Sustainable development control method for cascade reservoir system in Yellow River basin

Abstract

The application discloses a kind of Yellow River Basin cascade reservoir group system sustainable development regulation methods, comprising: the watershed system is divided into water and sediment, ecological and social subsystem, obtains multidimensional parameter data and identifies the order state flow variable of driving system evolution;The same vibration degree of order state flow variable is calculated, and the same vibration degree represents the coordination level of variable evolution;Overall harmonic contractility of system is calculated based on the same vibration degree;Select water and sediment regulation factor, construct the quantitative regulation model including water and sediment regulation factor, the same vibration degree of order state flow variable and the mapping relationship of system harmonic contractility;The target harmonic contractility interval of system is set, and based on quantitative regulation model, the water and sediment regulation factor regulation threshold required for realizing the target is calculated reversely.The application introduces evolution coordination analysis and reverse regulation mechanism, solves the problems that traditional method is difficult to quantify time sequence synchronism and cannot backstep regulation boundary, realizes the target-oriented accurate regulation of watershed system.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy project scheduling, and in particular, it is a method for sustainable development regulation of the Yellow River Basin cascade reservoir system. Background Technology

[0002] Cascade reservoir systems constitute a complex coupling of hydrodynamics, ecological maintenance, and water resource allocation. The core technical challenge in regulating such large-scale systems lies in quantifying the coupling relationships between multidimensional parameters and establishing a closed-loop control mechanism from engineering scheduling to system state management. Accurately identifying the sequential flow variables driving system evolution and quantitatively assessing the synergistic level of internal system parameters are prerequisites for determining reservoir group operation strategies and ensuring the stability of watershed system evolution.

[0003] Currently, research on the regulation of cascade reservoir groups typically employs sequential flow variable identification techniques to characterize the system's evolution. The prevailing technical approach involves: collecting historical multidimensional parameter data from subsystems such as water, sediment, and ecology; normalizing the data using methods like range standardization; calculating the static co-oscillation degree, which reflects the development level of these parameters; and then using statistical methods such as Pearson correlation analysis to screen for water and sediment regulation factors (such as reservoir outflow and sediment concentration) that are highly correlated with sequential flow variables. This allows for the construction of a positive evaluation model for the system, used to assess the harmonious state of the system under specific scheduling schemes.

[0004] However, existing technologies suffer from deep-seated technical problems, such as a disconnect between static numerical evaluation and dynamic evolution characteristics, and a mismatch between statistical correlation and physical controllability. Specifically, the co-vibration calculation based on static normalization only reflects the level of parameters, ignoring the synchronicity of evolution trends between parameters. When parameters are at high levels but evolve in opposite directions (such as one rising and the other falling), false co-vibration misjudgments can occur, failing to truly characterize the coordinated evolution of the system. Furthermore, the selection of control factors based on statistical correlation lacks verification of controllability. High correlation does not necessarily mean that the control factor has sufficient motivation to drive the system state into the target range within a finite time, making it difficult to establish an accurate reverse solution path from the target harmonicity to the specific engineering control threshold. Summary of the Invention

[0005] The purpose of this invention is to provide a sustainable development regulation method for the Yellow River Basin cascade reservoir system, in order to solve the aforementioned problems existing in the prior art.

[0006] Technical solution: A method for sustainable development regulation of the Yellow River basin cascade reservoir system, comprising:

[0007] The Yellow River Basin cascade reservoir system is divided into water and sediment, ecological and social subsystems, and multidimensional parameter data characterizing the operational status of each subsystem are obtained.

[0008] Identify the sequential flow variables driving the evolution of the subsystem from multidimensional parametric data;

[0009] Calculate the co-oscillation of each sequential flow variable to characterize the level of coordination in variable evolution;

[0010] Calculation of the system harmony degree of the Yellow River Basin cascade reservoir system based on the co-vibration degree;

[0011] A quantitative control model was constructed by selecting water and sediment control factors and constructing a mapping relationship between the co-vibration degree of water and sediment control factors, sequential flow variables, and system harmonicity.

[0012] The target harmony degree range of the Yellow River Basin cascade reservoir system is set, and the control threshold of water and sediment control factors that satisfy the target harmony degree range is solved in reverse based on the quantitative control model.

[0013] Beneficial effects: By introducing evolutionary synergistic analysis and reverse regulation mechanism, this invention solves the problems of traditional methods being unable to quantify temporal synchronization and unable to reverse the regulation boundary, thus realizing the targeted and precise regulation of the watershed system. Attached Figure Description

[0014] Figure 1 A flowchart illustrating the steps of a sustainable development regulation method for a cascade reservoir system in the Yellow River Basin, provided in this application embodiment.

[0015] Figure 2 A flowchart illustrating the steps for identifying sequential flow variables driving the evolution of a subsystem from multidimensional parameter data, as provided in this application embodiment.

[0016] Figure 3 A flowchart illustrating the steps for calculating the co-vibration of each sequential flow variable provided in this application embodiment.

[0017] Figure 4 A flowchart illustrating the steps for calculating the evolution co-variables between sequential flow variables and other parameters within the subsystem, as provided in this application embodiment.

[0018] Figure 5 A schematic diagram of a sustainable development regulation method for the Yellow River Basin cascade reservoir system provided in this application embodiment.

[0019] Figure 6 A diagram illustrating the variation process of the total harmonic coefficient in the Yellow River Basin, provided as an embodiment of this application. Detailed Implementation

[0020] 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.

[0021] It should be noted that the terms include and have, and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0022] like Figure 1 As shown, a sustainable development regulation method for the Yellow River Basin cascade reservoir system includes the following steps:

[0023] The Yellow River Basin cascade reservoir system is divided into water and sediment, ecological and social subsystems, and multidimensional parameter data characterizing the operational status of each subsystem are obtained.

[0024] Specifically, based on systems engineering theory, the Yellow River basin's cascade reservoir system is deconstructed into three interconnected subsystems: a water and sediment subsystem, an ecological subsystem, and a social subsystem, comprehensively covering the core elements of basin management. Furthermore, based on geographical spatial characteristics, the entire basin can be divided into three sections: upstream, middle reaches, and downstream, thus constructing a matrix-style parameter acquisition system with three subsystems and three sections.

[0025] For example, regarding multidimensional parameter data, in the water and sediment subsystem, specific physical parameters are acquired, including reservoir sediment discharge ratio, annual average flow, average flow during the flood season, annual average sediment concentration, average sediment concentration during the flood season, floodplain flow, river channel meander coefficient, and Tongguan elevation. These parameters directly reflect the river channel's scouring and deposition status and the sediment transport capacity of the water flow. In the ecological subsystem, specific ecological indicators are acquired, including ecological pulse compliance rate, ecologically suitable flow guarantee rate, and critical period ecological water demand flow guarantee rate, to quantify the degree of maintenance of the basin's ecological health. In the social subsystem, specific economic indicators are acquired, including water supply security rate, cascade reservoir group power generation guarantee rate, and total power generation of the cascade reservoir group, to assess the supporting capacity of water resources for socio-economic development.

[0026] Identify the sequential flow variables that drive the evolution of the subsystem from multidimensional parametric data.

[0027] In this embodiment, ordered flow variables refer to key parameters that play a dominant role in the system's evolution and determine its transition from disorder to order. Since the initially acquired multidimensional parameter data is large and dimensionally redundant, directly using the full dataset for modeling would lead to computational complexity and ambiguous physical meaning. Therefore, it is necessary to select the most representative variables using predetermined mathematical methods. Preferably, the identified ordered flow variables include: the upstream Sanhukou section's flat-shoal flow, the Toudaoguai section's ecologically suitable flow guarantee rate, and the Lanzhou section's water supply guarantee rate; the midstream Tongguan elevation, the Tongguan section's ecologically suitable flow guarantee rate, and the Huayuankou section's water supply guarantee rate; and the downstream Sunkou section's flat-shoal flow, the Lijin section's ecologically suitable flow guarantee rate, and the Lijin section's water supply guarantee rate. These respectively represent the core evolutionary characteristics of each river section in terms of water and sediment, ecology, and society.

[0028] Calculate the co-vibration of each sequential flow variable, which characterizes the level of coordination in variable evolution.

[0029] Specifically, co-oscillation is a quantitative indicator ranging from 0 to 1, used to measure the degree to which a sequential flow variable matches the overall development rhythm of the system during its temporal evolution. The calculation process considers not only the absolute level of the variable itself, but also its trend of change and its synchronicity with other parameters within the system. For example, when a sequential flow variable (such as flood discharge) is at a high level and grows synchronously with other related parameters (such as upstream inflow), its co-oscillation value is high, indicating that the variable is in a benign evolutionary state; conversely, if the variable level is high but shows a reverse evolutionary trend, the co-oscillation value will decrease accordingly, objectively reflecting potential system risks.

[0030] The system harmony degree of the Yellow River Basin cascade reservoir system is calculated based on the co-vibration degree.

[0031] In this embodiment, the system harmony degree is used to characterize the macroscopic coordination level of the entire watershed system. Specifically, a weighted aggregation method can be used to map the co-vibration of the sequential flow variables of each subsystem to a single comprehensive index. For example, the formula for calculating the system harmony degree is: U = ∑ x ∑ y (W xy ×U(P xy Where U is the system harmonicity, W xy Let U(P) be the weight of the y-th ordered flow variable in the x-th subsystem. xy ) represents the corresponding co-oscillation degree. In some embodiments, assuming that each subsystem is of equal status, the weights can be set to equal values, such as 1 / 3 for each.

[0032] Furthermore, to intuitively assess the system state, a preset grading standard can be used to classify and evaluate the calculated system harmony degree. The specific grading standard is as follows: harmony degree in the interval [0, 0.1] is extremely disharmony, [0.1, 0.2] is severely disharmony, [0.2, 0.3] is moderate disharmony, [0.3, 0.4] is slightly disharmony, [0.4, 0.5] is near disharmony, [0.5, 0.6] is barely harmonious, [0.6, 0.7] is primary harmony, [0.7, 0.8] is intermediate harmony, [0.8, 0.9] is good harmony, and [0.9, 1.0] is excellent harmony. This provides a clear quantitative basis for setting subsequent control targets.

[0033] A quantitative control model was constructed by selecting water and sediment control factors and constructing a mapping relationship between the co-vibration degree of the water and sediment control factors, the sequential flow variables, and the system harmonicity.

[0034] In other words, water and sediment control factors that are correlated with the sequential flow variables are selected from multidimensional parameter data, and a quantitative control model is constructed that includes the mapping relationship between water and sediment control factors, the co-vibration of the sequential flow variables, and the system harmonicity.

[0035] Specifically, water and sediment regulation factors refer to control variables that can be artificially intervened through reservoir scheduling. For different river sections and sequential flow variables, regulation factors with clear physical causal relationships are selected. For example, for the Sanhukou plain discharge in the upper reaches, the outflow, sediment coefficient, and flood season flow process parameters of Reservoir A are selected as regulation factors; for the Tongguan elevation in the middle reaches, the discharge ratio and sediment discharge ratio of Reservoir B are selected as regulation factors. The construction of the quantitative regulation model preferably adopts a hierarchical mapping strategy: establishing the first-level quantitative relationship between water and sediment regulation factors and the co-vibration of sequential flow variables, typically expressed as a logarithmic or linear regression equation; combining the weighting formula, establishing the second-level quantitative relationship between co-vibration and system harmony. Through the cascading of these two levels of relationships, a mathematical connection is achieved from microscopic engineering parameters to macroscopic system states.

[0036] The target harmony degree range of the Yellow River Basin cascade reservoir system is set, and the control threshold of water and sediment control factors that satisfy the target harmony degree range is solved in reverse based on the quantitative control model.

[0037] In this embodiment, unlike traditional forward evaluation, which assesses the effectiveness of a given scheduling scheme, a reverse solution logic is employed. Specifically, decision-makers set a target harmony degree range based on watershed management needs; for example, they might aim for a medium-level harmony state, where harmony degree U falls within the range of [0.7, 0.8]. Using a pre-constructed quantitative control model, this target value is substituted into the formula for reverse calculation, determining the lower limit of the co-vibration intensity required to maintain this harmony degree level. This, in turn, yields the specific boundary values ​​of the water and sediment control factors. For instance, it is calculated that the proportion of flood season outflow from reservoir A must exceed a certain threshold. The results are then directly converted into actionable reservoir scheduling instructions to guide actual engineering operations.

[0038] This embodiment establishes a logical closed loop of data-variable-state-control, realizing a scientific mapping from complex system state assessment to specific engineering control parameters.

[0039] like Figure 2 As shown, in one possible implementation, sequential flow variables driving the evolution of the subsystem are identified from multidimensional parametric data, including:

[0040] The multidimensional parameter data is classified, and the parameter data of the same category are processed by arithmetic mean to obtain a simplified parameter set.

[0041] Specifically, since the originally acquired parameters may contain multiple data sequences of the same attribute from different monitoring stations, such as the annual average flow from multiple upstream hydrological stations, directly processing this highly correlated and redundant data would interfere with model recognition. Therefore, parameters are classified according to their physical attributes, and similar parameters are grouped together. For example, the annual average flow data of each major upstream section are arithmetically averaged to generate a representative upstream average flow sequence; the sediment concentration data of each section are averaged to generate an upstream average sediment concentration sequence. Through preprocessing, the data dimensionality is reduced, resulting in a more compact and simplified parameter set.

[0042] Based on a simplified parameter set, a pre-configured sequential flow variable identification model is used for preliminary identification to obtain macroscopic sequential flow variables.

[0043] In this embodiment, a sequential flow variable identification model is used to perform macroscopic-level screening of the simplified parameter set.

[0044] In a preferred implementation, the ordered flow variable identification model identifies ordered flow variables by calculating the similarity coefficient between the value parameter structure and the ideal value parameter structure.

[0045] The similarity coefficient is calculated using a modified cosine similarity formula:

[0046] r ki = (∑ j=1 p (wij ×w* ij )) / (sqrt(∑ j=1 p (w ij ) 2 )×sqrt(∑ j=1 p (w* ij ) 2 ));

[0047] Where r ki Let w be the similarity coefficient under the k-th dominant mode. ij For the j-th value parameter component of the i-th parameter in the k-th dominant mode, w* ij Let p be the component corresponding to the ideal value parameter structure, and p be the dimension of the value parameter.

[0048] The dominant mode with the largest similarity coefficient is selected as the evolution direction of the system, and the parameter ranked first in the dominant mode is determined as the sequential flow variable.

[0049] Specifically, the sequential flow variable identification model preferably uses similarity analysis based on the value parameter structure. The value parameter structure is obtained by performing goal programming analysis on each parameter in the simplified parameter set; the ideal value parameter structure consists of the optimal value parameters for each parameter in its corresponding dimension. The dominant pattern is obtained by performing cluster analysis or principal component analysis on the simplified parameter set. The calculation process of the sequential flow variable identification model is as follows: Constructing the ideal target vector y... i * For the i-th parameter, its ideal objective vector is composed of the optimal value of that parameter across all sample years. If the parameter is a positive indicator (the larger the better), the optimal value is the maximum; if it is a negative indicator (the smaller the better), the optimal value is the minimum. Based on the goal programming concept, from the perspective of best reflecting the value of parameter i, its weight on the j-th evaluation indicator is calculated, forming the value parameter structure vector w. ij =(w i1 , ..., w ip ) T ;where w i1 w represents the weight of the i-th parameter in the first evaluation metric dimension. ip Let i be the weight of the i-th parameter in the p-th evaluation index dimension. T This is a transpose. An ideal value parameter structure w* is constructed, consisting of the optimal value parameters of all parameters in their corresponding dimensions, representing the ideal evolution direction of the system. The similarity between the value parameter structure of each parameter and the ideal value parameter structure is calculated. To more accurately reflect this similarity, a modified cosine similarity formula is preferred to calculate the similarity coefficient r. kiThrough calculation, the dominant pattern with the highest similarity coefficient is selected as the evolution direction of the system, and the parameter ranked first in this dominant pattern is determined as the macroscopic sequential flow variable. For example, in a water and sediment subsystem, after preliminary identification, the upstream flat discharge may be selected as the macroscopic sequential flow variable.

[0050] The original parameters corresponding to the macroscopic sequential flow variables are extracted from the multidimensional parameter data, and the sequential flow variable identification model is used for secondary identification to obtain the final sequential flow variables.

[0051] In this embodiment, after determining the macroscopic direction, the focus shifts back to the raw data level for refined positioning. Macroscopic sequential flow variables, such as upstream flood discharge, are mapped back to the raw multidimensional parameter data, and the specific raw parameters constituting these macroscopic variables are extracted, such as the flood discharge at the Sanhu River estuary and the flood discharge at the Toudaoguai section. For this subset, a similarity coefficient calculation method is used again for secondary identification.

[0052] For example, after secondary identification and calculation, the similarity coefficient of the plain discharge at the Sanhu River estuary section was the highest, and therefore it was identified as the final sequential flow variable of the upstream water and sediment subsystem. Similarly, through a multi-level identification process, the core indicator system characterizing the evolutionary state of each subsystem in the Yellow River Basin was finally determined.

[0053] In an optional embodiment, the multidimensional parameter data includes: water and sediment subsystem parameters: including reservoir sediment discharge ratio, average flood season flow, floodplain flow, tortuosity coefficient, and Tongguan elevation; ecological subsystem parameters: including ecological pulse compliance rate, ecologically suitable flow guarantee rate, and critical period ecological water demand flow guarantee rate; and social subsystem parameters: including water supply guarantee rate, cascade reservoir group power generation guarantee rate, and total power generation. This provides precise input variables for subsequent co-vibration calculation and control model construction.

[0054] like Figure 3 As shown, according to one aspect of this application, the co-oscillation of each sequential flow variable is calculated, including:

[0055] The historical sequence data of the sequential flow variable are normalized to obtain the normalized level value, which represents the static development level of the sequential flow variable.

[0056] Specifically, to eliminate the influence of different dimensions, the original data of the sequential flow variable needs to be mapped to the interval [0, 1]. Differentiated standardization formulas can be used for parameters with different physical properties. For example, normalization processing of the historical sequence data of the sequential flow variable includes: identifying the index attributes of the sequential flow variable: if the variable is a positive index, i.e., the larger the value, the more beneficial it is to system development, such as floodplain flow and water supply guarantee rate, then the range standardization formula is used to calculate: U*(t) = (p(t) - p min) / (p max - p min If the variable is a negative indicator, meaning that a smaller value is more beneficial to system development, such as the sedimentation coefficient or riverbed siltation, then the inverse standardization formula is used to calculate: U*(t) = 1 - (p(t) - p min ) / (p max - p min ); where U*(t) is the normalized level value for year t, p(t) is the original observation value for year t, and p max and p min These represent the maximum and minimum values ​​of the variable in the historical statistical sequence, respectively. Through the above processing, the obtained normalized level value U* can objectively reflect the relative position of this parameter in the historical timeline.

[0057] As a basic implementation method, the calculated normalized level value U* can be directly defined as the co-vibration. Preferably, in order to introduce dynamic characteristics, the normalized level value U* can also be cooperatively corrected.

[0058] Calculate the evolution coordination coefficient between the sequential flow variable and other parameters within the subsystem. The evolution coordination coefficient characterizes the temporal synchronization degree between the sequential flow variable and the overall evolution of the subsystem.

[0059] like Figure 4 As shown, in an exemplary embodiment, calculating the evolution co-variance coefficients between the sequential flow variables and other parameters within the subsystem includes:

[0060] Construct a reference parameter set, which consists of the remaining parameters of the subsystem except for the sequential flow variables.

[0061] Specifically, to evaluate the representativeness and synergy of ordered flow variables, they need to be examined within the overall context of the subsystem. Let S be a subsystem S. x It contains m parameters, of which the ordered flow variable is P. xy Then refer to the parameter set Ω. x Defined as the set of all non-order flow variables within this subsystem, i.e.: Ω x = {Q1, Q2, ..., Q} m}\{P xy}; where \ represents removal in set operators. For example, if the water and sediment subsystem includes three parameters: floodplain flow (sequential flow variable), annual average flow, and annual average sediment concentration, then the reference parameter set consists of annual average flow and annual average sediment concentration.

[0062] Calculate the evolution direction indicator function of the sequential flow variable and each parameter in the reference parameter set. The evolution direction indicator function is used to identify the change state of the parameter in adjacent years, including rising, remaining flat or falling.

[0063] In this embodiment, the arbitrary parameter Q is calculated. i First-order difference between adjacent years: ΔQ i (t) = Q i (t) - Q i (t-1). Based on the difference results, define the evolution direction indicator function D. i (t) is as follows: when the first-order difference ΔQ i When (t) > 0, D i (t) = +1, indicating an increase; when ΔQ i When (t) = 0, D i (t) = 0, indicating that the value remains unchanged; when ΔQ i When (t) < 0, D i (t) = -1 indicates a decrease. The evolution direction indicator function simplifies complex numerical fluctuations into clear directional signals, laying the foundation for subsequent consistency analysis.

[0064] Based on the evolution direction indicator function, the directional consistency between the sequential flow variable and any parameter in the reference parameter set at the same time is calculated, and the average directional consistency between the sequential flow variable and any parameter in the reference parameter set over the statistical period is also calculated.

[0065] Specifically, directional consistency is the product of the evolution direction indicator functions of the two, i.e., the sequential flow variable P. xy With reference parameter Q i The directional consistency C at time t xy，i (t) is defined as the product of the two direction indicator functions: C xy，i (t) = D P (t)×D Qi (t); where D P (t) is the direction indicator function for the evolution of the ordered flow variable at time t, D Qi (t) is the direction indicator function for the evolution of a parameter in the reference parameter set Ωx at time t. If the direction consistency result is +1, it indicates that both parameters rise and fall together, and their evolution directions are consistent; if the result is -1, it indicates that one parameter increases while the other decreases, and their evolution directions are opposite; if the result is 0, it indicates that at least one parameter maintains its current state. Based on this, the arithmetic mean of the result over the entire statistical period T is calculated to obtain the average direction consistency C. xy，i This reflects the long-term cooperative relationship between ordered flow variables and a specific reference parameter in a long sequence. In other words, the average directional consistency is the arithmetic mean of the directional consistency of parameter pairs across all statistical moments. For example, C... xy，i = [1 / (T-1)]×∑ t=2 T (D P (t)×DQi (t)).

[0066] Based on the average directional consistency of all parameters in the reference parameter set, the evolutionary synergy coefficient η is calculated using the following formula. xy :

[0067] η xy = [1 + (1 / |Ω x |)×∑ i∈Ωx (C xy，i )] / 2;

[0068] Where |Ω x |For the reference parameter set Ω x The number of parameters in C xy，i The average direction of the ordered flow variable is consistent with that of the i-th parameter in the reference parameter set, and the summation range is the summation of all parameters in the reference parameter set.

[0069] In this embodiment, the formula for calculating the evolutionary synergy coefficient maps the average consistency of the [-1, +1] interval to the [0, 1] interval. If η xy A value close to 1 indicates that the ordered flow variables are highly synchronized with the vast majority of parameters within the subsystem, demonstrating strong system representativeness; if η xy A value close to 0 indicates that it runs counter to the overall evolution trend of the system.

[0070] Calculate the degree of co-existence: U(P) xy ) = U*(P xy )×η xy ;where U(P xy ) represents the degree of co-vibration, U*(P) xy ) represents the normalized level value, η xy This is the evolutionary co-evolution coefficient.

[0071] Specifically, the co-oscillation degree is corrected by multiplying the static level with the dynamic coordination. For example, in a certain year, the level value U* of a certain sequential flow variable is as high as 0.8, but because its evolution direction is opposite to that of other parameters, the coordination coefficient η is only 0.4. Therefore, the corrected co-oscillation degree U is reduced to 0.32. This reveals that although the variable has a high value, it is in a state of artificially high or uncoordinated development, thus avoiding misjudgment of the system's health status.

[0072] This embodiment addresses the shortcomings of existing technologies that rely solely on static normalized values, which cannot reflect the dynamic evolution relationship between parameters. It introduces a time-series analysis perspective and corrects the normalization level value by calculating the evolution synergy coefficient, thus solving the pseudo-synchronous problem of high-level but reverse-evolutionary evolution.

[0073] In one embodiment of this application, a quantitative control model is constructed, comprising the mapping relationship between the water and sediment control factor, the co-vibration of the sequential flow variable, and the system harmonicity, including:

[0074] For each sequential flow variable, a corresponding water and sediment control factor is selected, and regression analysis is used to establish the first quantitative relationship between the water and sediment control factor and the co-oscillation of the sequential flow variable.

[0075] In a preferred implementation, before establishing the first quantitative relationship between the water and sediment regulation factor and the isodynamicity of the sequential flow variable, the following is also included:

[0076] The cumulative effect of water and sediment regulation factors was processed to construct a cumulative effect regulation factor that reflects the lag and superposition of regulation measures.

[0077] In this embodiment, before establishing the relationship, considering that the impact of reservoir regulation on downstream areas often has time lags and cumulative effects—for example, the impact of upstream reservoir sediment discharge on downstream river morphology may last for several years—directly using the regulation factor data from the current year for fitting often yields poor results. Therefore, a cumulative effect processing is introduced. Specifically, a cumulative effect regulation factor X is constructed. cum (t), which can be expressed as a weighted sum of the current year and the control factors of several past years, or as an exponential decay cumulative model.

[0078] The optimal cumulative parameter is identified by maximizing the correlation coefficient between the water and sediment control factor and the co-vibration of the sequential flow variable.

[0079] Specifically, a search space is defined for accumulation parameters such as time window length and attenuation coefficient. The correlation coefficients (e.g., Pearson coefficients) between the accumulation effect control factor and the isodynamicity of the sequential flow variable under different parameters are calculated. The parameter combination that maximizes the correlation coefficient is selected as the optimal accumulation parameter.

[0080] The cumulative effect control factor generated based on the optimal cumulative parameters is used as the independent variable, and the co-oscillation of the sequential flow variable is used as the dependent variable. Fitting calculations are performed to construct the first quantitative relationship.

[0081] In this embodiment, based on the data processed with the optimal cumulative parameters, regression analysis is preferably used to construct the first quantitative relationship. For different physical processes, the fitting function can be a logarithmic function, a power function, or a linear function. For example, for the flow isodynamic intensity of the Sanhu River estuary in the upstream area, its relationship with the flood season flow process parameters of Reservoir A (characteristic flow rate 1400 m³ / h) is established. 3 The quantitative relationship between / s) and the fitted power function formula is: Q1=0.7548×θ LJZ 0.1246 Where Q1 is an intermediate variable or normalized value related to the isodynamicity, and θLJZ Let H be the flow parameters of Reservoir A during the flood season. For the isodynamic intensity at Tongguan elevation in the middle reaches, a quantitative relationship is established between it and the discharge ratio of Reservoir B. The fitted logarithmic formula is: H = 0.4937 + 1.7325 × ln(α) SMX ); where H is the isodynamic variable, α SMX Let be the discharge ratio of reservoir B. The specific mathematical expression constitutes the first core layer of the model.

[0082] Based on the weights of each ordered flow variable, a second quantitative relationship is established between the co-vibration of the ordered flow variable and the system harmonicity.

[0083] Specifically, according to the weighted summation formula U=∑ x ∑ y (W xy ×U(P xy Since the weight W xy Typically, a preset constant, such as 1 / 3, is used; therefore, this embodiment essentially establishes a linear mapping relationship. This transforms the microscopic change in co-vibration intensity into a macroscopic change in system harmonicity.

[0084] By cascading the first and second quantitative relationships, a quantitative control model is obtained, which takes water and sediment control factors as input and system harmony degree as output.

[0085] In a further embodiment, based on a quantitative control model, the control threshold of the water and sediment control factor satisfying the target harmony degree range is solved in reverse, including:

[0086] Obtain the lower limit value of the target harmonicity interval, substitute the lower limit value into the second quantitative relationship for inverse calculation, and obtain the target isodynamic lower limit of the ordered flow variable required to maintain the target state of the system.

[0087] For example, the target state of the system is set as intermediate harmonicity, i.e., the system harmonicity U ≥ 0.7. Assuming the system consists of three equally weighted subsystems, and to simplify the calculation, assuming that the co-vibration of each subsystem develops in a balanced manner, the required lower limit of the co-vibration of the sequence current variable should also be about 0.7. Its specific value needs to be solved inversely based on the actual weights.

[0088] Identify the correlation direction between the water and sediment regulation factor and the co-vibration of the sequential flow variable; substitute the lower limit of the target co-vibration into the first quantitative relationship to calculate the corresponding boundary value of the water and sediment regulation factor; determine the regulation threshold based on the correlation direction and boundary value: if there is a positive correlation, the regulation threshold is determined to be greater than or equal to the boundary value; if there is a negative correlation, the regulation threshold is determined to be less than or equal to the boundary value.

[0089] In this embodiment, the direction of correlation is determined by the sign of the regression coefficient in the first quantitative relationship. For example, the flow rate at the Sanhu River estuary is known to be positively correlated with the flood season flow process parameter θ of Reservoir A. Substituting the target isodynamic correlation value into the formula: Q1 = 0.7548 × θ LJZ 0.1246 Perform the inverse operation. Assume the boundary value obtained from the inverse calculation is 0.25. Since there is a positive correlation, the final control threshold is determined as follows: the outflow from Reservoir A during the flood season is greater than 1400 m³ / h. 3 The proportion of water volume per second to the total outflow during the flood season should be greater than 0.25. For example, regarding the Tongguan elevation, its isodynamic intensity (the Tongguan elevation itself is a negative indicator, but its normalized isodynamic intensity is positive) and the outflow ratio α of reservoir B should be considered. SMX They are positively correlated. If the boundary value obtained by inverse calculation is 1.12, then the control threshold is: the discharge ratio of reservoir B should be greater than or equal to 1.12. This embodiment successfully transforms the abstract sustainable development goal into specific engineering control instructions such as flow ratio and discharge ratio.

[0090] In another embodiment of this application, constructing a quantitative control model that includes the mapping relationship between the co-vibration degree of water and sediment control factors, sequential flow variables, and system harmonicity can also be:

[0091] The Yellow River Basin cascade reservoir system is regarded as a dynamic control system, and a discrete-time state-space model is constructed with sequential flow variables as state variables and candidate water and sediment regulation factors as control variables.

[0092] In this embodiment, the variables are no longer viewed in isolation, but rather the Yellow River basin is considered as a holistic dynamic system. The state vector x(t) is defined as consisting of the ordered flow variables of each river segment, such as x = [plain flow, ecological pulse guarantee rate, water supply guarantee rate]. T The control vector u(t) is defined as consisting of all candidate water and sediment regulation factors, such as u = [outflow from reservoir A, sediment discharge ratio from reservoir B, discharge coefficient from reservoir C]. T The candidate water and sediment regulation factors are a set of parameters with potential regulatory effects pre-selected from multidimensional parameter data.

[0093] In a preferred implementation, the discrete-time state-space model is represented as:

[0094] x(t+1) = A×x(t) +B×u(t)+ w(t);

[0095] Where x(t) is the ordered flow variable vector at time t, u(t) is the water and sediment regulation factor vector at time t, w(t) is the random disturbance vector, A is the state matrix reflecting the natural evolution of the system, and B is the input matrix reflecting the influence of the regulation factor.

[0096] Constructing a discrete-time state-space model specifically involves using the least squares method to fit the state matrix A and the input matrix B based on pre-stored historical data.

[0097] Specifically, A is the state matrix, reflecting the evolution of the system under natural conditions, such as the natural transmission of water from upstream to downstream; B is the input matrix, reflecting the control effect of various water and sediment regulation factors on the sequential flow variables; w(t) is the random disturbance vector. Preferably, the least squares method or subspace identification algorithm is used to estimate the parameters of matrices A and B based on historical observation data.

[0098] For different combinations of candidate water and sediment control factors, the corresponding controllability Gramian matrix is ​​calculated based on the discrete-time state-space model.

[0099] For example, for any subset S of candidate water and sediment control factors, the controllability Gramian matrix Wc(S) in the finite time domain is calculated using the following formula:

[0100] Wc(S)=∑ k=0 N-1 (A k ×Bs×Bs T ×(A T ) k );

[0101] Where Bs is a submatrix consisting of column vectors corresponding to subset S in the input matrix B. T For the transpose, N is the length of the time window; k is the index of the discrete time step in the finite time domain; the summation range is k=0 to N-1. The matrix Wc(S) geometrically describes the range of the state space that the system state can reach under finite energy constraints, i.e., the controllable ellipsoid.

[0102] The harmonic controllability index is calculated based on the controllability Gramian matrix. The harmonic controllability index characterizes the ability of a combination of control factors to drive a sequential flow variable to a preset target state.

[0103] For example, the harmonic controllability index C is calculated using the following formula. ctrl (S):

[0104] C ctrl (S) = log(det(Wc(S) +εI));

[0105] Where det represents the matrix determinant, εI is the regularization term to prevent singularity, and log represents the logarithmic operation; the value of the determinant is proportional to the volume of the controllable ellipsoid.

[0106] If C ctrlThe larger the value of (S), the stronger the harmonic controllability of the combination of water and sediment regulation factors corresponding to the subset S. In other words, C ctrl The larger the value, the stronger the control ability of the combination of regulatory factors on the sequential flow variables, that is, the system can be driven to any desired harmonic state at a relatively low cost.

[0107] The optimal combination of control factors is selected when the controllability index of the harmonic fit meets the preset threshold, and a quantitative control model is constructed based on the optimal combination of control factors.

[0108] Alternatively, one can select the optimal combination of controllable factors when the harmonic controllability index meets the preset threshold or reaches its maximum value, and construct a quantitative control model based on this optimal combination of controllable factors.

[0109] In one possible implementation, when selecting the optimal combination of control factors that satisfies the preset threshold or reaches its maximum value for the harmonic controllability index, a greedy strategy can be adopted to select the most efficient combination from numerous candidate factors: initialize the control factor combination as an empty set; iterate through all unselected candidate water and sediment control factors, add them to the current combination respectively, and calculate the marginal harmonic controllability index increment ΔC after addition. ctrl The regulatory factor that will bring the largest increase in the marginal harmonic controllability index will be formally added to the portfolio until the harmonic controllability index C is reached. ctrl (S) Exceeds a preset threshold or the increment of the marginal harmony controllability index is less than the preset threshold, i.e., diminishing marginal returns. The factor combinations selected through a greedy strategy can not only effectively regulate the system but also avoid control redundancy caused by too many factors, achieving optimal regulation efficiency. As an alternative, if computational resources permit, integer programming or genetic algorithms can also be used to globally optimize all possible factor combinations.

[0110] This embodiment introduces modern control theory and uses a state-space model to screen the most driving regulatory factors from a mechanistic perspective, thus solving the spurious correlation problem that may exist in traditional correlation analysis.

[0111] like Figure 5As shown, according to one aspect of this application, the sustainable development regulation method for the Yellow River Basin cascade reservoir system can also be as follows: Divide the Yellow River Basin cascade reservoir system into multiple subsystems and select representative multi-parameters from each subsystem. Use mathematical methods to identify sequential flow variables at multiple levels for different subsystems, collect historical data of these sequential flow variables, and calculate the co-vibration of each sequential flow variable. Higher co-vibration indicates a higher degree of development of the sequential flow variable. Combined with the co-vibration of the sequential flow variables, calculate the harmony variation process of each river segment in the complex basin system. Select corresponding water and sediment regulation factors for each sequential flow variable and establish a quantitative relationship between the water and sediment regulation factors and the co-vibration of the sequential flow variables. Combining this with the previous quantitative relationship between the co-vibration of the sequential flow variables and the system harmony, a quantitative relationship between the water and sediment regulation factors and the system harmony can be obtained. Through this quantitative relationship, the water and sediment regulation factors can be quantified and targeted in reverse, thereby maintaining a high degree of harmony in the basin and achieving sustainable development of the complex basin system.

[0112] The sequential flow variable is a key parameter describing the degree of internal parameter fit during the system's evolution. It reflects the increase, decrease, and transformation of the system's harmony degree with factors such as time, energy, and information, and reflects the characteristics and trends of the system's flow and evolution between different states. It is a key element in understanding the system's harmony degree. The resonance degree emphasizes the degree of synchronization in the evolution of parameters within a subsystem, reflecting the synchronicity and consistency among parameters in terms of development rhythm and frequency. The harmony degree emphasizes the closeness of the coordination and fit between the various subsystems of the system, reflecting the system's inherent harmony.

[0113] In an exemplary embodiment, the Yellow River cascade reservoir system is divided into three major subsystems: water and sediment, ecology, and society. Based on the characteristics of different sections of the Yellow River, it is further divided into three sections: upper reaches, middle reaches, and lower reaches. Multiple parameters are selected for each system, including: water and sediment subsystem parameters: reservoir sediment discharge ratio, average annual flow, average flood season flow, average annual sediment concentration, average flood season sediment concentration, floodplain flow, tortuosity coefficient, Tongguan elevation, etc.; social subsystem parameters: water supply guarantee rate, cascade reservoir power generation guarantee rate, total power generation of the cascade reservoir system, etc.; ecological subsystem parameters: ecological pulse compliance rate, ecologically suitable flow guarantee rate, critical period ecological water demand flow guarantee rate, etc.

[0114] Assume a subsystem of the Yellow River cascade reservoir system has m parameters, and the state of each parameter is represented by a parameter system consisting of a p-dimensional vector index x. Given the different dimensions of each parameter, the original data is first processed to be dimensionless. An ideal target vector yi* is constructed, and then, following the idea of ​​goal programming, its value parameter structure is determined from the perspective that best reflects parameter i. The value parameter structure of the i-th parameter is: w ij =(w i1 ,…,w ij ,…,wip ) T This leads to the ideal value parameter structure. For all w within the system... ij Cluster analysis was performed to obtain multiple dominant patterns of the system, and the similarity coefficient between the value parameter structure of each dominant pattern and the ideal value parameter structure was calculated. Cosine similarity was used for improvement, which can more accurately reflect the degree of similarity between the value parameter structures of different dominant patterns and the ideal value parameter structure. The larger the similarity coefficient, the closer the value parameter structure of the k-th dominant pattern is to the ideal value parameter structure, and the stronger its role in the system evolution process. Therefore, among all the dominant patterns of the system, the dominant pattern with the largest similarity coefficient dominates the evolution and development of the system. The parameter ranked first in this dominant pattern has a guiding and controlling effect on the remaining parameters, and can influence the direction of the system's evolution and development, i.e., the order current variable.

[0115] Given the large number of parameters within the Yellow River Basin system, identifying all parameters often results in similarity coefficients across parameters, making it difficult to distinguish sequential flow variables. Therefore, a multi-level identification method is proposed. When the number of parameters is excessive, a preliminary screening is performed, averaging parameters of the same type (such as the annual average flow of upstream hydrological stations) to simplify the number of parameters. Then, a sequential flow variable identification model is used to obtain macroscopic sequential flow variables. A secondary identification is then performed on specific parameters within the macroscopic sequential flow variables to obtain the final sequential flow variables. Using the sequential flow variable identification model, the similarity coefficients and value structure parameters of macroscopic sequential flow variables in the three major subsystems of water, sediment, ecology, and economy within the Yellow River Basin cascade reservoir system are obtained, further leading to the sequential flow variables of each river section subsystem.

[0116] For example, in the upstream river section, within the water and sediment subsystem, the similarity coefficients and value structure parameters of the macroscopic sequential flow variables are 0.9934 / 0.1521, and those of the sequential flow variables are 0.9930 / 0.2489, respectively. The sequential flow variable is the plain discharge at the Sanhu River estuary. In the upstream river section, within the ecological subsystem, the similarity coefficients and value structure parameters of the macroscopic sequential flow variables are 0.9950 / 0.2806, and those of the sequential flow variables are 0.9976 / 0. .7402, the sequential flow variable is the ecologically suitable flow guarantee rate at the Toudaoguai section; in the upstream section, in the economic subsystem, the similarity coefficient and value structure parameter of the sequential flow variable are 0.9990 / 0.1831, and the sequential flow variable is the water supply guarantee rate at the Lanzhou section; in the midstream section, in the water and sediment subsystem, the similarity coefficient and value structure parameter of the sequential flow variable are 0.9948 / 0.1646, and the sequential flow variable is the Tongguan elevation; in the midstream section, in the ecological subsystem, the similarity coefficient and value structure parameter of the sequential flow variable are respectively... The sequential flow variable is 0.8924 / 0.2431, representing the ecologically suitable flow guarantee rate at the Tongguan section. In the middle reaches, within the economic subsystem, the similarity coefficient and value structure parameter of the sequential flow variable are 0.9933 / 0.1849, respectively, and the sequential flow variable is the water supply guarantee rate at the Huayuankou section. In the lower reaches, within the water and sediment subsystem, the similarity coefficient and value structure parameter of the macroscopic sequential flow variable are 0.9952 / 0.2258, and the similarity coefficient and value structure parameter of the sequential flow variable are 0.9884 / 0.3519, respectively. The sequential flow variable is the plain discharge at the Sunkou section; in the downstream river section, within the ecological subsystem, the similarity coefficient and value structure parameter of the macroscopic sequential flow variable are 0.9744 / 0.3076, and the similarity coefficient and value structure parameter of the sequential flow variable are 0.9997 / 0.5651, respectively. The sequential flow variable is the ecologically suitable flow guarantee rate at the Lijin section; in the downstream river section, within the economic subsystem, the similarity coefficient and value structure parameter of the sequential flow variable are 0.9995 / 0.2933, respectively. The sequential flow variable is the water supply guarantee rate at the Lijin section.

[0117] Let the Yellow River basin cascade reservoir system S consist of x interconnected subsystems, i.e., S = (S1, S2, ..., S...). x (x=3), the development and changes of each subsystem will be affected by the sequential flow variable P xy =(P x1 P x2 , ..., P xm The influence of ) is 1≤y≤m. Given the different dimensions and influences of the original data, the ordered flow variables are normalized to obtain the isodynamicity U(P) of the ordered flow variables. xyThe system harmony degree U is used to characterize the harmony level of the development process of n subsystems. The value of U ranges from [0, 1]. The larger the value, the higher the harmony level of the three subsystems. At least 10 harmony states can be divided according to the value of U.

[0118] The calculated process of the harmony degree variation of the Yellow River basin cascade reservoir system is as follows: Figure 6 As shown, from 1965 to 1985, the basin's harmony index fluctuated, with the annual variation range being upstream < downstream < midstream; from 1986 to 2001, the basin's harmony index fluctuated and decreased, with the decline range being upstream ≈ midstream < downstream; from 2002 to 2020, the basin's harmony index fluctuated and increased, with the increase range being upstream ≈ midstream < downstream.

[0119] The flow rate at the Sanhu River estuary mainly depends on the upstream water and sediment conditions, such as the inflow volume, sediment coefficient, and flood season flow parameters. Generally, a large upstream inflow volume, a small sediment coefficient, and high flood season flow parameters favor sediment transport, resulting in a corresponding increase in the flow rate at the estuary. The upstream water and sediment conditions at the Sanhu River estuary are closely related to the operation of Reservoir A. Therefore, the outflow volume, sediment coefficient, and flood season flow parameters of Reservoir A are selected as water and sediment control factors. Each factor can be controlled by adjusting the outflow volume and sediment concentration of Reservoir A. Considering that the flow rate at the estuary responds differently to the annual and flood season water and sediment conditions, the water and sediment control factors are analyzed separately for the annual and flood season periods. The fitted quantitative relationship is as follows: When the water and sediment control factor is the annual outflow volume, the fitted formula is Q1 = -1.1455 + 0.2517lnQ LJZ Goodness of fit R 2 The value is 0.2169; when the water and sediment control factor is the flood season outflow, the fitting formula is Q1=-1.1156+0.2390lnQ LJZ，汛 R 2 The value is 0.3392; when the water and sediment control factor is the annual sediment inflow and outflow coefficient, the fitting formula is Q1=0.5436-0.0010lnρ LJZ R 2 The value is 0.1360; when the water and sediment control factor is the sediment inflow coefficient during the flood season, the fitting formula is Q1=-0.0209-0.0749lnρ LJZ，汛 R 2 The value is 0.2913; when the water and sediment regulation factor is the flood season flow process, the characteristic flow is 1000 m³ / s. 3 When the value is 0.6454θ, the fitting formula is Q1 = 0.6454θ. LJZ，汛 0.1871 R 2 The value is 0.3182; when the water and sediment regulation factor is the flood season flow process, the characteristic flow is 1200 m³ / s. 3When the value is 0.7061θ, the fitting formula is Q1 = 0.7061θ. LJZ，汛 0.1439 R 2 The value is 0.3779; when the water and sediment regulation factor is the flood season flow process, the characteristic flow is 1400 m³ / s. 3 When the value is 0.7548θ, the fitting formula is Q1 = 0.7548θ. LJZ，汛 0.1246 R 2 It is 0.5166. Where Q... LJZ Let Q be the average annual outflow from reservoir A. LJZ，汛 Let ρ be the average outflow from reservoir A during the flood season. LJZ Let ρ be the annual sediment inflow coefficient of reservoir A. LJZ，汛 Let θ be the sediment inflow coefficient of reservoir A during the flood season. LJZ，汛 Q1 represents the characteristic parameters of the water flow process during the flood season in Reservoir A, and Q1 represents the flat beach flow at the Sanhu River Estuary section.

[0120] It can be seen that the flow rate at the Sanhu River estuary is directly proportional to the outflow from Reservoir A and the flow process, and inversely proportional to the sediment inflow coefficient. The characteristic flow rate is 1400 m³ / s. 3 The highest correlation was found in the water flow process at a rate of / s, so Q1=0.7548θ was chosen. LJZ，汛 0.1246 This represents the quantitative response relationship between upstream water and sediment regulation factors and the flow rate at the Sanhu River Estuary section.

[0121] The evolution of the Tongguan elevation is closely related to factors such as the operation mode of Reservoir B and the conditions of water and sediment inflow. The discharge ratio and sediment discharge ratio of Reservoir B are selected as water and sediment control factors. Each factor can be controlled by adjusting the outflow and sediment concentration of Reservoir B. The quantitative relationship obtained by fitting is as follows: When the water and sediment control factor is the discharge ratio, the fitting formula is H = 0.4937 + 1.7325lnα SMX Goodness of fit R 2 The value is 0.4862; when the water and sediment control factor is the sediment discharge ratio, the fitting formula is H=0.4600+0.0429lnβ. SMX Goodness of fit R 2 It is 0.1245. Where α SMX Let β be the discharge ratio of reservoir B. SMX H represents the sediment discharge ratio of reservoir B, and H represents the elevation of Tongguan.

[0122] It can be seen that the elevation of Tongguan is directly proportional to the discharge ratio of Reservoir B. Therefore, we choose H = 0.4937 + 1.7325lnα. SMX As a quantitative response relationship between the midstream water and sediment regulation factors and the Tongguan elevation.

[0123] The flow rate at the Sunkou section is also primarily dependent on the upstream water and sediment conditions, which are closely related to the operation of Reservoir C. Therefore, the water and sediment control factors selected are the outflow from Reservoir C, the sediment inflow coefficient, and the flood season flow process parameters. Each factor can be controlled by adjusting the outflow and sediment concentration of Reservoir C. Considering that the flow rate at the flat beach exhibits different responses to the water and sediment conditions throughout the year and during the flood season, the water and sediment control factors are analyzed separately for the whole year and the flood season. The fitted quantitative relationship is as follows: When the water and sediment control factor is the annual outflow, the fitted formula is Q2 = -0.7740 + 0.1821lnQ XLD Goodness of fit R 2 The value is 0.5971; when the water and sediment control factor is the flood season outflow, the fitting formula is Q2=-0.1312+0.0853lnQ XLD，汛 R 2 The value is 0.4425; when the water and sediment regulation factor is the flood season flow process, the characteristic flow is 2000 m³ / s. 3 When the value is 0.5 m / s, the fitting formula is Q2 = 0.4970θ. XLD 0.0818 R 2 The value is 0.2005; when the water and sediment regulation factor is the flood season flow process, the characteristic flow is 2200 m³ / s. 3 When the value is 0.5530θ, the fitting formula is Q2 = 0.5530θ. XLD 0.1433 R 2 The value is 0.2700; when the water and sediment regulation factor is the flood season flow process, the characteristic flow is 2400 m³ / s. 3 When the value is 0.5069θ, the fitting formula is Q2 = 0.5069θ. XLD 0.0505 R 2 The value is 0.4488; when the water and sediment regulation factor is the flood season flow process, the characteristic flow is 2600 m³ / s. 3 When the value is 0.5023θ, the fitting formula is Q2 = 0.5023θ. XLD 0.0410 R 2 It is 0.4237. Where Q... XLD Let Q be the average annual outflow from reservoir C. XLD，汛 Let θ be the average outflow from reservoir C during the flood season. XLD Q1 represents the characteristic parameters of the water flow process during the flood season in Reservoir C, and Q2 represents the flat beach flow at the Sunkou section.

[0124] It can be seen that the flow rate at Sunkou Pingtan is positively proportional to both the outflow from Reservoir C and the flow process. The strongest correlation is with the annual outflow from Reservoir C, so the formula Q2 = -0.7740 + 0.1821lnQ is chosen. XLD The quantitative response relationship between downstream water and sediment regulation factors and the plain flow at the Sunkou section.

[0125] By using the ordered flow variable as an intermediate quantity, a quantitative relationship between the water and sediment regulation factor and the system's harmony degree is established. This allows for the adjustment of the water and sediment regulation factor to alter the system's harmony degree, thereby maintaining the sustainable development of the Yellow River basin's cascade reservoir system. Based on the harmony degree calculation model, the quantitative relationship between the ordered flow variable and the harmony degree of each river segment in the system can be obtained:

[0126] U= n sqrt(∏ x=1 n (∑ y=1 m W xy U(P xy (J s ur X ur ))));

[0127] Where U is the system harmonicity, U(P) xy W represents the normalized value of the y-th sequential flow variable in the x-th subsystem. xy Let W be the weight of the y-th ordered flow variable in the x-th subsystem. Here, each subsystem in each river segment has only one ordered flow variable, therefore W... xy It can also be considered as the weight of the x-th subsystem. Assuming that the weights of the subsystems are the same, they are all taken as 1 / 3. J s un X is the water and sediment regulation factor (negative entropy flow). ur This is the system state vector; n sqrt() represents taking the nth root; ∏ is the product operator; n is the number of subsystems in the system, and m is the number of ordered stream variables in each subsystem.

[0128] Upstream: U(P) 11 ) = 0.7548θ LJZ，汛 0.1246 ;U(P 21 = -1.3503 + 0.3231lnQ LJX ;U(P 31 )={1.0, Q LJX ≥830m 3 / s; -3.6322 + 0.6870lnQ LJX Q LJX <830m 3 / s}. Midstream: U(P 12 ) = 0.4937 + 1.7325lnα SMX ;U(P 22 = -0.1152 + 0.1633lnQ WJZ ;U(P 32 )={1.0, Q XLD ≥800m3 / s; -4.2350 +0.7782lnQ XLD Q XLD <800m 3 / s}. Downstream: U(P 13 = -0.7740 + 0.1821lnQ XLD ;U(P 23 = -2.9373 + 0.5505lnQ XLD ;U(P 33 )={1.0, Q XLD ≥810m 3 / s; -8.6903 + 1.4446lnQ XLD Q XLD <810m 3 / s}. Where Q LJX Q represents the average or representative outflow from reservoir A throughout the year. WJZ This refers to the average or representative outflow from reservoir F throughout the year.

[0129] In the future process of water and sediment regulation in the Yellow River Basin, we can first calculate how to change the water and sediment regulation factors to maintain the basin at a high degree of harmony, that is, to achieve the sustainable development of the basin system through the water and sediment regulation of the reservoir group.

[0130] In 2020, the normalized flood discharge at the Sanhu River estuary reached 0.36 m³ / h. Setting the normalized flood discharge at the Sanhu River estuary to ≥0.5 m³ / h indicates a barely compatible condition; in this case, the flood discharge should be ≥2611 m³ / h. 3 / s, greater than the past 20 years' flood discharge. Based on the normalized quantitative response relationship between the flood discharge at the Sanhu River estuary and the flood season flow process of Reservoir A, the calculated flow process of Reservoir A during the flood season should be ≥0.25, meaning the outflow from Reservoir A during the flood season should be greater than 1400 m³ / s. 3 The proportion of water volume per second to the total outflow during the flood season should be greater than 0.25.

[0131] In 2020, the ecological suitability flow guarantee rate at the Toudaoguai section reached 100%. A guarantee rate of ≥0.9 is set at the Toudaoguai section, indicating a high-quality and coordinated state. Based on the quantitative response relationship between the ecological suitability flow guarantee rate at the Toudaoguai section and the average daily outflow from Reservoir A, the calculated average daily outflow from Reservoir A should be ≥1061 m³ / h. 3 / s.

[0132] In 2020, the water supply guarantee rate at the Lanzhou section reached 100%. This 100% guarantee rate indicates a high-quality, coordinated operation. Based on the response relationship between the Lanzhou section's water supply guarantee rate and the average daily outflow from Reservoir A, the calculated average daily outflow from Reservoir A should be ≥830 m³ / h. 3 / s.

[0133] Therefore, when the upper reaches of the Yellow River reach a medium-level coordinated state, the boundary for water and sediment regulation is: the outflow from Reservoir A during the flood season is greater than 1400 m³ / h. 3 The proportion of water volume per second to the total outflow during the flood season should be greater than 0.25; and the average daily outflow of Reservoir A should be ≥1061 m³ / s. 3 / s.

[0134] Since 2003, a 318 control system has been adopted, meaning that the highest operating water level during non-flood seasons will not exceed 318m, while during flood season and normal water levels it will be controlled at 305m, with a flow rate greater than 1500m³. 3 / s Open discharge and sediment removal. The elevation of Tongguan decreased to 327.38m in 2012, but gradually rose again since 2013, reaching 328.11m in 2018. Assuming the normalized elevation of Tongguan is ≥0.7, the elevation should be ≤326.88m. Based on the quantitative response relationship between the normalized elevation of Tongguan and the discharge ratio of Reservoir B, the discharge ratio of Reservoir B should be ≥1.12.

[0135] In 2020, the ecological suitability flow guarantee rate at the Tongguan section reached 100%. The ecological suitability flow guarantee rate at the Tongguan section is set at ≥0.95, indicating a high-quality and coordinated state. Based on the quantitative response relationship between the ecological suitability flow guarantee rate at the Tongguan section and the average daily outflow of reservoir F, the calculated average daily outflow of reservoir F should be ≥681 m³ / s. 3 / s.

[0136] In 2020, the water supply guarantee rate at the Huayuankou section reached 100%. This 100% guarantee rate indicates a high-quality, coordinated operation. Based on the response relationship between the Huayuankou section's water supply guarantee rate and the average daily discharge flow from Reservoir C, the calculated average daily discharge flow from Reservoir C should be ≥800 m³ / h. 3 / s.

[0137] From 2003 to 2020, although water and sediment levels were relatively low, Reservoir C was in its water storage and sediment retention operation phase. Except during water and sediment regulation and flood periods, it primarily discharged clear water. This led to continuous scouring of the main channel downstream, curbing the shrinking and siltation of the riverbed. Consequently, the flood-carrying capacity of the lower Yellow River channel recovered significantly, and the floodplain discharge increased to 4500 m³. 3 Approximately / s. With the normalized flow rate at the Sunkou section set at ≥0.5, it is in a barely compatible state; at this point, the flow rate should be ≥4150 m³ / s. 3 / s. Based on the normalized quantitative response relationship between the plain discharge at Sunkou section and the outflow from reservoir C, the outflow from reservoir C is calculated to be ≥1090m³ / s. 3 / s.

[0138] In 2020, the ecological suitability flow guarantee rate at the Tongguan section reached 100%. The ecological suitability flow guarantee rate at the Tongguan section is set at ≥0.9, indicating a high-quality and coordinated state. Based on the quantitative response relationship between the ecological suitability flow guarantee rate at the Lijin section and the average daily outflow from Reservoir C, the average daily outflow from Reservoir C is calculated to be ≥1065 m³ / h. 3 / s.

[0139] In 2020, the water supply guarantee rate at the Lijin section reached 100%. This 100% guarantee rate indicates a high-quality, coordinated operation. Based on the response relationship between the Lijin section's water supply guarantee rate and the average daily discharge flow from Reservoir C, the calculated average daily discharge flow from Reservoir C should be ≥810 m³ / h. 3 / s.

[0140] Therefore, when the middle and lower reaches of the Yellow River reach a moderate level of coordination, the boundary for water and sediment regulation is: the discharge ratio of reservoir B should be ≥1.12, and the calculated average daily discharge of reservoir F should be ≥681 m³ / s. 3 / s, the average daily outflow of reservoir C should be ≥1090m³ / s. 3 / s.

[0141] According to one aspect of this application, a computer system and hardware architecture for implementing the sustainable development regulation method of the Yellow River Basin cascade reservoir system as described in any of the above embodiments are provided, including: a data acquisition subsystem, a transmission network, a computing processing center, and a regulation execution terminal.

[0142] The data acquisition subsystem is responsible for performing multi-dimensional parameter acquisition tasks. Specifically, the data acquisition subsystem includes a network of hydrological monitoring stations deployed at key sections in the upper, middle, and lower reaches of the Yellow River, such as Sanhuhekou, Toudaoguai, Tongguan, Huayuankou, Sunkou, and Lijin. These stations are equipped with sensors such as water level gauges, flow meters, and online sediment concentration monitors to collect water and sediment subsystem parameters in real time. The subsystem also includes ecological monitoring buoys and biodiversity observation stations to acquire ecological subsystem parameters such as ecological pulses and suitable flow rates. Simultaneously, it acquires social subsystem parameters such as power generation and water supply guarantee rate through server interfaces connected to the power grid dispatch center and water supply company.

[0143] The computing center is typically a high-performance server or cloud computing platform. This center is equipped with memory and a processor. The memory pre-stores historical long-sequence hydrological data, a trained sequential flow variable identification model, a quantitative control model, and a preset harmonicity grading standard. The processor is configured to execute computer programs to implement the core algorithm steps in the aforementioned embodiments, including: multi-level identification of sequential flow variables using an improved cosine similarity algorithm; calculating the corrected dynamic co-oscillation using the evolutionary co-evolutionary coefficient formula; constructing a quantitative control relationship based on statistical regression or a state-space model; and inversely solving for the control threshold based on the target harmonicity interval.

[0144] The control execution terminal is connected to the dam control center of each cascade reservoir. When the calculation and processing center outputs the control threshold of the water and sediment control factor, for example, when the proportion of outflow from reservoir A during the flood season is >0.25, the control execution terminal converts the digital signal into specific gate opening instructions or scheduling plans to assist dispatchers or automatic control systems in performing water and sediment control operations, transforming theoretical calculation results into actual actions that change the physical state of the river.

[0145] In addition, a computer-readable storage medium, such as a hard disk, optical disk, or flash memory, is provided, on which computer instructions are stored. When these instructions are executed by a processor, they can implement all the steps of the sustainable development regulation method for the Yellow River Basin cascade reservoir system described in any of the above embodiments.

[0146] This invention abandons the traditional approach of focusing solely on numerical values ​​and proposes a method for calculating the co-vibration intensity based on evolutionary coordination coefficients. By constructing a temporal evolution trend vector, it quantifies the consistency of the sequential flow variables with other parameters in the direction of change. Multiplying the static level with the dynamic synchronization degree effectively identifies and eliminates artificially high states where parameter levels are high but the evolution trends are contradictory, ensuring that the evaluation results truly reflect the co-evolutionary characteristics of the system. A harmonic controllability screening method and a two-layer inverse control system based on a state-space model are constructed. On the one hand, a controllability Gramian matrix is ​​introduced to quantify the ability of control factors to drive system state changes from a mechanistic perspective, replacing simple correlation screening and giving the selected factors substantial physical driving force. On the other hand, an inverse algebraic solution path of target harmonicity—co-vibration intensity—control factor is established, and combined with cumulative effect parameter optimization, accurate back-calculation is achieved.

[0147] 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 sustainable development regulation of a cascade reservoir system in the Yellow River Basin, characterized in that, include: The Yellow River Basin cascade reservoir system is divided into water and sediment, ecological and social subsystems, and multidimensional parameter data characterizing the operational status of each subsystem are obtained. Identify the sequential flow variables driving the evolution of the subsystem from multidimensional parametric data; Calculate the co-oscillation of each sequential flow variable to characterize the level of coordination in variable evolution; Calculation of the system harmony degree of the Yellow River Basin cascade reservoir system based on the co-vibration degree; A quantitative control model was constructed by selecting water and sediment control factors and constructing a mapping relationship between the co-vibration degree of water and sediment control factors, sequential flow variables, and system harmonicity. The target harmony degree range of the Yellow River Basin cascade reservoir system is set, and the control threshold of water and sediment control factors that satisfy the target harmony degree range is solved in reverse based on the quantitative control model. Calculate the isodynamics of each ordered flow variable, including: The historical sequence data of the sequential flow variable are normalized to obtain the normalized level value, which characterizes the static development level of the sequential flow variable; Calculate the evolution coordination coefficient between the sequential flow variables and other parameters within the subsystem, which characterizes the temporal synchronization between the sequential flow variables and the overall evolution of the subsystem; Calculate the degree of co-existence: U(P) xy ) = U*(P xy )×η xy ;where U(P xy ) represents the isotropic degree, U*(P) xy ) represents the normalized level value, η xy Evolutionary co-evolution coefficient; A quantitative control model is constructed, incorporating the mapping relationship between the isodynamic intensity and system harmonicity of water and sediment control factors, sequential flow variables, and water-sediment harmony. For each sequential flow variable, a corresponding water and sediment control factor is selected, and regression analysis is used to establish the first quantitative relationship between the water and sediment control factor and the co-oscillation of the sequential flow variable; Based on the weights of each ordered flow variable, a second quantitative relationship is established between the co-vibration of the ordered flow variables and the system harmonicity. By cascading the first and second quantitative relationships, a quantitative control model is obtained with water and sediment control factors as input and system harmony degree as output. Before establishing the first quantitative relationship between the water and sediment regulation factor and the isodynamicity of the sequential flow variable, the following steps are also included: Cumulative effect processing was applied to water and sediment regulation factors to construct a cumulative effect regulation factor that reflects the lagged and superimposed effects of regulation measures; The optimal cumulative parameter is identified with the goal of maximizing the correlation coefficient between the water and sediment control factor and the co-vibration of the sequential flow variable. The cumulative effect control factor generated based on the optimal cumulative parameters is used as the independent variable, and the co-oscillation of the sequential flow variable is used as the dependent variable. Fitting calculations are performed to construct the first quantitative relationship.

2. The method according to claim 1, characterized in that, Identify the sequential flow variables driving the evolution of the subsystem from multidimensional parametric data, including: The multidimensional parameter data is classified, and the parameter data of the same category are processed by arithmetic mean to obtain a simplified parameter set; Based on a simplified parameter set, a pre-configured sequential flow variable identification model is used for preliminary identification to obtain macroscopic sequential flow variables; The original parameters corresponding to the macroscopic sequential flow variables are extracted from the multidimensional parameter data, and the sequential flow variable identification model is used for secondary identification to obtain the final sequential flow variables.

3. The method according to claim 2, characterized in that, The ordered flow variable identification model identifies ordered flow variables by calculating the similarity coefficient between the value parameter structure and the ideal value parameter structure; The similarity coefficient is calculated using a modified cosine similarity formula: r ki = (∑ j=1 p (w ij ×w* ij )) / (sqrt(∑ j=1 p (w ij ) 2 )×sqrt(∑ j=1 p (w* ij ) 2 )); Where r ki Let w be the similarity coefficient under the k-th dominant mode. ij For the j-th value parameter component of the i-th parameter in the k-th dominant mode, w* ij Let p be the component corresponding to the ideal value parameter structure, and p be the dimension of the value parameter. The dominant mode with the largest similarity coefficient is selected as the evolution direction of the system, and the parameter ranked first in the dominant mode is determined as the sequential flow variable.

4. The method according to claim 1, characterized in that, Calculate the evolution co-variance coefficients between the ordered flow variables and other parameters within the subsystem, including: Construct a reference parameter set, which consists of the remaining parameters in the subsystem except for the sequential flow variables; Calculate the evolution direction indicator function of the sequential flow variable and each parameter in the reference parameter set to identify the change state of the parameter in adjacent years, including rising, remaining flat or falling; Based on the evolution direction indicator function, the directional consistency between the sequential flow variable and any parameter in the reference parameter set at the same time is calculated, and the average directional consistency over the statistical period is calculated. Based on the average directional consistency of all parameters in the reference parameter set, the evolutionary synergy coefficient η is calculated using the following formula. xy : ； Where |Ω x |For the reference parameter set Ω x The number of parameters in C xy，i The average direction of the ordered flow variable is consistent with that of the i-th parameter in the reference parameter set.

5. The method according to claim 1, characterized in that, A quantitative control model that includes the mapping relationship between the co-vibration degree and the system harmonicity of water and sediment control factors and sequential flow variables can also be constructed as follows: The Yellow River Basin cascade reservoir system is regarded as a dynamic control system, and a discrete-time state-space model is constructed with sequential flow variables as state variables and candidate water and sediment regulation factors as control variables. For different combinations of candidate water and sediment control factors, the corresponding controllability Gramian matrix is ​​calculated based on the discrete-time state-space model; The harmonic controllability index is calculated based on the controllability Gramian matrix to characterize the ability of a combination of control factors to drive a sequential flow variable to a preset target state. The optimal combination of control factors is selected when the controllability index of the harmonic fit meets the preset threshold, and a quantitative control model is constructed based on the optimal combination of control factors.

6. The method according to claim 5, characterized in that, The discrete-time state-space model is represented as: x(t+1) = A×x(t) + B×u(t) + w(t); Where x(t) is the ordered flow variable vector at time t, u(t) is the water and sediment regulation factor vector at time t, w(t) is the random disturbance vector, A is the state matrix reflecting the natural evolution of the system, and B is the input matrix reflecting the influence of the regulation factor. Constructing a discrete-time state-space model specifically involves using the least squares method to fit the state matrix A and the input matrix B based on pre-stored historical data.

7. The method according to claim 5, characterized in that, Calculate the corresponding controllability Gramian matrix and harmonic controllability index, including: For any subset S of the candidate water and sediment control factors, the controllability Gramian matrix Wc(S) in the finite time domain is calculated using the following formula: Wc(S)=∑ k=0 N-1 (A k ×Bs×Bs T ×(A T ) k ); Where Bs is a submatrix consisting of column vectors corresponding to subset S in the input matrix B. T For transpose, N is the length of the time window; k is the index of the discrete time step in the finite time domain; Calculate the harmonic controllability index C using the following formula. ctrl (S): C ctrl (S) = log(det(Wc(S) +εI)); Where det represents the matrix determinant, and εI is a regularization term to prevent singularity; If C ctrl The larger the value of (S), the stronger the controllability of the water and sediment regulation factor combination corresponding to the subset S.

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