Method and equipment for co-optimization of water quality simulation degradation coefficient and internal source strength of large shallow lake

Abstract

A large shallow lake water quality simulation degradation coefficient and internal source strength collaborative optimization method and equipment are disclosed. The method is based on the topographic data and hydrological boundary conditions of the target shallow lake to construct a forward control model, calculate the predicted concentration field of the target pollutant; based on the measured water quality data of each monitoring station and the predicted concentration field, a target function is constructed; when the target function does not meet the preset convergence precision, the biochemical degradation coefficient k and the internal source strength S are taken as the parameters to be inverted, the collaborative variational adjoint equation is constructed and solved based on the variational principle, the partial derivative gradient of the target function with respect to the two parameters is obtained, the joint update correction is calculated by the quasi-Newton optimization algorithm, and the two parameters are updated simultaneously; the above process is executed in a loop until convergence, and the k and S after collaborative optimization are output. The disclosure realizes the collaborative rating of k and S in a unified variational framework, overcomes the problem of compensation distortion due to opposite mechanisms, and significantly reduces the calculation cost of parameter rating.

Description

Technical Field

[0001] This disclosure relates to the field of water conservancy engineering and water environment numerical simulation technology, and in particular to a method and equipment for synergistic optimization of water quality degradation coefficient and endogenous source strength in large shallow lakes. Background Technology

[0002] Large, shallow lakes play a vital role in regional freshwater supply and ecological balance maintenance, but their shallow depth makes them highly susceptible to eutrophication. Numerical simulation is a primary technique for analyzing the evolution of lake water environments and supporting management decisions. Since the horizontal dimensions of shallow lakes are much larger than their vertical dimensions, depth-averaged two-dimensional hydrodynamic-water-quality coupled models are widely used in water quality prediction and management research for these lakes. These models include two key kinetic parameters in their source-sink terms: the biochemical degradation coefficient of pollutants, characterizing the water body's self-purification capacity for the biochemical decomposition of pollutants; and the endogenous source strength, characterizing the ability of sediment to release pollutants into the overlying water. Accurate calibration of these two parameters is a prerequisite for ensuring the model's predictive accuracy.

[0003] Conventional methods for determining water quality model parameters can be divided into two categories: trial and error and automatic optimization. Trial and error methods rely on human experience to adjust parameters, such as the modified Morse code and orthogonal experimental design, and are usually combined with parameter sensitivity analysis to improve calibration efficiency. Automatic optimization methods take minimizing the error between simulated and observed values ​​as the objective function, and optimize through iterative algorithms. Existing research has introduced particle swarm optimization (PSO) and deep reinforcement learning algorithms into water quality parameter calibration, improving the objectivity of the calibration. However, the above methods have the following shortcomings when dealing with two-dimensional models of large shallow lakes.

[0004] Regarding the joint identification of parameters, the degradation coefficient and the endogenous source strength have opposite effects on the concentration of pollutants in water: the former reduces the concentration, while the latter increases it. Conventional optimization algorithms lack a unified physical constraint mechanism when simultaneously calibrating these two parameters, which easily leads to compensation between the two parameters. That is, although the overall model fitting error is small, the calibration values ​​of each parameter deviate from their true physical meaning, weakening the predictive reliability of the model.

[0005] In terms of computational efficiency, a single forward numerical calculation of a large two-dimensional lake water environment model often takes tens of minutes or even hours. Black-box intelligent optimization methods, such as particle swarm optimization and genetic algorithms, typically require hundreds or thousands of forward model calls to complete the parameter search, and the computational cost is difficult to meet the efficiency requirements of engineering applications.

[0006] The adjoint method, a gradient-based solution tool using variational principles, requires only a few forward and backward calculations to obtain the exact partial derivatives of the objective function with respect to all parameters to be optimized, making its computational efficiency far superior to black-box intelligent algorithms. Currently, the adjoint method has shown application potential in scenarios such as one-dimensional river pollution source inversion. However, existing applications of the adjoint method are mostly limited to one-dimensional open channel or single-parameter inversion scenarios. When simultaneously inverting multiple inverse parameters within a two-dimensional water quality model containing complex biochemical source-sink terms, the physical reliability of the parameter inversion results is difficult to guarantee.

[0007] In summary, how to achieve the synergistic calibration of degradation coefficient and endogenous source strength in a two-dimensional shallow lake water quality model, while overcoming the efficiency bottleneck caused by large-scale forward calculation, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0008] This disclosure proposes a synergistic optimization scheme for degradation coefficient and endogenous source strength in large shallow lake water quality simulation. It can achieve synergistic calibration of degradation coefficient and endogenous source strength in two-dimensional shallow lake water quality models, while overcoming the efficiency bottleneck caused by large-scale forward calculation.

[0009] According to one aspect of this disclosure, a method for synergistic optimization of water quality simulation degradation coefficient and endogenous source strength in large shallow lakes is proposed, comprising: Based on the topographic data and hydrological boundary conditions of the target shallow lake, a depth-averaged two-dimensional hydrodynamic and water quality coupled positive control model is constructed. The initialized biochemical degradation coefficient and endogenous source strength are input into the positive control model to calculate the predicted concentration field of the target pollutant in the corresponding spatiotemporal domain. Based on the measured water quality data from each monitoring station of the target shallow lake and the current predicted concentration field, an objective function for the observation error is constructed. If the current function value of the objective function does not meet the preset convergence accuracy threshold, the biochemical degradation coefficient and endogenous source strength are updated. The updated biochemical degradation coefficient and endogenous source strength are then substituted into the forward control model, and the predicted concentration field is recalculated until the current function value of the objective function meets the preset convergence accuracy threshold. The current biochemical degradation coefficient and endogenous source strength are then output as the objective parameter results. Updating the biochemical degradation coefficient and endogenous source strength includes: constructing a cooperative variational adjoint equation based on the variational principle using the biochemical degradation coefficient and endogenous source strength as the parameters to be inverted; solving the adjoint equation to obtain the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and endogenous source strength, respectively; calculating the joint update correction amount of the biochemical degradation coefficient and endogenous source strength using a quasi-Newton optimization algorithm based on the partial derivative gradients; and updating the current biochemical degradation coefficient and endogenous source strength based on the joint update correction amount.

[0010] In some implementations, the positive control model is constructed using the following formula: , in, , Using horizontal orthogonal spatial coordinates, For time, For instantaneous water depth, , This represents the depth-averaged velocity component in the horizontal orthogonal direction. For pollutant concentration, The biochemical degradation coefficient, For internal strength, This is the horizontal mixing coefficient.

[0011] In some implementations, the objective function is constructed as the sum of weighted squared errors at each monitoring station and at each observation time: , in, The total number of monitoring stations. For the first Spatial coordinates of each monitoring station For the first The number of observation times at each monitoring station For the first The first monitoring station At each observation time, For the first The monitoring station, at the The predicted concentration field values ​​at each observation time. This corresponds to the measured concentration value. These are the weighting coefficients.

[0012] In some implementations, using the biochemical degradation coefficient and endogenous source strength as the parameters to be inverted, a cooperative variational adjoint equation is constructed based on variational principles, including: With companion variables As a Lagrange multiplier, the objective function and the positive control model are combined to construct a Lagrange functional; Based on the variational principle, the Lagrange functional is derived using variational derivation, yielding the following cooperative variational adjoint equation: , in, , Using horizontal orthogonal spatial coordinates, For time, For instantaneous water depth, , This represents the depth-averaged velocity component in the horizontal orthogonal direction. The horizontal mixing coefficient, The biochemical degradation coefficient, As an accompanying variable, To compute arbitrary spatial coordinates within the domain, For the first Spatial coordinates of each monitoring station The total number of monitoring stations. For the first The number of observation times at each monitoring station For the first The first monitoring station At each observation time, This represents the predicted concentration field value output by the positive control model. This corresponds to the measured concentration value. These are the weighting coefficients. Let be the Dirac function, and the adjoint equation be... For terminal conditions, To simulate the termination time, from Solve by integrating backwards from the initial time step.

[0013] In some implementations, the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and the endogenous source strength are extracted according to the following analytical formulas: , , in, For spatial computational domain, This is to simulate the termination time.

[0014] In some implementations, the joint update correction of the biochemical degradation coefficient and the endogenous source strength is calculated using a quasi-Newton optimization algorithm, including: By concatenating the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and the endogenous source strength, a joint gradient vector in two-dimensional space is constructed. Calculate the difference between the biochemical degradation coefficient and endogenous source strength of the current iteration step and the biochemical degradation coefficient and endogenous source strength of the previous iteration step, as the first difference vector; and calculate the difference between the joint gradient vector of the current iteration step and the joint gradient vector of the previous iteration step, as the second difference vector. Input the first difference vector, the second difference vector, and the approximate inverse Hessian matrix of the previous iteration step into the BFGS recursive formula to update and generate the approximate inverse Hessian matrix of the current iteration step, wherein the initial approximate inverse Hessian matrix is ​​initialized as a positive definite diagonal matrix. Calculate the negative dot product of the approximate inverse Hessian matrix of the current iteration step and the joint gradient vector to determine the two-parameter descent search direction; The step size factor along the two-parameter descent search direction is determined based on the line search criterion, and the product of the step size factor and the two-parameter descent search direction is used as the joint update correction.

[0015] In some implementations, determining the step size factor along the dual-parameter descent search direction based on the line search criterion includes: Set the trial step size factor along the dual-parameter descent search direction; Calculate the trial function value of the objective function and the inner product of the gradient after introducing the trial step size factor; Determine whether the trial function value and the inner product of the gradient satisfy a preset line search criterion; When the trial function value and the gradient inner product satisfy a preset line search criterion, the trial step size factor is determined as the step size factor.

[0016] In some implementations, the preset line search criterion is a one-dimensional inaccurate line search criterion, which includes any one of the Armijo criterion, Wolfe criterion, or strong Wolfe criterion.

[0017] In some implementations, the target shallow lake has complex topography and spatially varying bed roughness. Based on the topographic data and hydrological boundary conditions of the target shallow lake, a depth-averaged two-dimensional hydrodynamic and water quality coupled positive control model is constructed, including: The digital elevation model data of the target shallow lake is extracted as the topographic data, and the computational domain constructed based on the topographic data is divided into a structured or unstructured two-dimensional planar computational grid to fit the lake bottom topography and shoreline that includes waterways, shoals and / or open lakes. Obtain substrate distribution data, and based on the substrate distribution data, set a substrate roughness with spatial distribution characteristics for each computing unit of the computing grid; The flow and water level data of rivers flowing into the lake, pumping stations or dams flowing out of the lake are extracted as the hydrological boundary conditions to drive the numerical solution of the two-dimensional shallow water fluid dynamics equations, and to obtain the instantaneous water depth and depth-average velocity field of each calculation node.

[0018] According to another aspect of this disclosure, an electronic device is provided, the device including a memory and a processor, the memory being used to store computer instructions executable on the processor, the processor being used to implement the method described above when executing the computer instructions.

[0019] This disclosure proposes a synergistic optimization scheme for the biochemical degradation coefficient and endogenous source strength in large shallow lake water quality simulation. It constructs a depth-averaged two-dimensional hydrodynamic-water quality coupled forward control model based on the topographic data and hydrological boundary conditions of the target shallow lake. The biochemical degradation coefficient and endogenous source strength are input into this model to calculate the predicted concentration field, providing a physically consistent forward computational foundation for subsequent parameter inversion. Based on this, the scheme constructs an objective function using the observed errors between the measured water quality data from each monitoring station and the predicted concentration field. The biochemical degradation coefficient and endogenous source strength are used as the parameters to be inverted. A synergistic variational adjoint equation is constructed based on variational principles, and the partial derivative gradients of the objective function with respect to the two parameters are analytically obtained by solving this adjoint equation. This gradient extraction mechanism requires only a very small number of forward and backward calculations, overcoming the efficiency deficiency of traditional black-box intelligent algorithms that require numerous calls to the forward model to complete parameter search, and significantly reducing the computational cost of parameter calibration for large two-dimensional water quality models. Furthermore, this scheme uses the partial derivative gradients of the two parameters as a joint gradient vector, and calculates the joint update correction using a quasi-Newton optimization algorithm. This simultaneously updates the biochemical degradation coefficient and endogenous source strength until the objective function meets a preset convergence accuracy threshold, at which point the final parameter result is output. This joint update mechanism constrains the synchronous correction process of two opposing mechanism parameters within a unified mathematical framework, overcoming the shortcomings of conventional optimization methods where the two parameters are prone to compensation distortion and the physical reliability of the inversion results is difficult to guarantee. This improves the accuracy of the calibration parameters in representing the real physical process.

[0020] Other features and advantages of this disclosure are described below. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this specification and, together with the description, serve to explain the principles of this specification.

[0022] Figure 1 This is a flowchart of a method for synergistic optimization of water quality simulation degradation coefficient and endogenous source strength in large shallow lakes, provided in an embodiment of this disclosure. Figure 2 This is a schematic diagram of the technical route for synergistic optimization of water quality simulation degradation coefficient and endogenous source strength in large shallow lakes provided by an exemplary embodiment of this disclosure; Figure 3 This is a schematic diagram of the complete iterative calculation route for the synergistic optimization of degradation coefficient and endogenous source strength provided by an exemplary embodiment of this disclosure; Figure 4 This is a schematic diagram of the hardware structure of an electronic device provided in at least one embodiment of this disclosure. Detailed Implementation

[0023] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0024] This disclosure can be applied to computer systems / servers that can operate with a wide range of other general-purpose or special-purpose computing system environments or configurations. Examples of well-known computing systems, environments, and / or configurations suitable for use with computer systems / servers include, but are not limited to: personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments that include any of the above systems, etc.

[0025] Computer systems / servers can be described in the general context of computer system executable instructions (such as program modules) executed by the computer system. Typically, program modules can include routines, programs, object programs, components, logic, data structures, etc., which perform specific tasks or implement specific abstract data types. Computer systems / servers can be implemented in distributed cloud computing environments, where tasks are performed by remote processing devices linked through a communication network. In distributed cloud computing environments, program modules can reside on local or remote computing system storage media, including storage devices.

[0026] This disclosure addresses the difficulty of simultaneously and accurately inverting the biochemical degradation coefficient and endogenous source strength—two opposing parameters—in water quality simulation of large shallow lakes. It proposes a synergistic optimization method based on variational adjoint equations. This method, building upon a depth-averaged two-dimensional hydrodynamic-water quality coupled model, constructs a Lagrange functional and derives the synergistic adjoint equation using variational principles. It simultaneously extracts the partial derivative gradients of the objective function with respect to the two inverted parameters in a single forward and reverse calculation. Then, it combines this with the BFGS quasi-Newton algorithm to calculate the joint update correction of the two parameters. This achieves synergistic optimization of the degradation and endogenous release processes within a unified mathematical framework, overcoming the similarity defect of parameter compensation balancing in traditional methods and avoiding the direct calculation of high-dimensional Hessian matrices.

[0027] Please refer to Figure 1 , Figure 1This is a flowchart illustrating a method for synergistic optimization of water quality simulation degradation coefficients and endogenous source intensity in large shallow lakes, as provided in one embodiment of this disclosure. The implementation environment for this method can be a computer system equipped with a numerical computing platform. This system can load topographic, hydrological, and water quality observation data of the target shallow lake and perform coupled hydrodynamic and water quality simulations and parameter optimization calculations. This method can be applied to scenarios requiring water quality simulation parameter calibration for large shallow lakes, such as lake eutrophication control, endogenous pollution assessment, and water environment management decision support.

[0028] The method includes the following steps S1 to S4.

[0029] Step S1: Based on the topographic data and hydrological boundary conditions of the target shallow lake, construct a depth-averaged two-dimensional hydrodynamic and water quality coupled positive control model.

[0030] Large, shallow lakes have a horizontal dimension much larger than their vertical dimension, and water movement is predominantly horizontal. The vertical mixing timescale of pollutants is much shorter than the horizontal transport timescale. Based on this physical characteristic, this scheme employs a depth-averaged two-dimensional planar hydrodynamic water quality model to simulate the transport, diffusion, degradation, and endogenous release processes of pollutants. The input data for constructing the forward control model includes: topographic data of the target shallow lake, used to generate the computational grid and describe the lakebed elevation distribution; and hydrological boundary conditions, used to drive the numerical solution of the hydrodynamic equations and obtain instantaneous water depth and velocity field information at each computational node at different times. After the hydrodynamic field is solved, the velocity field and water depth field can be input as known quantities into the water quality control equations. Combined with the biochemical degradation coefficients and endogenous source strength to be inverted, a forward control model describing the spatiotemporal evolution of pollutant concentrations is established.

[0031] This forward control model comprehensively describes the processes of pollutant transport by water flow, diffusion caused by turbulent mixing, biochemical degradation of pollutants by water, and endogenous release of pollutants from sediment to overlying water. The biochemical degradation coefficient and endogenous source strength in this equation are the two target parameters to be optimized in this scheme.

[0032] In some implementations, a depth-averaged two-dimensional hydrodynamic-water quality coupled positive control model is constructed as follows: , in, , Using horizontal orthogonal spatial coordinates, For time, For instantaneous water depth, , This represents the depth-averaged velocity component in the horizontal orthogonal direction. The target concentration of typical pollutants, such as the permanganate index, The biochemical degradation coefficient, For internal strength, The horizontal mixing coefficient is represented by the equation. The first term on the left-hand side is the local temporal rate of change of concentration, and the second term is the convective transport term, representing the horizontal migration of pollutants with depth-average velocity. The first term on the right-hand side is the horizontal turbulent diffusion term, describing the diffusion process driven by the concentration gradient; the second term is the biochemical degradation term, where the degradation coefficient k multiplied by the water depth h and concentration C indicates that the degradation rate is proportional to the total amount of pollutants in the water; the third term is the endogenous source strength S, characterizing the rate at which bottom sediments release pollutants to the overlying water. In this model, the degradation term decreases the concentration, while the endogenous term increases it; their effects on concentration are opposite, which explains the equivalence problem in traditional parameter joint inversion.

[0033] For depth-averaged two-dimensional models, the horizontal mixing coefficient exhibits anisotropic characteristics. In the transverse direction of the flow, lateral diffusion plays a dominant role, and its mixing coefficient can be calculated as the ratio of eddy viscosity to Prandtl-Schmidt concentration number, i.e. ,in The viscosity is eddy current. This is the Prandtl-Schmidt concentration number, which is typically set to 1. In the longitudinal direction of the water flow, longitudinal dispersion is much greater than lateral diffusion, and can be calculated using Elder's longitudinal dispersion formula, i.e. ,in The velocity is the frictional flow velocity.

[0034] The boundary conditions for the forward control model can be set as follows: , That is, a given inflow concentration at the inflow boundary. Zero normal concentration gradient conditions are set at the outflow boundary and the shore boundary; the initial concentration distribution of the lake water is set at the initial time. .

[0035] In some implementations, the target shallow lake has complex topography and spatially varying bed roughness. The process of constructing a positive control model includes the following steps: Digital elevation model (DEM) data of the target shallow lake can be extracted as topographic data, which contains spatial distribution information of the lakebed elevation. Based on this topographic data, the computational domain can be divided into structured or unstructured two-dimensional planar computational grids to fit the lakebed topography and shoreline boundaries, including channels, shoals, and / or open lakes. For example, unstructured grids have advantages in handling irregular boundaries and local refinement, and are suitable for large lakes with meandering shorelines and undulating topography; structured grids have advantages in computational efficiency and numerical accuracy, and are suitable for waters with relatively regular boundary shapes. After gridding, bed sediment distribution data can be obtained. Based on this data, a spatially distributed bed roughness can be set for each computational unit to reflect the differences in flow resistance caused by different bed sediment types. Subsequently, flow and water level data from inflowing rivers, outflowing pumping stations, or dams can be extracted as hydrological boundary conditions to drive the numerical solution of the two-dimensional shallow water hydrodynamic equations, obtaining the instantaneous water depth and depth-averaged velocity field at each computational node. This implementation method, through refined terrain processing and spatially varying roughness settings, enables the forward control model to more accurately characterize the hydrodynamic features of complex lake environments, providing reliable hydrodynamic field driving data for subsequent water quality simulation and parameter inversion.

[0036] Step S2: Input the initialized biochemical degradation coefficient and endogenous source strength into the positive control model to calculate the predicted concentration field of the target pollutant in the corresponding spatiotemporal domain.

[0037] After the forward control model is constructed, the biochemical degradation coefficient k and the endogenous source strength S can be initialized. The initial values ​​can be selected by referring to historical calibration experience of the target lake or literature reports of similar lakes. Specific values ​​can be adjusted according to the lake's water quality characteristics and pollution load level. Substituting the initialized k and S into the constructed forward control model and performing numerical integration from the simulation start time backward, the predicted concentration field of the target pollutant over the entire computational domain and simulation period can be obtained. This predicted concentration field can record the predicted pollutant concentration values ​​at each time step for each computation node.

[0038] Step S3: Based on the measured water quality data from each monitoring station of the target shallow lake and the current predicted concentration field, construct an objective function for the observation error.

[0039] In water quality simulation, the actual observations from monitoring stations can be used as the optimization objective for inversion. By constructing an objective function, the error between the model's predicted concentration and the actual observed value can be minimized. Since actual observations are only obtained at a finite number of discrete times from a finite number of spatial monitoring stations, the construction of the objective function needs to summarize the prediction errors at each measuring point and at each observation time into a quantifiable scalar index, which serves as the convergence criterion for subsequent optimization iterations.

[0040] In some implementations, the objective function is constructed as the sum of weighted squared errors at each monitoring station and at each observation time: , in, The total number of monitoring stations. For the first Spatial coordinates of each monitoring station For the first The number of observation times at each monitoring station For the first The first monitoring station At each observation time, For the first The monitoring station, at the The predicted concentration field values ​​at each observation time. This corresponds to the measured concentration value. The weighting coefficients are used. The objective function involves a weighted sum of the squared differences between the predicted and measured concentrations at each monitoring station and observation time. The pre-weighting coefficients are... To facilitate elimination of the exponent during subsequent variational differentiation, weighting coefficients are used. The default value is 1, but it can also be weighted according to the observation accuracy to reflect the differences in the reliability of data from different monitoring stations or different observation times.

[0041] To achieve the integral expression in the continuous space-time domain required for subsequent variational derivation, the Dirac function can be introduced. Utilizing its filtering properties in the spatial and temporal dimensions: .

[0042] Based on the above properties, the discrete summation form can be equivalently rewritten as an integral form over the entire time and space domain. This integral form is strictly equivalent to the discrete summation form, but the integrand is in the continuous time and space domain. It has a unified definition and can be used for joint integration by parts and variational operations with the Lagrange functional constructed from the water quality control equation. In the subsequent derivation of the adjoint equation, this integral form can naturally generate impulse error source terms that are non-zero only at the measurement points, providing a mathematical basis for the derivation of the covariant adjoint equation.

[0043] By constructing the objective function as a weighted sum of squared errors, a well-structured quadratic functional can be generated while ensuring full utilization of the observation data from each monitoring station. This facilitates the subsequent extraction of the partial derivative gradients of the objective function for the parameters to be inverted using variational methods.

[0044] Step S4: If the current function value of the objective function does not meet the preset convergence accuracy threshold, update the biochemical degradation coefficient and endogenous source strength. Substitute the updated biochemical degradation coefficient and endogenous source strength into the forward control model and recalculate the predicted concentration field until the current function value of the objective function meets the preset convergence accuracy threshold. Output the current biochemical degradation coefficient and endogenous source strength as the objective parameter result. Updating the biochemical degradation coefficient and endogenous source strength includes: constructing a cooperative variational adjoint equation based on the variational principle using the biochemical degradation coefficient and endogenous source strength as the parameters to be inverted; solving the adjoint equation to obtain the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and endogenous source strength, respectively; calculating the joint update correction amount using a quasi-Newton optimization algorithm based on the partial derivative gradients; and updating the current biochemical degradation coefficient and endogenous source strength based on the joint update correction amount.

[0045] This step constitutes the iterative control flow of the entire collaborative optimization method. In each iteration, the current biochemical degradation coefficient k and endogenous source strength S are first substituted into the forward control model to solve for the predicted concentration field. Then, the error between the predicted and measured concentrations is substituted into the objective function to calculate the current function value. If the function value does not meet the preset convergence accuracy threshold, the parameter update phase begins. Each parameter update includes: constructing the collaborative variational adjoint equation, solving the adjoint equation to obtain the partial derivative gradient, calculating the joint update correction using a quasi-Newton optimization algorithm, and updating the parameters based on the correction. The updated parameters are substituted into the forward control model to recalculate the predicted concentration field, starting the next iteration. This process is repeated until the objective function value meets the convergence accuracy threshold. The convergence accuracy threshold can be determined according to the actual accuracy requirements. For example, it can be set to the objective function value being less than a certain preset small amount, or the rate of change of the objective function value between two adjacent iterations being less than a certain proportional threshold.

[0046] In some implementations, a preset maximum number of iterations can be set as a stopping condition. When the number of iterations reaches this preset maximum value, the iteration is terminated even if the objective function has not yet met the convergence accuracy threshold, and the current degradation coefficient and intrinsic source strength are output as parameter results.

[0047] The parameter update process will be described in detail below.

[0048] The first step is to construct the co-variant adjoint equations. Specifically, within the framework of variational principles, a set of adjoint equations dual to the forward control equations is established, so that the partial derivatives of the objective function with respect to the inversion parameters can be directly extracted from the solution of the adjoint variables without having to perform perturbation calculations for each parameter separately.

[0049] In some implementations, using the biochemical degradation coefficient and endogenous source strength as the parameters to be inverted, a cooperative variational adjoint equation is constructed based on variational principles, including: using adjoint variables... As Lagrange multipliers, a Lagrange functional is constructed by combining the objective function and the positive control model; based on the variational principle, the Lagrange functional is derived variationally to obtain the cooperative variational adjoint equation: , in, , Using horizontal orthogonal spatial coordinates, For time, For instantaneous water depth, , This represents the depth-averaged velocity component in the horizontal orthogonal direction. The horizontal mixing coefficient, The biochemical degradation coefficient, As an accompanying variable, To compute arbitrary spatial coordinates within the domain, For the first Spatial coordinates of each monitoring station The total number of monitoring stations. For the first The number of observation times at each monitoring station For the first The first monitoring station At each observation time, This represents the predicted concentration field value output by the positive control model. This corresponds to the measured concentration value. These are the weighting coefficients. The Dirac function is given by the adjoint equation. For terminal conditions, To simulate the termination time, from Solve by integrating backwards from the initial time step.

[0050] The construction process of the adjoint equation is as follows. The minimization process of the objective function must be strictly controlled by the physical laws of water convection and diffusion. Based on the general principles of the adjoint equation method, continuous spatiotemporal adjoint variables can be introduced. As a Lagrange multiplier, the objective function is added to the water quality simulation control equation to construct the Lagrange functional: , in, A transformation of the water quality simulation governing equations: .

[0051] This operation transforms the inversion problem constrained by physical equations into an unconstrained functional extremum problem. To find the extrema of the Lagrange functional, functional analysis can be performed to obtain the differential operators of the Lagrange functional. By using the two-dimensional Green's theorem, substituting relevant boundary conditions and the mass conservation equation, and performing integration by parts and algebraic transformations on the integral terms containing partial derivatives, the differential operator can be transformed from a concentration perturbation variable... Transfer to adjoint variables Above. Order By setting the coefficient term to zero and moving the contribution term of the objective function to the right-hand side of the equation, the adjoint equation that the adjoint variable must satisfy can be extracted.

[0052] On the right-hand side of the adjoint equation, the error between the predicted and measured concentrations, under the influence of the Dirac function, forms a pulse-like error source term that is non-zero only at the monitoring station, serving as the reverse excitation for solving the adjoint equation in reverse time. The adjoint equation is... As the terminal condition, combined with the adjoint boundary condition, the solution is obtained by inverse integration from the simulation termination time T to the initial time, so that the adjoint variable... Record the sensitivity response of errors to different spatiotemporal locations.

[0053] Through the variational derivation described above, the two parameters to be inverted—the degradation coefficient and the intrinsic source strength—can be processed simultaneously within a unified mathematical framework, allowing their gradient information to share the same adjoint field. This approach avoids perturbing each parameter individually and repeatedly solving the forward model, thus reducing the cost of gradient calculation.

[0054] The second step is to solve the adjoint equation to obtain the partial derivative gradient. After solving the adjoint equation, the gradient can be obtained based on the adjoint variables. The solution results are used to extract the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient k and the endogenous source strength S.

[0055] In some implementations, the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and the endogenous source strength are extracted according to the following analytical formulas: , , in, For spatial computational domain, This is to simulate the termination time.

[0056] The two gradient formulas mentioned above are derived from the variational derivation of the Lagrange functional. Under the conditions that the adjoint equation holds and the boundary line integrals are eliminated, only the operators related to the Lagrange functional differential operator remain. and The relevant terms allow for the analytical extraction of the partial derivatives of the objective function with respect to k and S. The integrand is This reflects the accompanying variables , water depth With concentration The cumulative effect of the three across the entire temporal and spatial domain; The integrand contains only , representing the accumulation of the adjoint variable over the entire time and space domain. These two gradients can be obtained by considering the adjoint field. and positive concentration field Numerical integration over the computational domain and simulation period is obtained directly, without the need for finite difference approximation of the objective function.

[0057] By analyzing the gradient formula, only one forward solution and one adjoint inverse solution are needed to simultaneously obtain the partial derivatives of the objective function with respect to the two inverted parameters. Compared with the traditional finite difference method, which requires perturbing each parameter separately and performing a forward solution for each, the computational cost does not increase with the parameter dimension, making it suitable for parameter inversion of large two-dimensional lake grids.

[0058] The third step is to calculate the joint update correction using a quasi-Newton optimization algorithm. The correction direction and magnitude can be determined based on the obtained gradients of the two-parameter partial derivatives. When dealing with optimization problems in large two-dimensional lake meshes, directly calculating the second derivative of the objective function with respect to the parameters (Hessian matrix) and its inverse is computationally intensive. This scheme uses the BFGS quasi-Newton optimization algorithm, which approximates the solution by successively modifying the tangent stiffness matrix. This retains the fast convergence speed of the Newton method while avoiding the direct calculation and inversion of the Hessian matrix.

[0059] In some implementations, the joint update correction of the biochemical degradation coefficient and the endogenous source strength is calculated using a quasi-Newton optimization algorithm, including: By concatenating the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and the endogenous source strength, a joint gradient vector in two-dimensional space is constructed. Calculate the difference between the biochemical degradation coefficient and endogenous source strength of the current iteration step and the biochemical degradation coefficient and endogenous source strength of the previous iteration step, as the first difference vector; and calculate the difference between the joint gradient vector of the current iteration step and the joint gradient vector of the previous iteration step, as the second difference vector. Input the first difference vector, the second difference vector, and the approximate inverse Hessian matrix of the previous iteration step into the BFGS recursive formula to update and generate the approximate inverse Hessian matrix of the current iteration step, wherein the initial approximate inverse Hessian matrix is ​​initialized as a positive definite diagonal matrix. Calculate the negative dot product of the approximate inverse Hessian matrix of the current iteration step and the joint gradient vector to determine the two-parameter descent search direction; The step size factor along the two-parameter descent search direction is determined based on the line search criterion, and the product of the step size factor and the two-parameter descent search direction is used as the joint update correction.

[0060] The specific implementation of the above process is as follows. The degradation coefficient k to be inverted and the intrinsic source strength S can be combined into a two-parameter joint control vector. In the nth iteration, the partial derivatives extracted in the previous step can be used to construct the joint gradient vector for that iteration step. The goal of optimization algorithms is to continuously refine them. Make the gradient vector It approximates the zero vector.

[0061] Set the parameter increment for step n to be The gradient increment is The inverse Hessian matrix can be approximately constructed and updated using the classic recurrence relation of Broyden-Fletcher-Goldfarb-Shanno (BFGS). : , Where I is the identity matrix. The initial approximate inverse Hessian matrix can be initialized as a positive definite diagonal matrix to ensure that the matrix generated in subsequent iterations is... Both remain positive definite and symmetrical, ensuring that the optimization process always proceeds in the descent direction.

[0062] Based on the updated matrix, the two-parameter descent search direction in step n can be calculated. : .

[0063] Once the search direction is determined, a suitable step size factor can be determined along that direction. This allows the objective function to decrease sufficiently. The product of the step size factor and the search direction is the synchronous update correction amount for the degradation coefficient k and the intrinsic source strength S, which generates a new parameter combination for the next iteration: .

[0064] In some implementations, determining the step size factor along the dual-parameter descent search direction based on the line search criterion includes: Set the trial step size factor along the dual-parameter descent search direction; Calculate the trial function value of the objective function and the inner product of the gradient after introducing the trial step size factor; Determine whether the trial function value and the inner product of the gradient satisfy a preset line search criterion; When the trial function value and the gradient inner product satisfy a preset line search criterion, the trial step size factor is determined as the step size factor.

[0065] According to this embodiment, the search can proceed along a predetermined search direction. Set a trial step size factor By substituting the trial step size factor into the parameter update formula, the trial function value of the objective function after introducing this trial step size can be calculated. and the inner product of the gradient and the search direction Then, it can be determined whether the trial function value and the inner product of the gradient satisfy the preset line search criterion. If they do, the trial step size factor is determined as the final step size factor. If the criteria are not met, the trial step size factor can be adjusted and the calculation and judgment recalculated until the criteria are met.

[0066] By constraining the step size factor through the line search criterion, it can be ensured that the objective function value decreases sufficiently in each iteration, avoiding the situation where the step size is too large, causing the optimal point to be missed, or the situation where the step size is too small, causing the convergence to be too slow.

[0067] In some implementations, the line search criterion is one of the Armijo criterion, the Wolfe criterion, or the strong Wolfe criterion.

[0068] Armijo guidelines require To ensure the function decreases sufficiently, the Wolfe criterion adds a curvature condition to the Armijo criterion. This can simultaneously guarantee the positive definiteness of the BFGS inverse Hessian approximation matrix. The strong Wolfe criterion strengthens the curvature condition into an absolute value constraint. It exhibits higher numerical robustness. and These are preset criterion parameters. In practical applications, a suitable criterion can be selected based on the numerical characteristics of the problem. When using the Wolfe criterion or the strong Wolfe criterion, the introduction of the curvature condition ensures that the denominator in the BFGS recursive formula... This maintains the positive definiteness of the inverse Hessian matrix, ensuring that the search direction in subsequent iterations is always the descent direction.

[0069] The fourth step is to update the parameters based on the joint update correction. The calculated step size factor... With search direction Multiplying these values ​​yields the synchronous update corrections for the degradation coefficient k and the intrinsic source strength S. This correction is then added to the current parameter values ​​to generate a new parameter combination for the next iteration. The new parameter combination can be substituted back into the forward control model to start the next round of forward solving, cyclically executing the process of prediction, adjoint inversion, and parameter update until the objective function value meets the preset convergence accuracy threshold. The degradation coefficient and intrinsic source strength used during convergence are the objective parameter results after co-optimization.

[0070] The above iterative process can be implemented based on a numerical computing platform. For example, an optimization algorithm module can be embedded in the open-source computational fluid dynamics framework OpenFOAM to construct an automatic closed-loop control process from data input to joint parameter optimization. Hydrodynamic field (instantaneous water depth) and depth average flow velocity The solution can be obtained once by solving the two-dimensional shallow water hydrodynamic equations before the iteration begins, and can be reused in the forward water quality calculations and adjoint equation solutions of all subsequent iterations without repeated calculations, thereby reducing the overall computational cost.

[0071] Please refer to Figure 2 , Figure 2 This diagram illustrates a technical route for the synergistic optimization of water quality simulation degradation coefficient and endogenous source strength in large shallow lakes, as provided in an exemplary embodiment of this disclosure. The diagram shows the layered technical route of this solution from theoretical foundation to engineering application.

[0072] The basic principles of this scheme include: variational principles and Lagrange operators, which construct the objective function through the Lagrange multiplier method, providing a theoretical basis for the subsequent inversion and derivation of parameters; and quasi-Newton optimization theory, which uses quasi-Newton algorithms such as BFGS to accelerate the convergence process of the objective function and improve the computational efficiency of degradation coefficient optimization.

[0073] In designing the scheme, this disclosure considers several interrelated operational stages. Regarding data input, multi-dimensional water quality data from sensors, remote sensing, or manual monitoring can be integrated to provide input for the model. For error quantification, the error gradient between the forward simulation results and measured data can be quantified by deriving the adjoint equation. Regarding parameter optimization, the collected data and error analysis can be combined, and iterative algorithms can be used to collaboratively optimize the degradation coefficient and endogenous source strength, ensuring model accuracy.

[0074] In engineering implementation, this solution can be developed and deployed based on a numerical computing platform. For example, optimization algorithms can be embedded in the open-source computational fluid dynamics platform OpenFOAM to build a customized water quality simulation module. After development, the system's reliability can be verified through standard calculation examples to ensure the accuracy of the algorithm in theoretical scenarios. After successful verification through calculation examples, the entire optimization method can be applied to actual large shallow lake environments to verify its effectiveness under real and complex working conditions.

[0075] Please refer to Figure 3 , Figure 3 This diagram illustrates a complete iterative calculation route for the synergistic optimization of degradation coefficient and endogenous source strength, as provided in an exemplary embodiment of this disclosure. The diagram details the complete calculation process of this exemplary embodiment, from data preparation to parameter convergence output.

[0076] The entire process can be divided into three stages. The first stage is model building and initialization. First, starting with acquiring digital elevation model data, lakebed topography and shoreline boundary information are extracted. Based on this, an unstructured computational grid is created to fit complex terrains such as channels and shoals. Seabed distribution data can also be acquired, and spatially distributed seabed roughness is set for each computational unit. After the grid and roughness settings are completed, flow and water level data from inflow rivers, outflow pumping stations, or dams can be extracted as hydrological boundary conditions to drive the numerical solution of the two-dimensional shallow water hydrodynamic equations, obtaining the instantaneous water depth and depth-averaged velocity field at each node. Simultaneously, the degradation coefficient k and the intrinsic source strength S are initialized, and the approximate inverse Hessian matrix is ​​initialized as a positive definite diagonal matrix.

[0077] The second stage involves forward solving and error assessment. Substituting the current values ​​of k and S into the depth-averaged two-dimensional convection-diffusion equation, forward numerical integration is performed from the initial time to the final time to obtain the predicted concentration field. Subsequently, the difference between the predicted and measured concentrations at each monitoring station at each observation time is calculated, and the objective function value J is obtained by summing the weighted squared errors. It is then determined whether the function value of J meets the preset convergence accuracy threshold. If it does, the current values ​​of k and S are output as the co-optimized objective parameter result, and the calculation process ends.

[0078] The third stage involves adjoint inversion and joint parameter update. If the objective function value does not meet the convergence accuracy threshold, the adjoint inversion and parameter update process begins. First, the concentration residuals at each monitoring station are calculated. Using the Dirac function, the residuals are constructed as impulse error driving terms that are non-zero only at the measuring points. This source term is then substituted into the co-variable adjoint equation, with terminal conditions... Using the initial value, integrate backwards from the termination time to the initial time to obtain the all-spacetime adjoint field. After solving for the adjoint field, the adjoint field and concentration field can be integrated over the entire time and space domain to analytically obtain the partial derivatives of the objective function with respect to k. and partial derivatives with respect to S .

[0079] After obtaining the two-parameter partial derivatives, you can... and Concatenate into a two-dimensional joint gradient vector Then, the parameter difference vector between the current step and the previous step is calculated. and gradient difference vector Substitute into the BFGS recursive formula to update the approximate inverse Hessian matrix. In the first iteration, a positive definite diagonal matrix can be directly used as the initial matrix. Based on the updated Calculate the negative dot product of the gradient with the joint gradient vector to determine the two-parameter descent search direction. Set the trial step size factor along the search direction, calculate the inner product of the trial function value and the gradient, and determine whether the line search criterion is satisfied. For example, the Armijo criterion, Wolfe criterion, or strong Wolfe criterion can be selected to determine the step size factor. .Will and Multiplying the values ​​yields a joint update correction, which simultaneously updates k and S. The updated parameters can be substituted back into the positive control model of the second stage to initiate the next iteration until convergence.

[0080] like Figure 3 As shown, this iterative process only needs to perform one forward solution and one accompanying reverse solution in each iteration to simultaneously obtain the updated correction amounts of the degradation coefficient and the intrinsic source strength, avoiding repeated calculations of perturbation solutions for the two parameters separately.

[0081] In summary, this scheme constructs a Lagrange functional and derives a cooperative variational adjoint equation. Within a unified mathematical framework, it simultaneously extracts the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and the endogenous source strength. Combined with the BFGS quasi-Newton algorithm, it achieves joint updating of the two parameters, forming a closed-loop iterative process of forward prediction, adjoint inversion, and parameter updating. This method overcomes the isomorphism defect of degradation coefficient and endogenous source strength easily falling into compensatory equilibrium due to their opposite directions of action. It also avoids the direct calculation of the Hessian matrix, reducing the computational cost of parameter inversion in large-scale two-dimensional lake grids. This provides a technical approach that balances physical reliability and computational efficiency for the cooperative calibration of parameters in shallow lake water quality simulation.

[0082] Figure 4 An electronic device provided in at least one embodiment of the present disclosure includes a memory and a processor. The memory is used to store computer instructions that can be executed on the processor. The processor is used to implement the method for synergistic optimization of water quality simulation degradation coefficient and endogenous source strength in large shallow lakes as described in any embodiment or implementation of the present disclosure when executing the computer instructions.

[0083] At least one embodiment of this disclosure also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for synergistic optimization of water quality simulation degradation coefficient and endogenous source strength in large shallow lakes as described in any embodiment or implementation of this disclosure.

[0084] Those skilled in the art will understand that one or more embodiments of this specification can be provided as a method, system, or computer program product. Therefore, one or more embodiments of this specification may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, one or more embodiments of this specification may take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0085] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the data processing device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0086] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps described in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired results. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0087] The embodiments of the subject matter and functional operation described in this specification can be implemented in the following ways: digital electronic circuits, tangibly embodied computer software or firmware, computer hardware including the structures disclosed in this specification and their structural equivalents, or combinations thereof. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier for execution by a data processing apparatus or for controlling the operation of a data processing apparatus. Alternatively or additionally, the program instructions may be encoded on artificially generated propagation signals, such as machine-generated electrical, optical, or electromagnetic signals, which are generated to encode information and transmit it to a suitable receiving device for execution by the data processing apparatus. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or combinations thereof.

[0088] The processing and logic flow described in this specification can be executed by one or more programmable computers that execute one or more computer programs to perform corresponding functions by operating on input data and generating output. The processing and logic flow can also be executed by dedicated logic circuitry—such as FPGAs (Field-Programmable Gate Arrays) or ASICs (Application-Specific Integrated Circuits), and the device can also be implemented as dedicated logic circuitry.

[0089] Suitable computers for executing computer programs include, for example, general-purpose and / or special-purpose microprocessors, or any other type of central processing unit. Typically, the central processing unit receives instructions and data from read-only memory and / or random access memory. The basic components of a computer include a central processing unit for implementing or executing instructions and one or more memory devices for storing instructions and data. Typically, a computer will also include one or more mass storage devices for storing data, such as disks, magneto-optical disks, or optical disks, or the computer will be operatively coupled to such mass storage devices to receive data from or transfer data to them, or both. However, a computer is not required to have such devices. Furthermore, a computer can be embedded in another device, such as a mobile phone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device such as a universal serial bus (USB) flash drive, to name a few.

[0090] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media, and memory devices, such as semiconductor memory devices (e.g., EPROM, EEPROM, and flash memory devices), magnetic disks (e.g., internal hard disks or removable disks), magneto-optical disks, and CD-ROM and DVD-ROM disks. Processors and memory may be supplemented by or incorporated into dedicated logic circuitry.

[0091] While this specification contains numerous specific implementation details, these should not be construed as limiting the scope of any invention or the scope of the claims, but rather are primarily intended to describe features of specific embodiments of a particular invention. Certain features described in the various embodiments herein may also be implemented in combination in a single embodiment. Conversely, various features described in a single embodiment may also be implemented separately in various embodiments or in any suitable sub-combination. Furthermore, while features may function in certain combinations as described above and even initially claimed in this way, one or more features from a claimed combination may be removed from that combination in some cases, and a claimed combination may refer to a sub-combination or a variation thereof.

[0092] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or sequentially, or requiring all illustrated operations to be performed to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0093] Thus, specific embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings are not necessarily shown in a specific order or sequence to achieve the desired result. In some implementations, multitasking and parallel processing may be advantageous.

[0094] The above description is merely a preferred embodiment of one or more embodiments of this specification and is not intended to limit the scope of one or more embodiments of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments of this specification should be included within the protection scope of one or more embodiments of this specification.

Claims

1. A method for synergistic optimization of water quality simulation degradation coefficient and endogenous source strength in large shallow lakes, characterized in that, include: Based on the topographic data and hydrological boundary conditions of the target shallow lake, a depth-averaged two-dimensional hydrodynamic and water quality coupled positive control model is constructed. The initialized biochemical degradation coefficient and endogenous source strength are input into the positive control model to calculate the predicted concentration field of the target pollutant in the corresponding spatiotemporal domain. Based on the measured water quality data from each monitoring station of the target shallow lake and the current predicted concentration field, an objective function for the observation error is constructed. If the current function value of the objective function does not meet the preset convergence accuracy threshold, the biochemical degradation coefficient and endogenous source strength are updated. The updated biochemical degradation coefficient and endogenous source strength are then substituted into the forward control model, and the predicted concentration field is recalculated until the current function value of the objective function meets the preset convergence accuracy threshold. The current biochemical degradation coefficient and endogenous source strength are then output as the objective parameter results. Updating the biochemical degradation coefficient and endogenous source strength includes: constructing a cooperative variational adjoint equation based on the variational principle using the biochemical degradation coefficient and endogenous source strength as the parameters to be inverted; solving the adjoint equation to obtain the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and endogenous source strength, respectively; calculating the joint update correction amount of the biochemical degradation coefficient and endogenous source strength using a quasi-Newton optimization algorithm based on the partial derivative gradients; and updating the current biochemical degradation coefficient and endogenous source strength based on the joint update correction amount.

2. The method according to claim 1, characterized in that, The positive control model is constructed using the following formula: ， in, , Using horizontal orthogonal spatial coordinates, For time, For instantaneous water depth, , This represents the depth-averaged velocity component in the horizontal orthogonal direction. For pollutant concentration, The biochemical degradation coefficient, For internal strength, This is the horizontal mixing coefficient.

3. The method according to claim 1, characterized in that, The objective function is constructed as the sum of weighted squared errors at each monitoring station and at each observation time: ， in, The total number of monitoring stations. For the first Spatial coordinates of each monitoring station For the first The number of observation times at each monitoring station For the first The first monitoring station At each observation time, For the first The monitoring station, at the The predicted concentration field values ​​at each observation time. This corresponds to the measured concentration value. These are the weighting coefficients.

4. The method according to claim 1, characterized in that, Using the biochemical degradation coefficient and endogenous source strength as the parameters to be inverted, a cooperative variational adjoint equation is constructed based on the variational principle, including: With companion variables As a Lagrange multiplier, the objective function and the positive control model are combined to construct a Lagrange functional; Based on the variational principle, the Lagrange functional is derived using variational derivation, yielding the following cooperative variational adjoint equation: , in, , The coordinates are horizontally orthogonal in space. For time, For instantaneous water depth, , This represents the depth-averaged velocity component in the horizontal orthogonal direction. The horizontal mixing coefficient, The biochemical degradation coefficient, As an accompanying variable, To compute arbitrary spatial coordinates within the domain, For the first Spatial coordinates of each monitoring station The total number of monitoring stations. For the first The number of observation times at each monitoring station For the first The first monitoring station At each observation time, This represents the predicted concentration field value output by the positive control model. This corresponds to the measured concentration value. These are the weighting coefficients. Let be the Dirac function, and the adjoint equation be... For terminal conditions, To simulate the termination time, from Solve by integrating backwards from the initial time step.

5. The method according to claim 4, characterized in that, The partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and the endogenous source strength are extracted using the following analytical formulas: ， ， in, For spatial computational domain, This is to simulate the termination time.

6. The method according to claim 1, characterized in that, The joint update correction of the biochemical degradation coefficient and the endogenous source strength is calculated using a quasi-Newton optimization algorithm, including: By concatenating the partial derivative gradients of the objective function with respect to the biochemical degradation coefficient and the endogenous source strength, a joint gradient vector in two-dimensional space is constructed. Calculate the difference between the biochemical degradation coefficient and endogenous source strength of the current iteration step and the biochemical degradation coefficient and endogenous source strength of the previous iteration step, as the first difference vector; and calculate the difference between the joint gradient vector of the current iteration step and the joint gradient vector of the previous iteration step, as the second difference vector. Input the first difference vector, the second difference vector, and the approximate inverse Hessian matrix of the previous iteration step into the BFGS recursive formula to update and generate the approximate inverse Hessian matrix of the current iteration step, wherein the initial approximate inverse Hessian matrix is ​​initialized as a positive definite diagonal matrix. Calculate the negative dot product of the approximate inverse Hessian matrix of the current iteration step and the joint gradient vector to determine the two-parameter descent search direction; The step size factor along the two-parameter descent search direction is determined based on the line search criterion, and the product of the step size factor and the two-parameter descent search direction is used as the joint update correction.

7. The method according to claim 6, characterized in that, Determining the step size factor along the dual-parameter descent search direction based on the line search criterion includes: Set the trial step size factor along the dual-parameter descent search direction; Calculate the trial function value of the objective function and the inner product of the gradient after introducing the trial step size factor; Determine whether the trial function value and the inner product of the gradient satisfy a preset line search criterion; When the trial function value and the gradient inner product satisfy a preset line search criterion, the trial step size factor is determined as the step size factor.

8. The method according to claim 7, characterized in that, The preset line search criterion is a one-dimensional inaccurate line search criterion, which includes any one of the Armijo criterion, Wolfe criterion, or strong Wolfe criterion.

9. The method according to claim 1, characterized in that, The target shallow lake has complex topography and spatially varying bed roughness. Based on the topographic data and hydrological boundary conditions of the target shallow lake, a depth-averaged two-dimensional hydrodynamic and water quality coupled positive control model is constructed, including: The digital elevation model data of the target shallow lake is extracted as the topographic data, and the computational domain constructed based on the topographic data is divided into a structured or unstructured two-dimensional planar computational grid to fit the lake bottom topography and shoreline that includes waterways, shoals and / or open lakes. Obtain substrate distribution data, and based on the substrate distribution data, set a substrate roughness with spatial distribution characteristics for each computing unit of the computing grid; The flow and water level data of rivers flowing into the lake, pumping stations or dams flowing out of the lake are extracted as the hydrological boundary conditions to drive the numerical solution of the two-dimensional shallow water fluid dynamics equations, and to obtain the instantaneous water depth and depth-average velocity field of each calculation node.

10. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store computer instructions executable on the processor, and the processor being used to implement the method of any one of claims 1 to 9 when executing the computer instructions.

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