressure prediction method, and a device. Background Technology

[0002] Accurately predicting the pressure values ​​at each node in a water supply network is fundamental to optimizing the operation of the water supply system. For example, by predicting pressure, the start-up and shutdown of water pumps and the opening of valves can be scientifically scheduled to meet the water pressure needs of distant users while avoiding excessive pressure at nearby points, thereby achieving energy conservation and consumption reduction. Meanwhile, abnormal pressure is often the most direct precursor to network leakage or pipe bursts; an accurate pressure propagation model is crucial for quickly locating fault points and minimizing the impact area. Therefore, constructing a dynamic model that accurately reflects how pressure changes at the water supply end propagate through the network over time has significant engineering value and economic implications.

[0003] Currently, methods for establishing pipeline pressure relationships can be mainly divided into two categories: The first category is hydraulic model simulation based on physical mechanisms, which relies on professional simulation software (such as EPANET) and requires input of complete and accurate pipeline topology, pipe material parameters (such as pipe diameter and roughness), and prior knowledge such as real-time water consumption distribution. Simulation calculations are performed by solving a set of hydraulic equations. The second category is data-driven methods based on historical monitoring data. With the development of Internet of Things (IoT) technology, this type of method is gradually increasing. For example, machine learning models such as Long Short-Term Memory (LSTM) networks are directly used to train and predict pressure time-series data, or correlation analysis is used to explore the pressure relationships between nodes.

[0004] However, the aforementioned existing technologies have significant limitations in practical applications. First, most data-driven methods assume that the pressure response of the target node is synchronized with the pressure change at the water supply end, ignoring the time delay required for pressure waves to propagate in the pipeline. This results in their inability to accurately characterize the dynamic pressure propagation characteristics of long-distance pipe networks, leading to insufficient accuracy of the models in the spatiotemporal dimensions. Second, while hydraulic model simulation methods have physical meaning, their modeling process heavily relies on detailed pipe network infrastructure information, resulting in high modeling costs, complex implementation, and difficulty in applying them to actual pipe network systems with incomplete topological information or those that are constantly changing with urban development, thus exhibiting poor universality. Finally, although "black box" models based on pure machine learning can achieve a certain level of predictive accuracy under specific conditions, their internal parameters lack clear physical meaning, making it difficult to support in-depth analysis requirements such as pipe network fault tracing and leak location that require clear causal relationships. Their insufficient interpretability limits their guiding value in water supply system operation and maintenance decisions. Summary of the Invention

[0005] This application provides a method for constructing a pressure prediction model for a water supply network, a pressure prediction method, and an apparatus, to solve the following problems in the prior art:

[0006] Existing data-driven methods assume that the pressure response of target nodes in a water supply network is synchronized with the pressure changes at the supply end, ignoring the time required for pressure waves to propagate in the pipeline. This results in an inability to accurately characterize the dynamic pressure propagation characteristics of long-distance pipelines. Existing methods often require prior knowledge of the detailed topology of the pipeline network, pipe material parameters, and water consumption distribution, leading to high modeling costs, complex implementation, and difficulty in applying them to actual pipeline systems with incomplete or constantly changing topological information. While "black box" models based on pure machine learning can make predictions, they cannot provide parameters with clear physical meaning, making it difficult to support in-depth analysis needs such as fault tracing and leak location in pipeline networks.

[0007] In a first aspect, this application provides a method for constructing a water supply network pressure prediction model, the method comprising:

[0008] Determine the time of pressure wave generation in the water supply network;

[0009] Based on the time of generation, a target time window is determined, wherein the time of generation is within the target time window;

[0010] Acquire the first pressure time series data of the target node of the water supply network within the target time window, and the second pressure time series data of the water supply end of the water supply network within the target time window;

[0011] In the first pressure time series data and the second pressure time series data, one is determined as the reference data and the other is determined as the non-reference data. The time corresponding to the non-reference data is offset according to different time offsets, and the similarity between the offset non-reference data and the reference data is calculated.

[0012] Among the similarities corresponding to each time offset, a first target similarity greater than a preset similarity threshold is determined;

[0013] Based on the time offset corresponding to the first target similarity, the propagation delay time of the pressure wave from the water supply end to the target node is determined;

[0014] Based on the propagation delay time, determine the pressure value of the pressure wave at the target node, and compare it with the attenuation of the pressure value of the pressure wave at the water supply end;

[0015] Based on the propagation delay time and the attenuation rate, a pressure prediction model for the target node is constructed.

[0016] In one possible implementation, determining the time of pressure wave generation in the water supply network includes:

[0017] Obtain the rate of pressure change at the water supply end;

[0018] If the rate of pressure change is greater than a preset rate threshold, then the current moment is determined as the generation moment.

[0019] In one possible implementation, determining the pressure value of the pressure wave at the target node based on the propagation delay time, compared to the attenuation of the pressure wave at the water supply end, includes:

[0020] Using the propagation delay time as an offset, the time corresponding to the non-reference data is offset to obtain the offset data;

[0021] The offset data and the baseline data are subjected to linear regression fitting to determine the attenuation degree.

[0022] In one possible implementation, determining the pressure value of the pressure wave at the target node based on the propagation delay time, compared to the attenuation of the pressure wave at the water supply end, includes:

[0023] Calculate the amplitude attenuation ratio, energy attenuation coefficient, and waveform distortion between the offset data and the reference data, and determine the attenuation degree based on the amplitude attenuation ratio, the energy attenuation coefficient, and the waveform distortion.

[0024] In one possible implementation, performing linear regression fitting on the offset data and the baseline data to determine the attenuation degree includes:

[0025] Obtain the traffic time-series data of the target node within the target time window;

[0026] Based on the traffic time-series data, determine the abnormal time range in which traffic anomalies exist;

[0027] Data in the offset data and the reference data whose corresponding time falls within the abnormal time range are identified as disturbed data; data in the offset data and the reference data other than the disturbed data are identified as undisturbed data.

[0028] Based on the first weight corresponding to the disturbed data and the second weight corresponding to the undisturbed data, a linear regression fitting process is performed on the offset data and the benchmark data to obtain the calculation result of the attenuation degree, wherein the second weight is greater than the first weight.

[0029] In one possible implementation, determining the abnormal time range where traffic anomalies exist based on the traffic time-series data includes:

[0030] Based on the traffic time-series data, determine the rate of change of traffic at different times within the target time window;

[0031] Among the flow rate changes at different times, determine the target flow rate change that is greater than a preset rate change threshold;

[0032] The abnormal time range is determined based on the time corresponding to the target flow rate change.

[0033] In one possible implementation, determining the abnormal time range where traffic anomalies exist based on the traffic time-series data includes:

[0034] Based on the traffic time-series data, a pre-trained deep learning model identifies abnormal traffic data.

[0035] The abnormal time range is determined based on the time corresponding to the abnormal traffic data.

[0036] In one possible implementation, constructing the stress prediction model for the target node based on the propagation delay time and the attenuation degree includes:

[0037] In the first target similarity, the second target similarity corresponding to each target path is determined, wherein the target path is the propagation path of the pressure wave in the water supply network;

[0038] Calculate the ratio of the second target similarity corresponding to each target path to the sum of all second target similarities;

[0039] The weight of each target path is determined based on the ratio corresponding to each target path;

[0040] The pressure prediction model is constructed based on the propagation delay time, the attenuation degree, and the weight corresponding to each target path.

[0041] Secondly, this application provides a stress prediction method, which is implemented based on the stress prediction model constructed in the first aspect, and the method includes:

[0042] Based on the pressure prediction model of the target node in the water supply network, the propagation delay time of the pressure wave from the water supply end of the water supply network to the target node is determined, as well as the pressure value of the pressure wave at the target node and the attenuation degree of the pressure wave at the water supply end.

[0043] Subtract the propagation delay time from the first target time to obtain the second target time;

[0044] Obtain the actual pressure value of the water supply end at the second target time;

[0045] Based on the actual pressure value and the attenuation rate, the pressure value of the target node at the first target time is predicted.

[0046] Thirdly, this application provides a device for constructing a water supply network pressure prediction model, the device comprising:

[0047] The time window determination module is used to determine the moment when pressure waves are generated in the water supply network.

[0048] Based on the time of generation, a target time window is determined, wherein the time of generation is within the target time window;

[0049] The pressure data acquisition module is used to acquire first pressure time-series data of the target node of the water supply network within the target time window, and second pressure time-series data of the water supply end of the water supply network within the target time window.

[0050] The model building module is used to determine one of the first pressure time series data and the second pressure time series data as the reference data and the other as the non-reference data, offset the time corresponding to the non-reference data according to different time offsets, and calculate the similarity between the offset non-reference data and the reference data.

[0051] Among the similarities corresponding to each time offset, a first target similarity greater than a preset similarity threshold is determined;

[0052] Based on the time offset corresponding to the first target similarity, the propagation delay time of the pressure wave from the water supply end to the target node is determined;

[0053] Based on the propagation delay time, determine the pressure value of the pressure wave at the target node, and compare it with the attenuation of the pressure value of the pressure wave at the water supply end;

[0054] Based on the propagation delay time and the attenuation rate, a pressure prediction model for the target node is constructed.

[0055] Fourthly, this application provides an electronic device, including: a processor, and a memory communicatively connected to the processor;

[0056] The memory stores computer-executed instructions;

[0057] The processor executes computer execution instructions stored in the memory to implement the method as described in the first aspect, or to implement the method as described in the second aspect.

[0058] Fifthly, this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the method described in the first aspect, or to implement the method described in the second aspect.

[0059] The method for constructing a pressure prediction model for a water supply network, the pressure prediction method, and the apparatus provided in this application have the following technical advantages:

[0060] 1. This method determines the moment of pressure wave generation and sets an analysis time window based on that moment to ensure the capture of the complete pressure propagation process. Subsequently, by calculating the similarity of pressure time-series data from the water supply end and the target node under time offset, it can proactively identify the optimal time offset for signal matching, i.e., the propagation delay. Therefore, this method considers the time delay of pressure wave propagation in the pipeline and no longer assumes synchronous responses. By quantifying the propagation delay, this method can accurately characterize the dynamic propagation process of pressure waves from the water supply end to the target node, making it particularly suitable for long-distance pipelines with significant propagation delays. This overcomes the limitation of existing data-driven methods in handling time delays.

[0061] 2. This method relies solely on pressure time-series data from the water supply end and the target node, requiring no prior information such as pipeline topology, pipe material parameters, or water consumption distribution. By using a data-driven approach, it directly extracts propagation features such as propagation delay and attenuation from the pressure signal to construct the model, reducing modeling complexity and cost. This makes the method applicable to real-world pipeline systems with incomplete or dynamically changing topology information.

[0062] 3. This method constructs a pressure prediction model by calculating parameters with clear physical meaning, such as propagation delay time and attenuation degree. Since these parameters directly correspond to the physical characteristics of pressure wave propagation (such as wave speed and energy loss), the pressure prediction model is no longer a black box. Furthermore, the propagation delay can be used to trace the path of pressure changes, and the attenuation degree can reflect the condition of the pipe section, thereby supporting the needs of in-depth analysis such as fault tracing and leak location, and enhancing the practicality and credibility of the model in engineering practice. Attached Figure Description

[0063] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0064] Figure 1A schematic diagram of the method for constructing a water supply network pressure prediction model provided in this application embodiment;

[0065] Figure 2 This is a schematic flowchart of a possible method for determining attenuation degree provided in an embodiment of this application;

[0066] Figure 3 A schematic diagram of a possible method for constructing a pressure prediction model provided in an embodiment of this application;

[0067] Figure 4 A schematic diagram of the water supply network pressure prediction model construction device provided in the embodiments of this application;

[0068] Figure 5 A schematic diagram of an electronic device provided in an embodiment of this application.

[0069] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0070] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments matching this application. Rather, they are merely examples of apparatuses and methods matching some aspects of this application as detailed in the appended claims.

[0071] As described in the background section, existing data-driven methods assume that the pressure response of the target node in the water supply network is synchronized with the pressure change at the water supply end, ignoring the time required for pressure waves to propagate in the pipeline. This results in an inability to accurately characterize the dynamic pressure propagation characteristics of long-distance pipelines. Existing methods often require prior knowledge of the detailed topology of the pipeline network, pipe material parameters, and water consumption distribution, leading to high modeling costs, complex implementation, and difficulty in applying them to actual pipeline systems with incomplete or constantly changing topological information. While "black box" models based on pure machine learning can make predictions, they cannot provide parameters with clear physical meaning, making it difficult to support in-depth analysis needs such as fault tracing and leak location in pipeline networks.

[0072] To address the aforementioned problems in the prior art, the inventors of this application have considered that the inability of the prior art to accurately characterize the dynamic pressure propagation characteristics of long-distance pipelines is mainly due to the failure to consider the propagation delay and attenuation of pressure waves in the pipeline. If a pressure prediction model can be constructed that considers the propagation delay and attenuation of pressure waves arriving at pipeline nodes, the pressure values ​​at different nodes in the water supply network can be predicted more accurately. Compared to methods that require complex prior knowledge for modeling, a data-driven approach should be used for modeling, ultimately generating a pressure prediction model that includes physical quantities with clear meanings, such as the propagation delay and attenuation of pressure waves, thus overcoming the black box problem of machine learning.

[0073] Taking the above considerations into account, the inventors of this application chose to acquire pressure time-series data of the water supply end and the target node in the water supply network, and used a cross-correlation method to determine the propagation delay time and attenuation degree of the pressure wave from the water supply end to the target node. Specifically, a time window containing the moment of pressure wave generation is determined, and pressure time-series data of the target node and the water supply end in the water supply network are acquired within this time window. Then, one of these is determined as the reference data, and the other is designated as the non-reference data. The non-reference data is offset according to different time offsets, and the similarity between the offset non-reference data and the reference data is calculated. Among the similarities corresponding to each time offset, similarities greater than a preset threshold are determined, and the propagation delay time is determined based on the time offsets corresponding to these similarities. Then, the attenuation degree of the pressure value of the target node compared to the pressure value of the water supply end is calculated under the aforementioned propagation delay time.

[0074] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0075] Figure 1 This is a schematic flowchart of a method for constructing a water supply network pressure prediction model provided in an embodiment of this application. This method can be applied to servers, such as... Figure 1 As shown, the method includes:

[0076] S101. Determine the time of pressure wave generation in the water supply network;

[0077] First, it should be noted that in a water supply network, the starting and stopping of pumps and the adjustment of valve openings at the water treatment plant will generate pressure waves in the water flow within the network. These pressure waves carry the following key information that can be used for modeling during their propagation through the network:

[0078] Propagation delay time: The time required for a pressure wave to propagate from the water plant (origin) to a target node (end point) is largely determined by the path length and the wave velocity in the pipeline. The wave velocity, in turn, is related to the pipe material, diameter, and wall thickness. Therefore, by measuring the propagation delay time, the effective path length of the pressure wave and the pipeline characteristics can be indirectly inferred, which forms the basis for establishing the time dimension in a spatiotemporal pressure prediction model.

[0079] Pressure wave attenuation refers to the gradual loss of energy during the propagation of a pressure wave due to resistance from pipe wall friction, bends, branches, etc., resulting in a decrease in its amplitude (peak pressure). The degree of attenuation reflects the roughness, diameter, and local resistance along the pipeline.

[0080] In this step, the server can receive real-time time-series data streams from the water supply network monitoring system via a data interface. These data streams can include pressure values ​​at the water supply end (such as the water plant outlet), pump start / stop status signals, opening signals of key regulating valves, and pressure values ​​at each pressure monitoring node (target node). All data is accompanied by high-precision timestamps and synchronized by the server. The server can then store this data in a real-time database.

[0081] If the server receives a clear signal indicating that the pump unit has started or stopped or that the valve opening has changed abruptly, it will directly mark the time corresponding to that signal as... The server can also provide a human-machine interface, allowing maintenance personnel to manually input the time of events such as pump start / stop or valve opening adjustment. The server will then use this time as... .

[0082] Optionally, the timing of pressure wave generation in the water supply network can be determined, including:

[0083] Step 1: Obtain the rate of pressure change at the water supply end;

[0084] Specifically, in this step, the server calculates the instantaneous rate of change of pressure at the water supply end. Let the current time be... The water supply pressure is Then the rate of pressure change for:

[0085]

[0086] in The sampling interval (e.g., 1 minute).

[0087] Step 2: If the rate of pressure change is greater than the preset rate threshold, then the current moment is determined as the generation moment.

[0088] Specifically, if If the speed exceeds a preset experience threshold (e.g., 0.5 m / min), then the time will be... Marked as .

[0089] S102. Determine the target time window based on the generation time, ensuring that the generation time falls within the target time window;

[0090] The server determines Then, the analysis window including that moment can be determined, i.e., the target time window. Specifically, the start time of the target time window is... The target time window ends at... The target time window is:

[0091]

[0092] in, , For example, preset parameters, It can be 30 minutes. The window is set at 60 minutes to ensure that the window length (e.g., 90 minutes) covers the full time required for the pressure wave to travel from the water plant to the furthest node in the pipeline network.

[0093] S103. Obtain the first pressure time series data of the target node of the water supply network within the target time window, and the second pressure time series data of the water supply end of the water supply network within the target time window.

[0094] In this step, the server retrieves the following data from the real-time database:

[0095] The first pressure time series data of the target node within the target time window is denoted as... ;

[0096] The second pressure time series data of the water supply end within the target time window is denoted as... .

[0097] in, .

[0098] S104. In the first pressure time series data and the second pressure time series data, one of them is determined as the reference data and the other is determined as the non-reference data. The time corresponding to the non-reference data is offset according to different time offsets, and the similarity between the offset non-reference data and the reference data is calculated.

[0099] In this step, the server can transmit the second pressure time series data. Set as baseline data. Use the first pressure timing data. Set as non-baseline data.

[0100] Next, the server can set possible time offsets. The search scope, for example ,For example, It is 0 minutes. for Minutes. Time offset. The search range should cover the maximum possible propagation time of the pressure wave from the water plant to the node.

[0101] For each candidate time offset within the search range The server performs the following operations:

[0102] Non-benchmark data Shift forward on the timeline Units, resulting in a new sequence That is, non-benchmark data in The value at time was used to compare with the baseline data. The values ​​at each time point are compared.

[0103] The server then calculates the non-baseline data after the offset. Compared with benchmark data The similarity is calculated using a standardized cross-correlation coefficient. As a similarity metric, its calculation formula is as follows:

[0104]

[0105] for The average pressure value within the target time window; for The average pressure value within the target time window.

[0106] S105. Among the similarities corresponding to each time offset, determine the first target similarity that is greater than the preset similarity threshold;

[0107] In this step, the service can adjust the parameters based on a preset similarity threshold. (For example = 0.6), in In the sequence, find all that satisfy The local extreme points (peaks or troughs) of the pressure wave are identified, and these points represent the first target similarity. Each such point represents a potentially significant propagation path of the pressure wave. The server records each first target similarity. Corresponding time offset .

[0108] S106. Based on the time offset corresponding to the first target similarity, determine the propagation delay time of the pressure wave from the water supply end to the target node;

[0109] In this step, the similarity of each first target is... Corresponding time offset That is, the pressure wave passes through the first The propagation delay time required for a path to propagate from the water supply end to the target node.

[0110] S107. Determine the pressure value of the pressure wave at the target node based on the propagation delay time, and compare it with the attenuation of the pressure value of the pressure wave at the water supply end.

[0111] In this step, the server can obtain the second pressure timing data from the water supply end. Delay in time ,get This makes it consistent with the pressure sequence of the target node. Align with causal relationships.

[0112] Next, the server can calculate the following attenuation-related metrics:

[0113] Amplitude Attenuation Ratio (AAR): Calculated as the ratio of the amplitudes of two aligned pressure time series data points. The calculation method is as follows:

[0114]

[0115] Where RMS represents the root mean square value of the calculated sequence. This value is less than 1, and the smaller the value, the more severe the amplitude decay.

[0116] Energy attenuation coefficient (EAC): Calculates the energy loss of pressure waves. The calculation method is as follows:

[0117]

[0118] The closer this coefficient is to 1, the greater the energy loss.

[0119] Waveform Distortion (WDD): The minimum path distance between two aligned sequences is calculated using the Dynamic Time Warping (DTW) algorithm and then normalized. The calculation method is as follows:

[0120]

[0121] This distance value It quantifies the shape changes that occur during waveform propagation. The length of the optimal warped path found by the Dynamic Time Warping (DTW) algorithm.

[0122] S108. Based on propagation delay time and attenuation, construct a pressure prediction model for the target node.

[0123] In this step, the server can select the most reliable path from all the identified potential propagation paths of the pressure wave as the sole modeling basis. The principle is that for any target node, in a single pressure wave event, only the most significant and stable pressure propagation relationship between it and the water supply end is adopted.

[0124] Specifically, the server retrieves all the first target similarities determined in S105. The server compares all of these. Find the absolute value of each, and select the one with the largest absolute value. The corresponding path The principle behind this optimal path modeling is as follows: The largest absolute value indicates that the pressure response signal under this path has the highest similarity to the water source excitation signal and is least affected by random noise and local interference. Therefore, it can be considered the most reliable and primary propagation channel.

[0125] The server is based on the optimal path. Propagation delay time and overall attenuation Construct a stress prediction model, in which,

[0126]

[0127] The goal of a pressure prediction model is to predict the pressure value of a target node at the current moment using historical pressure data from the water supply end. The basic form of a pressure prediction model is a functional relationship, which can be expressed as follows:

[0128]

[0129] in, It is determined by the attenuation The determined pressure transformation function is designed to more accurately capture the nonlinear characteristics of pressure wave attenuation and waveform distortion. This can be achieved using neural networks (such as a multilayer perceptron), to... Using the pressure values ​​at and adjacent time points as input, the system is trained to output predicted values. The target value used to train this neural network is the actual value. And the attenuation eigenvector The decay rate index can be used as part of the loss function during training to guide the neural network to learn the correct decay pattern.

[0130] Figure 1 The method shown has the following technical effects:

[0131] 1. This method determines the moment of pressure wave generation and sets an analysis time window based on that moment to ensure the capture of the complete pressure propagation process. Subsequently, by calculating the similarity of pressure time-series data from the water supply end and the target node under time offset, it can proactively identify the optimal time offset for signal matching, i.e., the propagation delay. Therefore, this method considers the time delay of pressure wave propagation in the pipeline and no longer assumes synchronous responses. By quantifying the propagation delay, this method can accurately characterize the dynamic propagation process of pressure waves from the water supply end to the target node, making it particularly suitable for long-distance pipelines with significant propagation delays. This overcomes the limitation of existing data-driven methods in handling time delays.

[0132] 2. This method relies solely on pressure time-series data from the water supply end and the target node, requiring no prior information such as pipeline topology, pipe material parameters, or water consumption distribution. By using a data-driven approach, it directly extracts propagation features such as propagation delay and attenuation from the pressure signal to construct the model, reducing modeling complexity and cost. This makes the method applicable to real-world pipeline systems with incomplete or dynamically changing topology information.

[0133] 3. This method constructs a pressure prediction model by calculating parameters with clear physical meaning, such as propagation delay time and attenuation degree. Since these parameters directly correspond to the physical characteristics of pressure wave propagation (such as wave speed and energy loss), the pressure prediction model is no longer a black box. Furthermore, the propagation delay can be used to trace the path of pressure changes, and the attenuation degree can reflect the condition of the pipe section, thereby supporting the needs of in-depth analysis such as fault tracing and leak location, and enhancing the practicality and credibility of the model in engineering practice.

[0134] Optionally, based on the propagation delay time, the pressure value of the pressure wave at the target node is determined, compared to the attenuation of the pressure value of the pressure wave at the water supply end, including:

[0135] Step 1: Use the propagation delay time as an offset to offset the time corresponding to the non-baseline data to obtain the offset data;

[0136] Specifically, in this step, the server will process the non-baseline data (i.e., the first pressure time series data of the target node). At that moment, it shifts in the positive direction (future) of the timeline. To obtain the new offset data :

[0137]

[0138] Thus, the pressure response observed at the target node is aligned to the moment when pressure excitation occurs at the water supply end, triggering that response. After the offset, Compared with baseline data (i.e., pressure time series data at the water supply end) It achieves causal alignment in time.

[0139] Step 2: Perform linear regression fitting on the offset data and the baseline data to determine the attenuation degree.

[0140] server Let (X) be the independent variable, and let the aligned values ​​be the values ​​of the variables. Using Y as the dependent variable, perform a univariate linear regression analysis over the entire target time window. The goal of univariate linear regression analysis is to find a set of parameters (slope and intercept) such that a straight line best fits the data points. The linear regression model is expressed as:

[0141]

[0142] in:

[0143] It is the slope of the regression line;

[0144] It is the intercept of the regression line;

[0145] It is the residual term, representing the fitting error.

[0146] For specific servers, the least squares method can be used to solve for the slope and intercept, that is, to find the slope and intercept that minimize the sum of squared residuals of all data points.

[0147] It should be noted that the parameters obtained after linear regression fitting and Together, they constitute the attenuation of the pressure wave as it propagates from the water supply end to the target node.

[0148] slope The attenuation rate characterizes the pressure amplitude; ideally, if there is no energy loss, It should be equal to 1. This indicates that the pressure wave attenuated during propagation. The smaller the value, the more severe the attenuation.

[0149] intercept This reflects the systematic pressure deviation caused by factors such as differences in terrain elevation and static pressure benchmarks.

[0150] Therefore, the attenuation can be represented as a binary tuple. This binary tuple quantifies the overall change characteristics of the pressure value as the pressure wave propagates from the water supply end to the target node.

[0151] The above scheme uses linear regression fitting to determine the attenuation degree, characterizing the attenuation characteristics of pressure propagation with a simple linear equation, avoiding the application of complex hydraulic formulas, and reducing the complexity of modeling and computational costs. At the same time, the slope and intercept obtained from the regression have intuitive physical meaning; this clear quantitative index enhances the interpretability of the model and facilitates maintenance personnel's understanding of the pressure wave propagation characteristics at different locations in the water supply network.

[0152] Figure 2 This is a schematic flowchart illustrating a possible method for determining attenuation in an embodiment of this application, as shown below. Figure 2 As shown, optionally, linear regression fitting is performed on the offset data and the baseline data to determine the attenuation degree, including:

[0153] S201. Obtain the traffic time-series data of the target node within the target time window;

[0154] In this step, after completing the causal alignment of the pressure time series data in the aforementioned linear fitting process, the server sends a query request to the database to retrieve the traffic time series data of the target node within the target time window. and ensure It has the exact same timestamps and sampling frequencies as the existing pressure time series data, ensuring that the data is strictly aligned in time.

[0155] S202. Based on the traffic time series data, determine the abnormal time range in which traffic anomalies exist;

[0156] Optionally, in this step, based on the traffic time-series data, the abnormal time range in which traffic anomalies exist is determined, including:

[0157] Based on the time-series traffic data, determine the rate of change of traffic at different times within the target time window;

[0158] Among the flow rate changes at different times, determine the target flow rate change that is greater than a preset rate change threshold;

[0159] Determine the abnormal time range based on the time corresponding to the target flow rate change rate.

[0160] The server calculates traffic time-series data. The rate of change of flow is calculated using the following formula:

[0161]

[0162] in, The sampling interval (e.g., 1 minute).

[0163] The server will It is compared with a preset engineering threshold, which can be set based on the historical water usage patterns of the target node, for example, a fixed percentage of the target node's average daily flow, such as 15%. When the conditions are met... When the value is greater than or equal to the threshold, the time is determined. There is an abnormal traffic flow.

[0164] The server can merge consecutive abnormal traffic times and extend them appropriately before and after (e.g., extend by 5-10 minutes) to form one or more consecutive abnormal time ranges. The reason for this design is that a large water usage event usually lasts for a period of time, and its impact will also exist briefly before and after the water usage event begins.

[0165] Optionally, based on traffic time-series data, determine the abnormal time range in which traffic anomalies exist, including:

[0166] Step 1: Based on traffic time series data, the pre-trained deep learning model identifies traffic data with anomalies.

[0167] Specifically, during the deep learning model training phase, the server collects a large amount of historical flow time-series data from IoT devices such as smart water meters and flow sensors deployed in the water supply network. This data includes timestamps and corresponding flow values. The server then preprocesses the collected raw data, including:

[0168] Handling missing values, obviously erroneous outliers (such as negative flow), and smoothing noise caused by transient sensor malfunctions;

[0169] Normalize the flow values ​​to a specific range (such as 0-1) to accelerate the convergence of deep learning models.

[0170] Next, the server can divide the time-series data into multiple traffic sequences according to a certain time window length (such as 6 consecutive hours).

[0171] To address the characteristics of time-series data, deep learning models can choose LSTM (Long Short-Term Memory) or its variants because LSTM can effectively capture long-term dependencies in traffic data, such as daily peak / off-peak water usage cycles and weekly changes in water usage patterns. The server inputs the preprocessed traffic sequence into the LSTM for training. The training process can employ supervised learning, with the goal of teaching the LSTM to distinguish between normal and abnormal traffic patterns.

[0172] After model training is complete, the server acquires flow data streams from sensors in the water supply network within the target time window and performs preprocessing on these data streams similar to that used during training. The server can define a sliding time window (with the same length as the time sequence of the flow sequence during training), input the flow sequence within the current sliding window into the LSTM model already loaded into memory, and then determine whether there are any abnormal flow data points in the flow sequence within the current sliding window.

[0173] Step 2: Determine the abnormal time range based on the time corresponding to the abnormal traffic data.

[0174] In this step, the server can determine the abnormal time range based on the start and end times of abnormal traffic data points within the target time window.

[0175] S203. In the offset data and the reference data, the data whose corresponding time falls within the abnormal traffic flow time range is identified as disturbed data; the data in the offset data and the reference data other than the disturbed data is identified as undisturbed data.

[0176] In this step, the server iterates through every point in time within the target time window. If the current time point If the data falls within any time range of abnormal traffic, the server will record the corresponding stress data point. Mark as disturbed data. Conversely, if the time point... If a data point is not within any period of abnormal traffic, it is marked as undisturbed data.

[0177] S204. Based on the first weight corresponding to the disturbed data and the second weight corresponding to the undisturbed data, perform linear regression fitting on the offset data and the benchmark data to obtain the calculation result of the attenuation degree, wherein the second weight is greater than the first weight.

[0178] The server assigns a high second weight to all data points labeled as undisturbed, indicating a high level of trust in the pressure propagation relationships reflected by these data points. Simultaneously, the server assigns a low first weight to all data points labeled as disturbed. This suggests that the server considers these points, due to localized water usage interference, to have lower reliability in reflecting propagation relationships and should therefore have a smaller influence in the fitting process.

[0179] The server uses water supply pressure Let X be the independent variable, and let the target node pressure after offset be the value. For the dependent variable Y, a weighted linear regression is performed. The goal of the weighted linear regression is to find the parameters. (Slope) and (Intercept) that minimizes the following weighted sum of squared residuals:

[0180]

[0181] Among them, the weight function The value is taken when the data point is undisturbed. As the second weight; when the data point is disturbed data, The first weight is determined by the first weight, and the second weight is greater than the first weight.

[0182] Figure 2 The method shown has the following technical effects:

[0183] 1. Traditional data-driven methods treat all time points as equal, without distinguishing whether changes in water supply network pressure originate from pressure waves generated by the water plant (i.e., the signal to be modeled) or from random water usage at the target node (noise that needs to be filtered out). Using this noisy data for linear regression fitting can easily lead to distorted results. Figure 2 The method described introduces time-series flow data, analyzes the time range of abnormal flow, determines the time period of random local water use at the target node, thereby identifying which data is disturbed, and mainly uses undisturbed data for linear regression fitting, thus improving the accuracy of linear regression fitting and improving modeling precision.

[0184] 2. Figure 2 The method described employs a weighted "soft filtering" strategy (S204), assigning different weights (the second weight is greater than the first weight) to data of different confidence levels, rather than directly deleting data within abnormal time ranges. Thus, for undisturbed data, the high weight ensures their dominant role in the attenuation calculation results, guaranteeing that the model can capture the true pressure propagation pattern. For disturbed data, the low weight does not completely ignore these data, but greatly weakens their influence. This effectively suppresses the bias caused by local disturbances while preserving the continuity of data, avoiding a sharp decrease in samples due to drastic data deletion, which could lead to model instability. It achieves a balance between maximizing the use of effective data and maximizing the suppression of invalid noise.

[0185] Figure 3 This is a schematic diagram of a possible method for constructing a pressure prediction model provided in an embodiment of this application, as shown below. Figure 3 As shown, a stress prediction model for the target node is constructed based on propagation delay time and attenuation, including:

[0186] S301. In the first target similarity, determine the second target similarity corresponding to each target path. The target path is the propagation path of the pressure wave in the water supply network.

[0187] In this step, the server receives all the first target similarities, i.e., the cross-correlation function, from step S105. All of the above are satisfied ( The server identifies significant peak points (within a preset threshold). Each peak point represents a possible pressure propagation path. The server marks each significant peak point as an independent target path. .

[0188] Next, for each target path The server records two parameters:

[0189] Propagation delay time This refers to the time offset corresponding to the peak point.

[0190] Second target similarity That is, the cross-correlation function value at the peak point. This value quantifies the fidelity of the pressure signal along this propagation path.

[0191] S302. Calculate the ratio of the second target similarity corresponding to each target path to the sum of all second target similarities;

[0192] In this step, the server calculates the sum of the absolute values ​​of the second target similarity for all identified target paths:

[0193]

[0194] in, This represents the total number of target paths.

[0195] For each target path The server calculates the ratio of the absolute value of the second target similarity to the total relevance strength, using the following method:

[0196]

[0197] S303. Determine the weight of each target path based on the ratio corresponding to each target path;

[0198] In this step, the server can specify each target path. The corresponding weights are set as the calculated ratios. In this way, the sum of all path weights is 1, which allows the propagation path with higher signal fidelity to contribute a greater weight in the final stress prediction model.

[0199] S304. Based on the propagation delay time, attenuation degree, and the weight corresponding to each target path, a pressure prediction model is constructed.

[0200] Specifically, for each target path The attenuation of this path can be:

[0201]

[0202] The attenuation is the attenuation obtained through the aforementioned linear fitting method.

[0203] The final stress prediction model can be:

[0204]

[0205] in, for At any given time, the predicted pressure value of the target node;

[0206] Total number of target paths;

[0207] For the first The weight of each path;

[0208] , : No. The attenuation of each path, the specific method of obtaining it and its meaning are explained in the aforementioned linear fitting method;

[0209] Water supply end at a historical moment The actual pressure value;

[0210] Pressure wave passes through the first The propagation delay time of each path to the target node.

[0211] Figure 3 The method shown has the following technical effects:

[0212] Traditional methods struggle to address the challenge of multipath propagation and superposition of pressure waves in ring-shaped water supply networks. Figure 3 The method automatically discovers all effective propagation paths of pressure waves by identifying multiple significant peaks in the cross-correlation function, and integrates the contributions of each propagation path of pressure waves using a weighted pressure prediction model. This enables it to accurately describe the real propagation behavior of pressure in complex pipe networks and can be applied to scenarios of multi-path propagation of pressure waves in ring-shaped water supply networks.

[0213] Based on the stress prediction model constructed using the aforementioned method, the stress prediction method for the target node is as follows:

[0214] Based on the pressure prediction model of the target node in the water supply network, the propagation delay time of the pressure wave from the water supply end of the water supply network to the target node, as well as the pressure value of the pressure wave at the target node, are determined compared with the attenuation of the pressure value of the pressure wave at the water supply end.

[0215] Subtract the propagation delay time from the first target time to obtain the second target time;

[0216] Obtain the actual pressure value at the water supply end at the second target time;

[0217] Based on the actual pressure value and attenuation rate, predict the pressure value of the target node at the first target moment.

[0218] The specific method for determining the pressure value of the target node at the first target time can be found in the pressure prediction model formula provided in the foregoing embodiments, and will not be elaborated upon here.

[0219] Figure 4 This is a schematic diagram of the water supply network pressure prediction model construction device provided in the embodiments of this application, as shown below. Figure 4 As shown, the device 40 includes:

[0220] The time window determination module 401 is used to determine the time of generation of pressure waves in the water supply network.

[0221] Based on the time of generation, a target time window is determined, and the time of generation falls within the target time window;

[0222] The pressure data acquisition module 402 is used to acquire the first pressure time series data of the target node of the water supply network within the target time window, and the second pressure time series data of the water supply end of the water supply network within the target time window.

[0223] The model building module 403 is used to determine one of the first pressure time series data and the other of the second pressure time series data as the reference data and the other as the non-reference data, offset the time corresponding to the non-reference data according to different time offsets, and calculate the similarity between the offset non-reference data and the reference data.

[0224] Among the similarities corresponding to each time offset, the first target similarity that is greater than the preset similarity threshold is determined;

[0225] Based on the time offset corresponding to the first target similarity, the propagation delay time of the pressure wave from the water supply end to the target node is determined;

[0226] Based on the propagation delay time, determine the pressure value of the pressure wave at the target node, and compare it with the attenuation of the pressure value of the pressure wave at the water supply end;

[0227] Based on propagation delay time and attenuation, a pressure prediction model for the target node is constructed.

[0228] The apparatus provided in this embodiment can execute the method provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0229] Figure 5 This is a schematic diagram of an electronic device provided in an embodiment of this application. Figure 5 As shown, the electronic device 50 provided in this embodiment includes at least one processor 501 and a memory 502. Optionally, the device 50 further includes a communication component 503. The processor 501, memory 502, and communication component 503 are connected via a bus 504.

[0230] In a specific implementation, at least one processor 501 executes computer execution instructions stored in memory 502, causing at least one processor 501 to perform the above-described method.

[0231] The specific implementation process of processor 501 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0232] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0233] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0234] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0235] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0236] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0237] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0238] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0239] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0240] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0241] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0242] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0243] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0244] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for constructing a water supply network pressure prediction model, characterized in that, The method includes: Determine the moment when pressure waves are generated in the water supply network; Based on the time of generation, a target time window is determined, wherein the time of generation is within the target time window; Acquire the first pressure time series data of the target node of the water supply network within the target time window, and the second pressure time series data of the water supply end of the water supply network within the target time window; In the first pressure time series data and the second pressure time series data, one is determined as the reference data and the other is determined as the non-reference data. The time corresponding to the non-reference data is offset according to different time offsets, and the similarity between the offset non-reference data and the reference data is calculated. In each similarity corresponding to the time offset, at least one first target similarity greater than a preset similarity threshold is determined; each first target similarity corresponds to a target path from the water supply end to the target node; Based on the time offset corresponding to the first target similarity, the propagation delay time of the pressure wave from the water supply end to the target node is determined; Based on the propagation delay time, determine the pressure value of the pressure wave at the target node, and compare it with the attenuation of the pressure value of the pressure wave at the water supply end; Based on the propagation delay time, the attenuation rate, and the weight corresponding to each target path, a pressure prediction model for the target node is constructed. The step of determining the pressure value of the pressure wave at the target node based on the propagation delay time, compared with the attenuation of the pressure wave at the water supply end, includes: Using the propagation delay time as an offset, the time corresponding to the non-reference data is offset to obtain the offset data; Obtain the traffic time-series data of the target node within the target time window; Based on the traffic time-series data, determine the abnormal time range in which traffic anomalies exist; Data in the offset data and the reference data whose corresponding time falls within the abnormal time range are identified as disturbed data; data in the offset data and the reference data other than the disturbed data are identified as undisturbed data. Based on the first weight corresponding to the disturbed data and the second weight corresponding to the undisturbed data, a linear regression fitting process is performed on the offset data and the benchmark data to obtain the calculation result of the attenuation degree, wherein the second weight is greater than the first weight.

2. The method according to claim 1, characterized in that, Determining the generation time of pressure waves in the water supply network includes: Obtain the rate of pressure change at the water supply end; If the rate of pressure change is greater than a preset rate threshold, then the current moment is determined as the generation moment.

3. The method according to claim 1, characterized in that, The step of determining the pressure value of the pressure wave at the target node based on the propagation delay time, compared with the attenuation of the pressure wave at the water supply end, includes: Calculate the amplitude attenuation ratio, energy attenuation coefficient, and waveform distortion between the offset data and the reference data, and determine the attenuation degree based on the amplitude attenuation ratio, the energy attenuation coefficient, and the waveform distortion.

4. The method according to claim 1, characterized in that, The step of determining the abnormal time range where traffic anomalies exist based on the traffic time-series data includes: Based on the traffic time-series data, determine the rate of change of traffic at different times within the target time window; Among the flow rate changes at different times, determine the target flow rate change that is greater than a preset rate change threshold; The abnormal time range is determined based on the time corresponding to the target flow rate change.

5. The method according to claim 4, characterized in that, The step of determining the abnormal time range where traffic anomalies exist based on the traffic time-series data includes: Based on the traffic time-series data, a pre-trained deep learning model identifies abnormal traffic data. The abnormal time range is determined based on the time corresponding to the abnormal traffic data.

6. The method according to claim 1, characterized in that, Before constructing the pressure prediction model based on the propagation delay time, the attenuation degree, and the weights corresponding to each target path, the method further includes: In the first target similarity, the second target similarity corresponding to each target path is determined, wherein the target path is the propagation path of the pressure wave in the water supply network; Calculate the ratio of the second target similarity corresponding to each target path to the sum of all second target similarities; The weight of each target path is determined based on the ratio corresponding to each target path.

7. A pressure prediction method, characterized in that, The method is implemented based on the pressure prediction model constructed according to any one of claims 1-6, and the method includes: Based on the pressure prediction model of the target node in the water supply network, the propagation delay time of the pressure wave from the water supply end of the water supply network to the target node is determined, as well as the pressure value of the pressure wave at the target node and the attenuation degree of the pressure wave at the water supply end. Subtract the propagation delay time from the first target time to obtain the second target time; Obtain the actual pressure value of the water supply end at the second target time; Based on the actual pressure value and the attenuation rate, the pressure value of the target node at the first target time is predicted.

8. A device for constructing a water supply network pressure prediction model, characterized in that, The device includes: The time window determination module is used to determine the moment when pressure waves are generated in the water supply network. Based on the time of generation, a target time window is determined, wherein the time of generation is within the target time window; The pressure data acquisition module is used to acquire first pressure time-series data of the target node of the water supply network within the target time window, and second pressure time-series data of the water supply end of the water supply network within the target time window. The model building module is used to determine one of the first pressure time series data and the second pressure time series data as the reference data and the other as the non-reference data, offset the time corresponding to the non-reference data according to different time offsets, and calculate the similarity between the offset non-reference data and the reference data. In each similarity corresponding to the time offset, at least one first target similarity greater than a preset similarity threshold is determined; each first target similarity corresponds to a target path from the water supply end to the target node; Based on the time offset corresponding to the first target similarity, the propagation delay time of the pressure wave from the water supply end to the target node is determined; Based on the propagation delay time, determine the pressure value of the pressure wave at the target node, and compare it with the attenuation of the pressure value of the pressure wave at the water supply end; Based on the propagation delay time and the attenuation rate, a pressure prediction model for the target node is constructed; When determining the pressure value of the pressure wave at the target node based on the propagation delay time, and comparing it with the attenuation of the pressure value of the pressure wave at the water supply end, the model building module is specifically used for: Using the propagation delay time as an offset, the time corresponding to the non-reference data is offset to obtain the offset data; Obtain the traffic time-series data of the target node within the target time window; Based on the traffic time-series data, determine the abnormal time range in which traffic anomalies exist; Data in the offset data and the reference data whose corresponding time falls within the abnormal time range are identified as disturbed data; data in the offset data and the reference data other than the disturbed data are identified as undisturbed data. Based on the first weight corresponding to the disturbed data and the second weight corresponding to the undisturbed data, a linear regression fitting process is performed on the offset data and the benchmark data to obtain the calculation result of the attenuation degree, wherein the second weight is greater than the first weight.

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