Modeling method and system of rainwater collection system based on gamma distribution and computer equipment

Abstract

The invention relates to a modeling method and system for a rainwater collection system based on gamma distribution and computer equipment. The method comprises the following steps: based on rainfall parameters including rainfall depth, rainfall duration and non-rainfall duration, simulating rainfall characteristics, and constructing a rainfall characteristic probability density function based on gamma distribution; simulating the runoff collected in the rainfall period to obtain the water amount of the runoff intercepted by the roof; simulating the residual water volume to obtain the range of the residual water volume when the rainfall cycle starts; simulating overflow based on the residual water quantity to obtain overflow; the probability density function, the water amount intercepted by the roof and overflow are synthesized, and water-saving and waterlogging-reducing efficiency parameters are constructed. By adopting the method, random rainfall characteristics can be simulated with high precision, and the method has the characteristic of few occupied computing resources.

Description

Technical Field

[0001] This application relates to the field of hydrological modeling technology, and in particular to modeling methods, systems and computer equipment for rainwater harvesting systems based on gamma distribution. Background Technology

[0002] Rapid urbanization has led to an increase in impervious surface area, causing adverse hydrological impacts such as flooding and water quality deterioration. With population growth (especially in developing countries), the diversification of domestic, industrial, and agricultural water demands is placing increasing pressure on water supply. Therefore, water scarcity and stress have become pressing challenges for many countries worldwide, threatened by extreme climate events, intense human activity, rapid urbanization, and population growth. Realizing, enhancing, or maximizing the effectiveness of rainwater harvesting (RWH) in mitigating these challenges, promoting green building, and achieving the Sustainable Development Goals requires the scientific design, evaluation, planning, and management of RWHs. A key foundation for this is advanced modeling of hydrological processes within each RWH system.

[0003] Currently, Stochastic Rainwater Harvesting System (StRaHaS) modeling can improve the accuracy and applicability of hydrological modeling in the widespread and scientific application of Rainwater Harvesting Systems (RWH) in large data-scarce areas. It reveals the impact of water demand and rainfall characteristics on system reliability. However, from the perspective of stochastic RWH simulation, random rainfall characteristics do not perfectly conform to the memoryless exponential distribution; furthermore, the assumption that the RWSU is filled at the end of each rainfall event is unreasonable in areas with scarce rainfall events. This may introduce certain biases into the modeling of the entire system, affecting its objectivity and accuracy.

[0004] Existing technology includes a comprehensive evaluation method for the health of drainage systems. This method involves deep learning, mining, and modeling of multi-source data, such as meteorological, remote sensing, elevation, pipe network, and exploration data, to derive indicators for evaluating the health of urban drainage systems. The method also calculates the comprehensive weight of each indicator to reflect the health level of the drainage system.

[0005] However, existing technologies have the problem of not considering the characteristics of random rainfall and not conforming to the memoryless exponential distribution. Therefore, how to invent a modeling method that considers the characteristics of random rainfall and is applicable to universal rainwater harvesting systems is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] Therefore, it is necessary to provide a modeling method and system for a rainwater harvesting system that can accurately simulate the characteristics of random rainfall, which has the advantage of requiring less computing resources, in order to address the above-mentioned technical problems.

[0007] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows: A modeling method for rainwater harvesting systems based on gamma distribution includes the following steps: Based on rainfall depth Duration of rainfall Duration of non-rainfall The rainfall parameters are used to perform random simulations of rainfall characteristics and construct a probability density function (PDF) for rainfall characteristics based on the gamma distribution. Based on the probability density function, a stochastic simulation is performed on the runoff collected during rainfall to obtain the amount of runoff intercepted by the roof. ; Based on the probability density function, the remaining water volume in the rainwater storage unit is simulated to obtain the remaining water volume at the start of the rainfall cycle. Scope; Based on the remaining water volume The overflow of the rainwater storage unit was randomly simulated to obtain the overflow rate. ; Combining the probability density function and the amount of water intercepted by the roof and the overflow Construct parameters for water-saving and flood-reduction efficiency.

[0008] Preferably, the construction of the rainfall feature probability density function based on the gamma distribution specifically involves:

[0009]

[0010]

[0011] in, (*) This represents the probability density function of the gamma distribution. 、 They are respectively 、 The shape parameters primarily determine the shape of the distribution curve; 、 、 They are respectively 、 The inverse scaling parameter primarily determines how steep the curve is. ， ， They represent the corresponding 、 The sample.

[0012] Furthermore, any rainfall parameter satisfies:

[0013]

[0014] in, express 、 Any parameter, for The corresponding shape parameters, for The corresponding inverse scaling parameter, For gamma function, A function of the gamma distribution. The probability density function of a random variable. This represents the cumulative distribution function of a random variable.

[0015] Furthermore, the amount of runoff intercepted by the roof, VC, is determined by the following formula:

[0016] Where a is the drainage area of ​​the rainwater harvesting system, φ is the runoff coefficient, and df is the depth to which the initial runoff is diverted.

[0017] Furthermore, the remaining water volume in the rainwater storage unit It can be represented in the following way:

[0018] in, The volume of the rainwater storage unit. This refers to water demand during non-rainfall periods. This refers to the length of the non-rainy period.

[0019] Furthermore, a random simulation of the overflow of the rainwater storage unit is performed to obtain the overflow rate. Specifically, a portion of the collected runoff will be used for water demand during both rainfall and non-rainfall periods, while the remainder will overflow into the municipal sewer system as a random variable. : .

[0020] Furthermore, the water-saving and flood-reduction efficiency parameters include water-saving efficiency. :

[0021] in, For overflow Expected value Water intercepted by the roof The expected value.

[0022] Furthermore, the water-saving and flood-reduction efficiency parameters also include flood-reduction efficiency. :

[0023] in, Remaining water volume Expected value This represents the average water requirement during rainfall. Duration of rainfall Expected value Rainfall depth The expected value.

[0024] A rainwater harvesting system based on gamma distribution includes a random rainfall simulation module, a random runoff simulation module, a random residual water simulation module, a random overflow simulation module, and a water-saving and flood-reduction efficiency evaluation module. The random rainfall simulation module is used to simulate rainfall based on rainfall depth. Duration of rainfall Duration of non-rainfall The rainfall parameters are used to perform random simulations of rainfall characteristics and construct a probability density function (PDF) for rainfall characteristics based on the gamma distribution. The aforementioned random runoff simulation module is used to perform random simulations of runoff collected during rainfall based on the probability density function, to obtain the amount of runoff intercepted by the roof. ; The random residual water volume simulation module is used to simulate the residual water volume in the rainwater storage unit based on the probability density function, so as to obtain the residual water volume when the rainfall cycle begins. Scope; The random overflow simulation module is used to simulate the remaining water volume. The overflow of the rainwater storage unit was randomly simulated to obtain the overflow rate. ; The water-saving and flood-reduction efficiency evaluation module is used to comprehensively consider the probability density function and the amount of water intercepted by the roof. and the overflow Construct parameters for water-saving and flood-reduction efficiency.

[0025] A computer-readable storage medium includes a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method.

[0026] The beneficial effects of this invention are as follows: This invention discloses a modeling method for rainwater harvesting systems based on gamma distribution. By constructing a rainfall characteristic probability density function based on gamma distribution using rainfall parameters including rainfall depth, rainfall duration, and non-rainfall duration, it can be applied to the simulation of all stochastic processes. While improving the accuracy of selecting higher fitting, it avoids multiple random number generation and conditional branch judgments during random sampling due to mixed distributions, which greatly improves the execution efficiency of CPU pipelines. Thus, this method improves the accuracy of stochastic simulation with less computational resources. Attached Figure Description

[0027] Figure 1 This is a flowchart of a modeling method for a rainwater harvesting system based on gamma distribution in one embodiment; Figure 2 This is a schematic diagram of a rainwater harvesting system with gamma distribution in one embodiment. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0029] like Figure 1 As shown, a modeling method for a rainwater harvesting system based on gamma distribution includes the following steps: Based on rainfall depth Duration of rainfall Duration of non-rainfall The rainfall parameters are used to perform random simulations of rainfall characteristics and construct a probability density function (PDF) for rainfall characteristics based on the gamma distribution. Based on the probability density function, a stochastic simulation is performed on the runoff collected during rainfall to obtain the amount of runoff intercepted by the roof. ; Based on the probability density function, the remaining water volume in the rainwater storage unit is simulated to obtain the remaining water volume at the start of the rainfall cycle. Scope; Based on the remaining water volume The overflow of the rainwater storage unit was randomly simulated to obtain the overflow rate. ; Combining the probability density function and the amount of water intercepted by the roof and the overflow Construct parameters for water-saving and flood-reduction efficiency.

[0030] Preferably, the construction of the rainfall feature probability density function based on the gamma distribution specifically involves:

[0031]

[0032]

[0033] in, (*) This represents the probability density function of the gamma distribution. 、 They are respectively 、 The shape parameters primarily determine the shape of the distribution curve; 、 、 They are respectively 、 The inverse scaling parameter primarily determines how steep the curve is. ， ， They represent the corresponding 、 The sample.

[0034] Furthermore, any rainfall parameter satisfies:

[0035]

[0036] in, express 、 Any parameter, for The corresponding shape parameters, for The corresponding inverse scaling parameter, For gamma function, A function of the gamma distribution. The probability density function of a random variable. This represents the cumulative distribution function of a random variable.

[0037] Furthermore, the amount of runoff intercepted by the roof, VC, is determined by the following formula:

[0038] Where a is the drainage area of ​​the rainwater harvesting system, φ is the runoff coefficient, and df is the depth to which the initial runoff is diverted.

[0039] Furthermore, the remaining water volume in the rainwater storage unit It can be represented in the following way:

[0040] in, The volume of the rainwater storage unit. This refers to water demand during non-rainfall periods. This refers to the length of the non-rainy period.

[0041] Furthermore, a random simulation of the overflow of the rainwater storage unit is performed to obtain the overflow rate. Specifically, a portion of the collected runoff will be used for water demand during both rainfall and non-rainfall periods, while the remainder will overflow into the municipal sewer system as a random variable. : .

[0042] Furthermore, the water-saving and flood-reduction efficiency parameters include water-saving efficiency. :

[0043] in, For overflow Expected value Water intercepted by the roof The expected value.

[0044] Furthermore, the water-saving and flood-reduction efficiency parameters also include flood-reduction efficiency. :

[0045] in, Remaining water volume Expected value This represents the average water requirement during rainfall. Duration of rainfall Expected value Rainfall depth The expected value.

[0046] Example 2 To verify the advantages of the modeling method proposed in this application in terms of computational efficiency and simulation accuracy, the inventors set up a comparative experiment. The experiment selected daily rainfall observation data from humid regions from 1990 to 2020 as the basic sample.

[0047] Experimental environment: Hardware platform: Intel Core i9-13900K processor, 64GB DDR5 memory. Software environment: Python 3.9, NumPy math library.

[0048] In this embodiment, an existing technical solution is used as a comparative example. This solution uses a linear combination of two independent exponential distributions (i.e., a mixed exponential distribution) to construct the probability density function of rainfall characteristics. Its mathematical form involves fitting multiple parameters. In the random sampling process of Monte Carlo simulation, generating a sample each time requires two steps: first, generating a uniformly distributed random number to determine which exponential component to select, and then generating the corresponding exponentially distributed random number, involving a large number of conditional judgments and branch calculations.

[0049] The method employed in this embodiment utilizes the gamma distribution to construct the probability density function. During the random simulation process, an optimized standard gamma distribution sampling algorithm (such as the Marsaglia-Tsang algorithm) is directly called to generate samples, eliminating the need for intermediate branching steps.

[0050] In this embodiment, the two methods described above are used to fit parameters to the same set of historical rainfall data. Subsequently, the fitted model is used to simulate 1,000,000 random rainfall events to simulate the system's operation over a long period.

[0051] The metrics for the two sets of experiments are shown in Table 1; the number of parameters represents the number of independent parameters required by the model. Simulation time represents the CPU time required to generate the simulated events. Fit accuracy represents the Kolmogorov-Smirnov (KS) statistic D value calculated for the simulated and measured data (the smaller the D value, the closer the simulated distribution is to the actual distribution). Memory usage represents the peak memory consumption during the simulation process.

[0052] Table 1

[0053] As shown in Table 1, although Comparative Example 1 corrected the error of the single exponential distribution by introducing more parameters (linear combination) and achieved a better fitting accuracy (D value = 0.042), the cost was a significant increase in model complexity. When performing large-scale stochastic simulations, its complex sampling logic resulted in a long computation time (1450ms).

[0054] In comparison, the gamma distribution modeling method used in this application has the following significant advantages: While maintaining fitting accuracy (D-value = 0.041, even slightly better than the comparative method), the simulation speed of the proposed method is improved by approximately 4.5 times. This is because the gamma distribution, as a standard statistical distribution, avoids the multiple random number generation and conditional branch judgments required during random sampling in mixed distributions, greatly improving the execution efficiency of the CPU pipeline. The memory usage of the proposed method is only 25% of that of the comparative method, and the number of parameters is reduced by 60%. This efficient utilization of computing resources makes the modeling method of this application not only suitable for high-performance computers, but also directly deployable in embedded rainwater control terminals with limited computing power (such as controllers based on microcontrollers or low-power ARM chips), realizing real-time dynamic simulation and control of rainwater harvesting systems. This is difficult to achieve with the complex mixed distribution models in the prior art.

[0055] In summary, by selecting the gamma distribution, this application not only solves the problem that "random rainfall characteristics do not conform to the exponential distribution," but also unexpectedly addresses the technical shortcomings of existing complex models, such as "high computational cost and difficulty in real-time application," achieving significant progress.

[0056] Example 3 like Figure 2 As shown, a rainwater harvesting system based on gamma distribution includes a random rainfall simulation module, a random runoff simulation module, a random residual water simulation module, a random overflow simulation module, and a water-saving and flood-reduction efficiency evaluation module. The random rainfall simulation module is used to simulate rainfall based on rainfall depth. Duration of rainfall Duration of non-rainfall The rainfall parameters are used to perform random simulations of rainfall characteristics and construct a probability density function (PDF) for rainfall characteristics based on the gamma distribution. The aforementioned random runoff simulation module is used to perform random simulations of runoff collected during rainfall based on the probability density function, to obtain the amount of runoff intercepted by the roof. ; The random residual water volume simulation module is used to simulate the residual water volume in the rainwater storage unit based on the probability density function, so as to obtain the residual water volume when the rainfall cycle begins. Scope; The random overflow simulation module is used to simulate the remaining water volume. The overflow of the rainwater storage unit was randomly simulated to obtain the overflow rate. ; The water-saving and flood-reduction efficiency evaluation module is used to comprehensively consider the probability density function and the amount of water intercepted by the roof. and the overflow Construct parameters for water-saving and flood-reduction efficiency.

Claims

1. A modeling method for a rainwater harvesting system based on gamma distribution, characterized in that, Includes the following steps: Based on rainfall depth Duration of rainfall Duration of non-rainfall The rainfall parameters are used to perform random simulations of rainfall characteristics and construct a probability density function (PDF) for rainfall characteristics based on the gamma distribution. Based on the probability density function, a stochastic simulation is performed on the runoff collected during rainfall to obtain the amount of runoff intercepted by the roof. ; Based on the probability density function, the remaining water volume in the rainwater storage unit is simulated to obtain the remaining water volume at the start of the rainfall cycle. Scope; Based on the remaining water volume The overflow of the rainwater storage unit was randomly simulated to obtain the overflow rate. ; Combining the probability density function and the amount of water intercepted by the roof and the overflow Construct parameters for water-saving and flood-reduction efficiency.

2. The method according to claim 1, characterized in that, The construction of the rainfall feature probability density function based on the gamma distribution is specifically as follows: in, (*) This represents the probability density function of the gamma distribution. 、 They are respectively 、 The shape parameters primarily determine the shape of the distribution curve; 、 、 They are respectively 、 The inverse scaling parameter primarily determines how steep the curve is. ， ， They represent the corresponding 、 The sample.

3. The method according to claim 2, characterized in that, All rainfall parameters satisfy: in, express 、 Any parameter, for The corresponding shape parameters, for The corresponding inverse scaling parameter, For gamma function, A function of the gamma distribution. The probability density function of a random variable. This represents the cumulative distribution function of a random variable.

4. The method according to claim 3, characterized in that, The amount of runoff intercepted by the roof, VC, is determined by the following formula: Where a is the drainage area of ​​the rainwater harvesting system, φ is the runoff coefficient, and df is the depth to which the initial runoff is diverted.

5. The method according to claim 4, characterized in that, The remaining water volume in the rainwater storage unit It can be represented in the following way: in, The volume of the rainwater storage unit. This refers to water demand during non-rainfall periods. This refers to the length of the non-rainy period.

6. The method according to claim 5, characterized in that, The overflow of the rainwater storage unit was randomly simulated to obtain the overflow rate. Specifically, a portion of the collected runoff will be used for water demand during both rainfall and non-rainfall periods, while the remainder will overflow into the municipal sewer system as a random variable. : 。 7. The method according to claim 1, characterized in that, The water-saving and flood-reduction efficiency parameters include water-saving efficiency. : in, For overflow Expected value Water intercepted by the roof The expected value.

8. The method according to claim 4, characterized in that, The water-saving and flood-reduction efficiency parameters also include flood-reduction efficiency. : in, Remaining water volume Expected value This represents the average water requirement during rainfall. Duration of rainfall Expected value Rainfall depth The expected value.

9. A rainwater harvesting system based on gamma distribution, characterized in that, It includes modules for random rainfall simulation, random runoff simulation, random residual water simulation, random overflow simulation, and water-saving and flood-reduction effectiveness assessment. The random rainfall simulation module is used to simulate rainfall based on rainfall depth. Duration of rainfall Duration of non-rainfall The rainfall parameters are used to perform random simulations of rainfall characteristics and construct a probability density function (PDF) for rainfall characteristics based on the gamma distribution. The aforementioned random runoff simulation module is used to perform random simulations of runoff collected during rainfall based on the probability density function, to obtain the amount of runoff intercepted by the roof. ; The random residual water volume simulation module is used to simulate the residual water volume in the rainwater storage unit based on the probability density function, so as to obtain the residual water volume when the rainfall cycle begins. Scope; The random overflow simulation module is used to simulate the remaining water volume. The overflow of the rainwater storage unit was randomly simulated to obtain the overflow rate. ; The water-saving and flood-reduction efficiency evaluation module is used to comprehensively consider the probability density function and the amount of water intercepted by the roof. and the overflow Construct parameters for water-saving and flood-reduction efficiency.

10. A computer-readable storage medium, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.

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