Water delivery system air tank body type optimization method based on self-adaptive sampling
By optimizing the air tank shape through adaptive sampling and the DNN-PSO algorithm, the problems of low computational efficiency and high cost in the existing technology are solved, and efficient and accurate air tank shape design is achieved, which is suitable for the safety protection of long-distance water transmission projects.
Patent Information
- Application Number
- CN202511647245.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-11
- Publication Date
- 2026-02-06
AI Technical Summary
Existing optimization methods for air tank shapes in long-distance water conveyance projects are computationally inefficient and highly subjective, making it difficult to obtain the global optimum in complex nonlinear systems. Furthermore, time-consuming simulation models lead to high computational costs, and conventional neural network training requires a large number of samples, which can easily result in insufficient accuracy.
An adaptive sampling method is adopted, combining a deep neural network (DNN) surrogate model and a particle swarm optimization (PSO) algorithm. By constructing a log-exponential soft penalty function and a dual-criteria adaptive sampling rule, the air tank body parameters are optimized, the number of calls to the hydraulic transient simulation model is reduced, and the computational efficiency and accuracy are improved.
It significantly reduces the computational cost of the air tank optimization process, improves design efficiency, and dynamically enhances prediction accuracy in key areas, ensuring the protective performance of the air tank and making it suitable for long-distance water transmission projects.
Smart Images
Figure CN121479967A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of water hammer protection of long-distance water conveyance (regulation) projects, and relates to an air tank body type optimization method, in particular to a water conveyance system air tank body type optimization method based on adaptive sampling. BACKGROUND
[0002] Long-distance water conveyance (regulation) projects are an important way to realize optimal allocation of water resources and improve utilization efficiency, but water hammer is prone to occur in the process of valve opening and closing or pump shutdown, and in severe cases, can cause safety accidents such as pipe rupture, valve damage and pump station shutdown. As a commonly used water hammer protection device, the air tank has the advantages of simple structure, convenient maintenance, good buffering effect for positive and negative water hammer, etc. and is widely used. Generally speaking, the larger the air tank body type parameter, the more significant the protection effect of the system, but it will also significantly increase the project investment and operation cost. Therefore, it is urgent to seek the optimal body type parameter between safety and economy.
[0003] Existing engineering design mostly relies on empirical trial method, that is, the initial value is given first, and then the hydraulic transient simulation and parameter correction are repeatedly performed, which has low calculation efficiency, strong subjectivity, and is difficult to obtain global optimization in a complex nonlinear system. Although there have been attempts to combine numerical simulation and intelligent optimization, the high-time-consuming transient simulation model needs to be frequently called in the optimization process, resulting in high calculation cost. In order to reduce the calculation cost, some engineering practices introduce a neural network agent to replace the simulation model with high calculation cost, but the conventional offline one-time training requires a large number of samples, and the accuracy is insufficient in the key / boundary region, which makes the optimization result highly sensitive to the initial fitting, and even produces deviation or failure.
[0004] In summary, there is an urgent need for an air tank body type optimization method that takes into account calculation efficiency and prediction accuracy in the optimization process, and can dynamically improve the approximation ability in the key region. SUMMARY
[0005] The purpose of the application is to provide an efficient air tank body type optimization method to reduce the calculation cost in the optimization process of the air tank.
[0006] TECHNICAL SOLUTION
[0007] The air tank body type optimization method based on adaptive sampling of the water conveyance system of the application comprises the following steps:
[0008] S1: Taking the minimum air tank volume that meets the safety protection requirements of the water conveyance system as the optimization objective, the optimization problem is specifically expressed as follows: In the formula, V t is the total volume of the air tank; H air , S avThese are the height and cross-sectional area of the air tank chamber, respectively. H represents the magnitude of the drop in water level inside the tank. s The safe water depth inside the air tank; P min P max These represent the minimum and maximum pressures at various nodes along the pipeline during the transition process of the water conveyance system; P 0min P 0max These are the critical minimum and maximum pressure values of the system, respectively;
[0009] Construct a logarithmic-exponential soft penalty function to transform the constrained optimization problem into an unconstrained form: In the formula, , where is the weight coefficient of the corresponding penalty item;
[0010] The described logarithmic-exponential soft penalty function is continuously differentiable and has controllable growth, which can effectively avoid discontinuity or non-differentiability problems and improve the convergence of the algorithm.
[0011] S2: Select the air tank body shape parameters as optimization variables. The air tank body shape parameters include the cross-sectional area of the air tank, the height of the air chamber, and the cross-sectional area of the connecting pipe. Within the given range of variable values, Latin hypercube sampling is used to generate the input vector X of the initial training samples. Using the established hydraulic transient model, the simulation output P corresponding to the body shape parameters is calculated. min P max , The value is substituted into the log-exponential soft penalty function constructed in step S1 to calculate the objective function f(X). The air tank body shape parameters are used as inputs and the value of f(X) is used as outputs to form an initial training sample set. The number of the initial training samples is 3n, where n is the number of variables of the body shape parameters.
[0012] S3: Establish a deep neural network (DNN) surrogate model, complete the initial training using 3n initial training samples, and obtain the mapping relationship between the air tank body shape parameters and the objective function f(X);
[0013] S4: Apply the Particle Swarm Optimization (PSO) algorithm to the DNN surrogate model for global optimization to obtain the size parameter X of the air tank that minimizes f(X). 1,* Based on the dual-criteria adaptive sampling rule, incremental samples are selected from the parameter space to form an adaptively expanded training set.
[0014] S5: Update and train the DNN using the adaptively augmented training set, and repeat S4 until the following condition is met: In the formula, the relative error of the output results of the DNN in two consecutive iterations; a set convergence threshold; and the optimal values obtained by the kth and k-1th DNN and PSO, respectively; the maximum number of iterations.
[0015] Further, the air tank is arranged vertically.
[0016] Further, in step S3, in order to enhance the fitting accuracy of the extreme value of the transient pressure, higher weights are given to the samples close to the extreme value in the training process, and the DNN loss function and the weight distribution strategy are designed as follows: In the formula: N t is the number of training samples; f(·) is the true value of the objective function; is the predicted value of the DNN model; W(s) is the weight of the th training sample; is the input vector of the th training sample.
[0017] Further, the selection of the incremental samples to form the adaptively expanded training set in step S4 specifically includes:
[0018] (i) selecting the current optimal air tank body parameter X 1,* to enhance the local approximation ability of the DNN in the extreme value region;
[0019] (ii) selecting the parameter combination X 2,* that is farthest from the existing sample set in the parameter space to improve the global search ability of the model and avoid falling into local optimum; In the formula, N t,k is the number of training samples updated in the kth iteration; is the Euclidean distance; is the input vector of the th training sample in the kth iteration;
[0020] For X 1,* , X 2,* , the hydraulic transient model is called to obtain the corresponding f(X) to form incremental samples to expand the training set, wherein the parameter combination X 2,* that is farthest from the existing sample set is forcibly added only in the initial n cycles.
[0021] Further, the hydraulic transient model is used to simulate the maximum pressure extreme value and the minimum pressure extreme value along the water delivery system and the water level drop amplitude in the air tank under the condition of given air tank body type parameters, and is used for target function calculation accordingly.
[0022] Further, the global optimization phase of the particle swarm algorithm completes the target function evaluation by using the DNN surrogate model, and the hydraulic transient model is only used when new samples are added by adaptive sampling
[0023] Beneficial effects: the air tank body type optimization method based on adaptive sampling provided by the present application can significantly reduce the number of calls to the hydraulic transient simulation model by iteratively updating the surrogate model and targeted incremental sampling, thereby greatly reducing the optimization calculation cost and improving the design efficiency, which is conducive to the engineering application of the air tank body type in long-distance water delivery projects. BRIEF DESCRIPTION OF DRAWINGS
[0024] Figure 1 is an air tank body type optimization flowchart for adaptive sampling;
[0025] Figure 2 is a schematic diagram of the water delivery system of the present embodiment;
[0026] Figure 3 is a comparison diagram of the DNN-PSO adaptive optimization method and the Monte Carlo method;
[0027] Figure 4 is an envelope line diagram of the pressure extreme value of the water delivery system under the optimization of DNN-PSO and PSO; DETAILED DESCRIPTION
[0028] In order to facilitate the understanding of the present application, the embodiments thereof will be further described with reference to the accompanying drawings.
[0029] The present embodiment takes a certain long-distance pump station pressurized water delivery project as the research object. The pump station is arranged with four horizontal centrifugal pumps (design head of 300.0 m, single design flow of 0.55 m³ / s), of which three are in operation and one is standby. The upstream intake pool is designed at a water level of 1365.5 m, and is delivered to the downstream outlet pool through about 75.0 km of DN1400 ductile iron pipe, and the outlet pool is operated at a water level of 1602.5 m. In order to prevent water hammer caused by pump power failure and other working conditions from damaging the pipeline system, an air tank is arranged at the outlet of the pump station for protection (the system profile is shown in Figure 2
[0030] Referring to Figure 1 , the specific steps of the present embodiment are as follows:
[0031] S1: Take the minimum air tank volume that meets the water delivery system safety protection requirements as the optimization target, and construct a logarithmic-exponential type soft penalty function. Considering the safety margin, take P 0min = 2.0 m, P 0max = 340 m, take the safe water depth H s = 0.5 m in the air tank, and the unconstrained form of the air tank size optimization is written as:
[0032] S2: Select the main size parameters of the air tank, such as the cross-sectional area, the air chamber height, and the connecting pipe cross-sectional area, as the optimization variables. Therefore, the size parameter dimension of the air tank is 3, and the initial training sample number is 3n = 9. The value range of each parameter is listed in Table 1. Within the given value range of the variable, Latin hypercube sampling is used to generate the input vector X of the initial training sample; the established hydraulic transient model is used to simulate the P min , P max , value corresponding to the size parameters, and the target function f(X) is calculated. The size parameters of the air tank are input, and the f(X) value is output, to form the initial training sample set.
[0033] S3: A deep neural network (DNN) proxy model containing 5 hidden layers is constructed, and the initial training of 9 initial samples is completed to obtain the mapping relationship from the size parameters of the air tank to the target function f(X). The weight weighted loss function WMSE is used in the training process.
[0034] In this embodiment, the particle swarm optimization algorithm (the proposed adaptive optimization framework (denoted as DNN-PSO)) contains 5 hidden layers, and is integrated with the PSO algorithm, and the maximum number of iterations is also set to 100. 10 are randomly selected from the initial 500 samples as the initial training samples of DNN-PSO.
[0035] S4: The constructed DNN proxy model is integrated with the PSO algorithm (denoted as DNN-PSO), and the maximum number of iterations is set to 100. The population size of PSO is set to 200, and the maximum number of iterations is also set to 100. The DNN-PSO is used for global optimization. According to the double-criteria adaptive sampling rule, the current optimal air tank size parameter X 1,* is selected to enhance the local approximation ability of DNN in the extreme value region, and the parameter combination X 2,* that is farthest from the existing sample set in the parameter space is selected to improve the global search ability of the model and avoid falling into local optimum.
[0036] S5: update the DNN using the training set with adaptive expansion, repeat S4 until the maximum number of iterations 100 is reached, or the relative error of the DNN output results in two consecutive iterations is less than the convergence threshold 10 less than the convergence threshold 10 -4 .
[0037] To verify the computational efficiency of the method, it is compared with the traditional PSO method. The parameters in the PSO method and the developed DNN-PSO method are kept consistent, that is, the population size is set to 200, and the maximum number of iterations is set to 100. The optimal extreme value and the corresponding parameter statistical results obtained by the two methods are shown in Table 2. The results show that the optimal objective function values of the two methods are basically consistent, but the PSO method needs to call the simulation model about 20000 times, while the DNN-PSO only needs 182 times, which is about 0.91% of the PSO calculation amount. It should be pointed out that in the proposed optimization framework, the iteration process of the PSO optimization algorithm depends on the DNN surrogate model with low computational cost, and the real simulation model is only called when adding new samples. Therefore, this method significantly reduces the overall computational overhead.
[0038] To verify the accuracy of the results of the method, Monte Carlo simulation is also used to evaluate the output results, and 20 repeated experiments are performed for different sample sizes. Figure 3 The box plot of the estimation results is shown. As can be seen from the figure, the results of the method are highly consistent with those of the filled sampling (Monte Carlo). When directly relying on the simulation model for optimization, more than 10 7 samples are needed to obtain comparable accuracy, which is almost impossible to achieve in engineering practice. As can be seen, the method proposed in the invention significantly improves the computational efficiency while maintaining high computational accuracy.
[0039] To further verify the protection performance of the air tank parameters obtained by optimization, the air tank body type parameters obtained by different methods are substituted into the hydraulic transient simulation model for verification. Figure 4 The pressure envelope of the water conveyance system under the condition of pump pumping and power-off is shown under the protection of the air tank body type optimized by the two methods. As Figure 4 can be seen from Table 2, although there are some differences in the size parameters of the air tank optimized by the two methods, the pressure extreme value distribution is highly consistent, and the absolute error is less than 1 m. Analysis shows that the protection performance of the air tank is mainly affected by its total volume, and the total volume under different parameter combinations is basically consistent, so there are multiple groups of equivalent optimal solutions. This result fully verifies the accuracy, robustness and engineering applicability of the method described in the invention.
[0040] Table 1 Air tank body type parameter interval value Interval variable Lower limit value Upper limit value Air tank air chamber height H air (m)]]> 0.50 5.00 Air tank cross-sectional area S av (m 2 )]]> 1.00 40.0 Connection pipe cross-sectional area A cp (m 2 )]]> 0.10 1.00 .
[0041] Table 2 Statistics of the results of different methods Method Air tank total volume / m 3 ]] Gas chamber height / m Air tank cross-sectional area / m 2 ]]> Connection pipe cross-sectional area / m 2 ]]> Minimum pressure / m Maximum pressure / m Fitness value Call number / time PSO 23.31 3.33 3.75 0.10 0.84 337.82 28.098 20000 DNN-PSO 23.18 2.88 4.25 0.10 0.25 337.95 28.618 182 .
Claims
1. A method for optimizing the shape of an air tank in a water conveyance system based on adaptive sampling, characterized in that, Includes the following steps: S1: The optimization objective is to find the minimum air tank volume that meets the safety protection requirements of the water conveyance system. The optimization problem is specifically described as follows: In the formula, V t H represents the total volume of the air tank. air S av These are the height and cross-sectional area of the air tank chamber, respectively. H represents the magnitude of the drop in water level inside the tank. s The safe water depth inside the air tank; P min P max These represent the minimum and maximum pressures at various nodes along the pipeline during the transition process of the water conveyance system; P 0min P 0max These are the critical minimum and maximum pressure values of the system, respectively; Construct a logarithmic-exponential soft penalty function to transform the constrained optimization problem into an unconstrained form: In the formula, The weighting coefficients for the corresponding penalty items; S2: Select the air tank body shape parameters as optimization variables. The air tank body shape parameters include the cross-sectional area of the air tank, the height of the air chamber, and the cross-sectional area of the connecting pipe. Within the given range of variable values, Latin hypercube sampling is used to generate the input vector X of the initial training samples. Using the established hydraulic transient model, the simulation output P corresponding to the body shape parameters is calculated. min P max , The value is substituted into the log-exponential soft penalty function constructed in step S1 to calculate the objective function f(X). The air tank body shape parameters are used as inputs and the value of f(X) is used as outputs to form an initial training sample set. The number of the initial training samples is 3n, where n is the number of variables of the body shape parameters. S3: Establish a deep neural network (DNN) surrogate model, complete the initial training using 3n initial training samples, and obtain the mapping relationship between the air tank body shape parameters and the objective function f(X); S4: Apply the Particle Swarm Optimization (PSO) algorithm to the DNN surrogate model for global optimization to obtain the size parameter X of the air tank that minimizes f(X). 1,* Based on the dual-criteria adaptive sampling rule, incremental samples are selected from the parameter space to form an adaptively expanded training set. S5: Update and train the DNN using the adaptively augmented training set, and repeat S4 until the following condition is met: In the formula, This represents the relative error of the DNN output results in two consecutive iterations. The set convergence threshold; and These are the optimal values obtained by DNN and PSO for the kth and k-1th iterations, respectively; This represents the maximum number of iterations.
2. The method for optimizing the air tank shape of a water conveyance system based on adaptive sampling according to claim 1, characterized in that, The air tank is arranged vertically.
3. The method for optimizing the air tank shape of a water conveyance system based on adaptive sampling according to claim 1, characterized in that, In step S3, to enhance the fitting accuracy of transient stress extrema, samples closer to the extrema are assigned higher weights during training. The DNN loss function and weight allocation strategy are designed as follows: Where: N t The number of training samples is denoted as f(⦁); f(⦁) is the true value of the objective function. W(s) is the predicted value of the DNN model; W(s) is the value of the first... The weights of each training sample; For the first The input vector of each training sample.
4. The method for optimizing the air tank shape of a water conveyance system based on adaptive sampling according to claim 1, characterized in that, Step S4, which involves selecting incremental samples to form an adaptively expanded training set, specifically includes: (i) Select the current optimal air tank body type parameter X 1,* This is used to enhance the local approximation ability of DNNs in extreme regions; (ii) Select the parameter combination X that is furthest away from the existing sample set in the parameter space. 2,* This is used to improve the model's global search capability and avoid getting trapped in local optima; In the formula, N t,k This represents the number of training samples updated in the k-th iteration. The distance is Euclidean. For the k-th iteration The input vector of each training sample; For X 1,* X 2,* The hydraulic transient model is invoked to obtain the corresponding f(X), forming incremental samples to expand the training set. Among them, the parameter combination X that is furthest from the existing sample set is... 2,* Force the addition only within the initial n loops.
5. The method for optimizing the air tank shape of a water conveyance system based on adaptive sampling according to claim 1, characterized in that, The hydraulic transient model is used to simulate and output the maximum and minimum pressure extreme values along the water conveyance system, as well as the drop in water level inside the air tank, under given air tank body parameters, and to use these values for objective function calculation.
6. The method for optimizing the air tank shape of a water conveyance system based on adaptive sampling according to claim 1, characterized in that, The global optimization phase of the particle swarm optimization algorithm uses the DNN surrogate model to evaluate the objective function, while the hydraulic transient model is only used when adaptively sampling new samples.