Cost-benefit-risk synergistic method for optimization of water network engineering scale

Abstract

The application discloses a cost-effective risk coordination water network engineering scale optimization method. The method comprises the following steps: obtaining historical data and degradation characteristic parameters, and constructing a joint inflow-water demand scenario set; an engineering capacity time-varying constraint system is established, and the engineering capacity is defined as a function evolving with the running life; under the joint scenario set driving, the time-varying constraint is used to perform a whole life cycle water balance simulation to obtain a water supply deficit matrix; based on the hierarchical driving mechanism of planning decision variables and operation decision variables, a comprehensive evaluation index is calculated, the operation risk including scale redundancy and supply shortage is quantified by using the conditional risk value; and an optimization model is solved and a recommended engineering scale is output. By introducing the physical degradation evolution path and the risk quantification variable decoupling mechanism, the technical problems that the traditional model ignores the engineering performance aging and the scale redundancy item control failure are solved, and the safety and robustness of the water network engineering scale decision are improved.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering planning and design technology, and in particular to a method for optimizing the scale of water network engineering through cost-benefit-risk synergy. Background Technology

[0002] The feasibility study of water network project scale is one of the core technologies for ensuring the long-term service effectiveness of water conservancy infrastructure. Existing methods for determining the scale of water network projects are mostly based on static water balance analysis, employing cost-benefit comparisons under representative design years or stochastic scenarios. These methods typically treat the project's storage capacity and water conveyance flow as fixed design constants. Regarding risk quantification, existing technologies largely draw on the logic of the newsboy model in operations research, using probability-weighted expected values ​​to conduct a mixed assessment of water shortage risk and design redundancy risk at a single operational level.

[0003] However, in practical applications, this approach ignores the evolution of physical properties of the project during its service life, such as reservoir siltation and pipe wall aging, leading to an overestimation of the long-term water supply guarantee rate. In other words, the limitations of existing technology result in a lack of technical robustness in addressing the dynamic evolution throughout the entire life cycle of the water network. Summary of the Invention

[0004] Purpose of the invention: To propose a cost-benefit-risk synergy method for optimizing the scale of water network projects in order to solve the above-mentioned problems.

[0005] Technical solution: A method for optimizing the scale of water network projects through cost-benefit and risk synergy, comprising:

[0006] Acquire historical hydrological data, historical water demand data, engineering design parameters, and pre-stored engineering degradation characteristic parameters;

[0007] Based on historical hydrological data and historical water demand data, a joint scenario set is constructed that includes future water inflow scenarios and water demand scenarios;

[0008] Based on engineering design parameters and degradation characteristic parameters, a time-varying engineering capability constraint system is established, and engineering capability is defined as a time-varying function that evolves with the service life.

[0009] Driven by a joint scenario set, a full life-cycle water balance simulation is performed using a time-varying engineering capacity constraint system to obtain a full life-cycle water supply deficit matrix.

[0010] Based on the water supply deficit matrix and engineering design parameters, a comprehensive evaluation index including engineering operation risk is calculated, where the operation risk is quantified based on a hierarchical driving mechanism of planning decision variables and operation decision variables.

[0011] Based on comprehensive evaluation indicators, a recommended project scale is output.

[0012] Beneficial effects: By introducing physical degradation evolution paths and risk quantification variable decoupling mechanisms, the technical problems of traditional models ignoring engineering performance aging and scale redundancy control failure are solved, thereby improving the safety and robustness of water network engineering scale decision-making. Attached Figure Description

[0013] Figure 1 This is a flowchart of the method for optimizing the scale of water network projects based on cost-benefit risk synergy, as presented in this invention.

[0014] Figure 2 This is a flowchart of the time-varying engineering capability constraint system of the present invention.

[0015] Figure 3 This is a flowchart illustrating the determination of the time-varying storage capacity sequence of the present invention.

[0016] Figure 4 This is a flowchart of the present invention for determining the time-varying water conveyance capacity sequence.

[0017] Figure 5 This is a flowchart of the process for obtaining degradation characteristic parameters in advance according to the present invention. Detailed Implementation

[0018] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0019] As mentioned in the background section, traditional models suffer from a logical confusion between planning-level and operational-level drivers. This leads to overly ambitious planning flaws that can cause solution loopholes during mathematical optimization, resulting in the failure of redundant risk monitoring. Furthermore, the nonlinear superposition effects of performance degradation and extreme drought scenarios are diluted by traditional expected value indicators, making it difficult to accurately capture the tail-end extreme risks induced by the collapse of water storage and transport capacity in the later stages of service. For example, when the driving variables of the redundancy penalty term in the risk model are vaguely defined, the solver may manually adjust operational decision variables to circumvent the scale redundancy penalty during optimization, significantly reducing the constraint effectiveness on the planning scale.

[0020] To solve these problems, combined with Figures 1 to 5 The present invention will be specifically described through the following embodiments.

[0021] Example 1

[0022] According to one aspect of this application, this embodiment provides a method for optimizing the scale of water network engineering projects through cost-benefit and risk coordination. Specifically, it optimizes the scale of water network engineering projects by constructing a time-varying engineering capacity constraint and hierarchical risk assessment mechanism, including:

[0023] Step 101: Obtain historical hydrological data, historical water demand data, engineering design parameters, and pre-stored engineering degradation characteristic parameters.

[0024] The historical hydrological data includes monthly runoff observation records from hydrological stations in the study area. Historical water demand data includes phased water demand forecasts compiled by planning departments, covering water demand at different levels of socio-economic development. Engineering design parameters include reservoir characteristic curves, pump station installed capacity, and water conveyance system design flow rates from the preliminary design report. Pre-stored engineering degradation characteristic parameters are used to reflect the evolution of the physical performance of the engineering system throughout its entire life cycle, including reservoir sedimentation rate, pipeline roughness growth parameters, and cross-sectional area reduction rate.

[0025] Step 102: Based on historical hydrological data and historical water demand data, construct a joint scenario set that includes future water inflow scenarios and water demand scenarios.

[0026] A joint scenario set refers to a series of time-series samples describing an uncertain future operating environment. In constructing this set, a kernel density estimation method can be used to fit the marginal probability distribution of water inflow, while a parametric model is used to fit the median path of water demand forecasts and its uncertainty interval.

[0027] Building upon this foundation, a copula function is employed to characterize the dependency structure between water inflow and demand, and a Latin hypercube sampling method is used to generate random scenario samples covering the entire planning period. Each scenario sample contains paired sequences of water inflow and demand for each year and time period within the planning period. By constructing a joint scenario set, the scale optimization model can comprehensively consider possible combinations of abundant and scarce water availability in the future, improving the robustness of decision-making. For example, the Gaussian copula function is used to characterize the dependency structure, and its correlation coefficient matrix can be obtained by estimating the rank correlation coefficients of historical water inflow and demand.

[0028] Step 103: Based on the engineering design parameters and degradation characteristic parameters, establish a time-varying engineering capability constraint system, and define the engineering capability as a time-varying function that evolves with the service life.

[0029] A time-varying engineering capacity constraint system refers to replacing engineering parameters that were originally set as constants with variables that vary over time in a mathematical model. In this embodiment, engineering capacity mainly includes storage capacity and water conveyance capacity. Based on degradation characteristic parameters, evolution equations are constructed for the effective storage capacity decreasing year by year with the number of years of operation, and for the water conveyance flow decreasing year by year with pipe wall aging. The corresponding calculation formulas are as follows:

[0030] V _eff (s,t)=V _0 (s)×(1-r _V ×t);

[0031] Among them, V _eff (s,t) represents the effective storage capacity in year t when the construction scale is s, V _0 (s) represents the initial design effective storage capacity, r _V Here, t represents the normalized reservoir capacity decay rate coefficient, and t represents the number of years of operation. This embodiment explicitly introduces the physical degradation mechanism into the constraint system, overcoming the limitation of ignoring engineering aging in traditional scale demonstrations.

[0032] Furthermore, the degradation path can also be determined using the nonlinear self-feedback recursive method described in Example 3.

[0033] Step 104: Driven by the joint scenario set, the whole life cycle water balance simulation is carried out using the time-varying engineering capacity constraint system to obtain the whole life cycle water supply deficit matrix.

[0034] Water balance simulation refers to the time-period calculation of the dynamic transformation process between reservoir storage, inflow replenishment, and water release under given scheduling rules. In this embodiment, a joint scenario set is used as the external driving input, and the system is dynamically constrained by the engineering capacity at that time period. Accordingly, the actual water supply for each time period is taken as the smaller value between the instantaneous water supply capacity and the current available water volume, and the corresponding calculation formula is as follows:

[0035] V_ s_t_k =V _s_t_k -1+I _t_k -x _t_k -F _t_k ;

[0036] Among them, V _s_t_k Let I be the water storage at the end of the k-th period in year t. _t_k For the inflow of water under scenario-driven conditions, x _t_k F represents the actual water supply. _t_k This represents the amount of water lost. Under different scenarios, the life-cycle water supply deficit matrix records the water demand gap for each period. This embodiment demonstrates the robustness of the project scale in responding to relatively extreme climate events under degradation conditions through large-scale scenario-driven simulation.

[0037] Step 105: Based on the water supply deficit matrix and engineering design parameters, calculate a comprehensive evaluation index that includes the operational risks of the project. The operational risks are quantified based on a hierarchical driving mechanism of planning decision variables and operational decision variables.

[0038] In this embodiment, the hierarchical driving mechanism decomposes risk into supply shortage risk and scale redundancy risk. Supply shortage risk is driven by operational decision variables, reflecting water loss due to insufficient water supply or limited capacity. Scale redundancy risk is driven by engineering scale variables, reflecting efficiency losses when engineering capacity exceeds actual demand; the corresponding calculation formula is:

[0039] R(s,x)=R _short (s,x)+R _red (s);

[0040] Where R(s,x) represents the project operation risk, R _short (s,x) represents the risk of insufficient supply, R _red (s) represents the risk of scale redundancy.

[0041] To address the issue in traditional models where redundant penalty terms are easily avoided by the running variables during optimization, this embodiment uses a hierarchical quantification method to correct this, ensuring that the economic penalty is truly effective even with large-scale projects. In addition, the comprehensive evaluation indicators also include the present value of construction investment and operation and maintenance costs, which are determined by the project scale.

[0042] Step 106: Based on the comprehensive evaluation indicators, output the recommended project scale.

[0043] In this embodiment, the process of outputting the recommended project scale is a process of solving the objective function. That is, it involves searching for the scale point that maximizes the overall net benefit within the candidate scale range to determine the optimal construction plan. The overall net benefit is defined as the total benefit minus the total cost and total risk. The output includes the optimal single scale value, as well as the sensitivity curves of each evaluation sub-item as a function of scale.

[0044] In some alternative implementations, the output can be further extended to a reasonable scale range. For example, a candidate scale range that meets both safety and economic requirements can be determined based on a dual threshold criterion of economic performance degradation rate and acceptable risk upper limit. Accordingly, the final implementation scale can be selected within this range according to specific engineering environments or preferences, thereby enhancing the adaptability of the planning results.

[0045] Example 2

[0046] This embodiment achieves synergistic equilibrium optimization of scale-based solutions by uniformly quantifying economic costs, social benefits, and uncertainty risks. One possible implementation includes the following steps:

[0047] Step 201: Obtain historical hydrological data, historical water demand data, engineering design parameters, and pre-stored engineering degradation characteristic parameters.

[0048] Historical hydrological data refers to long-term runoff observation data of the study area that has undergone quality control and standardization, reflecting the natural endowment and fluctuation characteristics of local water resources. Historical water demand data includes historical statistical data on urban domestic water use, industrial production water use, and ecological environment water use. Engineering design parameters are the structural characteristic parameters of the proposed project, such as the characteristic water level-capacity curve of a reservoir and the rated flow capacity of a pumping station. Pre-stored engineering degradation characteristic parameters refer to empirical model parameters pre-constructed based on historical operating data of similar projects, used to describe the rate of annual decline in engineering capacity due to physical environmental influences. In the process of acquiring the above data, this embodiment performs data integrity checks, and imputs missing values ​​in the runoff sequence by cross-checking with neighboring stations, ensuring that the basic dataset input to the model is statistically complete and accurate.

[0049] Step 202: Based on historical hydrological data and historical water demand data, construct a joint scenario set that includes future water inflow scenarios and water demand scenarios.

[0050] In this embodiment, the joint scenario set is constructed using a random scenario generation method. Specifically, the marginal probability distribution of water inflow is fitted using historical hydrological data. Based on historical water demand data and a preset demand growth rate, the water demand distribution for each planning level year is fitted. On this basis, a connection function is used to characterize the dependency structure between water inflow and water demand, establishing a joint probability model of water inflow and water demand. Based on this model, a Latin hypercube sampling method is used to generate multiple equally probable synthetic sequences, each covering the entire process from the first year of planning to the last year of service.

[0051] For example, for projects with a planning period of 50 years, the generated joint scenario set contains a large number of simulated samples that can reflect the alternating characteristics of high water season, normal water season and continuous dry season, providing a comprehensive environmental background for subsequent assessment of the scale's performance under different hydrological frequencies.

[0052] Step 203: Based on the engineering design parameters and degradation characteristic parameters, establish a time-varying engineering capability constraint system, and define the engineering capability as a time-varying function that evolves with the service life.

[0053] In traditional scale justification, engineering capacity is typically treated as a constant design value. In contrast, the time-varying engineering capacity constraint system describes engineering capacity as a function of time. That is, based on degradation characteristic parameters, the engineering capacity is updated in each operating year t according to its state in the previous year, and the corresponding calculation formula is:

[0054] g(s,t)=g(s,0)×(1-ρ _deg ×t);

[0055] Where g(s,t) is the engineering storage capacity in year t, g(s,0) is the initial design storage capacity determined by the project scale s, and ρ _deg t represents the preset average annual capacity degradation rate, and t represents the number of years of operation.

[0056] It is understood that in this embodiment, the resource boundary available for allocation by the engineering system shrinks year by year throughout its entire life cycle, avoiding overestimation of the long-term water supply reliability.

[0057] Step 204: Driven by the joint scenario set, the whole life cycle water balance simulation is carried out using the time-varying engineering capacity constraint system to obtain the whole life cycle water supply deficit matrix.

[0058] During the water balance simulation, for each scenario in the joint scenario set, water balance calculations are performed time-by-time according to a set time step. Within each time period, the system prioritizes meeting the current water demand, while being constrained by the time-varying engineering capacity of the year, including time-varying water storage limits and time-varying water delivery flow restrictions. If the available water volume for a certain scenario cannot meet the water demand target within a preset time period, a water supply deficit occurs, and the corresponding calculation formula is as follows:

[0059] ξ(s,t,ω,k)=d(t,k)-q _sup (s,t,ω,k);

[0060] Where ξ(s,t,ω,k) represents the deficit in the k-th period of year t under scenario ω with scale s, d(t,k) represents the water demand in that period, and q _sup (s,t,ω,k) represents the actual water supply constrained by time-varying engineering capacity. By traversing various scenarios and time periods, a life-cycle water supply deficit matrix is ​​generated. This matrix can quantitatively capture the risk effects of engineering capacity degradation and the superposition of extreme weather events, and can then be used for subsequent risk indicator calculations.

[0061] Step 205: Based on the water supply deficit matrix and engineering design parameters, calculate a comprehensive evaluation index that includes engineering operation risks, where the operation risks are quantified based on a hierarchical driving mechanism of planning decision variables and operation decision variables.

[0062] In this embodiment, the calculation process of the comprehensive evaluation index includes benefit monetization, cost aggregation, and risk cost quantification, and the corresponding calculation formula is as follows:

[0063] B(s,x)=∑(α _k ×B _k (s,x));

[0064] Where B(s,x) represents the overall project benefit, and α _k B is the dimensionless weighting coefficient for the k-th type of benefit. _k (s,x) represents the k-th category of benefit sub-items converted to monetary units, and ∑ represents the summation operation. Benefit sub-items include water supply benefits, power generation benefits, etc. Water supply benefits can be determined by multiplying the unit water supply value by the actual water supply volume.

[0065] C(s,x)=C _cap (s)+∑(Δ _t ×(C _fix (s)+C _var (x,t)));

[0066] Where C(s,x) is the total lifecycle cost, C _cap (s) represents the one-time construction investment dependent on the project scale s, Δ _t C is the discount factor. _fix (s) represents the fixed operating costs related to scale, C _var (x,t) represents the variable costs related to the amount of operation.

[0067] R(s,x)=R _short (s,x)+R _red (s);

[0068] Where R(s,x) represents the engineering operation risk determined by the hierarchical driving mechanism, R _short (s,x) represents the supply shortage risk driven by operational decision variables, R _red (s) represents the scale redundancy risk directly driven by the project scale variable. This decoupled calculation allows for the explicit measurement of both the efficiency loss caused by a large scale and the service gap caused by an excessively small scale.

[0069] Step 206: Based on the comprehensive evaluation indicators, output the recommended project scale.

[0070] In this embodiment, the recommended scale can be determined by solving for the optimal value of the comprehensive evaluation index. Specifically, a model is constructed with the objective of maximizing the overall net benefit:

[0071] Z(s) = B(s,x) - C(s,x) - R(s,x);

[0072] Where Z(s) represents the overall net benefit, B(s,x) represents the overall project benefit, C(s,x) represents the life-cycle cost, and R(s,x) represents the project operation risk. All evaluation indicators and their components are uniformly expressed in monetary units.

[0073] In some alternative implementations, the model behavior can also be diagnosed based on normalized examples.

[0074] Example 3

[0075] This embodiment further explains the process of establishing a time-varying engineering capacity constraint system. Specifically, by establishing a dynamic feedback relationship between sediment interception efficiency and remaining reservoir capacity, the degradation path of the water network engineering's regulation capacity throughout its entire life cycle is simulated. One possible implementation includes the following steps:

[0076] Step 301: Determine the initial engineering capability based on the engineering design parameters, and determine the degradation rate of the engineering capability based on the degradation characteristic parameters.

[0077] The engineering design parameters include the characteristic storage capacity curve of the proposed reservoir, the reservoir basin geometry, and the initial beneficial water level. Based on these engineering design parameters, the initial regulation and storage capacity is defined as a parameterized function of the construction scale variable 's', and the corresponding calculation formula is as follows:

[0078] V _0 (s)=γ×s k ;

[0079] Among them, V _0 (s) represents the initial design effective reservoir capacity, γ is the shape coefficient determined based on the reservoir basin topography, s is the construction scale decision variable, and k is the reservoir capacity scale index. The degradation rate in the degradation characteristic parameters reflects the expected level of effective reservoir capacity loss per unit time, which can be obtained through statistical analysis of historical siltation data of similar projects.

[0080] Furthermore, taking the initial engineering capacity as the starting point for recursion, the time-varying storage capacity sequence and time-varying water conveyance capacity sequence corresponding to each operating year within the planning period are calculated using the degradation rate; based on the time-varying storage capacity sequence and time-varying water conveyance capacity sequence, a time-varying engineering capacity constraint system is constructed.

[0081] Step 302: Obtain the historical siltation measurement sequence and inspection attenuation record corresponding to the project.

[0082] The historical sedimentation measurement sequence includes the results of all depth sounding sections in the reservoir area and the cumulative sedimentation amount estimated by the section method. Inspection attenuation records document data such as the surface erosion depth of hydraulic structures and the reduction in gate sealing performance. After obtaining the relevant data, the sliding window method was used to identify and remove abrupt changes in the data sequence, improving the reliability of the fitted benchmark data.

[0083] Step 303: Fit the reservoir capacity loss in the measured siltation sequence with the corresponding operating years to obtain the reservoir siltation rate parameter.

[0084] Specifically, regression analysis was used to correlate historical reservoir capacity loss with operating time. The reservoir siltation rate parameter was obtained through fitting, which includes the multi-year average annual sediment inflow L and the interception efficiency shape parameter κ.

[0085] Furthermore, the time-varying storage capacity sequence is determined through the following self-feedback recursive method:

[0086] Step 304: Based on the shape parameter of interception efficiency in the degradation characteristic parameters and the multi-year average annual water volume determined based on historical hydrological data, construct a nonlinear function of interception efficiency with respect to the remaining effective reservoir capacity.

[0087] In this embodiment, the nonlinear function is used to characterize the dynamic change of the reservoir's sediment interception capacity with the water storage regulation space, and the corresponding calculation formula is:

[0088] η(s,t)=1-(1 / (1+κ×(V _eff (s,t-1) / W)));

[0089] Where η(s,t) is the sediment interception efficiency in year t, κ is the shape parameter of the interception efficiency, and V _eff (s,t-1) represents the remaining effective reservoir capacity at the end of year t-1, and W represents the multi-year average annual water volume. This nonlinear function reflects the self-feedback characteristic of interception efficiency, that is, the siltation intensity in the current year is limited by the remaining space state caused by previous siltation.

[0090] Step 305: In any operating year within the planning period, calculate the sediment interception efficiency for the current year based on the remaining effective reservoir capacity at the end of the previous year and the nonlinear function.

[0091] In this embodiment, the calculation process is recursively applied year by year, starting from the first year of operation. In any given year *t*, the remaining effective reservoir capacity data from the previous year's end is read from memory. Using a nonlinear function, the sediment interception efficiency for that year is calculated based on the current remaining reservoir capacity ratio. Since the remaining effective reservoir capacity decreases monotonically with age, the interception efficiency also exhibits a corresponding evolutionary trend, thus constituting a path-dependent characteristic in the degradation path.

[0092] Step 306: Based on the multi-year average annual sediment transport in the sediment interception efficiency and degradation characteristic parameters, determine the annual sedimentation volume for the current year, and update the effective reservoir capacity at the end of the current year accordingly to obtain the time-varying regulation capacity sequence.

[0093] Specifically, the total siltation amount for the current year is the product of the amount of sand entering the reservoir and the interception efficiency, and the corresponding calculation formula is:

[0094] sed(s,t)=η(s,t)×L;

[0095] Where sed(s,t) is the annual sedimentation volume in year t; L is the multi-year average annual sediment inflow, in units of volume / year.

[0096] Next, update the current effective storage capacity status. The corresponding calculation formula is:

[0097] V _eff (s,t)=V _eff (s,t-1)-sed(s,t) / (1-p _pore );

[0098] Among them, V _eff (s,t) represents the updated remaining effective storage capacity at the end of year t, p _pore This is the preset porosity of the sediment. In this embodiment, by repeatedly executing the above steps until the end of the planning period, a complete time-varying storage capacity sequence can be obtained. When the calculated V... _eff When (s,t) is less than or equal to zero, it is truncated to zero, and the interception efficiency of subsequent years is set to zero.

[0099] In some alternative implementations, the range of shape parameters is adjusted for different reservoir basin shapes to adapt to canyon-type or plain-type reservoir projects. The annual sediment load can also be set as a distribution function with annual random fluctuations to more realistically reflect the impact of flood pulses on the sedimentation process.

[0100] Example 4

[0101] This embodiment analyzes the physical evolution of roughness increase and cross-sectional area reduction to establish a dynamic decay model of the water conveyance system's capacity throughout its entire life cycle. In some optional implementations, the following steps are specifically included:

[0102] Step 401: Parametric modeling of the evolution characteristics of water conservancy indicators in the inspection attenuation record is performed to obtain the water conveyance attenuation rate parameter.

[0103] Specifically, the inspection attenuation records include data from periodic physical surveys of long-distance water conveyance tunnels or pipelines, such as records of pipe wall erosion depth, scale thickness measurements, and biofouling statistics. In this embodiment, feature extraction is performed on these unstructured records to identify key physical indicators reflecting increased water conveyance resistance and shrinkage of the flow space. Parametric modeling refers to using nonlinear regression methods to correlate these indicators with the years of operation to determine the attenuation dynamic parameters of the water conveyance system. The water conveyance attenuation rate parameters include the roughness growth coefficient λ and the cross-sectional linear reduction slope θ. This embodiment, through the parameterization of measured records, enables the model to reflect the evolution of engineering performance under a pre-defined engineering environment.

[0104] Furthermore, the reservoir siltation rate parameter and the water conveyance attenuation rate parameter are encapsulated as degradation characteristic parameters.

[0105] As one possible implementation, the time-varying water conveyance capacity sequence is determined through the following multi-mechanism coupling method:

[0106] Step 402: Based on the water conveyance attenuation rate parameter in the degradation characteristic parameters, construct the roughness equation that increases saturatedly with the years of operation and the effective flow cross-section reduction equation that decreases linearly with the years of operation.

[0107] In water conveyance systems, increased resistance typically originates from pipe wall corrosion or biofouling. This process increases rapidly in the initial stages of operation and then tends to stabilize later. Therefore, the roughness equation is described using a saturated growth model, and the corresponding calculation formula is:

[0108] n(t) = n _0 +(n _max -n _0 )×(1-exp(-λ×t));

[0109] Where n(t) is the roughness coefficient in year t, n _0 Let n be the initial design roughness. _max λ is the preset upper limit of saturated roughness, t is the roughness growth coefficient, and t is the number of years of operation.

[0110] Correspondingly, due to sediment deposition or scale buildup, the flow cross-section undergoes physical geometric shrinkage. Therefore, a linear model is used to describe the effective flow cross-section reduction equation, and the corresponding calculation formula is:

[0111] A(t) = A _0 ×(1-θ×t);

[0112] Where A(t) is the effective cross-sectional area of ​​the flow in the t-th year of operation, A _0 Let θ be the initial design cross-sectional area, and θ be the slope of the linear reduction of the cross-section. That is, we construct the roughness equation and the cross-sectional equation respectively, and fully characterize the attenuation mechanism from two directions: the increase of drag and the reduction of space.

[0113] Step 403: In any operating year within the planning period, use the roughness equation to determine the roughness of the current year, and use the cross-sectional reduction equation to determine the effective flow cross-sectional area and corresponding hydraulic radius of the current year.

[0114] Specifically, the hydraulic radius is dynamically updated based on the geometric relationship of the effective flow section, and the corresponding calculation formula is as follows:

[0115] R _h (t)=A(t) / P(t);

[0116] Among them, R _hLet A(t) be the hydraulic radius in year t, A(t) be the effective cross-sectional area in year t, and P(t) be the wetted perimeter in year t. During the reduction of the cross-sectional area, the wetted perimeter P(t) typically changes. For example, for a circular cross-section pipe, as the sediment thickness increases, the effective flow shape gradually evolves from a circle to a partially circular shape. Based on this, the system automatically calculates the corresponding hydraulic radius according to the current geometric parameters.

[0117] Step 404: The Manning formula is used to perform coupled calculations on roughness, effective cross-sectional area and hydraulic radius to obtain a time-varying water conveyance capacity sequence.

[0118] The time-varying water conveyance capacity sequence records the maximum flow capacity corresponding to each operating year. In this embodiment, multiple attenuation mechanisms are physically coupled using the Manning formula, and the corresponding calculation formula is as follows:

[0119] Q _max (s,t)=(1 / n(t))×A(t)×(R _h (t) 2 / 3 )×sqrt(J);

[0120] Among them, Q _max (s,t) represents the maximum water conveyance capacity in year t when the construction scale is s, n(t) represents the roughness coefficient in year t, A(t) represents the effective cross-sectional area in year t, and R _h (t) represents the hydraulic radius in year t, J represents the hydraulic gradient designed for the project, sqrt represents the square root operation, and the exponent 2 / 3 is the inherent exponent of the Manning formula. This formula can be understood as quantifying the multiplicative amplification effect of roughness increase and cross-sectional reduction on flow reduction. Since n(t) is in the denominator and A(t) is in the numerator, the simultaneous deterioration of both factors will lead to a decrease in the water conveyance capacity Q. _max The trend is accelerating. Through this multi-mechanism coupling, it is possible to assess whether the project can still meet the design water delivery target in the later stages of its service life.

[0121] In some alternative implementations, different cross-sectional shape models can be used for different types of water conveyance structures. For example, for rectangular open channels, the nonlinear changes in the flow cross-sectional area and wetted perimeter can be automatically calculated based on the siltation height. Furthermore, for projects with multi-stage pumping stations, the effective hydraulic gradient can be dynamically corrected based on the real-time head characteristics of each pump, thereby realistically simulating the water conveyance degradation behavior of complex water network systems.

[0122] Furthermore, the water conveyance attenuation rate parameter can be adjusted according to the water hardness or pH of the planned area to adapt to the corrosive environment of different regions.

[0123] Example 5

[0124] This embodiment establishes the physical coupling relationship between reservoir siltation and uplift and the hydraulic gradient of the water conveyance system, and performs cross-mechanism correction on the water conveyance capacity throughout its entire life cycle. When the siltation surface is much lower than the intake sill elevation and the reservoir water level fluctuation is small, in one possible implementation, after obtaining the time-varying water conveyance capacity sequence, the step of performing regulation-transfer interactive feedback correction on the time-varying water conveyance capacity sequence is also included.

[0125] Step 501: Extract the cumulative siltation amount for each year within the planning period from the time-varying regulation capacity sequence, and convert the cumulative siltation amount into the siltation surface rise height at the reservoir intake in the corresponding year based on the pre-stored reservoir topographic feature parameters.

[0126] Specifically, the time-varying storage capacity sequence records the annual loss of effective storage capacity due to sediment interception. In year t of operation, the difference between the initial design effective storage capacity and the current remaining effective storage capacity is calculated to determine the total cumulative sedimentation for that year. The sedimentation surface uplift height refers to the vertical distance by which the reservoir bottom elevation rises after sediment accumulates at the bottom. In this embodiment, based on the reservoir area's topographical features, the total cumulative sedimentation is converted into the vertical uplift. For example, in a plain reservoir, assuming that sediment is uniformly distributed within the beneficial storage capacity area, the uplift height is determined by dividing the cumulative sedimentation by the average water storage area of ​​the reservoir. The corresponding calculation formula is:

[0127] Δh(s,t)=V _silt (s,t) / A _mean ;

[0128] Where Δh(s,t) is the height of the siltation surface uplift in year t when the construction scale is s, and V _silt (s,t) represents the cumulative sediment volume in year t, A _mean The average water storage area of ​​the reservoir is represented by this figure. This embodiment constructs the link in the physical evolution from the storage end to the water conveyance end, namely, sediment occupies the water storage space and changes the boundary conditions of hydraulic operation.

[0129] Step 502: Based on the height of the siltation surface rise and the pre-stored water conveyance line length, the initial hydraulic gradient in the engineering design parameters is corrected to obtain the effective hydraulic gradient for each year.

[0130] In gravity-fed or pressurized water conveyance systems, the driving force for water conveyance mainly comes from the potential energy difference between the intake and outlet. As the siltation surface at the intake rises, the effective depth of water flow at the intake decreases, or the proximity of the siltation layer to the intake leads to increased local head loss during water intake, reducing the effective hydraulic drive of the water conveyance line.

[0131] Initial hydraulic gradient refers to the head loss per unit length of a project in its initial state. In this embodiment, the initial gradient is corrected by subtracting from the siltation surface uplift height; the corresponding calculation formula is as follows:

[0132] J _eff (s,t)=J _0 -(Δh(s,t) / L _line );

[0133] Among them, J _eff (s,t) represents the corrected effective hydraulic gradient in year t, J _0 Let L be the initial design hydraulic gradient, Δh(s,t) be the height of the siltation surface rise at the intake, and L be the initial design hydraulic gradient. _line This represents the pre-stored total length of the water conveyance line. The corrected effective hydraulic gradient reflects the decrease in water conveyance dynamics due to the degradation of the upstream storage system. When J _eff When (s,t)≤0, the gravity flow function of the water conveyance system is deemed lost for that year, and the corresponding water conveyance capacity is set to zero.

[0134] Step 503: Substitute the effective hydraulic gradient back into the Manning formula to update the time-varying water conveyance capacity sequence, and obtain the time-varying water conveyance capacity sequence after interactive feedback correction.

[0135] In this embodiment, this step achieves multi-mechanism coupling of storage degradation and water conveyance degradation. In Embodiment 4, the time-varying water conveyance capacity considers the increase in pipeline roughness and cross-sectional reduction. Based on this, this embodiment superimposes the effect of decreased driving force. That is, by substituting the corrected effective hydraulic gradient back into the Manning formula, the final corrected flow rate is obtained, and the corresponding calculation formula is:

[0136] Q _final (s,t)=Q _max (s,t)×sqrt(J _eff (s,t) / J _0 );

[0137] Among them, Q _final (s,t) represents the actual water conveyance capacity in year t after interactive feedback correction, Q _max (s,t) represents the water conveyance capacity considering only the degradation of the pipeline itself, J _eff (s,t) represents the effective hydraulic gradient, J _0 This is the initial design hydraulic gradient.

[0138] It is understandable that, under certain circumstances, the reservoir may still have sufficient water storage, but due to siltation, the effective head at the intake is insufficient, preventing the water conveyance system from supplying water to the receiving area at the designed flow rate. This is because the increased resistance due to internal aging of the water conveyance pipeline, coupled with the decreased power due to siltation in the regulating reservoir, can lead to performance degradation, resulting in an actual water supply guarantee rate far lower than expected in the later stages of the project's service life. In some optional implementations, for pressurized water conveyance systems, the impact of the rise height on the gradient can be corrected based on the specific pump station characteristic curves. For example, when the inlet head decreases, the pump's operating point shifts, further reducing the flow rate. Under this condition, using pre-stored pump performance parameters, a nonlinear mapping of flow rate with respect to the inlet head is established, achieving precise flow rate correction. For multi-source water networks, siltation and degradation of one source may affect the water supply capacity of other sources through the network pressure distribution. This can be addressed using system-level topological dynamics equations for overall correction, reflecting the cascading failure characteristics of the water network system.

[0139] Furthermore, when the sedimentation surface exceeds the intake threshold, the primary controlling factor shifts to the direct compression of the flow cross-section by sediment. Consequently, the flow rate reduction caused by cross-sectional narrowing will be far greater than the effect of a reduction in head of equal value. Therefore, a threshold for sedimentation surface elevation is introduced. When the sedimentation surface exceeds the intake threshold, the submerged orifice flow formula is used, ensuring the model maintains physical fidelity throughout its entire lifecycle. The submerged orifice flow formula is an empirical formula in hydrology that can be selected by those skilled in the art.

[0140] Example 6

[0141] This implementation decomposes engineering risks into supply shortage risks driven by operational decision variables and scale redundancy risks driven by planning scale variables. Both types of risks are rooted in long-term statistical results of supply and demand balance throughout the entire life cycle. That is, the supply shortage risk is statistically lower than the water shortage and damage events that meet the guarantee rate target, and the scale redundancy risk is statistically higher than the excess capacity that meets the guarantee rate target. This enables a hierarchical measurement of risks at the operational and planning levels.

[0142] In one possible implementation, the risk of scale redundancy is calculated based on the engineering scale variables in the engineering design parameters and the demand in the joint scenario set, specifically including the following steps:

[0143] Step 601: Calculate the supply shortage risk based on the operational supply determined in the full life cycle water balance simulation. The supply shortage risk is driven by operational decision variables and is used to reflect the water supply service gap at the operational level. Calculate the scale redundancy risk based on the engineering design capacity determined by the engineering scale decision variables and the demand in the joint scenario set. The scale redundancy risk is driven by engineering scale decision variables and is used to reflect the capacity excess at the planning level.

[0144] In traditional models, redundancy penalties are often linked to actual water supply. The solver, in order to minimize this penalty, may artificially lower water supply decisions, leading to model failure. In this embodiment, the risk of insufficient supply is defined as the economic loss incurred when the actual water supply capacity cannot meet the water demand target. The corresponding calculation formula is as follows:

[0145] R _short (s,x)=∑ _ω p _ω ×∑ _t Δ _t ×L _s (d _t,ω -x _t,ω );

[0146] Among them, R _short (s,x) represents the risk of insufficient supply, p _ω Let Δ be the probability of scenario ω occurring. _t Let L be the discount factor for year t. _s For the supply shortage loss function, d _t,ω Let ω be the water demand in year t, and x be the water demand in scenario ω. _t,ω This represents the actual water supply volume driven by operational decision variables. In this embodiment, the expected value is essentially a discounted statistical representation of the depth, duration, and frequency of water shortages throughout the entire life cycle. It reflects the degree of disruption to the water supply guarantee rate under long-term scheduling and is a risk measure at the operational level.

[0147] Correspondingly, scale redundancy risk is defined as the efficiency loss and fixed cost waste that occurs when the design capacity corresponding to the scale of an engineering project exceeds the actual social demand. This risk is driven by engineering scale variables at the planning level. To avoid redundancy evaluation being affected by annual demand fluctuations, the redundancy risk in this embodiment is constructed based on long-series statistical expectations. The expected value is obtained by comparing the water demand series after safety reserve correction under each scenario year by year, thus obtaining a comprehensive statistical value reflecting capacity surplus throughout the entire life cycle. Through this hierarchical setting, the scale redundancy term becomes a monotonically increasing term with respect to the scale variable s, while the supply shortage term becomes a monotonically decreasing term with respect to the scale variable s. Together, they construct a stable extreme value structure in the objective function.

[0148] Furthermore, the loss function L _s The form of the loss function can be selected according to different engineering needs. For example, the loss function can be a linear function, and the corresponding calculation formula is:

[0149] L _s (Δq)=c _unit ×Δq;

[0150] Among them, L _s For losses due to insufficient supply, c _unitLet be the unit water shortage loss coefficient, and Δq be the water demand gap. This linear function is applicable to general water supply objectives that are not sensitive to the consequences of water shortage.

[0151] Furthermore, in a preferred embodiment, the loss function can be in the form of a convex function to characterize the marginal increasing characteristics of the nonlinear growth of loss as the degree of water shortage intensifies.

[0152] In complex schemes involving multi-objective water supply, the loss function can also take a piecewise linear form.

[0153] Step 602: Obtain the preset reasonable reserve capacity threshold β _0 , where 0≤β _0 <1; Calculate the difference between the engineering design capacity determined by the engineering scale variable and the demand after correction by a reasonable reserve capacity threshold; if the difference is greater than zero, the difference is mapped using a preset redundancy loss function to obtain the scale redundancy risk; if the difference is less than or equal to zero, the scale redundancy risk is zero.

[0154] A reasonable reserve capacity threshold is used to define the necessary safety margin in an engineering system. This threshold can be determined based on the importance level of the water-receiving area and the frequency of historical extreme events. Those skilled in the art can refer to the reserve capacity requirements in relevant water supply engineering safety specifications to set it. Water network projects typically need to retain a pre-set, over-construction scale to cope with emergencies; this scale should not be considered redundant. In this embodiment, when the engineering design capacity exceeds β... _0 When the revised demand ceiling is applied, redundancy risk is factored in, and the corresponding calculation formula is:

[0155] R _red (s)=∑ _ω p _ω ×∑ _t Δ _t ×H(Q _des (s)-(1+β _0 )×d _t,ω );

[0156] Among them, R _red (s) represents the risk of scale redundancy, p _ω Let Δ be the probability. _t Here, H is the discount factor, H is the preset redundancy loss function, and Q is the redundancy loss function. _des (s) represents the engineering design water supply capacity determined by the scale variable s, β _0 d is the preset reasonable reserve capacity threshold. _t,ωLet ω represent the water demand in year t. Based on this, the formula describes the statistical loss of excess capacity over the entire life cycle, using the expected value of a long series of water demand scenarios. β0 essentially anchors the redundancy assessment benchmark to the water demand level corresponding to the design water supply guarantee rate. When β0 is determined based on the water demand frequency analysis of the guarantee rate, only surplus capacity exceeding the safety-added demand under the corresponding guarantee rate is included in the redundancy. This avoids misjudging short-term excess capacity caused by natural demand troughs during the wet season as structural waste, ensuring that redundancy risk accurately reflects the long-term excess consequences at the planning level.

[0157] This embodiment introduces a reasonable reserve capacity threshold, enabling the optimization model to retain necessary engineering safety redundancy while pursuing compactness, thus achieving a balance between economic efficiency and water supply security.

[0158] In some alternative solutions, the redundancy loss function H can be a linear function or dynamically adjusted in conjunction with the specific payback period.

[0159] Example 7

[0160] This embodiment utilizes Conditional Value at Risk (VaR) to measure the extreme deficit risk in the later stages of degradation and reveals the interactive amplification effect between water storage degradation and water conveyance degradation through factor isolation analysis. In one possible implementation, operational risk is measured based on VaR when calculating the comprehensive evaluation index, specifically including the following steps:

[0161] Step 701: Based on the preset tail probability level, sort the deficit samples in the water deficit matrix according to the size of the loss, determine the risk value of the corresponding tail probability level, and identify extreme deficit samples that exceed the conditional risk value from the water deficit matrix; calculate the conditional expected loss of the extreme deficit samples to obtain the conditional value of risk.

[0162] Specifically, the water supply deficit matrix records the distribution of deficit under different combinations of water inflow and demand scenarios. Since the safety indicators of water conservancy projects usually focus on more extreme and unfavorable situations, traditional expected value indicators are prone to submerging small-probability large-scale losses in the large-probability minor deficits, leading to an underestimation of risk.

[0163] In this embodiment, the tail probability level α is used to define the severity of the risk assessment, and α can be determined according to the water supply safety level of the water-receiving area. The deficit samples under a preset scale are sorted in descending order of loss magnitude to identify the deficit data corresponding to the probability interval. This data constitutes the extreme deficit samples, and the corresponding calculation formula is as follows:

[0164] CVaR _α =(1 / α)×∑ _ω∈Ωtail p _ω ×L(ω);

[0165] Among them, CVaR _α Let α be the conditional value at risk, Ωtail be the set of extreme scenarios exceeding the risk value, and p be the conditional value at risk. _ω Let L(ω) be the probability of scenario ω occurring, and L(ω) be the deficit loss under that scenario. In other words, by focusing on tail risks, we can capture the potentially catastrophic deficits that water network projects may face under degradation conditions, thereby determining a reasonable initial scale.

[0166] Step 702: Based on the ratio of the engineering capacity value corresponding to each operating year to the initial engineering capacity value in the time-varying engineering capacity constraint system, calculate the comprehensive degradation intensity corresponding to each operating year; divide the planning period into several degradation stages according to the comprehensive degradation intensity, and reorganize the water supply deficit matrix according to the degradation stages to obtain the condition deficit sample set corresponding to each degradation stage; calculate the conditional risk value CVaR under each condition deficit sample set to obtain the staged tail risk index set that evolves with the degradation stage.

[0167] Because engineering performance dynamically declines over the years, risks are not evenly distributed throughout the entire life cycle. The comprehensive degradation intensity refers to the rate of loss of system regulation capacity caused by both reservoir siltation and water conveyance reduction.

[0168] Specifically, the comprehensive degradation intensity is obtained by weighted summation of the relative degradation intensity of water storage and the relative degradation intensity of water conveyance. The corresponding calculation formula is as follows:

[0169] ρ _total (s,t)=ω _V ×φ _V (s,t)+ω _Q ×ρ _Q (s,t);

[0170] φ _V (s,t)=1-V _eff (s,t) / V _0 (s);

[0171] ρ _Q (s,t)=1-Q _final (s,t) / Q _max (s,0);

[0172] Where, φ _V (s,t) represents the relative degradation intensity, ρ _Q (s,t) represents the relative degradation intensity of water transport, ω _V With ω _Q These are the preset weighting coefficients.

[0173] For example, based on the numerical range of the comprehensive degradation intensity, the entire planning period is divided into three stages: the initial operation phase, the middle operation phase, and the later operation phase. For each stage, deficit data under all scenarios within that time window are extracted to construct a conditional deficit sample set. The CVaR for each stage is calculated separately. The staged tail risk index set is used to present the evolutionary trend of risk accelerating with the aging of the project. The CVaR in the later operation phase will be higher than that in the initial phase, meaning that the shrinkage of the project's capacity leads to a decrease in its resilience to extreme drought.

[0174] Step 703: By isolating a single degradation mechanism, construct a first counterfactual scenario that only considers storage degradation, a second counterfactual scenario that only considers water conveyance degradation, and a baseline scenario with no degradation; perform water balance simulations under the first counterfactual scenario, the second counterfactual scenario, and the baseline scenario respectively, and calculate the conditional risk value under each scenario; based on the conditional risk value under each scenario, decompose the conditional risk value increment at each degradation stage into a storage degradation contribution component, a water conveyance degradation contribution component, and an interaction amplification term using a factor comparison method; based on the contribution components and the interaction amplification term, determine the main control risk factors of the project at different degradation stages.

[0175] In this embodiment, factor isolation is achieved by artificially freezing certain degradation parameters in the simulation model. Specifically, the baseline scenario assumes that the reservoir capacity and water flow rate remain unchanged at their initial design values; the first counterfactual scenario activates the reservoir sedimentation module, while maintaining the initial values ​​for water flow roughness and cross-section; the second counterfactual scenario activates the water flow attenuation module. The risk increment is decomposed by calculating the difference in CVaR under different scenarios, and the corresponding calculation formula is as follows:

[0176] ΔCVaR _total =ΔCVaR _storage +ΔCVaR _convey +R _inter ;

[0177] Wherein, ΔCVaR _total ΔCVaR represents the total risk increment. _storage ΔCVaR contributes to the degradation of storage capacity. _convey Contribution to water conveyance degradation, R _inter This refers to the interactive amplification factor. The interactive amplification factor reflects the additional risks arising from the combined effects of reduced storage capacity and insufficient water conveyance power. The identification results of the interactive amplification factor can serve as a priority basis for formulating later-stage dredging plans or pipeline renovation plans.

[0178] In some alternative implementations, differentiated α values ​​can be set for different levels of importance of the water-receiving areas. Furthermore, risk attribution analysis can be extended to include third-party attribution of demand fluctuations, that is, decomposing risk increments into contributions from capacity degradation and demand growth.

[0179] Example 8

[0180] In this embodiment, the step of outputting the recommended project scale involves constructing and solving an optimization model based on comprehensive evaluation indicators. The optimization model employs a two-stage stochastic programming framework for further explanation. One possible implementation includes the following steps:

[0181] Step 801: The first-stage decision variable is the project scale variable s, which is determined and cannot be changed before the uncertain scenario is realized.

[0182] In this embodiment, the first-stage decision is an early decision, typically completed during the feasibility study and preliminary design phases. The project scale variable *s* represents scale parameters in the water network project that have physical entity attributes and are difficult to adjust, such as the beneficial storage capacity between the dead water level and normal storage level of a reservoir, the installed capacity of pumping stations, and the inner diameter of water conveyance tunnels. The first-stage decision adopts the current decision, that is, determining a fixed scale in advance when the specific water inflow sequence and water demand fluctuations over the next few decades are difficult to predict. This scale decision will determine the initial construction investment of the project and serve as the physical boundary conditions for subsequent operational simulations.

[0183] Step 802: The decision variables for the second stage are the operational plans under various uncertain scenarios, including the operational supply and water storage for each time period, which are adaptively adjusted after the uncertain scenarios are realized.

[0184] The second-stage decision is a posterior decision, reflecting the system's response strategy after a pre-defined uncertain scenario occurs. The operational plan refers to the optimal scheduling plan executed for each independent scenario sample ω under the constraint of the scale s determined in the first stage. Within each computational period, the system adaptively determines the current reservoir storage and the operational supply to each water-receiving area based on the actual inflow scenario. For example, in a high-water scenario, the second-stage decision tends to increase water storage for later use; in a low-water scenario, it maximizes water supply efficiency by utilizing previously stored water. Based on the two-stage structure, the model can evaluate the adaptability of the current-scale plan s in dealing with various extreme scenarios, and the corresponding calculation formula is:

[0185] TC(s)=C _cap (s)+∑ _ω∈Ω p _ω ×Q(s,ω);

[0186] Where TC(s) is the total objective function value, C _cap (s) is the construction investment function when the scale of the first stage project is s, p _ω Let ω be the probability of occurrence of the uncertain scenario, and Q(s,ω) be the second-stage minimization cost function for scenario ω under the size constraint s.

[0187] In this embodiment, a Benders decomposition strategy based on an exact algorithm is used for solving the problem. That is, the original model is decomposed into a main problem containing variable 's' and several sub-problems for preset scenarios. The main problem generates candidate sizes. Under preset sizes, the sub-problems perform water balance simulations and calculate risks and deficit costs. If the feedback from the sub-problems indicates that the current size is insufficient to support operational requirements, a feasibility cut or optimality cut is generated and returned to the main problem. The main problem adjusts its size based on the feedback results and iterates again until the lower bound of the main problem and the overall upper bound of the sub-problems converge within a preset error tolerance range.

[0188] In an alternative approach, for complex water network scalability optimization problems involving highly nonlinear degradation constraints or discrete expansion characteristics, this embodiment also provides a heuristic algorithm-based solution, such as using a genetic algorithm (GA) or a particle swarm optimization (PsO) algorithm. This involves initializing a population containing multiple scalability schemes. For each individual in the population, the water balance simulation module is invoked in parallel to perform all scenario simulations in the second stage, calculating its overall fitness. By performing crossover, mutation, or velocity update operations, the population is guided to evolve towards high-net-worth areas.

[0189] In some alternative implementations, the solution strategy can also incorporate a massively parallel computing framework. Since the second-stage simulations of each scenario are completely independent, multi-core processors can be used to simultaneously execute time-by-time water balance recursions for thousands of scenarios, reducing computation time on large-scale scenario sets.

[0190] Furthermore, for complex water networks with multiple interconnected nodes, the sub-problems in the second stage can be solved by linear programming using the interior point method or the simplex method, so that the operational decisions can maximize the benefits of a single scenario while satisfying the constraints of water balance and flow upper limit.

[0191] Example 9

[0192] This embodiment expands the single optimal size solution into a reasonable size range with engineering adaptability by establishing a dual control boundary of economic performance and operational risk, and outputs the corresponding risk gradient matrix. In one possible implementation, the process of outputting the recommended engineering size specifically includes:

[0193] Step 901: Determine the optimal scale and its corresponding comprehensive evaluation index value and supply shortage risk based on the comprehensive evaluation index.

[0194] Optimal size s *This refers to the engineering construction scale point that maximizes the overall net benefit over the entire life cycle. In this embodiment, the peak coordinates of the overall net benefit curve are identified by performing an exhaustive search or gradient optimization algorithm on the candidate scale sequence. Because the decision-making process for the scale of water conservancy projects has significant uncertainties, a single optimal solution is insufficient to cope with complex future changes in boundary conditions.

[0195] Therefore, in determining the optimal size s * At the same time, record the corresponding maximum comprehensive net benefit value, as well as the life-cycle supply shortage risk under this scale, and use it as a benchmark for subsequently defining the boundaries of a reasonable range.

[0196] Step 902: Obtain the preset acceptable economic performance degradation rate ε and the upper limit threshold R for supply shortage risk. _allow .

[0197] Among them, the acceptable rate of decline in economic performance ε reflects the degree to which policymakers tolerate the loss of economic efficiency caused by deviations from the optimal scale. The upper limit threshold for supply shortage risk R... _allow This represents the bottom line of safety that the project needs to maintain, and this threshold is usually determined based on the importance level of the water-receiving area. These two parameters together constitute the horizontal economic constraints and vertical safety constraints on the scale of the project decision.

[0198] Step 903: Determine the set of sizes that meet the following dual threshold criteria: First, the comprehensive evaluation index value is not less than (1-ε) times the comprehensive evaluation index value corresponding to the optimal size; Second, the risk of insufficient supply does not exceed the upper limit threshold R. _allow .

[0199] In this embodiment, the system automatically performs dual verification for each candidate scale. Specifically, an economic performance verification is performed, calculating the ratio of the net benefit of the current scale to the optimal net benefit, and determining whether it is within a preset allowable attenuation range. The corresponding calculation formula is as follows:

[0200] Z _limit =Z _star ×(1-ε);

[0201] Among them, Z _limit To meet the lower limit of net benefit requirements for economic performance, Z _star The overall net benefit corresponding to the optimal scale is ε, which is the preset acceptable rate of decline in economic performance.

[0202] Next, an operational risk check is performed to determine whether the supply shortage risk at the current scale is below the safety threshold. The corresponding formula for this check is:

[0203] R _short (s)≤R _allow ;

[0204] Among them, R _short (s) represents the life-cycle supply shortage risk when the scale is s, R _allow This is a preset upper limit threshold for supply shortage risk. In this embodiment, a dual-threshold filtering mechanism is used to exclude schemes that are economically viable but have excessively high risks, or schemes that are safe but have high economic costs. As the scale *s* increases, the supply shortage risk decreases monotonically, and the net economic benefit shows a characteristic of first increasing and then decreasing. Therefore, the dual-threshold criterion is actually a segment of scale near the peak region of the benefit curve that ensures investment efficiency while meeting the safety bottom line.

[0205] Step 904: Define the boundary of the scale set as a reasonable engineering scale range and output it.

[0206] Specifically, the reasonable range of project scale is represented by [s] _min ,s _max The form ] s _min Typically determined by a risk ceiling threshold R _allow Locked in indicates the minimum construction size required to meet minimum security requirements; s _max It is usually locked by the economically acceptable rate of decline ε, which represents the maximum construction scale without causing excessive investment waste.

[0207] Building upon this, this embodiment also outputs a staged risk gradient matrix corresponding to a reasonable engineering scale range. The risk gradient matrix is ​​a two-dimensional data structure, where the row dimension represents different degradation stages and the column dimension represents different candidate scales within the range. Each element in the matrix stores the conditional value of risk (CVaR) for the corresponding scale at the corresponding degradation stage. By outputting this matrix, decision-makers can examine the risk evolution path of different scale schemes after long-term performance degradation.

[0208] In some optional implementations, the output also includes resilient decision-making recommendations. Furthermore, the system automatically identifies the most robust scaling point within the interval based on the risk gradient matrix. Furthermore, the reasonable interval can be adjusted based on future expansion possibilities; if conditions for future expansion are reserved, the current s can be appropriately lowered. _min .

[0209] In another specific embodiment, the dual threshold criterion can be fused using dynamic weighting. By constructing a penalty function for benefit decay and risk level, a single point that balances both objectives can be found as the final recommended value.

[0210] Example 10

[0211] This embodiment performs a stability assessment of the scale scheme. By simulating uncertainties and disturbances in key parameters, it determines the engineering robustness margin that can withstand environmental changes, ensuring that the recommended engineering scale has sufficient performance margin during actual operation. As one possible implementation, it specifically includes the following steps:

[0212] Step 1001: Based on the comprehensive evaluation indicators, output the recommended project scale.

[0213] Specifically, the process of outputting the recommended project scale includes sensitivity verification of the initially determined scale scheme. Due to the long service life of water network projects, the degradation parameters, hydrological parameters, and economic parameters input into the model often contain estimation errors, which may lead to deviations in the optimal scale decision. In this embodiment, key input parameters affecting the decision are identified, including reservoir siltation rate parameters, water conveyance attenuation rate parameters, multi-year average annual sediment inflow, water supply efficiency coefficient, and financial discount rate.

[0214] Furthermore, a preset range of numerical perturbation is applied to each key input parameter. For each parameter perturbation, the water balance simulation and scale optimization module is automatically invoked again to calculate the rate of change of the parameter with respect to the optimal scale. The corresponding calculation formula is as follows:

[0215] σ _j =abs((s _new -s _star ) / s _star ) / (ΔΦ _j / Φ _j );

[0216] Where, σ _j Let s be the sensitivity coefficient of the j-th parameter. _new s is the optimal size after parameter perturbation. _star The optimal size under the baseline parameters, ΔΦ _j Let Φ be the disturbance displacement of the j-th parameter. _j This is the baseline value for the parameter, and abs is the preset absolute value function.

[0217] Based on this, parameters are classified according to their sensitivity coefficients. If the sensitivity coefficient of a parameter is greater than a preset sensitivity threshold, it is classified as a highly sensitive parameter.

[0218] Furthermore, a robustness verification scenario under the most unfavorable conditions is constructed. This involves simultaneously setting all identified highly sensitive parameters to extreme perturbation values ​​in the unfavorable direction. For example, the degradation rate is set as the upper limit of the maximum perturbation, the future water volume as the lower limit of the minimum perturbation, and the water supply efficiency coefficient as the reduced lower value. Under this combination of unfavorable scenarios, scale optimization is performed again to obtain the optimal scale under the most unfavorable conditions. The corresponding calculation formula is:

[0219] Δs _robust =s _worst -s _star ;

[0220] Where, Δs _robust For robustness margin, s _worst This represents the optimal size under the most unfavorable conditions.

[0221] Accordingly, the recommended size is adjusted based on the robustness margin. If the robustness margin is within the preset engineering margin ratio, the initially determined optimal size is deemed to have satisfactory robustness. Otherwise, it is recommended to add a robustness margin to the initially optimal size to obtain the final recommended engineering size, in order to cope with the risk of complex parameter drift in the future and improve the robustness of the size decision throughout the entire life cycle.

[0222] In some alternative implementations, a multi-dimensional parameter response curve can be output, which shows the dynamic trajectory of the optimal size as it continuously changes with a preset highly sensitive parameter. For example, by plotting the curve of the optimal size as a function of the discount rate, decision-makers can determine whether the project size needs to be proactively adjusted under different macroeconomic expectations. For projects with multi-stage expansion potential, robustness margins can also serve as a guide for phased construction plans, allocating a portion of the margin to later expansion phases to reduce the sunk risk of initial investment.

[0223] In another specific embodiment, Monte Carlo simulation can be used instead of single-parameter perturbation. By setting a preset probability distribution function for all sensitive parameters, parallel computation is performed using a large number of randomly sampled parameter combinations to statistically obtain the probability density distribution of the optimal scale. The recommended project scale can be determined based on the upper limit of the confidence interval of the optimal scale distribution, thereby providing a more probabilistic and statistically significant risk protection for project decisions.

[0224] Example 11

[0225] This embodiment constructs a dimensionless relative degradation intensity index to achieve a horizontal comparison of the performance degradation degree of different construction scale schemes throughout their entire life cycle. One possible implementation includes the following steps:

[0226] Step 1101: Calculate the relative degradation intensity of water storage based on the ratio of the current year's effective storage capacity to the initial effective storage capacity; calculate the relative degradation intensity of water conveyance based on the ratio of the current year's maximum water conveyance flow to the initial maximum water conveyance flow; wherein, the relative degradation intensity of water storage and the relative degradation intensity of water conveyance are used to measure the severity of performance degradation under different construction scales when calculating operational risks.

[0227] Specifically, the relative degradation intensity of the reservoir is used to quantify the degree of erosion of its regulating capacity by sedimentation. In year t of operation, the remaining effective reservoir capacity for the current year is extracted and compared with the initial design capacity under this scale scheme. The corresponding calculation formula is as follows:

[0228] φ _V (s,t)=1-(V _eff (s,t) / V _0 (s));

[0229] Where, φ _V (s,t) represents the relative degradation intensity of water storage in year t when the construction scale is s, and V _eff (s,t) represents the remaining effective storage capacity in year t, V _0 (s) represents the initial design effective storage capacity.

[0230] Accordingly, the relative degradation intensity of water conveyance is used to quantify the loss of flow capacity caused by pipeline aging and cross-sectional shrinkage, and the corresponding calculation formula is:

[0231] ρ _Q (s,t)=1-(Q _final (s,t) / Q _max (s,0));

[0232] Where, ρ _Q (s,t) represents the relative degradation intensity of water conveyance in year t when the construction scale is s, and Q _final (s,t) represents the corrected actual water conveyance capacity in year t, Q _max (s,0) represents the initial design maximum water conveyance capacity.

[0233] Since the absolute value of the initial capacity q differs for different construction scales, directly comparing absolute losses cannot objectively reflect the vulnerability of smaller-scale projects to degradation. Therefore, a proportional strength index is used to identify which scaled projects will experience performance collapse in the later stages of operation. For example, under the same environmental conditions, smaller-scale projects have higher ρ... _V The growth curve of (q,t) is usually steeper than that of large-scale projects, reflecting that small-scale projects lose their regulatory capacity earlier in the later stages of degradation and are more likely to induce higher tail risks.

[0234] Furthermore, the relative degradation intensity of water storage and the relative degradation intensity of water conveyance are used as key intermediate parameters and passed to the operational risk calculation module. When calculating the staged conditional value of risk (CVaR), the deficit samples are weighted or classified using the two intensity indices, so that the risk assessment results can reflect the nonlinear impact of physical degradation depth on water supply security.

[0235] In some alternative implementations, the formula for calculating the overall degradation intensity is:

[0236] ρ _total (s,t)=ω _V ×φ _V (s,t)+ω _Q ×ρ _Q (s,t);

[0237] Where, ρ _total (s,t) represents the overall degradation intensity, ω _V With ω _Q ω are preset weighting coefficients, representing the contribution weights of water storage degradation and water conveyance degradation to system failure, respectively. In this embodiment, ω _V With ω _Q The value of can be determined based on the relative importance of the water storage and water transmission links in the engineering system to the reliability of water supply. Those skilled in the art can determine this by analyzing the marginal impact of the two types of capacity decline on the water supply guarantee rate during historical operation. By comprehensively assessing the degradation intensity, the system health throughout its entire lifecycle can be monitored in real time under a single indicator. When the comprehensive degradation intensity reaches a preset warning threshold, an early warning signal recommending major repairs or dredging operations can be automatically output, thus extending the functionality of the scale demonstration model to maintenance decision support during the engineering operation period.

[0238] Based on the above embodiments, this application also provides a cost-benefit-risk synergy water network engineering scale optimization system. The system includes a processor coupled to a memory. The memory stores instructions, which are executed by the processor to implement the methods described in the above method embodiments.

[0239] This application also provides an electronic device, including: one or more processors and a memory, wherein the one or more processors are coupled to the memory, the memory is used to store computer program code, the computer program code including computer instructions, and when the one or more processors execute the computer instructions, the electronic device executes the methods executed in the above-described method embodiments.

[0240] This application also provides a chip, including: a processor and a communication interface, wherein the processor calls a computer program or instruction through the communication interface to execute the methods executed in the above-described method embodiments.

[0241] This application also provides a computer program product, which, when run on a computer, executes the methods described in the above-described method embodiments.

[0242] This application also provides a computer-readable storage medium storing a computer program. When the computer program is run on a computer, the computer executes the methods described in the above-described method embodiments.

[0243] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for optimizing the scale of water network engineering projects through cost-benefit-risk synergy, characterized in that, include: Acquire historical hydrological data, historical water demand data, engineering design parameters, and pre-stored engineering degradation characteristic parameters; Based on historical hydrological data and historical water demand data, a joint scenario set is constructed that includes future water inflow scenarios and water demand scenarios; Based on engineering design parameters and degradation characteristic parameters, a time-varying engineering capability constraint system is established, and engineering capability is defined as a time-varying function that evolves with the service life. Driven by a joint scenario set, a full life-cycle water balance simulation is performed using a time-varying engineering capacity constraint system to obtain a full life-cycle water supply deficit matrix. Based on the water supply deficit matrix and engineering design parameters, a comprehensive evaluation index including engineering operation risk is calculated, where the operation risk is quantified based on a hierarchical driving mechanism of planning decision variables and operation decision variables. Based on comprehensive evaluation indicators, a recommended project scale is output.

2. The method according to claim 1, characterized in that, Establish a time-varying engineering capability constraint system, including: The initial engineering capability is determined based on the engineering design parameters, and the degradation rate of the engineering capability is determined based on the degradation characteristic parameters. Using the initial engineering capacity as the starting point for recursion, the time-varying storage capacity sequence and time-varying water conveyance capacity sequence corresponding to each operating year within the planning period are calculated using the degradation rate. A time-varying engineering capacity constraint system is constructed based on time-varying storage capacity sequence and time-varying water conveyance capacity sequence.

3. The method according to claim 2, characterized in that, The time-varying storage capacity sequence is determined through the following self-feedback recursive method: Based on the shape parameter of interception efficiency in the degradation characteristic parameters and the multi-year average annual water volume determined based on historical hydrological data, a nonlinear function of interception efficiency with respect to the remaining effective reservoir capacity is constructed. In any operating year within the planning period, the sediment interception efficiency for the current year is calculated based on the remaining effective reservoir capacity at the end of the previous year and the nonlinear function. Based on the multi-year average annual sediment transport in the parameters of sediment interception efficiency and degradation characteristics, the annual sedimentation volume of the current year is determined, and the effective reservoir capacity at the end of the current year is updated accordingly to obtain the time-varying regulation capacity sequence.

4. The method according to claim 2, characterized in that, Time-varying water conveyance capacity sequences are determined through the following multi-mechanism coupling method: Based on the water conveyance attenuation rate parameter in the degradation characteristic parameters, roughness equations that increase saturally with the number of years of operation and effective flow cross-section reduction equations that decrease linearly with the number of years of operation are constructed respectively. In any operating year within the planning period, the roughness of the current year is determined using the roughness equation, and the effective cross-sectional area and corresponding hydraulic radius of the current year are determined using the cross-sectional reduction equation. The Manning formula was used to perform coupled calculations on roughness, effective cross-sectional area and hydraulic radius to obtain a time-varying water conveyance capacity sequence.

5. The method according to claim 4, characterized in that, After obtaining the time-varying water conveyance capacity sequence, the process also includes a step of performing regulation-water conveyance interactive feedback correction on the time-varying water conveyance capacity sequence: The cumulative sedimentation volume for each year within the planning period is extracted from the time-varying regulation and storage capacity sequence, and the cumulative sedimentation volume is converted into the sedimentation surface uplift height at the reservoir intake in the corresponding year based on the reservoir topographic feature parameters. Based on the height of the siltation surface rise and the length of the water conveyance line, the initial hydraulic gradient in the engineering design parameters is corrected to obtain the effective hydraulic gradient for each year. By substituting the effective hydraulic gradient back into the Manning formula, the time-varying water conveyance capacity sequence is updated, resulting in a time-varying water conveyance capacity sequence corrected by interactive feedback.

6. The method according to claim 2, characterized in that, When calculating the time-varying storage capacity sequence and water conveyance capacity sequence corresponding to each operating year during the planning period, the following are also included: Calculate the relative degradation intensity of water storage based on the ratio of the current year's effective storage capacity to the initial effective storage capacity; Calculate the relative degradation intensity of water conveyance based on the ratio of the current year's maximum water conveyance to the initial maximum water conveyance; Among them, the relative degradation intensity of water storage and the relative degradation intensity of water conveyance are used to measure the severity of performance degradation under different construction scales when calculating operational risks.

7. The method according to claim 1, characterized in that, When calculating the comprehensive evaluation indicators, operational risk is measured based on conditional value of risk, specifically including: Based on the preset tail probability level, the deficit samples in the water supply deficit matrix are sorted according to the size of the loss, the risk value of the corresponding tail probability level is determined, and extreme deficit samples exceeding the conditional risk value are identified from the water supply deficit matrix; the conditional expected loss of the extreme deficit samples is calculated to obtain the conditional value of risk.

8. The method according to claim 1, characterized in that, Output recommended project size, including: Determine the optimal scale and its corresponding comprehensive evaluation index value and supply shortage risk based on the comprehensive evaluation index; obtain the preset acceptable economic performance decay rate ε and the upper limit threshold of supply shortage risk; determine the scale set that meets the following dual threshold criteria: first, the comprehensive evaluation index value is not less than (1-ε) times the comprehensive evaluation index value corresponding to the optimal scale; second, the supply shortage risk does not exceed the upper limit threshold; define the boundary of the scale set as the reasonable engineering scale range and output it.

9. The method according to claim 1, characterized in that, The degradation feature parameters are obtained in advance in the following way: Obtain the historical siltation measurement sequence and inspection attenuation records corresponding to the project; By fitting the reservoir capacity loss in the measured siltation sequence with the corresponding years of operation, the reservoir siltation rate parameter is obtained. The evolution characteristics of water conservancy indicators in the inspection attenuation records are parametrically modeled to obtain the water conveyance attenuation rate parameters. The reservoir siltation rate parameter and the water conveyance attenuation rate parameter are encapsulated as degradation characteristic parameters.

10. The method according to claim 1, characterized in that, In the step of outputting the recommended project scale, an optimization model is constructed and solved based on comprehensive evaluation indicators. The optimization model adopts a two-stage stochastic programming framework: The decision variable in the first stage is the project scale variable s, which is determined and cannot be changed before the uncertain scenario is realized; The decision variables for the second stage are the operational plans under various uncertain scenarios, including the operational supply and water storage for each time period, which are adaptively adjusted after the uncertain scenarios are realized.

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