Water-saving ship lock water level division method based on variable cross-section water-saving basin

Abstract

This invention discloses a method for classifying water levels in a water-saving lock based on a variable cross-section water-saving pool. The method includes: acquiring upstream and downstream water level information and lock chamber geometric parameters; constructing a physical model of the variable cross-section water-saving pool based on a preset number of pool levels, wherein the physical model includes a sequence of area ratios between each level of water-saving pool and the lock chamber, and the area ratio sequence allows at least some levels of water-saving pools to have unequal area ratios; calculating the graded head and operating water level of each level of water exchanged between each level of water-saving pool and the lock chamber based on the upstream and downstream water level information and the area ratio sequence; and determining and outputting the design parameters of each level of water-saving pool according to the operating water level. This invention reduces rock excavation and slope support costs in high-head lock applications in mountainous areas, improves robustness, and reduces safety risks.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering technology, and in particular to a method for classifying water levels in a water-saving lock based on a variable cross-section water-saving pool. Background Technology

[0002] As inland waterway shipping extends into mountainous and canyon areas, the demand for high-head ship locks is increasing. Water-saving ship locks, by incorporating multi-stage water-saving pools to recover and utilize the energy released from discharged water, are a key engineering measure to reduce operational water consumption and improve navigation efficiency. The rational determination of the number, area, and elevation of the water-saving pools (i.e., water stage division) directly determines the water-saving efficiency, flow pattern, and project investment scale of the ship lock, making it a crucial aspect of the design process.

[0003] Currently, conventional water-saving lock designs are mainly based on the assumption of equal cross-sections, that is, assuming that the horizontal area of ​​each level of water-saving pool is equal, and using the equal head method for parameter calculation accordingly. This design method is relatively mature in plain areas, and construction is relatively standardized. In practice, designers usually determine the number of levels based on the total design head and target water-saving rate, by referring to tables or using simplified formulas, and arrange each level of water-saving pool as a concrete structure with regular shape and uniform size.

[0004] However, strictly adhering to the constant cross-section design faces severe challenges in mountainous canyon sections with steep terrain and complex geology. Limited by V-shaped or U-shaped valley topography, excavation space at low elevations is extremely restricted, making it difficult to arrange large-area water-saving pools. Forced excavation would lead to a surge in slope support costs and ecological damage. Traditional deterministic design methods ignore uncertainties such as water level fluctuations, construction errors, and siltation, causing ideal parameters under design conditions to fail in actual operation. This can result in overflow accidents where small pools contain large amounts of water or suction problems where large pools pump out small amounts of water, threatening the structural safety and operational stability of the lock. Therefore, a robust non-constant cross-section water-saving lock design method that can adapt to complex terrain constraints is urgently needed.

[0005] The water-saving principle of a water-saving lock lies in the orderly exchange of water between the lock chamber and multiple levels of water-saving pools. These pools are typically arranged in layers along one or both sides of the lock chamber, from highest to lowest level. During water discharge, as ships sail downstream, the water level in the lock chamber must drop from the upstream level to the downstream level. Discharge proceeds in descending order: first, the valve between the lock chamber and the highest-level water-saving pool is opened, allowing water to flow from the lock chamber into the pool. Once the water levels are equal, the valve is closed, and water exchange continues with the next highest-level water-saving pools. Only after all pools are full is the remaining water discharged downstream. During filling, as ships sail upstream, filling proceeds in ascending order: first, the valve between the lowest-level water-saving pool and the lock chamber is opened, using water stored in the pool to replenish the lock chamber. Once the water levels in the pool and lock chamber are equal, the valve is closed, and higher-level pools are used to replenish the lock chamber. Any remaining water is supplied from upstream. The tiered exchange operation mode ensures that each passage through the gate only consumes the water volume corresponding to the last stage of exchange, rather than the water volume corresponding to the entire upstream and downstream water level difference, thus achieving water conservation. Summary of the Invention

[0006] The purpose of this invention is to provide a water-saving lock water level classification method based on a variable cross-section water-saving pool, in order to solve the above-mentioned problems existing in the prior art.

[0007] According to one aspect of this application, a method for classifying water-saving lock water levels based on a variable cross-section water-saving pool includes:

[0008] Obtain upstream and downstream water level information and lock chamber geometric parameters of the water-saving ship lock;

[0009] A physical model of a variable cross-section water-saving pool is constructed based on a preset number of water-saving pool levels. The physical model of the variable cross-section water-saving pool includes a sequence of area ratio relationships between each level of water-saving pool and the gate chamber, and the area ratio relationship sequence allows at least some levels of water-saving pools to have different area ratios.

[0010] Based on upstream water level information, downstream water level information and area ratio relationship sequence, calculate the graded head and operating water level of the water exchanged between each level of provincial water pool and gate chamber;

[0011] Based on the operating water levels at each level, determine and output the design parameters for each level of the provincial water tank;

[0012] Among them, the area ratio sequence is composed of the ratio of the area of ​​each level of provincial water tank to the area of ​​the gate chamber in the geometric parameters of the gate chamber;

[0013] In the physical model of the variable cross-section water-saving pool, the area ratio of each level of water-saving pool is not constant as the elevation of the water-saving pool changes, resulting in at least two levels of water-saving pools having different area ratio values.

[0014] Beneficial effects: This invention reduces rock excavation and slope support costs in the application of high-head ship locks in mountainous areas, improves robustness, and reduces safety risks. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the overall process of the water-saving lock water level classification method based on the variable cross-section water-saving pool provided in the embodiments of this application.

[0016] Figure 2 The constraint set provided in this application embodiment includes robust water-saving efficiency constraints, and is a flowchart illustrating the process of determining whether the calculated graded head and operating water level of each grade meet the constraint set.

[0017] Figure 3 This is a schematic diagram of the water-saving lock arrangement of the equal-section water-saving pool provided in the embodiments of this application.

[0018] Figure 4 This is a schematic diagram of the water-saving lock arrangement of the variable cross-section water-saving pool provided in the embodiments of this application. Detailed Implementation

[0019] 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 of the present invention. 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.

[0020] In this invention, unless otherwise stated, the following terms have the following meanings:

[0021] Water level classification refers to the design process of determining the number, volume, elevation arrangement, and water exchange parameters between the water-saving pools of each level in the water-saving lock and the lock chamber.

[0022] The graded head refers to the water level difference between the gate chamber and the single-stage water-saving pool before one water exchange is completed, denoted by the symbol H in this invention. w express.

[0023] The area ratio refers to the ratio of the horizontal projected area of ​​the water-saving pool to the effective water area of ​​the gate chamber. In this invention, the area ratio of the i-th level water-saving pool is denoted by the symbol k. i This indicates that when the water-saving pool has a non-uniform cross-section structure, the area ratio is taken as the ratio of the average projected area within the range of operating water level fluctuations to the area of ​​the gate chamber.

[0024] The working head of a water-saving tank refers to the change in water level within the tank during a single water exchange. In this invention, the working head of the i-th stage water-saving tank is denoted by the symbol H. iexpress.

[0025] Robust water-saving efficiency refers to the lower limit of water-saving efficiency calculated when the input parameters take the most unfavorable combination of boundary values. It is used to ensure that the actual operating efficiency is not lower than the design threshold. In this invention, it is represented by the symbol η. rob express.

[0026] The upper limit of the staged head refers to the maximum staged head value that may occur under the most unfavorable combination of operating conditions, denoted by the symbol H in this invention. w + express.

[0027] Example 1: A detailed explanation of the overall process of the water-saving lock water level classification method based on a variable cross-section water-saving pool, such as... Figure 1 As shown, this paper addresses how to overcome the limitations of traditional constant-section water-saving tank designs under complex terrain constraints. Through the synergistic optimization of physical structure and hydraulic calculations, the paper achieves an optimal balance between water-saving efficiency, earthwork excavation volume, and project investment.

[0028] Step 101: Obtain the upstream water level information, downstream water level information, and lock chamber geometric parameters of the water-saving lock.

[0029] In this embodiment, upstream and downstream water level information are the basic boundary conditions for water level classification. Specifically, upstream water level information can be represented as the maximum design navigable water level, the minimum design navigable water level, or the measured water level at a specific moment in the upstream channel; the same applies to downstream water level information.

[0030] In some basic implementations, the water level information described above can be considered as a deterministic scalar value, for example, an upstream design water level of 85.0 meters and a downstream design water level of 40.0 meters. In other, more complex implementations (such as those described in subsequent embodiments), the water level information may also be represented as a set of intervals containing statistical uncertainty to cover seasonal fluctuations or tidal changes in water levels.

[0031] The geometric parameters of the lock chamber mainly include its effective length, effective width, bottom elevation, and the draft of vessels designed to pass through. These parameters directly determine the volume of water that needs to be exchanged during a single filling and emptying process, and are crucial for determining the volume of the water-saving pool. Data can be obtained by reviewing the engineering feasibility study report, retrieving historical records from the waterway hydrological monitoring database, or directly receiving real-time measurement data transmitted by engineering surveying instruments.

[0032] Step 102: Construct a variable cross-section water-saving pool physical model based on the preset number of water-saving pool levels. The variable cross-section water-saving pool physical model includes a sequence of area ratio relationships between each level of water-saving pool and the gate chamber, and the area ratio relationship sequence allows at least some levels of water-saving pools to have different area ratios. The area ratio relationship sequence is determined based on the ratio of the area of ​​each level of water-saving pool to the area of ​​the gate chamber in the geometric parameters of the gate chamber.

[0033] The variable cross-section water-saving pool physical model is a mathematical abstraction of the actual water-saving lock engineering structure. Traditional water-saving lock designs typically assume that all water-saving pools have equal areas, i.e., a constant cross-section model, which is reasonable in flat terrain. However, in mountainous or canyon terrain, excavating large areas of flat ground is difficult and costly. The variable cross-section concept proposed in this step breaks the constraint that the areas of water-saving pools at all levels must be equal.

[0034] Specifically, the number of water-saving tank stages, m, is usually preset based on the total head difference and the target water-saving efficiency, for example, m=3 or 4. The area ratio sequence K consists of a set of ordered values ​​(k1,k2,...,k...). m Composed of, where k i A represents the horizontal projected area of ​​the i-th level water-saving pool. i With the effective water area A of the lock chamber c The ratio of the area of ​​the water-saving pools is allowed to be different for at least some levels, meaning that designers can flexibly adjust the size of each level of water-saving pool according to the distribution of topographic contour lines.

[0035] For example, in a V-shaped canyon terrain, the excavation face is narrower at lower elevations, allowing for a smaller area ratio, such as k1=1.2; while at higher elevations, the mountain body is wider, allowing for a larger area ratio, such as k m =4.5. The site-specific physical model construction method can significantly reduce the amount of rock excavation and slope support costs, while providing a physical basis for subsequent optimization of head distribution through hydraulic calculations.

[0036] Step 103: Based on upstream water level information, downstream water level information, and area ratio relationship sequence, calculate the graded head and operating water level of the water exchanged between each level of the provincial water reservoir and the gate chamber. The operating water level at each level is estimated from the graded head and upstream or downstream water level information.

[0037] The graded head calculated in this step is a predetermined hydraulic index, referring to the water level difference between the gate chamber and the water-saving pool, under the premise of satisfying the water exchange balance between the water-saving pools and the gate chambers at each level. Through this calculation, the system can automatically solve for the optimal head distribution scheme suitable for the current area ratio sequence K. The operating water levels at each level include the highest storage water level, the lowest discharge water level, and the intermediate equilibrium water level of each water-saving pool. The determination process of the above water levels follows the principle of communicating vessels and the law of volume conservation, ensuring that under the action of gravity, the water can flow smoothly between the gate chamber and the water-saving pools at each level in a preset order.

[0038] Step 104: Determine and output the design parameters of each level of water-saving tank based on the operating water level at each level.

[0039] Based on this, specific engineering design parameters can be derived from the calculated operating water levels at each level. Specifically, the bottom elevation of each level of water-saving tank is usually set as the lowest operating water level of that level minus a certain dead water depth (to accommodate sediment), while the top elevation is set as the highest operating water level plus a certain safety freeboard (to prevent wave overflow). In addition, key indicators such as the effective volume of each level of water-saving tank and the elevation of the water conveyance corridor can be further determined.

[0040] The design parameters will be output as engineering design drawings, parameter reports, or configuration files for digital twin models. The output can be displayed directly on a computer screen or generated as standard CAD files or BIM model data for construction units to perform on-site layout and construction. This complete process achieves a scientific transformation from basic hydrological data to specific engineering structures.

[0041] Example 2 elaborates on how to construct a mathematical and physical model of a variable cross-section water-saving tank under the premise that the water level and structural parameters are deterministic values, and derives its hydraulic control formula. This not only solves the technical difficulty of traditional constant cross-section design in adapting to complex terrain, but also proves the theoretical feasibility of variable cross-section design in maintaining high water-saving efficiency through rigorous mathematical derivation.

[0042] Step 201: The area ratio sequence is composed of the ratio of the area of ​​each level of water-saving pool to the area of ​​the gate chamber in the geometric parameters of the gate chamber. In the physical model of the variable cross-section water-saving pool, the area ratio of each level of water-saving pool exhibits a non-constant distribution as the elevation of the water-saving pool changes, resulting in at least two levels of water-saving pools having different area ratio values. The area of ​​each level of water-saving pool is a design value pre-set according to the engineering terrain conditions.

[0043] In this embodiment, the geometric characteristics of the variable cross-section physical model are further defined. The area ratio sequence K serves as a bridge connecting topographic constraints and hydraulic characteristics. Specifically, for a lock with an m-level water-saving pool, this sequence can be represented as K={k1,k2,...,k...} m} Wherein, the subscript 1 usually represents the lowest elevation of the first-level water-saving reservoir, and the subscript m represents the highest elevation of the first-level water-saving reservoir. k i The calculation formula is:

[0044] k i =A i / A c ;

[0045] Among them, A i Let A be the effective water surface area of ​​the i-th level water-saving pool. c This refers to the effective water surface area of ​​the gate chamber. In actual engineering calculations, if the inclination of the gate chamber sidewalls or the slope of the water-saving pool is taken into account, the above area is usually taken as the average area within the range of operating water level fluctuations.

[0046] A non-constant distribution means that the values ​​of each element in the sequence K are not all equal. This characteristic is to adapt to the terrain and geological conditions in actual engineering projects. For example, in typical V-shaped canyons or steep mountain slopes, the natural excavation width available for arranging water-saving ponds usually changes with increasing elevation. To reduce the enormous amount of engineering work and geological disaster risks caused by deep excavation and high filling, the preferred implementation is to design the area of ​​the water-saving pond to increase or decrease monotonically with elevation.

[0047] As a specific preferred implementation method, for canyon terrain that is wider at the top and narrower at the bottom, the area ratio sequence can be designed as an increasing sequence, i.e., k1 <k2<...<k m For example, setting k1=1.5, k2=2.0, and k3=3.0 indicates that the lower-level water-saving pools are smaller and embedded in the narrow space at the bottom of the valley; the upper-level water-saving pools are larger and utilize the open space above. This layout can best conform to the original terrain and reduce the amount of earthwork excavation. Conversely, if it is in an inverted trapezoidal artificial excavated channel, in order to maintain slope stability, a layout with a smaller top and a larger bottom may be adopted, in which case the area ratio sequence shows a decreasing trend.

[0048] Step 202: Both upstream and downstream water level information are constant values. In calculating the graded head and operating water level for each level of water exchange between the provincial water reservoir and the gate chamber, the graded head is calculated using the following formula:

[0049] H w =(z u -z d ) / (m+1-Σ i=1 m [1 / (k i +1)]);

[0050] Among them, H w For graded head, z u For upstream water level information, z d This provides downstream water level information, where m represents the number of stages in the provincial water reservoir, and k... i It represents the area ratio between the i-th level water-saving pool and the gate chamber in the area ratio relationship sequence.

[0051] To enable those skilled in the art to clearly understand the derivation process of the graded head formula, a detailed explanation is provided below in conjunction with the structure of a three-stage water-saving tank.

[0052] Let the effective water surface area of ​​the gate chamber be A. c The effective water surface area of ​​the i-th level water-saving pool is A. i The ratio of the area of ​​provincial water tanks to sluice gates at all levels is k. i , i.e., k i =A i / A cLet the water depth changes of each level of the provincial water reservoir during one water exchange be x1, x2, and x3, respectively. The final water depth discharged downstream during the gate chamber discharge process is x4, and the water depth from upstream during the filling process is also x4. The upstream water level is z. u The downstream water level is z d .

[0053] The analysis is based on the water balance conditions between the gate chamber and the primary-level water-saving pools during the gate chamber's discharge process. When water exchange occurs between the gate chamber and the primary-level water-saving pool, the height of the drop in water level in the gate chamber multiplied by the gate chamber's area should equal the height of the rise in water level in the primary-level water-saving pool multiplied by the primary-level water-saving pool's area. Since the water levels are equal at the end of the exchange, let the lowest water level in the primary-level water-saving pool be z. s1 Then we have:

[0054] z s1 =z u -x1-k1*x1=z u -(1+k1)*x1;

[0055] Among them, z s1 This refers to the lowest water level in the first-level provincial water reservoir, measured in meters; z u 1 represents the upstream water level in meters; x1 represents the water depth change of the first-stage water-saving pool in meters; k1 represents the area ratio of the first-stage water-saving pool to the gate chamber, dimensionless.

[0056] Similarly, the minimum water level of the secondary provincial water tank is:

[0057] z s2 =z s1 -(1+k2)*x2;

[0058] Among them, z s2 This refers to the lowest water level in the secondary provincial reservoir, measured in meters; z s1 x2 represents the minimum water level of the first-level water-saving pool, in meters; x2 represents the water depth variation of the second-level water-saving pool, in meters; k2 represents the area ratio of the second-level water-saving pool to the gate chamber, dimensionless.

[0059] The lowest water level in the Level III water-saving reservoir is:

[0060] z s3 =z s2 -(1+k3)*x3;

[0061] Among them, z s3 This is the lowest water level in the third-level provincial water reservoir, in meters; z s2 x3 represents the lowest water level of the secondary water-saving pool, in meters; x3 represents the water depth variation of the tertiary water-saving pool, in meters; k3 represents the area ratio of the tertiary water-saving pool to the gate chamber, dimensionless.

[0062] The relationship between the downstream water level and the lowest water level of the third-level provincial water reservoir is as follows:

[0063] z d =z s3 -x4;

[0064] Among them, z d This is the downstream water level, in meters; z s3 x4 represents the lowest water level in the third-level water-saving pool, in meters; x4 represents the water depth change between the gate chamber and the downstream area, in meters.

[0065] Solving the four equations simultaneously, we get:

[0066] (1+k1)*x1=(1+k2)*x2=(1+k3)*x3=x4;

[0067] Where k1, k2, and k3 are the area ratios of the first, second, and third level water-saving pools to the gate chamber, respectively, and are dimensionless; x1, x2, and x3 are the water depth changes of the first, second, and third level water-saving pools, respectively, in meters; and x4 is the water depth change between the gate chamber and the downstream area, in meters.

[0068] The above equation shows that regardless of whether the area ratios of the various levels of the water-saving pools are equal, the grading head between the water-saving pools and the gate chambers is the same. This grading head is defined as H. w Then we have:

[0069] H w =(1+k1)*x1=(1+k2)*x2=(1+k3)*x3=x4;

[0070] Among them, H w The unit for graded head is meters.

[0071] Based on the above equation, the formula for calculating the water depth changes of each level of water-saving pool can be derived:

[0072] x i =H w / (1+k i );

[0073] Where, x i H represents the water depth variation of the i-th level water-saving pool, in meters; w This refers to the graded head, measured in meters (k). i Let be the ratio of the area of ​​the i-th level water-saving pool to the area of ​​the gate chamber, which is dimensionless.

[0074] Expanding the total head difference between the upstream and downstream water levels, we have:

[0075] z u -z d =(1+k1)*x1+(1+k2)*x2+(1+k3)*x3+x4;

[0076] H w Substituting the expression into the above formula, for the case of a three-stage water-saving tank, we get:

[0077] z u -z d =H w +(k1 / (1+k1))*H w +(k2 / (1+k2))*H w +(k3 / (1+k3))*H w ;

[0078] After sorting, we get:

[0079] z u -z d =H w *(1+k1 / (1+k1)+k2 / (1+k2)+k3 / (1+k3));

[0080] Extending the formula above for a three-stage water-saving tank to the general case of an m-stage water-saving tank, we can obtain a general calculation formula for the graded head.

[0081] To verify the correctness of the above formula, we examine the special case of water-saving tanks with equal cross-sections. When all water-saving tanks have the same area, k1 = k2 = k m =k, at which point the above formula degenerates into:

[0082] H w =(z u -z d ) / (1+m*k / (k+1));

[0083] Further analysis reveals:

[0084] H w =(k+1)*(z u -z d ) / (m*k+k+1);

[0085] Among them, H w This refers to the graded head, measured in meters; z u This refers to the upstream water level, in meters; z d The downstream water level is in meters; m is the number of the water-saving pool level, taken as a positive integer; k is the area ratio of each water-saving pool to the gate chamber, dimensionless.

[0086] The above degradation results are completely consistent with the calculation results of the water level classification method for equal cross-section water-saving tanks in existing technical literature, which verifies the correctness of the graded head calculation formula for variable cross-section water-saving tanks proposed in this invention.

[0087] This embodiment details the physical meaning and derivation logic of the graded head calculation formula. Upstream water level information z u and downstream water level information z d This serves as a deterministic design boundary condition. For example, let z... u This is the normal water level upstream. d This represents the average navigable water level downstream.

[0088] To ensure smooth water exchange between the various levels of water-saving pools and sluice chambers, it is essential to guarantee that the head difference (i.e., driving force) is uniform and reasonable during each exchange process. Let H... w This is a graded head system. Based on the principle of communicating vessels and the law of volume conservation, when the water level in the gate chamber exchanges with the i-th stage water-saving pool, the exchanged water volume V... i Two conditions must be met: first, the water level change caused on the gate chamber side must be Δh. c Secondly, the water level change caused by the water level change on the provincial water tank side should eventually make the water levels of the two tanks equal.

[0089] Based on the above physical processes, a single-stage water balance equation can be established:

[0090] V i =A c *Δh c =A i *Δh i ;

[0091] Where, Δh i Let be the water level variation of the i-th level water-saving pool.

[0092] Because the water levels were level at the end of the exchange, and the water level in the gate chamber changed by Δh during the exchange process. c The water level in the provincial water tank changed by Δh i Based on geometric relationships, it can be deduced that:

[0093] Δh i =Δh c / k i ;

[0094] Gate chamber graded head H w =Δh i +Δh c =[(k i +1) / k i ]Δh c

[0095] The formula for calculating the volume of a single-stage exchange is obtained as follows:

[0096] V i =[k i / (k i +1)]*Ac *H w .

[0097] Considering the entire water filling or releasing process as a whole, the gate chamber is lowered from the downstream water level z. d Rising to upstream water level z u Total head H=z u -z d It consists of three parts:

[0098] (1) The remaining water head in the gate chamber itself, that is, the height of the water replenished to the upstream water level after the last stage of exchange, is equal to H. w ;

[0099] (2) The total effective head contributed by provincial reservoirs at all levels;

[0100] (3) Head loss during water exchange (usually ignored or included in the coefficient in theoretical derivation).

[0101] In an ideal situation, the total head H is equal to the sum of the water level rise caused by each stage of exchange.

[0102] The meanings of the symbols in the formula are as follows: H w This refers to the graded head, measured in meters; z u This is upstream water level information, in meters; z d This represents downstream water level information, in meters; m is the number of stages in the provincial water reservoir, taken as a positive integer; k i Let be the area ratio of the i-th level water-saving pool, which is dimensionless; Σ represents the summation of i from 1 to m.

[0103] This formula reveals the inherent operating principle of the variable cross-section water-saving lock: staged head H w It depends not only on the total head difference, but also on the specific area configuration of each level of water-saving pool. When all k i When the values ​​are equal, the formula automatically degenerates into the traditional calculation formula for water-saving locks with equal cross-sections, which indirectly verifies the universality and theoretical correctness of the formula.

[0104] Step 203, before determining and outputting the design parameters for each level of water-saving tank, also includes calculating the theoretical water-saving efficiency of the variable cross-section water-saving tank, specifically using the following formula:

[0105] η=1-1 / (1+Σ i=1 m [k i / (k i +1)]);

[0106] Where η is the theoretical water-saving efficiency, a decimal between 0 and 1, m is the number of water-saving tank stages, and k i It represents the area ratio between the i-th level water-saving pool and the gate chamber in the area ratio relationship sequence.

[0107] The theoretical water-saving efficiency can be output as part of the design parameters of water-saving tanks at all levels, or used to compare and verify with the preset target water-saving efficiency.

[0108] To enable those skilled in the art to clearly understand the derivation process of the water-saving efficiency formula, a detailed explanation is provided below.

[0109] Let the area of ​​the gate chamber be A. c The area of ​​the i-th level provincial water tank is A. i The ratio of the area of ​​the water tank to the area of ​​the sluice gate is k. i A i =k i *A c Let the working head of the gate chamber be z. u -z d The working head of a single-stage water-saving tank is H. i H i This indicates the range of change in the water level of the water-saving reservoir itself.

[0110] When the gate chamber discharges water into the water-saving pool, let the water level in the gate chamber drop by a height of H. i_star According to the principle of water balance:

[0111] A c *H i_star =A i *H i ;

[0112] Among them, A c H represents the area of ​​the gate chamber, in square meters. i_star The drop in water level in the sluice chamber is expressed in meters; A i H represents the area of ​​the i-th level water-saving pool, in square meters; i The working head of the i-th level water-saving tank is expressed in meters.

[0113] Because of A i =k i *A c Substituting into the above formula, we get:

[0114] H i_star =k i *H i ;

[0115] Among them, H i_star The drop in water level in the sluice chamber is expressed in meters; k i H represents the ratio of the area of ​​the i-th level water-saving pool to the area of ​​the gate chamber, which is dimensionless; i The working head of the i-th level water-saving tank is expressed in meters.

[0116] Furthermore, because the working head H of the water-saving tank iWith the drop in water level H in the gate chamber i_star The sum equals the staged head H between the gate chamber and the water-saving pool. w ,Right now:

[0117] H i +H i_star =H w ;

[0118] Among them, H i H represents the working head of the i-th level water-saving tank, in meters. i_star H represents the drop in water level in the sluice chamber, in meters. w The unit for graded head is meters.

[0119] H i_star =k i *H i Substituting into the above equation, we get:

[0120] H i =H w / (1+k i );

[0121] H i_star =k i *H w / (1+k i );

[0122] During the gate chamber filling process, only the water added to the gate chamber by the water-saving tank represents the actual water saving. The water-saving efficiency η of a single-stage water-saving tank... i The height H of the water level rise in the gate chamber i_star With graded head H w The ratio:

[0123] η i =H i_star / H w =k i / (1+k i );

[0124] Where, η i H represents the water-saving efficiency of the i-th stage water-saving pool, which is dimensionless; i_star H represents the drop in water level in the sluice chamber, in meters. w This refers to the graded head, measured in meters (k). i Let be the ratio of the area of ​​the i-th level water-saving pool to the area of ​​the gate chamber, which is dimensionless.

[0125] For a water-saving lock with m-level water-saving pools, the water-saving contributions of each level of pool are summed. Considering the proportion of head contributed by each level of pool in the total head difference, the overall water-saving efficiency of the multi-level pool system is:

[0126] η=Σ i=1m (k i / (1+k i ))*H w / (z u -z d );

[0127] The graded head formula H w =(z u -z d ) / (1+Σ i=1 m (k i / (k i Substituting +1))) into the above formula and rearranging it, we can obtain the theoretical water-saving efficiency calculation formula for the variable cross-section water-saving tank.

[0128] To verify the correctness of the above formula, we examine a special case of water-saving tanks with equal cross-sections. When all water-saving tanks have the same area, k1 = k2 = k m =k, at which point the above formula degenerates into:

[0129] η = 1 - 1 / (1 + m * k / (k + 1));

[0130] Further analysis reveals:

[0131] η = m*k / (m*k+k+1);

[0132] Where η is the theoretical water-saving efficiency, dimensionless; m is the number of water-saving pool stages, taking a positive integer; and k is the area ratio of each water-saving pool to the gate chamber, dimensionless.

[0133] The above degradation results are completely consistent with the calculation results of water-saving efficiency of constant cross-section water-saving tanks in existing technical literature, verifying the correctness of the water-saving efficiency calculation formula of variable cross-section water-saving tanks proposed in this invention.

[0134] This step further provides an important indicator for evaluating the merits of variable cross-section design schemes – water-saving efficiency η. Water-saving efficiency is defined as the ratio of the amount of water saved by using a water-saving pool to the total amount of water required without using a water-saving pool (i.e., discharging all the water in the gate chamber downstream at once).

[0135] Using the relationship derived in step 202, the amount of water that needs to be replenished (or discharged) from upstream during a single gate passage corresponds only to the head section of the last replenishment (or the first discharge), and its height is exactly H. w Actual water consumption V cost =A c *H w The total water consumption V without a water-saving tank. total =A c *(z u -z d ).

[0136] H w Substituting the expression into the efficiency definition η=1-(V cost / V total )=1-(H w / (z u -z d After algebraic transformation, the above characteristic formula can be obtained.

[0137] This formula demonstrates that, given a fixed series m, water-saving efficiency can be fine-tuned by adjusting the area ratio sequence K. It proves that even if the areas of the water-saving pools at each stage are unequal (to adapt to the terrain), a high water-saving efficiency can still be maintained, and even improved by optimizing k, as long as the hydraulic design rules of this embodiment are followed. i Combining different approaches, such as increasing the area ratio of the high-head section, can achieve better overall benefits than the uniform cross-section design under certain specific working conditions. This provides solid theoretical support for constructing high-head, water-saving ship locks in complex mountainous areas.

[0138] Example 3 elaborates on a robust design method for uncertainties such as water level fluctuations and construction errors. It solves the technical problem that traditional fixed-value design methods may lead to safety hazards such as overflow of the water-saving tank, evacuation and air intake, or deterioration of the flow pattern when the actual operating conditions deviate from the design values. By introducing interval mathematics and worst-case analysis, a solid safety barrier is built for the lock.

[0139] Step 301: The upstream water level information is represented by the range of upstream water level changes, the downstream water level information is represented by the range of downstream water level changes, and the area ratio relationship sequence is represented by the area ratio fluctuation range of each level of provincial water pool.

[0140] In this embodiment, water level and structural parameters are no longer treated as single deterministic values, but rather modeled as a set of intervals containing all possible values. This is a more rigorous engineering mathematical description method that can cover various extreme cases in actual operation.

[0141] Specifically, the range of upstream water level changes is represented as [z u - ,z u + ], where z u - This refers to the lower limit of the upstream water level, such as the minimum navigable water level during the dry season. u + This represents the upper limit of the upstream water level, such as the highest navigable water level during flood season. Similarly, the downstream water level variation range is represented as [z]. d - ,z d +The data for the interval can be derived from statistical analysis of long-term hydrological data, or from the design water level envelope determined according to waterway grade specifications.

[0142] The area ratio fluctuation range is represented as [k] i - ,k i + The introduction of this interval is primarily to address the uncertainties arising from construction errors and operational losses. In actual engineering projects, due to over- or under-excavation of soil and rock, deformation of concrete pouring formwork, or siltation and structural deformation after long-term operation, the actual constructed water-saving pool area A... i The results often deviate from the theoretical design values. For example, if the design area ratio is 2.0, considering a construction tolerance of + / - 5%, it can be modeled as an interval [1.9, 2.1]. This modeling method ensures that the subsequent calculation results have strong adaptability (robustness) to engineering realities.

[0143] The specific calculation method for the area ratio fluctuation range is as follows:

[0144] Let the fluctuation range of the bottom width of the i-th level water-saving pool be [b i_min ,b i_max The fluctuation range of the slope angle is [θ]. i_min ,θ i_max If the area is less than the lower limit k, then... i_min The calculation formula is:

[0145] k i_min =A i_min / A c ;

[0146] Among them, A i_min A represents the minimum average water surface area of ​​the i-th level water-saving pool under the most unfavorable parameter combination, expressed in square meters. c The area of ​​the gate chamber is expressed in square meters.

[0147] A i_min =L i *(b i_min +(H i / 2)*cot(θ i_max ));

[0148] Among them, A i_min L represents the minimum average water surface area of ​​the i-th level water-saving pool, in square meters; i b is the length of the i-th level water-saving pool along the direction of the gate chamber, in meters; i_min H represents the lower limit of the bottom width of the i-th level water-saving pool, in meters; i The working head of the i-th level water-saving tank is expressed in meters; θ i_maxis the upper limit of the slope angle of the i-th level water-saving pool, in degrees; cot represents the cotangent function.

[0149] As an alternative implementation, uncertainty can also be described using a geometric parametric model. For example, for a water-saving pool with a trapezoidal cross-section, its area A... i It can be expressed as a function of the base width b and the slope angle α:

[0150] A i =L*(b+2*h*cot(α)).

[0151] At this point, the bottom width b and the slope angle α can be modeled as intervals [b...]. - ,b + ] and [α - ,α + The area ratio k is derived through interval operations. i The fluctuation range provides a flexible modeling approach for different types of water-saving tank structures.

[0152] As a specific implementation of the geometric parameter model, for a water-saving pond with a trapezoidal slope cross-section, its water surface area can be expressed as a function of geometric parameters:

[0153] A i (z)=L i *(b i +2*(zz i_bot )*cot(θ i ));

[0154] Among them, A i (z) represents the water surface area of ​​the i-th level water-saving pool at water level z, in square meters; L i b is the length of the i-th level water-saving pool along the direction of the gate chamber, in meters; i z is the bottom width of the i-th level water-saving tank, in meters; z is the calculated water level, in meters; z i_bot θ represents the elevation of the bottom of the i-th level water-saving reservoir, in meters; i denoted as the slope angle of the i-th level water-saving pool, in degrees; cot represents the cotangent function.

[0155] When the pool bottom width b i The range of values ​​for b is i_min to b i_max Between, slope angle θ i The range of values ​​for θ is i_min to θ i_max When the range is between these values, the fluctuation range of the equivalent area ratio can be derived through interval calculations. In the most unfavorable working condition analysis, the parameter combination that minimizes the area is selected, i.e., b is chosen. i =b i_min And take θ i =θi_max The slope angle value at that time yields the area ratio lower limit k. i_min Then, the aforementioned robustness calculation formula is applied.

[0156] Step 302: The upstream water level change range is defined by the upper limit and lower limit of the upstream water level, the downstream water level change range is defined by the upper limit and lower limit of the downstream water level, and the area ratio fluctuation range is defined by the upper limit and lower limit of the area ratio.

[0157] This step further clarifies the above-mentioned interval definition. Defining upper and lower limits is a prerequisite for interval operations. In practice, the determination of boundary values ​​should follow a conservative principle. For example, the upper limit of the upstream water level should be the highest possible physical water level, and the lower limit of the area ratio should be the minimum possible area value after considering the maximum negative deviation (such as construction necking or severe siltation).

[0158] Step 303: Based on the upstream water level change range, the downstream water level change range, and the area ratio fluctuation range, determine the most unfavorable working condition combination.

[0159] The most unfavorable operating condition combination refers to the state most likely to cause the system's operational safety boundary to be breached among all possible parameter combinations. For water-saving locks, one of the most critical safety risks is excessive staged head. Excessive staged head may lead to water overflowing from the top of the water-saving pool (dam overflow risk), air entering the valves due to the pumping of water during discharge (air intake risk), or excessively high flow velocity in the water conveyance channel, causing cavitation erosion (flow regime risk).

[0160] Theoretical analysis shows that the staged head H w It is directly proportional to the total head difference H, and proportional to the denominator (including the area ratio k). i The function is inversely proportional to the stage head H. w The most unfavorable operating condition combination that reaches the maximum value must simultaneously satisfy the following two conditions:

[0161] Condition 1: The total head difference reaches its maximum. This corresponds to the upstream water level being at an extremely high value z. u + Meanwhile, the downstream water level is at an extremely low value. d - At that moment.

[0162] Condition 2: The system's hierarchical adjustment capability is the weakest. Mathematically, this represents the denominator term Σ[k] i / (k i +1)] reaches its minimum value. Since the function f(k) = k / (k+1) is a monotonically increasing function with respect to k, when all k i Take its lower limit value k i - When the denominator is minimized, the calculated H is... w maximum.

[0163] The most unfavorable combination of operating conditions is determined as follows: upstream water level = z u + Downstream water level = z d - And the area ratio of each level is k i - .

[0164] Step 304: Calculate the upper limit of the staged head based on the most unfavorable combination of working conditions; whereby the upper limit of the staged head is the maximum staged head value that may occur under the condition of satisfying the interval constraints.

[0165] This step is used to quantify risk and calculate the upper limit of the graded head H. w + This is a critical safety threshold. It represents the maximum hydraulic load the system might encounter under extreme conditions, such as a flood season coinciding with a dry season and construction errors resulting in an undersized pool. If the design can achieve this, then... w + If safety is still guaranteed, such as no overflow or cavitation, then the solution will certainly be safe under other normal operating conditions as well.

[0166] Step 305, determining the most unfavorable combination of conditions includes calculating the maximum total head difference and selecting the area ratio boundary value that maximizes the staged head.

[0167] This step describes the specific operations of step 303. In terms of algorithm implementation, the subtraction operation H is performed first. + =z u + -z d - Obtain the maximum total driving head; simultaneously, traverse the area ratio sequence and extract each k i The lower boundary value k i - Construct the most unfavorable area ratio vector K - ={k1 - k2 - ,...,k m -}

[0168] Step 306, calculating the upper limit of the staged head is performed using the following formula:

[0169] H w + =H + / (1+m-Σ i=1 m [1 / (k i - +1)]);

[0170] In this embodiment, the calculation of H is given. w + The explicit mathematical formula. The physical meaning and units of each symbol in the formula are as follows:

[0171] H w + The upper limit of the graded head (unit: meters) is the benchmark load for subsequent safety verification;

[0172] H + Maximum total head difference (unit: meters), determined by z u + -z d - Calculated;

[0173] z u + :The upper limit of the upstream water level variation range (unit: meters);

[0174] z d - : Lower limit of the downstream water level variation range (unit: meters);

[0175] m: Level of the provincial water tank (dimension 1);

[0176] k i - : The lower limit of the fluctuation range of the area ratio of the i-th level water-saving pool (dimensionless).

[0177] Σ i=1 m : This indicates a summation operation on all terms from level 1 to level m.

[0178] Example 4 elaborates on how, after calculating the staged head under the most unfavorable working conditions, a comprehensive check of the design scheme is carried out by establishing a constraint set that includes multiple dimensions such as efficiency, water level, and flow regime. This solves the problem that simply pursuing water-saving efficiency may neglect engineering safety. Through rigorous logical judgment, the final output design parameters are guaranteed to be both effective and safe.

[0179] Step 401: Construct a set of constraints, which includes safe operating thresholds and efficiency thresholds for the most unfavorable operating conditions.

[0180] In this embodiment, the constraint set is a multi-objective evaluation matrix used to determine the feasibility of the preliminary design scheme by ensuring that all constraints are met simultaneously. Failure to meet any constraint condition indicates that the scheme is infeasible. It's like a multi-layered security gate; exceeding any indicator will trigger an alarm. The safe operation threshold covers multiple dimensions, including structural safety (overflow prevention) and hydraulic safety (cavitation prevention); the efficiency threshold focuses on economic indicators.

[0181] Specifically, the set of constraints typically includes, but is not limited to, the following three important subsets:

[0182] (1) Robust water-saving efficiency constraint: ensure that the water-saving effect still meets the standard even under the worst case;

[0183] (2) Overflow control at the highest water level: to ensure that water will not overflow the top of the pool when the extreme flood level is superimposed with the maximum operating amplitude;

[0184] (3) Graded head flow constraint: ensure that the energy of a single water delivery is not too large, and avoid vibration or cavitation of the water delivery valve.

[0185] In some more detailed implementation plans, minimum water level anti-air intake constraints (to prevent air from being drawn in when the water level is too low) or maximum single water transfer time constraints (to ensure navigation efficiency) can also be added.

[0186] Step 402: Determine whether the calculated graded head and operating water level of each grade meet the constraint condition set.

[0187] This step is the logical action to perform the verification. The system will then use the H calculated in the previous steps... w + The upper limit of the water head for each stage and the derived extreme values ​​of the water level at each stage are substituted into the inequalities in the above constraint set for comparison. If all inequalities are true, the scheme is deemed qualified; otherwise, it is deemed unsatisfactory, and the subsequent optimization and adjustment process needs to be triggered.

[0188] Step 403: The set of constraints includes robust water-saving efficiency constraints.

[0189] This embodiment focuses on the robustness assessment of efficiency. Traditional designs often only consider efficiency under design conditions, which can easily overestimate actual performance. This method introduces robust water-saving efficiency, that is, assessing the minimum efficiency under the most unfavorable operating conditions. (Referring to H...) w + and H + This is for calculating this indicator.

[0190] Determine whether the calculated graded head and operating water level at each level meet the set of constraints, such as... Figure 2 As shown, it specifically includes:

[0191] Step 404: Using the calculated upper limit of the staged head and the maximum total head difference, calculate the robust water-saving efficiency using the following formula:

[0192] η rob =1-(H w + / H + );

[0193] Where, η rob Robust water-saving efficiency (dimensionless percentage); H w + The upper limit of the graded head (meters); H + The maximum total head difference (meters).

[0194] The physical meaning of this formula is: Under the most unfavorable operating conditions, in order to fill the lock (total head H) + The additional head section that needs to be supplied from upstream is H. w + The proportion of water head saved is 1 - (H) w + / H + For example, if H + =30m, H w + =10m, then η rob =1-10 / 30=66.7%. This means that even under the worst conditions, the plan can still save 66.7% of water consumption.

[0195] Step 405: Determine whether the robust water-saving efficiency is greater than or equal to the preset minimum water-saving efficiency threshold.

[0196] This step compares the calculation results with preset standards. The minimum water-saving efficiency threshold is usually specified by the owner in the project proposal or set according to relevant navigation structure specifications, such as 50% or 60%. If η rob If the value is less than the threshold, it indicates that the current scheme has too few levels m or the area ratio k is too low. i The configuration is incorrect and needs to be adjusted.

[0197] Step 406: Obtain the preset top elevation of each level of water-saving pool; determine whether the upper limit of the highest operating water level of any level of water-saving pool is less than its corresponding preset top elevation.

[0198] This step performs a specific security comparison. Preset pool top elevation z i,top It is the physical boundary determined by the civil engineering structural design. The judgment logic is: if z i,max + <z i,top If the water level in the provincial water tank does not overflow, the constraint is satisfied.

[0199] As a preferred implementation, a safety margin Δ is usually added to the inequality, that is, z is required to be... i,max + +Δ <z i,top This is to cope with the rising waves. This process will be further refined in step 408.

[0200] Step 407: The set of constraints also includes graded head flow state safety constraints; determine whether the calculated graded head and operating water level of each level meet the set of constraints, specifically including: obtaining the maximum allowable graded head threshold, the maximum graded head threshold is determined based on the allowable flow velocity or cavitation criterion of the water-saving lock water conveyance valve; determine whether the upper limit of the graded head is less than or equal to the maximum graded head threshold.

[0201] In this embodiment, a flow regime check is added. This is an easily overlooked but crucial implicit constraint. (Sequencing head H) w + The initial flow velocity v within the water conveyance channel is directly determined. According to Bernoulli's equation, v ≈ μ*sqrt(2*g*H) w + ), where μ is the flow coefficient.

[0202] If H w + If the velocity is too high, the flow velocity v will exceed the critical cavitation resistance velocity of the valve material, or the local pressure in the channel will drop below the vaporization pressure of water, causing destructive cavitation phenomena.

[0203] Maximum graded head threshold H w,max It is a hard parameter determined based on hydraulic tests. For example, for conventional concrete galleries, the height (H) is typically limited. w,max Between 6.0 meters and 8.0 meters. If the calculated H... w + >H w,max In this case, it is necessary to forcibly increase the number of water-saving tank stages (m) to distribute the water head, regardless of whether the water-saving efficiency has met the standard.

[0204] Step 408, in determining and outputting the design parameters for each level of water-saving tank, specifically includes determining the top elevation of each level of water-saving tank; the top elevation is determined using the following formula:

[0205] z i,top =z i,max + +Δf i ;

[0206] Among them, z i,top Let z be the elevation (in meters) of the top of the i-th level water-saving pool. i,max + Δf represents the upper limit of the maximum operating water level (in meters) of the i-th level water-saving pool. i The preset safety margin (in meters) for the i-th level structure.

[0207] This step provides a method for determining the final construction parameters. After successful verification, the specific construction parameters need to be output.

[0208] Safety margin Δfi The calculation is typically based on the engineering grade and wind and wave factors, with values ​​generally ranging from 0.5 meters to 1.5 meters. For example, if the calculated highest water level of a certain level of pool is 60.0 meters, and a freeboard of 1.0 meter is taken, then the design pool top elevation is set at 61.0 meters. This formula directly guides the pouring height of the retaining wall and has strong practical engineering applicability.

[0209] Example 5 elaborates on how to automatically find the optimal solution through a systematic feedback adjustment mechanism when the preliminary design scheme is difficult to meet the multi-dimensional constraint set, thus endowing the design method with self-optimization ability and upgrading it from a simple calculation tool to an intelligent design system.

[0210] Step 501: If the judgment result is that the set of constraints is not met, adjust the area ratio relationship sequence or the number of water-saving tank levels in the physical model of the variable cross-section water-saving tank, and return to the step of calculating the graded head and the graded operating water level of the water exchanged between each level of water-saving tank and the gate chamber, until the set of constraints is met.

[0211] In other words, if the judgment result is that the set of constraints is not met, the sequence of water-saving pool levels and / or area ratios is updated according to the preset adjustment strategy, and the process returns to the step of calculating the graded head and the graded operating water level of the water exchanged between each level of water-saving pool and the gate chamber, until the set of constraints is met.

[0212] This embodiment describes the key logic of a closed-loop control system. When any constraint (efficiency, overflow prevention, flow state) fails the verification, the system does not simply report an error and stop, but triggers an adjustment-recalculation loop.

[0213] The default adjustment strategy serves as the navigation graph for this cycle, containing a series of priority adjustment rules. The strategy will differ depending on the cause of failure.

[0214] Scenario 1: Only the flow state constraint is not satisfied, H w + >H w,max .

[0215] The problem at this point is that the head of a single stage is too high. The most direct and effective adjustment is to increase the number of stages in the water-saving tank, m (for example, m = m + 1). Increasing the number of stages will directly reduce the head distributed at each stage.

[0216] The adjustment action is, m _new =m _old +1(m) _new To update the number of water-saving tank stages, m _old (The current or original provincial water tank level); keep the K-series distribution unchanged or re-interpolate.

[0217] Scenario 2: Overflow prevention constraint alone is not satisfied, zi,max + >z i,top .

[0218] The problem at this point is that the volume of a certain stage's water-saving pool is too small to hold the exchanged water. The solution is to increase the area A of that stage's water-saving pool. i That is, increase k i .

[0219] The adjustment action is to locate the i-th stage of the overflow and let k i_new =k i_old *(1+step)(k i_new To update the area ratio of the i-th level water-saving pool, k i_old (where step is the ratio of the current or original area of ​​the i-th level water-saving pool), where step is the step size, such as 0.1.

[0220] Scenario 3: Only the water-saving efficiency constraint is not met, η rob Less than the threshold.

[0221] This indicates that the total water storage capacity is insufficient. The capacity of all k can be increased globally. i Alternatively, the number of stages m could be increased. Considering earthwork costs, a better strategy might be to first try fine-tuning k. i For example, prioritize increasing the k value in high-altitude, large-scale excavation areas. m If it is ineffective, add m.

[0222] Scenario 4: Multiple constraints are not satisfied simultaneously.

[0223] At this point, the operation of increasing the level m is usually prioritized, as it is the most powerful way to improve system performance.

[0224] As a specific automated implementation method, this process can be achieved through computer algorithms:

[0225] Initialization: Set m=2, K={1.0,1.0}.

[0226] Calculation: Determine the most unfavorable working condition combination and calculate the upper limit H of the staged head. w + .

[0227] Verification: Determine whether the calculated graded head and operating water level of each grade meet the set of constraints.

[0228] Discrimination:

[0229] If successful, output the solution and end.

[0230] If it fails, analyze the violations:

[0231] If H w +If the limit is exceeded, m = m + 1, reset K, and jump to step 2.

[0232] If H w + Qualified but with localized overflow, adjust the corresponding k. i Jump to step 2.

[0233] If there is still no solution after more than 1000 iterations, an error message will be displayed indicating that the terrain conditions cannot meet the design requirements.

[0234] The iterative optimization mechanism ensures that the final output solution is a feasible solution under the current constraints, and is often close to the optimal solution, meaning that it minimizes the number of stages and the amount of excavation while meeting safety requirements. This replaces the inefficient design mode of traditional manual trial and error and decision-making based on experience.

[0235] The specific implementation of the iterative optimization mechanism is as follows:

[0236] Step 1: Set the initial area ratio sequence k1, k2 to k m The initial value can be estimated based on the terrain conditions or by adopting the area ratio of the equal cross section scheme;

[0237] Step 2: Based on the initial area ratio sequence, calculate the upper limit H of the staged head using the staged head formula and the robustness calculation formula. w + Upper limits of operating water levels at all levels and robust water-saving efficiency η rob ;

[0238] Step 3: Determine if all constraints are met, including robust water-saving efficiency constraints, overflow prevention constraints, and flow regime safety constraints. If all constraints are met, proceed to Step 5; if any constraints are not met, proceed to Step 4.

[0239] Step 4: Adjust the area ratio sequence according to the type of constraint not met. If the robust water-saving efficiency does not meet the lower limit requirement, increase the area ratio of the smaller water-saving tank; if the overflow prevention constraint is not met, decrease the area ratio of the corresponding level of water-saving tank or increase the tank top elevation; if the flow safety constraint is not met, adjust the stage head or increase the number of water-saving tank stages. After adjustment, return to Step 2;

[0240] Step 5: Output the final design parameters, including the area of ​​each level of water-saving pool, the top elevation of the pool, the bottom elevation of the pool, and the operating water level range.

[0241] The iterative convergence criterion is: the change in the area ratio sequence between two consecutive iterations is less than a preset threshold ε, where ε ranges from 0.01 to 0.05. If the number of iterations exceeds a preset maximum number N... max If convergence is still not achieved, the current series scheme is deemed infeasible, and the number of water-saving tank stages needs to be increased before recalculation. N maxThe typical value is 50.

[0242] Numerical examples of the iterative optimization process are as follows:

[0243] Based on a high-head water-saving ship lock in a mountainous area, the initial design scheme is assumed to be m=2, K={1.0,1.5}, the target efficiency threshold is 60%, and the maximum graded head threshold is 8.0 meters.

[0244] Round 1 iteration:

[0245] Calculate H w =45.0 / (1+0.5+0.6)=45.0 / 2.1≈21.43 meters;

[0246] Flow constraint verification: 21.43 meters > 8.0 meters, not satisfied;

[0247] Trigger adjustment: Increase level m=3.

[0248] Second iteration:

[0249] Let K = {1.0, 1.5, 2.0};

[0250] Calculate H w =45.0 / (1+0.5+0.6+0.667)=45.0 / 2.767≈16.26 meters;

[0251] Flow constraint verification: 16.26 meters > 8.0 meters, still not satisfied;

[0252] Trigger adjustment: Continue to increase the level m=4.

[0253] Third iteration:

[0254] Let K = {1.0, 1.5, 2.0, 3.0};

[0255] Calculate H w =45.0 / (1+0.5+0.6+0.667+0.75)=45.0 / 3.517≈12.79 meters;

[0256] Flow constraint verification: 12.79 meters > 8.0 meters, still not satisfied;

[0257] Trigger adjustment: Try increasing the area ratio of high-rise buildings, let K={1.0,2.0,4.0,6.0}.

[0258] 4th iteration:

[0259] Calculate H w =45.0 / (1+0.5+0.667+0.8+0.857)=45.0 / 3.824≈11.77 meters;

[0260] Continue adjusting until the constraints are met.

[0261] As can be seen from the above iterative process, the system can automatically select and adjust strategies according to the type of constraint violation, and eventually converge to a feasible solution.

[0262] Example 6: Through specific engineering numerical examples, the complete application process of the method of the present invention is comprehensively demonstrated. By comparing the calculation results of conventional constant cross-section design and the variable cross-section design of the present invention, the engineering effectiveness of the present invention in handling high water head and complex terrain constraints is proved.

[0263] Step 601: Obtain the upstream water level information, downstream water level information, and lock chamber geometric parameters of the water-saving lock.

[0264] In this embodiment, the engineering background is a high-head, water-saving ship lock in a mountainous area.

[0265] The basic input parameters obtained are as follows:

[0266] Upstream design maximum navigable water level z u =85.0 meters.

[0267] Downstream minimum navigable water level z d =40.0 meters.

[0268] Therefore, the maximum design head difference H = z u -z d =45.0 meters.

[0269] Effective area A of the gate chamber c Normalized to 1.0 unit area (subsequent area ratio calculations are based on this).

[0270] Preset water-saving efficiency target: η target ≥60%.

[0271] Step 602, perform design calculations based on a conventional constant cross-section model, such as... Figure 3 As shown.

[0272] First, the design results using a constant cross-section model are presented. In traditional methods, it is mandatory that the area ratio of each level of the sluice tank to the gate chamber be equal, i.e., k1=k2=k m =k.

[0273] Assuming that the maximum excavable water-saving pool area is limited by terrain, reaching only 1.1 times the gate chamber area (i.e., limit k=1.1), and a four-stage water-saving pool is used (m=4), the head calculation is performed using the staged head formula under constant cross-section conditions:

[0274] H w =(z u -z d) / (1+m*k / (k+1));

[0275] Substitute the value z u =85 meters, z d =40 meters, m=4, k=1.1, the calculation process is as follows:

[0276] Calculation of denominator: k / (k+1) = 1.1 / 2.1 = 0.5238;

[0277] m*k / (k+1)=4*0.5238=2.0952;

[0278] 1+m*k / (k+1)=1+2.0952=3.0952;

[0279] H w =45 / 3.0952=14.54 meters.

[0280] Calculate water-saving efficiency:

[0281] η=m*k / (m*k+k+1)=4*1.1 / (4*1.1+1.1+1)=4.4 / 6.5=0.677;

[0282] That is, the water-saving efficiency is approximately 67.7%.

[0283] Step 603, perform design calculations based on the variable cross-section model, such as... Figure 4 As shown.

[0284] The strategy of applying the method described in this invention is to break the limitation that the area ratios of each level are equal. Although the lower areas are limited and can only be made small, the higher areas have open terrain and can be made large.

[0285] The series is set to m=3, and the area ratio sequence is set to k1=1.1, k2=3.4, and k3=4.0. This is a typical increasing sequence, suitable for V-shaped canyon terrain. Here, k1=1.1 indicates that the bottom is restricted, k2=3.4 indicates that the middle is open, and k3=4.0 indicates that the top is wide.

[0286] Calculate using the graded head formula of this invention:

[0287] H w =(z u -z d ) / (1+m-Σ i=1 m (1 / (k i +1)));

[0288] Calculate the summation part of the denominator:

[0289] First term: 1 / (k1+1) = 1 / 2.1 = 0.476;

[0290] The second term: 1 / (k²+1) = 1 / 4.4 = 0.227;

[0291] The third term: 1 / (k3+1) = 1 / 5.0 = 0.200;

[0292] Sum: 0.476 + 0.227 + 0.200 = 0.903;

[0293] H w =45 / (1+3-0.903)=14.53 meters.

[0294] Calculate water-saving efficiency:

[0295] η=1-1 / (1+2.0965)=1-1 / 3.0965=1-0.323=0.677;

[0296] That is, the water-saving efficiency is approximately 67.7%.

[0297] The variable cross-section three-stage water-saving tank layout has a stage head of approximately 14.53 meters, which is basically consistent with the stage head of approximately 14.54 meters for the constant cross-section four-stage water-saving tank layout. Both layouts achieve a water-saving efficiency of approximately 67.7%. However, the variable cross-section layout requires only three stages of water-saving tanks, while the constant cross-section layout requires four. The variable cross-section layout reduces the construction of one stage of water-saving tank, thereby reducing the number of water conveyance valves, shortening the lock's water conveyance time, and improving the lock's water conveyance efficiency. It also makes full use of the excavated space on the high slope near the lock.

[0298] Step 604: Perform a robustness check based on uncertainty.

[0299] Assuming the above variable cross-section scheme K={1.1,3.4,4.0}, the construction error is -5%.

[0300] Then the most unfavorable area ratio sequence K - ={1.045,3.23,3.8}.

[0301] Assuming the upstream water level may rise by 1 meter, z u + =86.0, H + =46.0 meters.

[0302] Recalculate the denominator term D - (Based on K) - ):

[0303] Item 1: 1.045 / 2.045 ≈ 0.511;

[0304] Item 2: 3.23 / 4.23 ≈ 0.763;

[0305] Item 3: 3.8 / 4.8 ≈ 0.791;

[0306] D - =1 + 2.065 = 3.065;

[0307] Calculate H w + =46.0 / 3.065≈15.01 meters.

[0308] Calculate robust efficiency η rob =1-15.01 / 46.0≈67.3%.

[0309] Robust efficiency 67.3% > 60%, satisfying efficiency constraints.

[0310] The maximum head for a given water level is 15.01 meters. If the valve limit is 15 meters, it is in a critical state, and it is recommended to make minor adjustments by increasing the area or strengthening the valve selection.

[0311] Calculate the water level z of the highest-level pool 3,max + =86.0 - 15.01 = 70.99 meters. If the preset pool top height is 72.0 meters, then the overflow requirement is met.

[0312] The numerical demonstration in this embodiment clearly shows the entire process from parameter setting, model selection, formula calculation to security verification, verifying the operability and practical effect of the method of the present invention.

[0313] This application employs a variable cross-section physical model design. By constructing a physical model that allows for unequal area ratios at each level of the water-saving tank, the lower-level water-saving tank can be designed with a smaller area in narrow valleys, while the upper-level tanks can be designed with a larger area utilizing open spaces. This approach adapts to the terrain, significantly reduces rock excavation and slope support costs, and automatically balances the hydraulic characteristics at each level using a graded head formula. It solves the problem of difficult and costly excavation for constant cross-section designs due to the limited terrain in mountainous areas.

[0314] This application introduces interval uncertainty modeling and robust design. By modeling water level and structural dimensions as fluctuation intervals, the most unfavorable operating condition leading to the maximum graded head is identified, and the upper limit of the graded head is calculated accordingly. Based on this, a multi-dimensional constraint system is established, including overflow prevention (based on the derived maximum operating water level), flow regime safety (based on the maximum flow velocity criterion), and robust efficiency. This ensures that even under extreme conditions (such as flooding combined with construction necking), the lock will not overflow, cavitation will not occur, and water conservation standards will be met, thus improving the safety margin of the project. This solves the problem that deterministic design ignores water level fluctuations and construction errors, leading to overflow or cavitation risks.

[0315] 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 classifying water-saving lock water levels based on a variable cross-section water-saving tank, characterized in that, include: Obtain upstream and downstream water level information and lock chamber geometric parameters of the water-saving ship lock; A physical model of a variable cross-section water-saving pool is constructed based on a preset number of water-saving pool levels. The physical model of the variable cross-section water-saving pool includes a sequence of area ratio relationships between each level of water-saving pool and the gate chamber, and the area ratio relationship sequence allows at least some levels of water-saving pools to have different area ratios. Based on upstream water level information, downstream water level information and area ratio relationship sequence, calculate the graded head and operating water level of the water exchanged between each level of provincial water pool and gate chamber; Based on the operating water levels at each level, determine and output the design parameters for each level of the provincial water tank; Among them, the area ratio sequence is composed of the ratio of the area of ​​each level of provincial water tank to the area of ​​the gate chamber in the geometric parameters of the gate chamber; In the physical model of the variable cross-section water-saving pool, the area ratio of each level of water-saving pool is not constant as the elevation of the water-saving pool changes, resulting in at least two levels of water-saving pools having different area ratio values.

2. The method according to claim 1, characterized in that, Both upstream and downstream water level information are constant values; In calculating the graded head and the operating water level at each level for the water exchange between the provincial water tanks and the gate chambers, the graded head is calculated using the following formula: H w =(of u -With d ) / (1+m-Σ i=1 m [1 / (k i +1)]); Among them, H w For graded head, z u For upstream water level information, z d This provides downstream water level information, where m represents the number of stages in the provincial water reservoir, and k... i It represents the area ratio between the i-th level water-saving pool and the gate chamber in the area ratio relationship sequence.

3. The method according to claim 2, characterized in that, Upstream water level information is represented by the range of upstream water level changes, downstream water level information is represented by the range of downstream water level changes, and the area ratio relationship sequence is represented by the range of area ratio fluctuations of each level of provincial water pool; The range of upstream water level changes is defined by the upper limit and lower limit of upstream water level, the range of downstream water level changes is defined by the upper limit and lower limit of downstream water level, and the range of area ratio fluctuations is defined by the upper limit and lower limit of area ratio.

4. The method according to claim 3, characterized in that, The calculation of the graded head and operating water level for the water exchanged between the provincial water tanks and gate chambers at each level includes: Based on the upstream water level change range, the downstream water level change range, and the area ratio fluctuation range, the most unfavorable combination of working conditions is determined. Calculate the upper limit of the graded head based on the most unfavorable combination of operating conditions; Among them, the upper limit of the graded head is the maximum graded head value that occurs under the condition of satisfying the interval constraints.

5. The method according to claim 4, characterized in that, Determining the most unfavorable combination of operating conditions involves calculating the maximum total head difference and selecting the area ratio boundary value that maximizes the staged head. The upper limit of the stage head is calculated using the following formula: H w + =H + / (1+m-Σ i=1 m [1 / (k i - +1)]); Among them, H w + H is the upper limit of the graded head. + For the maximum total head difference, and H + =z u + -z d - , z u + The upper limit of the upstream water level, z d - The lower limit of the downstream water level, m is the number of stages in the water-saving reservoir, and k is the number of stages in the reservoir. i - This represents the lower limit of the area ratio of the i-th level water-saving pool.

6. The method according to claim 5, characterized in that, After calculating the graded head and operating water level of the water exchanged between the provincial water tanks and gate chambers at each level, the following is also included: Construct a set of constraints, which includes safe operating thresholds and efficiency thresholds for the most unfavorable operating conditions; Determine whether the calculated graded head and operating water level at each level meet the set of constraints. If the judgment result is that the set of constraints is not met, the area ratio relationship sequence or the number of water-saving tank levels in the physical model of the variable cross-section water-saving tank is adjusted, and the process returns to the step of calculating the graded head and the operating water level of each level of water-saving tank and gate chamber, until the set of constraints is met.

7. The method according to claim 6, characterized in that, The constraint set includes robust water-saving efficiency constraints. It determines whether the calculated staged head and operating water level at each stage satisfy the constraint set, including: Referencing the upper limit of graded head and the maximum total head difference; Calculate robust water-saving efficiency using the following formula: or rob =1-(H w + / H + ); Where, η rob For robust water-saving efficiency, H w + H is the upper limit of the graded head. + This represents the maximum total head difference. Determine whether the robust water-saving efficiency is greater than or equal to the preset minimum water-saving efficiency threshold.

8. The method according to claim 2, characterized in that, Before determining and outputting the design parameters for each level of water-saving tank, the theoretical water-saving efficiency of the variable cross-section water-saving tank is calculated using the following formula: n=1-1 / (1+Σ i=1 m [k i / (k i +1)]); Where η is the theoretical water-saving efficiency, m is the number of water-saving tank stages, and k i This represents the area ratio between the i-th level water-saving pool and the gate chamber in the area ratio sequence. The theoretical water-saving efficiency can be output as part of the design parameters of water-saving tanks at all levels, or used to compare and verify with the preset target water-saving efficiency.

9. The method according to claim 6, characterized in that, The constraint set also includes staged head flow regime safety constraints; determining whether the calculated staged heads and operating water levels at each stage satisfy the constraint set includes: The maximum permissible graded head threshold is obtained, which is determined based on the permissible flow rate or cavitation criterion of the water-saving lock's water conveyance valve; Determine whether the upper limit of the graded head is less than or equal to the maximum graded head threshold.

10. The method according to claim 1, characterized in that, In determining and outputting the design parameters for each level of provincial water tank, the top elevation of each level of provincial water tank is determined. The elevation of the pool top is determined using the following formula: z i,top =z i,max + +Δf i ; Among them, z i,top Let z be the elevation of the top of the i-th level water-saving pool. i,max + Δf represents the upper limit of the maximum operating water level of the i-th level water-saving pool. i The pre-defined i-th level structural safety margin is extremely high.

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