Water supply network pressure prediction method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention discloses a water supply pipe network pressure prediction method and device, electronic equipment and a storage medium, and relates to the technical field of water supply pipe network pressure prediction.The method comprises the steps that feature engineering of mechanism constraint is constructed based on a pipe network hydraulics basic principle, and feature variables and target pressure values of a water supply pipe network are collected; a data set is formed and preprocessed; a multi-task LightGBM is adopted to construct a pressure prediction model, and parameters are adjusted through a loss function and an optimization algorithm based on a data set to train the model; calculating a multi-period absolute error mean value of the model, and constructing a feature contribution degree quantification system based on an SHAP framework to calculate a contribution degree proportion of each feature to the model; and the model is optimized and retrained according to the error mean value and the contribution degree proportion until the set requirement is met, and pressure prediction is carried out on the water supply pipe network. The problems that in the prior art, a dynamic pressure fluctuation rule is difficult to capture, prediction errors are high, interpretability is weak, optimization lags, and deployment flexibility is poor are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of water supply network pressure prediction, and in particular to a water supply network pressure prediction method, device, electronic equipment and storage medium. Background Art

[0002] With the acceleration of urbanization, the scale of water supply networks continues to expand, and water demand becomes increasingly complex and changeable, which puts higher demands on the real-time and accuracy of water supply network pressure prediction.

[0003] However, traditional water supply network pressure prediction methods, such as hydraulic modeling and data-driven approaches, have demonstrated significant limitations when addressing the complexities of modern water supply network management. While the hydraulic modeling method relies on hydraulic equations to construct a mathematical model of the network, while having a solid theoretical foundation, it requires extremely high quality data for the underlying network, a complex parameter calibration process, and the need for ongoing maintenance by a specialized team, resulting in high implementation and maintenance costs. Furthermore, this method exhibits relatively low modeling efficiency, making it difficult to quickly respond to changes in the network's operating status.

[0004] In addition, the data-driven method is too dependent on the quality of time series data, and its black box characteristics make it weak in interpretability, making it difficult to understand the physical meaning of the model prediction results. When the boundary conditions of the pipeline network change, the prediction accuracy of the data-driven model will drop significantly, which cannot meet the needs of actual engineering applications.

[0005] Therefore, there is an urgent need for a water supply network pressure prediction method that can effectively integrate hydraulic mechanisms and data-driven technology to improve the water supply network pressure prediction accuracy, computational efficiency and interpretability. Summary of the Invention

[0006] The embodiments of the present invention provide a water supply network pressure prediction method to address the problems of existing technologies such as difficulty in capturing dynamic pressure fluctuation patterns, high prediction errors and poor interpretability, optimization lags, and poor deployment flexibility. The technical solution is as follows: According to one aspect of the present invention, a method for predicting pressure in a water supply network includes: constructing a feature engineering with mechanism constraints based on the basic principles of network hydraulics, collecting characteristic variables and target pressure values of the water supply network according to the feature engineering, forming a data set and preprocessing it; constructing a pressure prediction model using multi-task LightGBM, and training the pressure prediction model by adjusting parameters through a loss function and an optimization algorithm based on the data set; calculating the multi-period absolute error mean of the pressure prediction model, and constructing a feature contribution quantification system based on the SHAP framework to calculate the contribution ratio of each feature in the feature engineering to the pressure prediction model; optimizing and retraining the pressure prediction model according to the error mean and contribution ratio until the trained pressure prediction model meets the set requirements, and performing pressure prediction on the water supply network.

[0007] In one embodiment, the feature engineering for constructing mechanism constraints based on the basic principles of pipeline hydraulics is achieved by the following steps: analyzing the influencing factors of pressure based on the pipeline hydraulic equation, and dividing the influencing factors into static characteristics that constitute the basic physical framework of pipeline pressure distribution and dynamic characteristics that directly drive real-time pressure fluctuations; according to the impact of the dynamic characteristics on pipeline pressure and the time lag effect of pipeline hydraulic response, the dynamic characteristics are divided into flow type, pressure type, state type and time lag type; and constructing the feature engineering for mechanism constraints based on the flow type, pressure type, state type and time lag type of the dynamic characteristics.

[0008] In one embodiment, the pipe network hydraulic equations include the mass conservation equation, the energy conservation equation, and the head loss equation along the pipeline; the static characteristics include pipe length, pipe diameter, roughness, topological structure, and elevation; the flow type includes regional water inlet, water plant outlet, booster pump station outlet, and large user water volume; the pressure type includes water plant outlet pressure and booster pump station outlet pressure; the state type includes valve opening and water pump operating status; the time series lag type includes minute lag characteristics and sliding window statistics.

[0009] In one embodiment, characteristic variables and target pressure values of the water supply network are collected according to the feature engineering to form a data set and preprocess the data set by the following steps: multi-source monitoring data of the water supply network are collected according to the feature engineering as input data; the input data covers the target pressure value and the characteristic variables included in the feature engineering; the input data are aligned according to timestamps and merged to form a structured data set, and the data set is marked as abnormal and missing values are filled by setting thresholds and data filling; monitoring points in the data set whose missing rate exceeds the set threshold are eliminated, sample data with missing values in the data set are deleted, and abnormal data statistics report and missing rate report are generated.

[0010] In one embodiment, a multi-task LightGBM is used to construct a pressure prediction model, and the pressure prediction model is trained by adjusting parameters based on the data set through a loss function and an optimization algorithm through the following steps: a two-layer architecture of a shared feature layer and an independent output layer and a multi-task LightGBM are used to construct a pressure prediction model, and the data set is input into the pressure prediction model to obtain a predicted value; the shared feature layer is used to process the dynamic features to generate a common feature representation; the independent output layer is used to generate a predicted value based on the common feature representation; the loss value is calculated based on the predicted value and the target pressure value using a loss function that minimizes the mean square error, and the pressure prediction model is trained and hyperparameters are tuned based on the loss value and a Bayesian optimization algorithm, and a regularization term is introduced to prevent overfitting.

[0011] In one embodiment, the multi-time period absolute error mean of the pressure prediction model is calculated, and a feature contribution quantification system is constructed based on the SHAP framework to calculate the contribution ratio of each feature in the feature engineering to the pressure prediction model by the following steps: defining the time period length, calculating the absolute error according to the predicted value and the target pressure value in each time period, and obtaining the multi-time period absolute error mean based on the average of multiple absolute errors; calculating the contribution of each feature in the feature engineering to the predicted value based on the Shapley value in cooperative game theory based on the SHAP framework to obtain the SHAP value of each feature; calculating the average of the SHAP values of each feature to obtain the global average contribution of each feature, and normalizing each global average contribution to obtain the contribution ratio of each feature to the pressure prediction model.

[0012] In one embodiment, the pressure prediction model is optimized and retrained based on the error mean and contribution ratio by the following steps: cross-analyzing the error mean and contribution ratio to identify monitoring points whose prediction accuracy is lower than the set requirements; adopting a feature enhancement strategy for the monitoring points to supplement the mechanism-driven dynamic feature variables; the feature enhancement strategy includes adding time series lag features and introducing new time series features.

[0013] According to one aspect of the present invention, a water supply network pressure prediction device includes: a feature engineering construction and acquisition module, which is used to construct a mechanism-constrained feature engineering based on the basic principles of network hydraulics, collect characteristic variables and target pressure values of the water supply network according to the feature engineering, form a data set and perform preprocessing; a model construction and training module, which is used to use multi-task LightGBM to construct a pressure prediction model, and train the pressure prediction model by adjusting parameters through loss function and optimization algorithm based on the data set; an error calculation and feature analysis module, which is used to calculate the multi-period absolute error mean of the pressure prediction model, and construct a feature contribution quantification system based on the SHAP framework to calculate the contribution ratio of each feature in the feature engineering to the pressure prediction model; a model optimization and application module, which is used to optimize and retrain the pressure prediction model according to the error mean and contribution ratio until the trained pressure prediction model meets the set requirements, and performs pressure prediction on the water supply network.

[0014] According to one aspect of the present invention, an electronic device includes at least one processor and at least one memory, wherein the memory stores computer-readable instructions; the computer-readable instructions are executed by one or more of the processors, so that the electronic device implements the water supply network pressure prediction method as described above.

[0015] According to one aspect of the present invention, a storage medium stores computer-readable instructions thereon, wherein the computer-readable instructions are executed by one or more processors to implement the water supply network pressure prediction method as described above.

[0016] The beneficial effects brought about by the technical solution provided by the present invention are: In the above technical scheme, the present invention first constructs a feature engineering with mechanism constraints based on the hydraulic principles of the pipeline network, systematically analyzes the pressure influencing factors and classifies them into static and dynamic features, and constructs feature engineering based only on dynamic features (flow, pressure, state and time lag), and then collects multi-source monitoring data to form a structured data set, so as to achieve efficient integration and preprocessing of data, adopts multi-task LightGBM to build a prediction model, utilizes a shared feature layer and an independent output layer architecture, combines the minimization of the mean square error loss function and the Bayesian optimization algorithm for model training and hyperparameter tuning, effectively improves the prediction accuracy, and accurately evaluates the model performance and the importance of each feature by calculating the mean absolute error of multiple time periods and quantifying the feature contribution based on the SHAP framework, providing data support for model optimization, and adopts a feature enhancement strategy for monitoring points with insufficient prediction accuracy based on the cross-analysis results of the mean error and the contribution ratio to supplement the mechanism-driven dynamic feature variables. This solution not only significantly improves the accuracy of water supply network pressure prediction, but also enhances the model's adaptability, thereby effectively solving the problems of existing technologies that are difficult to capture dynamic pressure fluctuation patterns, have high prediction errors and weak interpretability, and suffer from optimization lags and poor deployment flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort.

[0018] Figure 1 is a flow chart of a method for predicting water supply network pressure according to an exemplary embodiment; Figure 2 is a flow chart of a method for predicting water supply network pressure in an exemplary embodiment; Figure 3 is a block diagram of a water supply network pressure prediction device according to an exemplary embodiment; Figure 4 is a hardware structure diagram of an electronic device according to an exemplary embodiment; Figure 5 It is a block diagram of an electronic device according to an exemplary embodiment. DETAILED DESCRIPTION

[0019] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0020] It will be understood by those skilled in the art that, unless expressly stated otherwise, the singular forms "a", "an", "said" and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of the present disclosure refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, "connected" or "coupled" as used herein may include wireless connections or wireless couplings. The term "and / or" used herein includes all or any units and all combinations of one or more associated listed items.

[0021] The present invention provides a water supply network pressure prediction method. By integrating hydraulic mechanism constraints with data-driven technology, adopting the LightGBM model in combination with the Bayesian optimization algorithm, and combining the SHAP framework for feature contribution analysis, the method achieves a simultaneous improvement in model accuracy and interpretability. This solves the problems of existing technologies such as difficulty in capturing dynamic pressure fluctuation patterns, high prediction errors and weak interpretability, optimization lags, and poor deployment flexibility. The water supply network pressure prediction method is suitable for use in a water supply network pressure prediction device, which can be an electronic device. The water supply network pressure prediction method in the embodiment of the present invention can be applied to a variety of scenarios, such as pressure prediction of urban water supply systems, etc.

[0022] See also Figure 1 , an embodiment of the present invention provides a water supply network pressure prediction method, which is applicable to electronic equipment.

[0023] In the following method embodiments, for ease of description, the execution subject of each step of the method is taken as an electronic device as an example for illustration, but this does not constitute a specific limitation.

[0024] like Figure 1 As shown, the method may include the following steps: Step 110 , constructing a feature engineering of mechanism constraints based on the basic principles of pipe network hydraulics, collecting characteristic variables and target pressure values of the water supply pipe network according to the feature engineering, forming a data set and performing preprocessing.

[0025] In one possible implementation, the factors affecting pressure are analyzed based on the hydraulic equations of the pipeline network. The influencing factors are divided into static characteristics that constitute the basic physical framework of the pipeline network pressure distribution and dynamic characteristics that directly drive the real-time fluctuation of pressure. According to the impact of the dynamic characteristics on the pipeline network pressure and the time lag effect of the pipeline network hydraulic response, the dynamic characteristics are divided into flow type, pressure type, state type and time lag type. According to the flow type, pressure type, state type and time lag type of dynamic characteristics, feature engineering with mechanism constraints is constructed.

[0026] Among them, the hydraulic equations of the pipeline network include the mass conservation equation, the energy conservation equation, and the head loss equation along the pipeline (such as the Darcy-Weisbach formula); static characteristics include pipe length, pipe diameter, roughness, topological structure, and elevation; flow types include regional water inflow, water plant outflow, booster pump station outflow, and large user water volume; pressure types include water plant outflow pressure and booster pump station outflow pressure; state types include valve opening and water pump operating status; time series lag types include minute lag characteristics and sliding window statistics, all of which are not limited here.

[0027] In one possible implementation, multi-source monitoring data of the water supply network is collected as input data based on feature engineering. The input data is aligned according to timestamps and merged to form a structured data set. The data set is anomaly marked and missing values are filled by setting thresholds and data filling. Monitoring points in the data set with a missing rate exceeding the set threshold are eliminated, and sample data with missing values in the data set are deleted. Finally, a statistical report on abnormal data and a missing rate report are generated.

[0028] The input data includes target pressure values and feature variables included in feature engineering.

[0029] Specifically, abnormal data marking and processing: set reasonable thresholds for feature variables and target variables, and data out of the range will be marked as abnormal and processed accordingly (such as deletion or replacement); missing value filling: fill the missing values in the original data, and for data segments with short consecutive missing time, use the previous and next valid values to generate an arithmetic sequence for filling; for missing values of lagged features or sliding window statistics, use the backward filling method; invalid monitoring points and samples are eliminated: based on the filled data, the monitoring points and samples with missing rates exceeding the threshold are eliminated to ensure the integrity and reliability of the data set; data quality assessment: generate abnormal data statistical reports and missing rate reports after interpolation, record the abnormal frequency, missing rate and repair results of each monitoring point, and provide data quality assurance for subsequent modeling.

[0030] Specifically, through dynamic feature classification, the dynamic features of flow (regional water inlet, water plant outlet), pressure (water plant outlet pressure), state (valve opening) and time lag (minute lag features, sliding window statistics) are incorporated into feature engineering to characterize the real-time pressure fluctuation pattern.

[0031] Furthermore, multi-source monitoring data from the SCADA system of the water supply plant network are collected to form an input dataset containing target pressure values and characteristic variables. The data are merged by timestamp to generate a structured dataset to ensure the spatiotemporal consistency of the characteristics and pressure values.

[0032] In the above process, the embodiment of the present invention marks outliers by setting thresholds, fills missing data with means and medians, deletes monitoring points with missing rates exceeding the threshold, generates anomaly and missing rate reports, ensures data quality, captures real-time fluctuations through dynamic features, ensures that feature engineering complies with hydraulic laws, and improves the reliability of model input data and reduces noise interference through anomaly marking and missing value processing.

[0033] In step 120 , a pressure prediction model is constructed using a multi-task LightGBM, and the pressure prediction model is trained by adjusting parameters using a loss function and an optimization algorithm based on the data set.

[0034] In one possible implementation, a two-layer architecture with a shared feature layer and an independent output layer and a multi-task LightGBM are used to build a pressure prediction model. The dataset is input into the pressure prediction model to obtain the predicted value. The loss value is calculated based on the predicted value and the target pressure value using the minimum mean square error loss function. The pressure prediction model is trained and hyperparameters are tuned based on the loss value and the Bayesian optimization algorithm, and a regularization term is introduced to prevent overfitting.

[0035] Among them, the shared feature layer is used to process dynamic features to generate common feature representations, and the independent output layer is used to generate prediction values based on the common feature representations. The shared feature layer integrates common features to simplify the model complexity, and the independent output layer personalizes the pressure characteristics to improve modeling efficiency and accuracy. This design aims to take into account the versatility and specificity of the model and improve the adaptability and prediction performance of the model.

[0036] Specifically, the personalized responses of different monitoring points are captured, and the mean square error loss is used as the loss function to quantify the deviation between the predicted value and the target pressure value. As the core goal of model training, the optimal hyperparameters (such as learning rate and tree depth) are automatically searched through Bayesian optimization parameter adjustment. Regularization terms are combined to prevent overfitting, and the generalization ability of the main task (pressure prediction) is improved through a multi-task learning mechanism.

[0037] Among them, after comprehensively comparing multiple algorithms, the embodiment of the present invention selects LightGBM as the core prediction model, because LightGBM is based on the gradient boosting framework of the decision tree, and uses the histogram algorithm to accelerate feature splitting, which can greatly improve data processing speed and memory efficiency. It adopts a two-layer architecture of shared feature layer-independent output layer to improve modeling efficiency and accuracy.

[0038] In the above process, the embodiment of the present invention uses a two-layer architecture to simplify the model complexity and improve the model's expressiveness. By combining Bayesian optimization with regularization, it avoids the inefficiency of manual tuning of hyperparameters and reduces the risk of overfitting.

[0039] Step 130 , calculate the multi-period absolute error mean of the pressure prediction model, and construct a feature contribution quantification system based on the SHAP framework to calculate the contribution ratio of each feature in the feature engineering to the pressure prediction model.

[0040] In one possible implementation, the length of a time period is defined, the absolute error is calculated based on the predicted value and the target pressure value in each time period, the average of multiple absolute errors is calculated to obtain the average absolute error of multiple time periods, and the contribution of each feature in feature engineering to the predicted value is calculated based on the Shapley value in cooperative game theory based on the SHAP framework to obtain the SHAP value of each feature. The average of the SHAP values of each feature is calculated to obtain the global average contribution of each feature, and the global average contribution is normalized to obtain the contribution ratio of each feature to the pressure prediction model.

[0041] Specifically, the absolute error between the predicted value and the target value is counted in a fixed time period (such as 15 minutes), the average absolute error of multiple time periods is calculated, and the overall prediction deviation of the model is quantified. Based on cooperative game theory, the marginal contribution of each feature to the predicted value is decomposed, and the mean SHAP value of the feature is normalized to the contribution ratio to intuitively reflect the importance of the feature. Monitoring points with high mean error and abnormal feature contribution are identified to locate the weak links of the model.

[0042] In the above process, the embodiment of the present invention reflects the model stability through the multi-period error mean, reveals the feature action mechanism through SHAP contribution, associates the error with the feature through cross-analysis, and provides a precise direction for model optimization.

[0043] Step 140 , optimize and retrain the pressure prediction model according to the error mean and contribution ratio until the trained pressure prediction model meets the set requirements, and perform pressure prediction on the water supply network.

[0044] In one possible implementation, the error mean and contribution ratio are cross-analyzed to identify monitoring points where the prediction accuracy is lower than the set requirements. A feature enhancement strategy is adopted for the monitoring points to supplement the mechanism-driven dynamic feature variables.

[0045] Specifically, for monitoring points where the prediction error exceeds the limit, priority is given to supplementing mechanism-driven dynamic feature variables, such as the operating data of surrounding pump rooms; combining the SHAP feature contribution analysis and model accuracy evaluation results, dynamically adjust the LightGBM hyperparameters to suppress the risk of overfitting; establish a closed-loop mechanism of "feature optimization-model iteration" to improve the model prediction accuracy and interpretability by continuously optimizing the feature set and model parameters.

[0046] Among them, feature enhancement strategies include adding time series lag features and introducing new time series features, etc.

[0047] Specifically, dynamic data (such as parameters of surrounding pump room operation) are added to monitoring points with high mean error to improve local prediction accuracy.

[0048] Specifically, the trained model is deployed to the water supply network monitoring system to achieve real-time pressure prediction. The model can quickly output prediction results based on the current monitoring data, provide decision support for network scheduling, and dynamically adjust the model input features and parameters according to changes in the network operation status to ensure the model's prediction accuracy under different working conditions. The prediction results and model performance indicators are displayed through a visual interface, which makes it easier for technical personnel to monitor the network operation status, promptly discover and deal with potential problems, regularly collect new monitoring data, and continuously optimize and iterate the model to ensure that the model always maintains high prediction accuracy and adaptability.

[0049] In the above process, the embodiment of the present invention improves the model's responsiveness to fluctuating scenarios through dynamic feature engineering and feature enhancement strategies.

[0050] Through the above process, the present invention first constructs a feature engineering with mechanism constraints based on the hydraulic principles of the pipeline network, systematically analyzes the pressure influencing factors and classifies them into static and dynamic features, and then collects multi-source monitoring data to form a structured data set, realizing efficient data integration and preprocessing, and adopts multi-task LightGBM to construct a prediction model. The shared feature layer and independent output layer architecture are used, combined with the minimization of the mean square error loss function and the Bayesian optimization algorithm for model training and hyperparameter tuning, which effectively improves the prediction accuracy. By calculating the mean absolute error of multiple time periods and quantifying the feature contribution based on the SHAP framework, the model performance and the importance of each feature are accurately evaluated, providing data support for model optimization. Based on the cross-analysis results of the mean error and the contribution ratio, dynamic features are supplemented for monitoring points with insufficient prediction accuracy, and a feature enhancement strategy is adopted, which not only significantly improves the accuracy of water supply network pressure prediction, but also enhances the adaptability of the model, effectively solving the problems that the existing technology is difficult to capture the dynamic pressure fluctuation law, the prediction error is high and the interpretability is weak, the optimization is delayed and the deployment flexibility is poor.

[0051] In an exemplary embodiment, the process of predicting the pressure of a water supply network using the water supply network pressure prediction method of the present invention is demonstrated.

[0052] like Figure 2 As shown, the following steps may be included: Step S1, mechanism constraint feature screening.

[0053] Step S1.1, impact factor analysis.

[0054] Specifically, based on the network hydraulic equations (mass conservation equation, energy conservation equation, and Darcy-Weisbach equation), the paper deeply analyzes the various factors affecting network pressure. These factors are categorized into static and dynamic characteristics. Static characteristics, such as pipe length, diameter, roughness, topology, and elevation, form the fundamental physical framework for network pressure distribution. Dynamic characteristics directly drive real-time pressure fluctuations and include flow (regional inflow, water plant outflow, and booster station outflow), pressure (water plant outflow pressure, booster station outflow pressure), state (valve opening and pump operating frequency), and time series lags (such as minute lag features t-1 and t-5, and the 5-minute mean of sliding window statistics).

[0055] Step S1.2, feature engineering construction.

[0056] Based on the core factors influencing pipe network pressure identified in the above process, feature engineering was developed based on the flow, pressure, state, and time lag categories of dynamic features. Based on these core factors, feature engineering encompasses multi-dimensional dynamic features, focusing on screening key factors that directly drive pressure fluctuations, such as water plant discharge pressure, water plant water output, and regional total water inflow.

[0057] Step S2: data collection and preprocessing.

[0058] Step S2.1, data acquisition.

[0059] Specifically, feature engineering is used to collect multi-source monitoring data from the water supply network as input. This multi-source monitoring data includes real-time operational data from the SCADA system (such as flow, pressure, and valve opening). The input data must include the target pressure value and the characteristic variables included in feature engineering.

[0060] Step S2.2, data preprocessing.

[0061] Specifically, the collected data is aligned according to the timestamps and then merged to form a structured data set. For example, dynamic data such as flow and pressure collected every minute can be combined.

[0062] Anomaly marking and missing value filling: Set thresholds to mark data as abnormal. For example, flow data outside the normal range (0-15,000 cubic meters / hour) or pressure data outside the normal range (0-0.8 MPa) are considered abnormal. Data filling methods are used to handle missing values, such as using the mean or median.

[0063] Eliminate low-quality data: Eliminate monitoring points in the data set whose missing rate exceeds the set threshold (such as 30%), and generate abnormal data statistics reports and missing rate reports.

[0064] Step S3: model construction and evaluation.

[0065] Step S3.1, model construction.

[0066] Specifically, a multi-task LightGBM model was used to construct a pressure prediction model, employing a two-layer architecture consisting of a shared feature layer and an independent output layer. The shared feature layer processes dynamic features extracted through feature engineering to generate common feature representations applicable to all monitoring points. The independent output layer generates a predicted value for each monitoring point using an independent model based on the output of the shared feature layer.

[0067] The preprocessed dataset is then fed into the pressure prediction model. A loss function, minimizing the mean squared error (MSE), is used to calculate the loss value based on the predicted and target pressure values. The pressure prediction model is trained and hyperparameters are tuned using the loss value and a Bayesian optimization algorithm. Regularization is introduced to prevent overfitting. For example, Bayesian optimization is used to adjust hyperparameters such as the learning rate and tree depth to achieve optimal model performance.

[0068] Step S3.2, accuracy evaluation.

[0069] Specifically, the multi-period absolute error mean is calculated. A time period is defined (e.g., 1 minute). The absolute error is calculated based on the predicted and target pressure values within each time period. The average of these absolute errors is then used to obtain the multi-period absolute error mean. For example, the absolute error between the predicted and actual pressure values for each 1-minute period within a given day can be calculated, and the average absolute error for the entire day can be calculated.

[0070] Step S4: iterative optimization of the model.

[0071] Step S4.1, feature contribution analysis.

[0072] Based on the SHAP framework, the contribution of each feature to the predicted value in feature engineering is calculated using the Shapley value in cooperative game theory, resulting in a SHAP value for each feature. The average SHAP value of each feature is calculated to obtain the global average contribution of each feature. After normalizing each global average contribution, the contribution percentage of each feature to the pressure prediction model is obtained.

[0073] Step S4.2, model dynamic optimization.

[0074] Specifically, a cross-analysis of mean error and contribution ratios was performed to identify monitoring points where prediction accuracy fell below the set requirement (e.g., MAE > 0.02 MPa). A feature enhancement strategy was then implemented, adding time-series lag features (e.g., 3-minute and 5-minute sliding averages) and introducing new time-series features (e.g., pump station operating parameters). After retraining the model, accuracy was reassessed until the set requirements were met.

[0075] Step S5: determine whether the accuracy requirement is met.

[0076] Specifically, a precision requirement threshold is set (such as the mean absolute error (MAE) is less than a certain value), and the error index obtained by model evaluation (such as the mean absolute error in multiple time periods) is compared with the threshold. If the precision requirement is not met, the model returns to the iterative optimization step, and the error and contribution calculation, model optimization and retraining are continued until the precision requirement is met.

[0077] Step S6: If the accuracy requirement is met, the model is applied to engineering projects.

[0078] Specifically, the pressure prediction model, which meets the required accuracy, is applied to actual water supply network systems to provide decision support for network operation and maintenance. For example, in network scheduling, the pump operating frequency and valve opening can be reasonably adjusted based on the pressure prediction results to optimize the network pressure distribution and ensure water supply stability.

[0079] Furthermore, in practical applications, real-time pipeline network data is continuously collected and input into the pressure prediction model to obtain real-time pressure prediction results. At the same time, the actual pressure monitoring value is compared with the predicted value. If a large deviation is found, the model iteration optimization mechanism can be triggered in a timely manner to update and optimize the model to adapt to the changes in the pipeline network operation status.

[0080] Furthermore, the effectiveness of the pressure prediction model in engineering applications will be regularly evaluated, analyzing indicators such as prediction accuracy and stability under different working conditions. Based on the evaluation results, targeted improvements and refinements will be made to the model to continuously enhance its performance in practical applications.

[0081] Through the above process, the pressure prediction accuracy of the water supply network has been significantly improved. By calculating the mean absolute error of multiple time periods, analyzing feature contributions, and constructing the mechanism of dynamic feature engineering for pressure prediction, the model's adaptability under different working conditions is enhanced, and it can more accurately capture the law of pressure fluctuations, providing reliable technical support for the optimized scheduling and fault warning of the water supply network.

[0082] In one application scenario, there are 154 pipe network pressure monitoring points within the jurisdiction of a certain city. The water supply pipe network pressure prediction method proposed in the present invention is used to predict the water supply pipe network pressure in this city, which specifically includes the following steps.

[0083] The first step is the screening of mechanism constraint features.

[0084] Specifically, a feature matrix containing 12-dimensional dynamic features was constructed for 154 pressure monitoring points, focusing on screening key factors that directly drive pressure fluctuations, such as water plant outlet pressure, water plant water output, and regional total water inflow.

[0085] The second step is data collection and preprocessing.

[0086] Specifically, 15 days of minute-by-minute historical monitoring data within the jurisdiction was collected, covering the characteristic variables required by the feature matrix (such as water plant outlet pressure, flow rate, and pipeline pressure monitoring point data) and the target pressure (pipeline pressure). SCADA system data was integrated to form a structured data set of 21,600 items.

[0087] Data preprocessing includes the following: first, abnormal data is marked, thresholds are set (such as pressure <0.05MPa or >1MPa), and outliers are marked. A total of 24,112 data are marked; then missing values are filled, and data segments with consecutive missing values of ≤5 minutes are interpolated, with a total of 24,267 interpolated data; then invalid monitoring points are eliminated, and 5 monitoring points with missing rates >5% and 4 equipment abnormality monitoring points are eliminated, resulting in 145 prediction points; finally, invalid samples are deleted, and samples that are still missing after filling are deleted, with a total of 310 rows deleted; the final total number of valid data rows is 21,290, and the number of valid data rows accounts for 98.6%.

[0088] The third step is model construction and evaluation.

[0089] Specifically, the model was constructed using the LightGBM multi-task learning model, with initial parameters set to learning_rate=0.12, max_depth=9, and n_estimators=350. The model employs a two-layer architecture of "shared feature layer-independent output layer," where the shared feature layer integrates common features, while the independent output layer personalizes pressure characteristics.

[0090] Furthermore, during model training, the preprocessed dataset is fed into the model, which uses a loss function that minimizes the mean squared error (MSE). Regularization is also introduced to prevent overfitting. The total training time is less than 3 minutes, and the single-step (multi-point) prediction response time is less than 5ms.

[0091] Furthermore, the model's accuracy was evaluated using the mean absolute error over multiple time periods. The initial evaluation results for 145 monitoring points are as follows: the overall performance average absolute error ε = 0.0032 MPa, with a maximum ε = 0.0248 MPa and a minimum ε = 0.0097 MPa. The error distribution shows that 88.3% of the monitoring points have ε ≤ 0.005 MPa, 96.6% have ε ≤ 0.01 MPa, 98.6% have ε ≤ 0.02 MPa, and 100% have ε ≤ 0.04 MPa.

[0092] The fourth step is iterative optimization of the model.

[0093] Specifically, the absolute error is first calculated based on the predicted value and target pressure value in each time period, and the average is obtained. Then, the contribution of each feature to the predicted value is calculated based on the SHAP framework to obtain the SHAP value of each feature, and the contribution ratio is obtained by normalization. The error mean and contribution ratio are cross-analyzed to identify monitoring points whose prediction accuracy is lower than the set requirement (such as MAE>0.01MPa).

[0094] The feature optimization includes: for the four monitoring points in the S area, four types of pressure characteristics and four types of flow characteristics are added, and the average error is reduced from 0.0045MPa to 0.0029MPa; for the two monitoring points in the W area, two types of pressure characteristics, two types of flow characteristics and time series lag characteristics (feature lag value of 1 minute, sliding average of 5 minutes) are added, and the average error is reduced from 0.0069MPa to 0.0050MPa.

[0095] Specifically, taking the monitoring point A near the water plant and the monitoring point B at the end of the pipeline network as examples, the average initial prediction errors were 0.0015MPa and 0.0031MPa, respectively. After optimizing the model according to the closed-loop mechanism of feature enhancement and model iteration, the average prediction errors were controlled within 0.01MPa. It can be seen that the two-layer architecture of shared feature layer-independent output layer combined with the mechanism constraint characteristics effectively realizes the collaborative modeling of global laws and local characteristics of different hydraulic positions, verifies the high-precision fitting ability of the fusion framework for pipeline pressure fluctuations, and effectively improves the model prediction accuracy in different scenarios.

[0096] Through the above process, the water supply network pressure prediction method of the present invention was implemented in the city, and the accuracy of the network pressure prediction within the jurisdiction was significantly improved. The average absolute error of the initial evaluation of 145 monitoring points was 0.0032MPa, and the errors of most monitoring points met the requirements of industry regulations. After optimizing the model through feature enhancement, the point accuracy was further improved, the monitoring point error was significantly reduced, and the model's single-step prediction response time was <5ms, meeting the real-time pressure prediction needs of the network. At the same time, the feature contribution analysis based on the SHAP framework gives the model a clear physical meaning, which is convenient for technical personnel to understand and analyze the prediction results. It not only significantly improves the accuracy of the water supply network pressure prediction, but also enhances the model's adaptability, effectively solving the problems of the existing technology being difficult to capture the dynamic pressure fluctuation law, high prediction error and weak interpretability, optimization lag and poor deployment flexibility.

[0097] The following is an embodiment of the device of the present invention, which can be used to implement the water supply network pressure prediction method involved in the present invention. For details not disclosed in the device embodiment of the present invention, please refer to the method embodiment of the water supply network pressure prediction method involved in the present invention.

[0098] See also Figure 3, an embodiment of the present invention provides a water supply network pressure prediction device 800.

[0099] The water supply network pressure prediction device 800 includes but is not limited to: a feature engineering construction and acquisition module 810, a model construction and training module 830, an error calculation and feature analysis module 850 and a model optimization and application module 870.

[0100] Among them, the feature engineering construction and collection module 810 is used to construct feature engineering with mechanism constraints based on the basic principles of pipe network hydraulics, collect characteristic variables and target pressure values of the water supply pipe network according to the feature engineering, form a data set and perform preprocessing.

[0101] The model building and training module 830 is used to build a pressure prediction model using a multi-task LightGBM, and train the pressure prediction model by adjusting parameters through a loss function and an optimization algorithm based on the data set.

[0102] The error calculation and feature analysis module 850 is used to build a pressure prediction model using a multi-task LightGBM, and to train the pressure prediction model by adjusting parameters through a loss function and an optimization algorithm based on a data set.

[0103] The model optimization and application module 870 is used to optimize and retrain the pressure prediction model according to the error mean and contribution ratio until the trained pressure prediction model meets the set requirements and performs pressure prediction on the water supply network.

[0104] It should be noted that the water supply network pressure prediction provided in the above embodiment is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the water supply network pressure prediction device will be divided into different functional modules to complete all or part of the functions described above.

[0105] In addition, the water supply network pressure prediction device and the water supply network pressure prediction method provided in the above embodiments belong to the same concept, and the specific manner in which each module performs operations has been described in detail in the method embodiment and will not be repeated here.

[0106] Figure 4 The following is a schematic diagram of the structure of an electronic device according to an exemplary embodiment.

[0107] It should be noted that the electronic device is only an example adapted to the present invention and cannot be considered to provide any limitation on the scope of use of the present invention. The electronic device cannot be interpreted as needing to rely on or must have Figure 4 One or more components of exemplary electronic device 2000 are shown.

[0108] The hardware structure of the electronic device 2000 may vary greatly due to different configurations or performances, such as Figure 4 As shown, the electronic device 2000 includes a power supply 210 , an interface 230 , at least one memory 250 , and at least one central processing unit (CPU) 270 .

[0109] Specifically, the power supply 210 is used to provide operating voltage for various hardware devices on the electronic device 2000 .

[0110] The interface 230 includes at least one wired or wireless network interface 231 for interacting with external devices. Of course, in other examples adapted by the present invention, the interface 230 may further include at least one serial-to-parallel conversion interface 233, at least one input / output interface 235, and at least one USB interface 237, etc. Figure 4 As shown, this does not constitute a specific limitation.

[0111] The memory 250 serves as a carrier for resource storage and can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon include an operating system 251, application 253 and data 255, etc. The storage method can be temporary storage or permanent storage.

[0112] Among them, the operating system 251 is used to manage and control the various hardware devices and application programs 253 on the electronic device 2000, so as to enable the central processing unit 270 to calculate and process the massive data 255 in the memory 250. It can be WindowsServerTM, Mac OS XTM, UnixTM, LinuxTM, FreeBSDTM, etc.

[0113] The application 253 is a computer-readable instruction that performs at least one specific task based on the operating system 251, and may include at least one module ( Figure 4 (not shown), each module may include computer-readable instructions for the electronic device 2000. For example, the water supply network pressure prediction device may be considered as an application 253 deployed on the electronic device 2000.

[0114] The data 255 may be signal information, etc., and is stored in the memory 250 .

[0115] The central processing unit 270 may include one or more processors and is configured to communicate with the memory 250 via at least one communication bus to read computer-readable instructions stored in the memory 250, thereby performing operations and processing on the massive amount of data 255 in the memory 250. For example, the water supply network pressure prediction method can be implemented by the central processing unit 270 reading a series of computer-readable instructions stored in the memory 250.

[0116] In addition, the present invention can also be implemented through hardware circuits or hardware circuits combined with software. Therefore, the implementation of the present invention is not limited to any specific hardware circuits, software, or combination thereof.

[0117] See also Figure 5 In an embodiment of the present invention, an electronic device 4000 is provided. The electronic device 4000 may include: a desktop computer, a laptop computer, a server, etc. with sensor recognition capabilities.

[0118] exist Figure 5 In the embodiment, the electronic device 4000 includes at least one processor 4001 and at least one memory 4003.

[0119] The data exchange between the processor 4001 and the memory 4003 can be achieved through at least one communication bus 4002. The communication bus 4002 may include a path for transmitting data between the processor 4001 and the memory 4003. The communication bus 4002 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus. The communication bus 4002 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 5 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0120] Optionally, the electronic device 4000 may further include a transceiver 4004, which may be used for data exchange between the electronic device and other electronic devices, such as data transmission and / or data reception. It should be noted that in actual applications, the number of transceivers 4004 is not limited to one, and the structure of the electronic device 4000 does not constitute a limitation on the embodiments of the present invention.

[0121] Processor 4001 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic device, transistor logic device, hardware component, or any combination thereof. It may implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the present disclosure. Processor 4001 may also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, and the like.

[0122] The memory 4003 can be a ROM (Read Only Memory) or other types of static storage devices that can store static information and instructions, a RAM (Random Access Memory) or other types of dynamic storage devices that can store information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), a CD-ROM (Compact Disc Read Only Memory) or other optical disk storage, optical disc storage (including compact disc, laser disc, optical disc, digital versatile disc, Blu-ray disc, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store desired program instructions or codes in the form of instructions or data structures and can be accessed by the electronic device 4000, but is not limited to these.

[0123] Computer-readable instructions are stored in the memory 4003 , and the processor 4001 can read the computer-readable instructions stored in the memory 4003 through the communication bus 4002 .

[0124] The computer-readable instructions are executed by one or more processors 4001 to implement the water supply network pressure prediction method in the above-mentioned embodiments.

[0125] In addition, an embodiment of the present invention provides a storage medium having computer-readable instructions stored thereon. The computer-readable instructions are executed by one or more processors to implement the water supply network pressure prediction method as described above.

[0126] A computer program product is provided in an embodiment of the present invention. The computer program product includes computer-readable instructions, which are stored in a storage medium. One or more processors of an electronic device read the computer-readable instructions from the storage medium, load and execute the computer-readable instructions, so that the electronic device implements the water supply network pressure prediction method as described above.

[0127] Compared with the related art, the present invention has the following beneficial effects: 1. This invention can significantly improve the accuracy of water supply network pressure prediction; by integrating hydraulic mechanism constraints with data-driven technology, a feature engineering system with clear physical meaning is constructed, and combined with the LightGBM multi-task learning model, high-precision prediction of pipeline network pressure is achieved.

[0128] 2. The present invention has fast computational response capabilities. By adopting the LightGBM histogram algorithm and Bayesian hyperparameter optimization, the model training process is greatly accelerated, making the model single-step (145 points) prediction response time less than 5ms, which can meet the needs of real-time pressure prediction of the pipeline network.

[0129] 3. This invention enhances the interpretability of the model; by introducing the feature contribution analysis of the SHAP framework, it can quantify the impact of each feature on pressure, providing technicians with a clear basis for analyzing the prediction results, facilitating understanding and application.

[0130] 4. The present invention has good adaptability; through the collaborative optimization of mechanism constraint feature screening and data-driven modeling, as well as the online data iterative optimization mechanism, the model has good adaptability to pipeline network structure adjustments, boundary condition changes, etc., and can continuously ensure the stability of prediction accuracy.

[0131] 5. The present invention reduces implementation and maintenance costs. Compared with the traditional hydraulic model method, this method does not require complex parameter calibration, which reduces the difficulty of implementation. At the same time, through the online data iterative optimization mechanism, it reduces long-term operating costs.

[0132] 6. The present invention realizes dynamic optimization; by establishing a "feature enhancement-model iteration" closed-loop mechanism based on SHAP feature contribution analysis and model accuracy evaluation, the model can be continuously optimized according to actual operation data, thereby improving the accuracy and reliability of the prediction.

[0133] 7. The present invention comprehensively covers the pipe network area; by collaboratively modeling global laws and local characteristics, it ensures that the prediction results can comprehensively cover each monitoring point in the pipe network, providing comprehensive decision support for pipe network operation and maintenance.

[0134] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown in sequence as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

[0135] The above descriptions are only partial embodiments of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and modifications without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A water supply network pressure prediction method, characterized in that: The method comprises: Based on the basic principles of pipe network hydraulics, a feature engineering with mechanism constraints is constructed. According to the feature engineering, characteristic variables and target pressure values of the water supply pipe network are collected to form a data set and preprocessed. A pressure prediction model is constructed using a multi-task LightGBM, and the pressure prediction model is trained based on the dataset by adjusting parameters using a loss function and an optimization algorithm; Calculate the multi-period absolute error mean of the pressure prediction model, and construct a feature contribution quantification system based on the SHAP framework to calculate the contribution ratio of each feature in the feature engineering to the pressure prediction model; The pressure prediction model is optimized and retrained according to the error mean and contribution ratio until the trained pressure prediction model meets the set requirements, and the pressure of the water supply network is predicted.

2. The water supply network pressure prediction method according to claim 1, characterized in that: The feature engineering of mechanism constraints based on the basic principles of pipe network hydraulics includes: The factors affecting pressure are analyzed based on the hydraulic equations of the pipeline network. The factors are divided into static characteristics that constitute the basic physical framework of the pipeline network pressure distribution and dynamic characteristics that directly drive the real-time fluctuation of pressure. According to the influence of the dynamic characteristics on the pipe network pressure and the time lag effect of the pipe network hydraulic response, the dynamic characteristics are divided into flow type, pressure type, state type and time lag type; Feature engineering of mechanism constraints is constructed based on the flow type, pressure type, state type and time lag type of the dynamic characteristics.

3. The water supply network pressure prediction method according to claim 2, characterized in that: The pipe network hydraulic equations include mass conservation equation, energy conservation equation and head loss equation along the pipe network; The static features include pipe length, pipe diameter, roughness, topology, and elevation; The flow types include regional water inflow, water plant outflow, booster pump station outflow, and large user water volume; The pressure category includes the water plant outlet pressure and the booster pump station outlet pressure; the status category includes the valve opening and the water pump operating status; The time series lag class includes minute lag features and sliding window statistics.

4. The water supply network pressure prediction method according to claim 1, wherein: The method of collecting characteristic variables and target pressure values of the water supply network according to the feature engineering to form a data set and preprocessing the data set includes: Collecting multi-source monitoring data of the water supply network as input data according to the feature engineering; the input data includes the target pressure value and the characteristic variables included in the feature engineering; The input data are aligned according to timestamps and merged to form a structured data set, and anomaly marking and missing value filling are performed on the data set by setting thresholds and data filling; The monitoring points in the data set whose missing rate exceeds the set threshold are eliminated, the sample data with missing values in the data set are deleted, and an abnormal data statistical report and a missing rate report are generated.

5. The water supply network pressure prediction method according to claim 2, wherein: The multi-task LightGBM is used to build a pressure prediction model, and the pressure prediction model is trained based on the data set by adjusting parameters using a loss function and an optimization algorithm, including: A pressure prediction model is constructed using a two-layer architecture of a shared feature layer and an independent output layer and a multi-task LightGBM. The dataset is input into the pressure prediction model to obtain a predicted value. The shared feature layer is used to process the dynamic features to generate a common feature representation. The independent output layer is used to generate a predicted value based on the common feature representation. A loss value is calculated based on the predicted value and the target pressure value using a mean square error minimization loss function. The pressure prediction model is trained and hyperparameters are tuned based on the loss value and a Bayesian optimization algorithm, and a regularization term is introduced to prevent overfitting.

6. The water supply network pressure prediction method according to claim 4, characterized in that: The calculation of the multi-period absolute error mean of the pressure prediction model and the construction of a feature contribution quantification system based on the SHAP framework to calculate the contribution ratio of each feature in the feature engineering to the pressure prediction model include: Define the time period, calculate the absolute error based on the predicted value and the target pressure value in each time period, and calculate the average of the absolute errors in multiple time periods based on the average of multiple absolute errors; Based on the SHAP framework, the contribution of each feature in the feature engineering to the predicted value is calculated by the Shapley value in cooperative game theory to obtain the SHAP value of each feature; The SHAP values of the features are calculated to obtain the global average contribution of the features, and the contribution ratio of the features to the pressure prediction model is obtained by normalizing the global average contribution.

7. The water supply network pressure prediction method according to claim 2, wherein: The optimizing and retraining of the pressure prediction model according to the error mean and contribution ratio includes: Cross-analyze the error mean and contribution ratio to identify monitoring points where the prediction accuracy is lower than the set requirement; A feature enhancement strategy is adopted for the monitoring points to supplement the mechanism-driven dynamic feature variables; the feature enhancement strategy includes adding time series lag features and introducing new time series features.

8. A water supply network pressure prediction device, characterized in that: The device comprises: A feature engineering construction and collection module is used to construct a feature engineering with mechanism constraints based on the basic principles of pipe network hydraulics, collect characteristic variables and target pressure values of the water supply pipe network according to the feature engineering, form a data set and perform preprocessing; A model building and training module is used to build a pressure prediction model using a multi-task LightGBM, and to train the pressure prediction model based on the dataset by adjusting parameters using a loss function and an optimization algorithm; The error calculation and feature analysis module is used to calculate the multi-period absolute error mean of the pressure prediction model and to build a feature contribution quantification system based on the SHAP framework to calculate the contribution ratio of each feature in the feature engineering to the pressure prediction model; The model optimization and application module is used to optimize and retrain the pressure prediction model according to the error mean and contribution ratio until the trained pressure prediction model meets the set requirements and performs pressure prediction on the water supply network.

9. An electronic device, characterized in that: include: at least one processor and at least one memory, wherein: The memory has computer-readable instructions stored thereon; The computer-readable instructions are executed by one or more of the processors, so that the electronic device implements the water supply network pressure prediction method according to any one of claims 1 to 7.

10. A storage medium having computer-readable instructions stored thereon, characterized in that: The computer-readable instructions are executed by one or more processors to implement the water supply network pressure prediction method according to any one of claims 1 to 7.

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