Robust Cooperative Design Method for Post-Pump Air Tank Considering Time-Varying Hydraulic Parameters

Abstract

This invention discloses a robust collaborative design method for a post-pump air tank considering the time-varying characteristics of hydraulic parameters. The method includes defining the uncertainty fluctuation range of hydraulic parameters throughout the entire life cycle of the water conveyance system, and setting the range of decision variables for the shape and structure of the post-pump air tank. It involves using experimental design methods to perform joint sampling within the uncertainty fluctuation range of hydraulic parameters and the range of shape and structure decision variables to generate an initial sample set. Steady-state and transient coupled simulations are performed on the initial sample set. A steady-flow operating condition of the water conveyance system is constructed using hydraulic equations, updating the pump operating point and pipeline pressure distribution. Transient simulations are performed using the method of characteristics to obtain hydraulic response indices, and a water hammer response surrogate model is trained. A robust optimization objective function based on failure probability constraints is constructed. An intelligent optimization algorithm is used to globally optimize the objective function, and the water hammer response surrogate model is invoked for random simulation to evaluate the failure probability and output the target design scheme.

Description

Technical Field

[0001] This invention relates to the field of safety protection technology for water conservancy projects and long-distance water transmission pipelines, and in particular to a robust collaborative design method for post-pump air tanks that considers the time-varying characteristics of hydraulic parameters. Background Technology

[0002] In long-distance, high-lift water conveyance projects, sudden shutdowns of pumping station units or valve malfunctions can easily trigger severe water hammer effects, causing significant fluctuations in pipeline pressure and seriously threatening the safe operation of the water conveyance system. Air tanks, by utilizing the compressibility of gas to absorb or release energy, can effectively reduce extreme pressure values ​​and prevent pipeline rupture or negative pressure damage, making them a widely used water hammer protection device.

[0003] The design of air tanks has evolved from the traditional empirical chart method to an intelligent optimization stage based on numerical simulation. Typically, intelligent algorithms are coupled with one-dimensional hydraulic transient flow simulation models to find the optimal shape and structural parameters under the premise of meeting pipeline pressure standards, with the goal of minimizing air tank volume or investment. Under deterministic conditions, this can reduce engineering costs and improve design efficiency.

[0004] However, traditional design methods, based on static parameter calculations, have significant limitations. Throughout the entire lifecycle of a water conveyance system, pipelines are affected by internal wall corrosion, scaling, and biofilm adhesion, causing the roughness to change with the years of operation, altering the head loss along the pipeline and the initial steady flow condition of the system. Water hammer wave velocity is also affected by factors such as water temperature, pressure, and gas content, exhibiting random fluctuations. Traditional methods ignore these time-varying characteristics and uncertainties, resulting in theoretically optimal solutions lacking robust safety margins against disturbances, and deviations from actual parameters can easily lead to protection failures. Furthermore, traditional numerical simulations assess risks by simulating and evaluating massive combinations of parameters one by one, leading to exponentially increasing computation time, which is insufficient to meet the timeliness requirements of engineering design. Therefore, there is an urgent need to develop robust design methods that consider both the time-varying characteristics of parameters and efficient risk quantification. Summary of the Invention

[0005] The purpose of this invention is to provide a robust collaborative design method for post-pump air tanks that takes into account the time-varying characteristics of hydraulic parameters.

[0006] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0007] This invention includes the following steps:

[0008] S1: Define the uncertainty fluctuation range of hydraulic parameters of the water conveyance system throughout its entire life cycle, and set the range of decision variables for the shape and structure of the air tank after the pump; the hydraulic parameters include the comprehensive roughness of the pipeline and the water hammer wave velocity that change with the years of operation;

[0009] S2: Using experimental design methods, joint sampling is conducted within the uncertainty fluctuation range of the hydraulic parameters and the decision variables of body structure to generate an initial sample set;

[0010] S3: Perform steady-state and transient coupled simulations on each group of samples in the initial sample set, construct the steady-flow operating condition of the water conveyance system using hydraulic equations, update the pump operating point and pipeline pressure distribution, perform transient simulation using the method of characteristics, obtain hydraulic response indices, and train a water hammer response surrogate model using machine learning; the water hammer response surrogate model is used to characterize the nonlinear mapping relationship between the air tank and hydraulic uncertainty parameters and the hydraulic response indices; the hydraulic response indices include the maximum and minimum pipeline pressure and the minimum water level in the air tank;

[0011] S4: Construct a robust optimization objective function based on failure probability constraints; the failure probability refers to the probability that the pressure of the water pipeline exceeds the safe pressure bearing standard within the uncertainty fluctuation range.

[0012] S5: Use intelligent optimization algorithm to perform global optimization of the objective function, call the water hammer response proxy model to perform random simulation when calculating the fitness value, evaluate the failure probability, and output a robust design scheme for the air tank that meets the preset reliability index.

[0013] Furthermore, the method for determining the uncertainty fluctuation range includes:

[0014] Based on historical operational monitoring data of water pipelines, the distribution characteristics of roughness and wave velocity are statistically analyzed through data inversion, and their 90% confidence interval is selected as the fluctuation range; alternatively, the range is set based on the pipe aging curve and engineering experience; the structural decision variables include the total volume of the air tank. V The height-to-diameter ratio of the air tank H / D Impedance orifice diameter of air tank connecting pipe d And the initial air-to-water volume ratio Raw, the installation position of the air tank is fixed to be close to the rear side of the pump station outlet valve;

[0015] For water pipelines with different service lives, data on pipe material properties, initial roughness, design wave velocity, operating environment, and historical monitoring data were obtained. The corrosion rate of the pipeline was calculated using empirical and mechanistic models, expressed as follows:

[0016]

[0017] in Operating life t corrosion depth, Let be the corrosion rate constant. For time index, The activation energy for the corrosion reaction, Absolute temperature It is the gas constant;

[0018] Based on pipeline corrosion detection data, the least squares method was used for fitting. k , Parameters were used to establish a mapping relationship between corrosion depth and service life.

[0019] A time-varying prediction model for roughness and wave velocity is constructed using a long short-term memory network, where the input layer is input with the number of years of operation. t Corrosion depth, water quality indicators, flow rate; output layer output is roughness. Wave speed The predicted values ​​and 90% confidence intervals;

[0020] Based on current monitoring data, the corrosion rate model parameters are updated, and LSTM is used to predict the roughness over the next 5 years. With wave speed The model uses Bayesian posterior estimation and combines it with the prediction error distribution to generate 90% confidence intervals for parameters in each year. When the prediction interval exceeds the engineering safety threshold, an early warning is triggered and the model is recalibrated. The model outputs a dynamic uncertainty fluctuation range.

[0021] Furthermore, the method for constructing the steady-flow operating condition of the water conveyance system using hydraulic equations includes:

[0022] S31: Pipeline roughness extracted based on the current sample n The resistance characteristic curve equation of the water pipeline is updated using the Manning formula or the Darcy-Wiesbach formula, and the expression is:

[0023]

[0024] in To meet the head requirements of the pipeline system, For Jingyang Cheng, The drag coefficient is related to roughness. This refers to the water flow rate.

[0025] S32: The updated equations for the pipeline resistance characteristic curve and the pump characteristic curve are combined, and the expression is:

[0026]

[0027] in To provide head for the water pump, This refers to the virtual head when the flow rate is zero. This is the virtual resistance coefficient within the pump body. m For index;

[0028] Solving the nonlinear equations yields the corrected constant flow rate.Q and water pump head H ;

[0029] S33: With the revised Q and H As boundary conditions, the initial hydraulic gradient line along the pipeline and the initial pressure head at each node are calculated to complete the initial steady flow condition construction for this set of samples.

[0030] Furthermore, the method for constructing the water hammer response proxy model includes:

[0031] The sample set is normalized and divided into training and test sets according to a preset ratio. A nonlinear fitting function for the input and output parameters is constructed using machine learning models such as BP neural network or Gaussian process regression. The input parameters include pipeline comprehensive roughness, water hammer wave velocity and air tank type structural decision variables. The output parameters are hydraulic response indices.

[0032] Furthermore, the robustness optimization objective function based on failure probability constraints is expressed as follows:

[0033] ;

[0034] in For body structure decision variables vector, The economic cost function is related to the volume and materials of the air tank. This represents the system failure probability of the current solution. This represents the maximum allowable failure probability threshold for the project. This is the penalty weighting coefficient.

[0035] Furthermore, the method for calculating the failure probability includes:

[0036] In each iteration of the optimization algorithm, the current decision variables are maintained. X The hydraulic parameters remain unchanged within the uncertainty fluctuation range. N The Monte Carlo random simulation was performed, and the response index for each simulation was quickly predicted using the water hammer response surrogate model. The number of times any of the following failure conditions were met was counted. :

[0037] (1) The maximum pressure of the pipeline exceeds the pressure bearing standard of the pipe material;

[0038] (2) The minimum pressure of the pipeline is lower than the vaporization pressure or negative pressure standard;

[0039] (3) The water level in the air tank is lower than the minimum safe water level;

[0040] The failure probability is then calculated as follows:

[0041]

[0042] in The system failure probability of the current solution is... For the number of Monte Carlo random simulations, The number of times any of the following failure conditions are satisfied.

[0043] Furthermore, the intelligent optimization algorithm is either the Grey Wolf Optimization Algorithm or the Particle Swarm Optimization Algorithm.

[0044] The beneficial effects of this invention are:

[0045] This invention is a robust collaborative design method for post-pump air tanks that considers the time-varying characteristics of hydraulic parameters. Compared with the prior art, this invention has the following technical advantages:

[0046] This invention fully considers the time-varying characteristics of hydraulic parameters, incorporates failure probability into constraints, improves the operational reliability of the air tank throughout its entire life cycle, and avoids safety risks caused by aging; it integrates the characteristic equations of pipelines and water pumps, corrects initial operating condition deviations, ensures accurate water hammer simulation boundary conditions, and improves the credibility of design results; it constructs a machine learning proxy model to replace traditional numerical simulation, achieves millisecond-level response prediction, significantly reduces computation time, and improves robust design efficiency. Attached Figure Description

[0047] Figure 1 This is a flowchart of the steps of a robust collaborative design method for a post-pump air tank that considers the time-varying characteristics of hydraulic parameters according to the present invention.

[0048] Figure 2 This is a sample distribution diagram of an embodiment of this specification, taking volume and impedance aperture diameter as an example;

[0049] Figure 3 This is a 1:1 fitting graph of each model on the hydraulic response index in the embodiments of this specification. Figure 3 (a) For each model in H max The 1:1 fitting plot on the top Figure 3 (b) For each model in H min The 1:1 fitting plot on the top Figure 3 (c) Each model in H Wmin 1:1 fitting plot on;

[0050] Figure 4 This is a convergence curve diagram of the optimization of the model parameters in the embodiments of this specification. Detailed Implementation

[0051] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0052] The present invention provides a robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters, comprising the following steps:

[0053] like Figure 1 As shown, this embodiment includes the following steps:

[0054] S1: Define the uncertainty fluctuation range of hydraulic parameters of the water conveyance system throughout its entire life cycle, and set the range of decision variables for the shape and structure of the air tank after the pump; the hydraulic parameters include the comprehensive roughness of the pipeline and the water hammer wave velocity that change with the years of operation;

[0055] In practical assessments, taking a long-distance, high-lift water pumping station project as an example, the project's water pipeline is 11km long, with a designed water flow rate of 6.5m³ / h. 3 / s, the pump has a rated head of 186m and a rated flow rate of 3.25m³ / s. 3 / s, the water transmission pipeline uses DN2400 steel pipe, with a design roughness of 0.012 and a wave velocity of 1000m / s; in order to prevent water hammer pressure caused by pump shutdown due to accident from damaging the pipeline system, it is proposed to install an air tank after the pump station outlet valve for protection;

[0056] S2: Using experimental design methods, joint sampling is conducted within the uncertainty fluctuation range of the hydraulic parameters and the decision variables of body structure to generate an initial sample set;

[0057] In the actual assessment, the range of uncertain parameters and the range of decision variables are defined as follows: First, based on the aging characteristics analysis of the pipe materials in this project, the range of uncertainty fluctuations in hydraulic parameters throughout the entire life cycle is determined; considering internal wall corrosion and scaling, the overall roughness of the pipe is set to fluctuate within a range of approximately [0.01, 0.013], and considering the changes in water gas content and pipe wall elastic modulus, the fluctuation range of water hammer wave velocity is set to [900, 1100] m / s; simultaneously, according to the design criteria of the air tank, the design parameters of the air tank are initially determined, and on this basis, the range of decision variables for the shape and structure of the air tank after the pump is set: air tank volume ∈ [110, 150] m³. 3 The air tank height-to-diameter ratio is [0.67, 1.33], the diameter of the connecting pipe impedance hole is [0.4, 0.7] m, and the initial air-to-water volume ratio is [0.5, 2].

[0058] Initial sample set generation: Using the Latin hypercube sampling method, joint sampling is performed within the uncertainty interval and decision variable range defined above to generate M=200 initial samples. The sample distribution, taking volume and impedance orifice diameter as examples, is as follows: Figure 2As shown, the generated samples have good spatial uniformity;

[0059] S3: Perform steady-state and transient coupled simulations on each group of samples in the initial sample set, construct the steady-flow operating condition of the water conveyance system using hydraulic equations, update the pump operating point and pipeline pressure distribution, perform transient simulation using the method of characteristics, obtain hydraulic response indices, and train a water hammer response surrogate model using machine learning; the water hammer response surrogate model is used to characterize the nonlinear mapping relationship between the air tank and hydraulic uncertainty parameters and the hydraulic response indices; the hydraulic response indices include the maximum and minimum pipeline pressure and the minimum water level in the air tank;

[0060] In the actual evaluation, steady-state-transient coupled simulation calculations are performed for each set of samples generated by S2. For the first set of samples... i Roughness in the group of samples n i The pipeline resistance coefficient was recalculated using the Darcy-Wiesbach formula. S i The updated pipeline characteristic curves were obtained. Solve the system of pipe characteristic curves and pump characteristic curves simultaneously to obtain the true steady flow operating point under this roughness condition. Q , H ;

[0061] Using the corrected steady-state conditions as initial values, the hydraulic transient process of the pump during power failure is simulated using the method of characteristics, and the maximum pressure along the pipeline is extracted. Minimum pressure and the lowest water level in the tank ;

[0062] A training set was constructed using the input variables and output responses of M sets of samples. Five machine learning models—BPNN, SVR, GPR, RF, and LightGBM—were selected for comparison. The Optuna Bayesian optimization framework was used to automatically optimize the model hyperparameters. Under limited sample conditions, a surrogate model was used to estimate the posterior distribution of the objective function, and the R-squared of each model on the test set was calculated. 2 Based on metrics such as RMSE, RSR, MAE, and computation time, the model most suitable for this project is selected according to its generalization ability, stability, and ability to express the characteristics of multi-output water hammer.

[0063] The hyperparameter ranges for each model were determined based on experience and prior debugging as follows: For BPNN: number of hidden layer neurons h∈[5,30], batch size b∈[4,16], learning rate Regularization coefficient The maximum number of iterations is set to ;

[0064] For SVR: Penalty coefficient The insensitive interval ε∈[0.001,0.1], kernel width parameter For GPR: length scale noise variance Regularization parameters ;

[0065] For RF: the number of base learners is nested. Maximum depth Minimum number of split samples Minimum number of leaf node samples Maximum feature sampling ratio For LightGBM: the number of weak learners nested, Number of leaf nodes Maximum depth Learning rate Minimum number of leaf samples Subsampling rate , column sampling rate Regularization parameters The optimal hyperparameter configurations and predictive performance of the five models under various output metrics are shown in Table 1. The 1:1 fitting results on the corresponding test set are shown in [Table 1]. Figure 3 See [link / reference] for optimized convergence characteristics. Figure 4 ;

[0066] Table 1. Hyperparameter optimization results and prediction performance metrics of each machine learning model

[0067]

[0068] Through comprehensive comparison and selection, the GPR with the highest prediction accuracy was determined as the air tank proxy model;

[0069] S4: Construct a robust optimization objective function based on failure probability constraints; the failure probability refers to the probability that the pressure of the water pipeline exceeds the safe pressure bearing standard within the uncertainty fluctuation range.

[0070] S5: Use intelligent optimization algorithm to perform global optimization of the objective function, call the water hammer response proxy model to perform random simulation when calculating fitness value, evaluate failure probability, and output air tank robust design scheme that meets preset reliability index.

[0071] In practical assessments, failure probability refers to the probability of meeting any of the following failure conditions within the uncertainty fluctuation range of hydraulic parameters: ① the maximum pressure of the pipeline exceeds the pressure bearing standard of the pipe material; ② the minimum pressure of the pipeline is lower than the vaporization pressure or negative pressure standard; ③ the water level in the air tank is lower than the minimum safe water level.

[0072] After iterative optimization, the target robust design scheme is: air tank volume 130.67m³. 3 To verify the beneficial effects of the present invention, the target robust design scheme is compared with the traditional deterministic optimization scheme that does not consider time-varying parameters: (1) Traditional scheme: based on a fixed roughness of 0.012, the volume is 126.93m³. 3 Although the solution is small in size, under extreme conditions where pipe aging leads to a roughness increase of 0.014, simulations show a failure probability as high as 85%, posing a serious risk of pipe bursting. (2) Solution of this invention: Volume is 130.67m 3 Although the volume increases slightly, the system failure probability is always controlled within 0.1% (reliability > 99.9%) within the range of parameter fluctuations throughout the entire life cycle. This scheme is a robust design that can balance economic cost and operational reliability after considering the risk of parameter drift throughout the entire life cycle.

[0073] In this embodiment, the method for determining the uncertainty fluctuation range includes:

[0074] Based on historical operational monitoring data of water pipelines, the distribution characteristics of roughness and wave velocity are statistically analyzed through data inversion, and their 90% confidence interval is selected as the fluctuation range; alternatively, the range is set based on the pipe aging curve and engineering experience; the structural decision variables include the total volume of the air tank. V The height-to-diameter ratio of the air tank H / D Impedance orifice diameter of air tank connecting pipe d And the initial air-to-water volume ratio Raw, the installation position of the air tank is fixed to be close to the rear side of the pump station outlet valve;

[0075] For water pipelines with different service lives, data on pipe material properties, initial roughness, design wave velocity, operating environment, and historical monitoring data were obtained. The corrosion rate of the pipeline was calculated using empirical and mechanistic models, expressed as follows:

[0076]

[0077] in Operating life t corrosion depth, Let be the corrosion rate constant. For time index, The activation energy for the corrosion reaction, Absolute temperature It is the gas constant;

[0078] Based on pipeline corrosion detection data, the least squares method was used for fitting. k , Parameters were used to establish a mapping relationship between corrosion depth and service life.

[0079] A time-varying prediction model for roughness and wave velocity is constructed using a long short-term memory network, where the input layer is input with the number of years of operation. t Corrosion depth, water quality indicators, flow rate; output layer output is roughness. Wave speed The predicted values ​​and 90% confidence intervals;

[0080] Based on current monitoring data, the corrosion rate model parameters are updated, and LSTM is used to predict the roughness over the next 5 years. With wave speed Using Bayesian posterior estimation and combining it with the prediction error distribution, 90% confidence intervals for parameters in each year are generated; when the prediction interval exceeds the engineering safety threshold, an early warning is triggered and the model is recalibrated; the dynamic uncertainty fluctuation interval is output.

[0081] In practical evaluation, the training of the time-varying prediction model for roughness and wave velocity involves: dividing the preprocessed historical data into a training set and a validation set in a 7:3 ratio; optimizing the network parameters using the backpropagation algorithm with the goal of minimizing the root mean square error; and introducing an attention mechanism to enhance the ability to capture key influencing factors.

[0082] Output the parameter fluctuation range for each operating stage with a 5-year usage period: when the operating period is 0, the roughness... The predicted value and 90% confidence interval are [0.010, 0.013], wave speed The predicted value and 90% confidence interval are [900, 1100]; when the operating life is 10 years, the roughness is... The predicted value and 90% confidence interval are [0.012, 0.015], wave speed The predicted value and 90% confidence interval are [850, 1050]; when the operating life is 20 years, the roughness is... The predicted value and 90% confidence interval are [0.014, 0.017], wave speed The predicted value and 90% confidence interval are [800, 1000];

[0083] In this embodiment, the method for constructing the steady flow operating condition of the water conveyance system using hydraulic equations includes:

[0084] S31: Based on the overall roughness n of the pipeline extracted from the current sample, update the resistance characteristic curve equation of the water transmission pipeline using the Manning formula or the Darcy-Wiesbach formula. The expression is:

[0085]

[0086] in To meet the head requirements of the pipeline system, For Jingyang Cheng, The drag coefficient is related to roughness. This refers to the water flow rate.

[0087] S32: The updated equations for the pipeline resistance characteristic curve and the pump characteristic curve are combined, and the expression is:

[0088]

[0089] in To provide head for the water pump, This refers to the virtual head when the flow rate is zero. This is the virtual resistance coefficient within the pump body. m For index;

[0090] Solving the nonlinear equations yields the corrected constant flow rate. Q and water pump head H ;

[0091] S33: With the revised Q and H As boundary conditions, the initial hydraulic gradient line along the pipeline and the initial pressure head at each node are calculated to complete the initial steady flow condition construction for this set of samples.

[0092] In actual assessment, m The static head is 2, which is the water level difference between the starting and ending points of the water conveyance system. It is calculated and determined according to the "Outdoor Water Supply Design Standard" based on engineering topographic survey data and user water pressure requirements. The virtual head when the flow rate is zero is the theoretical head when the pump flow rate is zero. It is extracted by polynomial fitting using the performance curve provided by the pump manufacturer. The virtual resistance coefficient in the pump body represents the coefficient of water flow resistance inside the pump. It is determined by fitting the characteristic curve based on the pump's rated flow rate and rated head data, or by using the design parameters provided by the manufacturer. The pump characteristic curve equation exponent represents the degree of nonlinearity in the relationship between pump head and flow rate. For centrifugal pumps, it is usually taken as 2 to 3, which is specifically determined by fitting the pump characteristic curve.

[0093] In this embodiment, the method for constructing the water hammer response proxy model includes:

[0094] The sample set is normalized and divided into training and test sets according to a preset ratio. A nonlinear fitting function for the input and output parameters is constructed using machine learning models such as BP neural network or Gaussian process regression. The input parameters include pipeline comprehensive roughness, water hammer wave velocity and air tank type structural decision variables. The output parameters are hydraulic response indices.

[0095] In this embodiment, the robustness optimization objective function based on failure probability constraints is expressed as:

[0096] ;

[0097] in For body structure decision variables vector, The economic cost function is related to the volume and materials of the air tank. This represents the system failure probability of the current solution. This represents the maximum allowable failure probability threshold for the project. This is the penalty weighting coefficient;

[0098] ,in The unit volume cost coefficient is determined by the market price of air tank materials and manufacturing process. This refers to the total volume of the air tank. The maintenance cost factor is related to the aspect ratio and impedance aperture. The fixed installation cost is determined by the construction process and the conditions of the installation location;

[0099] The penalty weighting coefficient is a weighting factor that balances economic costs and failure risks; the maximum allowable failure probability threshold is the upper limit of the system failure risk acceptable to the project, which is determined according to the safety level of the water supply system; the number of Monte Carlo random simulations is determined through convergence analysis based on the accuracy requirements of failure probability calculation; the initial gas-water volume ratio is the ratio of the gas volume to the water volume in the tank in the initial state after the air tank is installed.

[0100] In this embodiment, the method for calculating the failure probability includes:

[0101] In each iteration of the optimization algorithm, the current decision variables are maintained. X The hydraulic parameters remain unchanged within the uncertainty fluctuation range. N The Monte Carlo random simulation was performed, and the response index for each simulation was quickly predicted using the water hammer response surrogate model. The number of times any of the following failure conditions were met was counted. :

[0102] (1) The maximum pressure of the pipeline exceeds the pressure bearing standard of the pipe material;

[0103] (2) The minimum pressure of the pipeline is lower than the vaporization pressure or negative pressure standard;

[0104] (3) The water level in the air tank is lower than the minimum safe water level;

[0105] The failure probability is then calculated as follows:

[0106]

[0107] in The system failure probability of the current solution is... For the number of Monte Carlo random simulations, The number of times any of the following failure conditions are satisfied.

[0108] In this embodiment, the intelligent optimization algorithm is either the Grey Wolf Optimization Algorithm or the Particle Swarm Optimization Algorithm.

[0109] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters, characterized in that, Includes the following steps: S1: Define the uncertainty fluctuation range of hydraulic parameters of the water conveyance system throughout its entire life cycle, and set the range of decision variables for the shape and structure of the air tank after the pump; the hydraulic parameters include the comprehensive roughness of the pipeline and the water hammer wave velocity that change with the years of operation; S2: Using experimental design methods, joint sampling is performed within the uncertainty fluctuation range of the hydraulic parameters and the decision variables of the body structure to generate an initial sample set; S3: Perform steady-state and transient coupled simulations on each group of samples in the initial sample set, construct the steady-flow operating condition of the water conveyance system using hydraulic equations, update the pump operating point and pipeline pressure distribution, perform transient simulation using the method of characteristics, obtain hydraulic response indices, and train a water hammer response surrogate model using machine learning; the water hammer response surrogate model is used to characterize the nonlinear mapping relationship between the air tank and hydraulic uncertainty parameters and the hydraulic response indices; the hydraulic response indices include the maximum and minimum pipeline pressure and the minimum water level in the air tank; S4: Construct a robust optimization objective function based on failure probability constraints; the failure probability refers to the probability that the pressure of the water pipeline exceeds the safe pressure bearing standard within the uncertainty fluctuation range. S5: Use intelligent optimization algorithm to perform global optimization of the objective function, call the water hammer response proxy model to perform random simulation when calculating the fitness value, evaluate the failure probability, and output a robust design scheme for the air tank that meets the preset reliability index.

2. The robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters as described in claim 1, characterized in that, The method for determining the uncertainty fluctuation range includes: Based on historical operational monitoring data of water pipelines, the distribution characteristics of roughness and wave velocity are statistically analyzed through data inversion, and their 90% confidence interval is selected as the fluctuation range; alternatively, the range is set based on the pipe aging curve and engineering experience; the structural decision variables include the total volume of the air tank. V The height-to-diameter ratio of the air tank H / D Impedance orifice diameter of air tank connecting pipe d And the initial air-to-water volume ratio Raw, the installation position of the air tank is fixed to be close to the rear side of the pump station outlet valve; For water pipelines with different service lives, data on pipe material properties, initial roughness, design wave velocity, operating environment, and historical monitoring data were obtained. The corrosion rate of the pipeline was calculated using empirical and mechanistic models, expressed as follows: ； in Operating life t corrosion depth, Let be the corrosion rate constant. For time index, The activation energy for the corrosion reaction, Absolute temperature It is the gas constant; Based on pipeline corrosion detection data, the least squares method was used for fitting. k , Parameters were used to establish a mapping relationship between corrosion depth and service life. A time-varying prediction model for roughness and wave velocity is constructed using a long short-term memory network, where the input layer is input with the number of years of operation. t Corrosion depth, water quality indicators, flow rate; output layer output is roughness. Wave speed The predicted values ​​and 90% confidence intervals; Based on current monitoring data, the corrosion rate model parameters are updated, and LSTM is used to predict the roughness over the next 5 years. With wave speed The model uses Bayesian posterior estimation and combines it with the prediction error distribution to generate 90% confidence intervals for parameters in each year. When the prediction interval exceeds the engineering safety threshold, an early warning is triggered and the model is recalibrated. The model outputs a dynamic uncertainty fluctuation range.

3. The robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters as described in claim 1, characterized in that, A method for constructing the steady-flow operating condition of the water conveyance system using hydraulic equations includes: S31: Pipeline roughness extracted based on the current sample n The resistance characteristic curve equation of the water pipeline is updated using the Manning formula or the Darcy-Wiesbach formula, and the expression is: ； in To meet the head requirements of the pipeline system, For Jingyang Cheng, The drag coefficient is related to the roughness. This refers to the water flow rate. S32: The updated equations for the pipeline resistance characteristic curve and the pump characteristic curve are combined, and the expression is: ； in To provide head for the water pump, This refers to the virtual head when the flow rate is zero. This is the virtual resistance coefficient within the pump body. m For index; Solving the nonlinear equations yields the corrected constant flow rate. Q and water pump head H ; S33: With the revised Q and H As boundary conditions, the initial hydraulic gradient line along the pipeline and the initial pressure head at each node are calculated to complete the initial steady flow condition construction for this set of samples.

4. The robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters as described in claim 1, characterized in that, The method for constructing the water hammer response proxy model includes: The sample set is normalized and divided into training and test sets according to a preset ratio. A nonlinear fitting function for the input and output parameters is constructed using machine learning models such as BP neural network or Gaussian process regression. The input parameters include pipeline comprehensive roughness, water hammer wave velocity and air tank type structural decision variables. The output parameters are hydraulic response indices.

5. The robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters as described in claim 1, characterized in that, The robustness optimization objective function based on failure probability constraints is expressed as follows: ； in For body structure decision variables vector, The economic cost function is related to the volume and materials of the air tank. This represents the system failure probability of the current solution. This represents the maximum allowable failure probability threshold for the project. This is the penalty weighting coefficient.

6. The robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters according to claim 1, characterized in that, The method for calculating the failure probability includes: In each iteration of the optimization algorithm, the current decision variables are maintained. X The hydraulic parameters remain unchanged within the uncertainty fluctuation range. N The Monte Carlo random simulation was performed, and the response index for each simulation was quickly predicted using the water hammer response surrogate model. The number of times any of the following failure conditions were met was counted. : (1) The maximum pressure of the pipeline exceeds the pressure bearing standard of the pipe material; (2) The minimum pressure of the pipeline is lower than the vaporization pressure or negative pressure standard; (3) The water level in the air tank is lower than the minimum safe water level; The failure probability is then calculated as follows: ； in The system failure probability of the current solution is... For the number of Monte Carlo random simulations, The number of times any of the following failure conditions are satisfied.

7. The robust collaborative design method for a post-pump air tank considering time-varying hydraulic parameters according to claim 1, characterized in that, The intelligent optimization algorithm is either the Grey Wolf Optimization Algorithm or the Particle Swarm Optimization Algorithm.

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