Axial flow pump fish-friendly design method based on multi-objective optimization

Abstract

The application discloses a kind of based on multi-objective optimization's axial flow pump fish friendly design method, to solve the problem that fish damage evaluation index is difficult to engineering, insufficient calculability and difficult to be optimization objective function or constraint in engineering design stage, the present application obtains threshold value parameter of axial flow pump design variable and target fish, establishes three-dimensional model and carries out unsteady computational fluid dynamics simulation to obtain pressure field, velocity field and shear rate field, pressure change rate field;Based on flow tracking, the passing probability distribution is obtained to determine the effective area of fish passing and the weight of release position, and the risk assessment driven adaptive encryption sampling is carried out in the effective area until the evaluation index converges;Along the convergence trajectory, the damage dose is obtained by time integration of the super-threshold exposure of shear, pressure and pressure change rate, and the cumulative collision damage dose of collision event is identified;Based on the survival model of the cause-specific hazard rate, the survival probability is obtained and weighted to form the fish-friendly evaluation index, and then the multi-objective optimization is constructed together with the efficiency and head, and the iterative solution is obtained, which realizes the technical effect of calculability of fish-friendly index and collaborative optimization with hydraulic performance.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering technology, and in particular to a fish-friendly design method for axial flow pumps based on multi-objective optimization. Background Technology

[0002] Axial flow pumps, due to their large flow rate, compact structure, and suitability for low-head conditions, are widely used in farmland irrigation, urban drainage, water diversion projects, and various pumping station systems. In recent years, with increasing demands for river ecological restoration and aquatic life protection, pumping station intake and drainage projects, while meeting hydraulic performance requirements such as head and efficiency, are also increasingly focusing on the safety of fish passing through the pumping system. This has gradually led to a demand for the design and evaluation of fish-friendly hydraulic machinery, aiming to reduce the risk of fish injury and death without significantly sacrificing hydraulic performance.

[0003] In existing technologies, safety studies of fish using hydraulic machinery typically employ a combination of experimental observation and numerical simulation. On one hand, statistical data on fish injury and mortality are obtained through on-site monitoring, operational tests, or biological experiments. On the other hand, computational fluid dynamics numerical simulations are used to obtain unsteady pressure and velocity fields within the pump, and further extract flow field indicators related to potential damage, such as shear rate, pressure change rate, minimum pressure, turbulent kinetic energy, and vortex structure. Some studies also introduce Lagrange flow tracking methods to calculate the trajectories of tracer particles or simplified fish released at the inlet, estimating potential risks such as shear, pressure drop, pressure changes, and collisions. These studies also attempt to use these indicators as design constraints or additional evaluation metrics to assist in the improvement and optimization of pump types and blade parameters.

[0004] Existing technologies still have shortcomings in the engineering design phase, making it difficult to formulate computable criteria that can be directly used for optimization for fish-friendly targets. These shortcomings are mainly reflected in the following aspects:

[0005] 1. Insufficient engineering of evaluation indicators. Existing evaluations often rely on extreme value indicators or empirical thresholds for judgment, making it difficult to transform fish injury or death into a unified quantitative objective function or constraint that can be used for optimization. Furthermore, there is a lack of consistent comprehensive expression among different damage mechanisms.

[0006] 2. Insufficient efficiency and convergence in trajectory statistics. Uniform sampling or global tracking is often used for entry release positions, which easily generates a large number of invalid or low-contribution trajectories. The computational cost is high, and it is difficult to adaptively encrypt high-risk channels, resulting in unstable risk assessment results or difficulty in convergence.

[0007] 3. Insufficient characterization of the cumulative and competitive relationships of multi-mechanism damage. Existing methods mostly use over-threshold recording or simple superposition, which makes it difficult to reflect the cumulative dose effects of factors such as shear, pressure drop, pressure change rate and collision and their contribution from each cause. Therefore, it is not easy to output a comprehensive index of survival probability or damage probability that can be directly used for design optimization.

[0008] Therefore, a fish-friendly design method for axial flow pumps that can overcome the shortcomings of the existing technology is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0009] One objective of this invention is to propose a fish-friendly design method for axial flow pumps based on multi-objective optimization. Addressing the problems in existing technologies where fish damage assessment indices are difficult to engineer and lack computability, are unsuitable as design optimization objective functions or constraints, and suffer from low trajectory statistical efficiency and difficulty in characterizing multi-mechanism damage accumulation and outputting survival probability indices, the following technical solution is proposed: Based on given axial flow pump design variables, operating conditions, and target fish threshold parameters, a three-dimensional model is established, and unsteady computational fluid dynamics simulations are performed to obtain pressure, velocity, shear rate, and pressure change rate fields. Based on flow tracking, the passage probability distribution is obtained to determine the effective passage area for fish and the weight of release positions. Fish trajectories are generated only within the effective area, and the weights are adaptively updated and sampling is intensified based on risk assessment results until the fish-friendly assessment index converges. The damage dose is obtained by time integration of shear, pressure, and pressure change rate exceeding the threshold exposure along the converged trajectory, and the cumulative collision damage dose of collision events is identified. The survival probability is calculated based on a multi-causal hazard rate survival model and weighted summaries are used to form a fish-friendly assessment index. This index, along with efficiency and head indices, is then used to construct a multi-objective optimization and iteratively solved. This invention has the technical effect of quantifying fish damage risk into a calculable target, improving assessment convergence and statistical efficiency, and achieving synergistic optimization of fish-friendly and hydraulic performance.

[0010] This invention provides a fish-friendly design method for axial flow pumps based on multi-objective optimization, comprising:

[0011] S1. Obtain the design variable set, design constraints, operating condition parameters, and target fish parameters for the axial flow pump. Target fish parameters include fish length, shear rate threshold, pressure threshold, pressure change rate threshold, and collision determination threshold. S2. Establish a three-dimensional geometric model of the axial flow pump based on the design variable set and generate a computational mesh. Perform unsteady computational fluid dynamics simulation under operating condition parameters to obtain the pressure field and velocity field. This yields the shear rate field and pressure change rate field for fish risk assessment, along with efficiency and head indices. S3. Based on the velocity field, at the axial flow pump inlet... S4. Set a set of release locations at the boundary and track them with the current to obtain the passage probability distribution, and determine the effective passage area for fish and its corresponding release location weights; S5. Generate fish trajectories based on release location weights within the effective passage area for fish, and conduct risk assessments on the fish trajectories based on shear rate field, pressure field, pressure change rate field and corresponding thresholds. Update the release location weights according to the risk assessment results and perform encrypted sampling to generate encrypted fish trajectories until the fish friendliness evaluation index meets the preset convergence conditions, and obtain the converged fish trajectories and updated release location weights; S6. For each converged fish trajectory... The trajectory is determined by the shear rate field, pressure field, and pressure change rate field, and the excess shear, pressure, and pressure change rate on the trajectory are integrated over time to obtain the shear damage dose, pressure damage dose, and pressure change rate damage dose. The collision event is determined based on the distance and relative velocity between the converged fish trajectory and the solid boundary of the axial flow pump's three-dimensional geometric model, and the collision event intensity is accumulated to obtain the collision damage dose. S6. Based on the shear damage dose, pressure damage dose, pressure change rate damage dose, and collision damage dose, a multi-cause hazard rate survival model is established to obtain the survival probability corresponding to each converged fish trajectory, and the fish-friendly evaluation index is calculated in combination with the updated release position weight. S7. Using the fish-friendly evaluation index as the fish-friendly objective function, and the efficiency index and head index as the hydraulic performance objective functions, a multi-objective optimization problem is formed under the design constraints. S8. The multi-objective optimization problem is solved iteratively. In each iteration, the candidate design variable set is updated, and S2 to S7 are executed based on the updated candidate design variable set to obtain the corresponding objective function values. When the preset termination condition is met, the optimized design variable set is output, and the fish-friendly design scheme of the axial flow pump is output accordingly.

[0012] Optionally, S1 includes:

[0013] Obtain the structural boundary conditions and installation boundary conditions corresponding to the axial flow pump to be designed, and determine the design variable set and the value range of the design variable set based on the structural boundary conditions and installation boundary conditions. The design variable set includes impeller blade geometric parameters, guide vane geometric parameters, hub geometric parameters and blade tip clearance parameters.

[0014] Obtain the operating condition parameters corresponding to the axial flow pump to be designed. The operating condition parameters include flow rate parameters, speed parameters, inlet boundary condition parameters, and outlet boundary condition parameters.

[0015] Obtain the species information and body length information of the target fish, and determine the body length parameter based on the body length information;

[0016] Based on the pre-established correspondence between target fish parameters and thresholds, the shear rate threshold, the pressure threshold, the pressure change rate threshold, and the collision determination threshold are determined according to the target fish species information and the fish body length parameter.

[0017] Optionally, S2 includes:

[0018] A three-dimensional geometric model of the axial flow pump is established based on the design variable set, and the computational domain is divided. The computational domain includes the impeller rotation domain and the stationary domain connected to the impeller rotation domain.

[0019] A computational mesh is generated within the computational domain based on the three-dimensional geometric model of the axial flow pump.

[0020] Based on the operating condition parameters, inlet and outlet boundary conditions are applied to the computational domain, and rotational speed parameters corresponding to the operating condition parameters are applied to the impeller rotation domain.

[0021] Unsteady computational fluid dynamics simulation was used to solve the control equations in the computational domain by time-progression, and the pressure field and velocity field at each time step were obtained.

[0022] The shear rate field is calculated based on the velocity gradient of the velocity field.

[0023] Calculate the pressure rate of change field based on the pressure field of adjacent time steps;

[0024] The head index is determined based on the shaft power, flow parameters, and pressure field obtained from the unsteady computational fluid dynamics simulation, and the efficiency index is determined based on the head index, the flow parameters, and the shaft power.

[0025] Optionally, S3 includes:

[0026] The inlet section of the axial flow pump is divided into multiple grid cells at the inlet boundary, and a set of release positions is set in each grid cell;

[0027] Using each release position in the set of release positions as the initial position, the massless tracer particle is tracked by the flow based on the velocity field to obtain the corresponding tracer particle trajectory.

[0028] Based on the number of tracer particle trajectories that can reach the axial flow pump outlet boundary from the axial flow pump inlet boundary, the passage probability of each grid cell is calculated and a passage probability distribution is formed.

[0029] Grid cells with a passage probability not less than a preset passage probability threshold are used as effective passage areas for fish.

[0030] Based on the passage probability distribution, release position weights are assigned to each release position within the effective passage area for fish, and the release position weights are positively correlated with the passage probability of the corresponding grid cell.

[0031] Optionally, S4 includes:

[0032] Within the effective area for fish passage, release positions are extracted from the set of release positions according to the weight of the release positions, and each extracted release position is used as the initial position. Based on the velocity field, the initial fish trajectory is obtained by following the flow.

[0033] For each initial fish trajectory in the initial fish trajectory, the shear rate sequence, pressure sequence, and pressure change rate sequence on the initial fish trajectory are extracted based on the shear rate field, the pressure field, and the pressure change rate field, respectively. The shear rate sequence, pressure sequence, and pressure change rate sequence are then compared with the shear rate threshold, the pressure threshold, and the pressure change rate threshold, respectively. Based on the comparison results, the risk value corresponding to the initial fish trajectory is calculated.

[0034] The risk values ​​of each initial fish trajectory are aggregated according to their initial positions to obtain the risk weight distribution corresponding to the set of release positions. The release position weights are then updated and normalized based on the risk weight distribution to obtain the updated release position weights.

[0035] According to the updated release position weight, the release position is encrypted and extracted within the effective area for fish passage, and the encrypted fish trajectory is obtained by following the flow based on the velocity field.

[0036] Based on the encrypted fish trajectory, S5 and S6 are executed to obtain the corresponding fish-friendly evaluation index. The change in the fish-friendly evaluation index obtained in two adjacent iterations is not greater than the convergence threshold as the convergence condition. The risk weight distribution calculation, release position weight update and encrypted extraction of release position are executed cyclically until the convergence condition is met, and the converged fish trajectory and the updated release position weight corresponding to the converged fish trajectory are obtained.

[0037] Optionally, S5 includes:

[0038] For each convergent fish trajectory in the set of convergent fish trajectories, the shear rate, pressure and pressure change rate values ​​are obtained by interpolation at the corresponding fish position at each time step of the unsteady computational fluid dynamics simulation, forming the shear rate sequence, the pressure sequence and the pressure change rate sequence respectively.

[0039] The shear rate sequence is compared with the shear rate threshold to obtain the shear rate excess sequence, the pressure sequence is compared with the pressure threshold to obtain the pressure excess sequence, and the pressure change rate sequence is compared with the pressure change rate threshold to obtain the pressure change rate excess sequence. The shear rate excess sequence, the pressure excess sequence, and the pressure change rate excess sequence are numerically integrated at their respective time steps to obtain the shear damage dose, the pressure damage dose, and the pressure change rate damage dose, respectively.

[0040] Simultaneously, collision events are determined based on the minimum distance between the fish position at each time step on the converged fish trajectory and the solid boundary of the three-dimensional geometric model of the axial flow pump. When the minimum distance is less than or equal to the collision determination threshold, a collision event is determined to have occurred. The collision event intensity is calculated based on the relative velocity between the fish velocity and the solid boundary at the time step where the collision event occurs and is accumulated to obtain the collision damage dose.

[0041] Optionally, S6 includes:

[0042] For each convergent fish trajectory in the set of convergent fish trajectories, the shear damage dose, pressure damage dose, pressure change rate damage dose, and collision damage dose corresponding to the convergent fish trajectory are used as independent variables, and the shear damage rate, pressure damage rate, pressure change rate damage rate, and collision damage rate are calculated according to a preset functional relationship. The model parameters of the preset functional relationship are determined or calibrated by the target fish parameters.

[0043] The total hazard rate is obtained by adding the shear hazard rate, the pressure hazard rate, the pressure change rate hazard rate, and the collision hazard rate, and the survival probability corresponding to the convergent fish trajectory is calculated based on the total hazard rate.

[0044] The survival probabilities corresponding to each convergent fish trajectory are weighted and summed according to the updated release position weights to obtain the fish-friendly evaluation index.

[0045] Optionally, the S7 includes:

[0046] The fish-friendly evaluation index is defined as the first objective function, the efficiency index is defined as the second objective function, the head index is defined as the third objective function, and the design constraints are used as constraints to form a multi-objective optimization problem.

[0047] Wherein, the first objective function is to maximize the fish-friendly evaluation index, the second objective function is to maximize the efficiency index, and the third objective function is to make the head index meet the preset head range or maximize the head index.

[0048] Optionally, S8 includes:

[0049] Multiple sets of candidate design variables are initialized within the value range of the design variable set;

[0050] For each set of candidate design variables, S2 to S7 are executed sequentially to obtain the corresponding fish-friendly evaluation index, efficiency index, head index, and constraint satisfaction.

[0051] In the set of candidate design variables that satisfy the design constraints, the non-dominated solution set is determined according to the non-dominated sorting, and the set of candidate design variables for generating the next iteration is selected from the non-dominated solution set according to the crowding distance.

[0052] The candidate design variable set used to generate the next iteration is updated by crossover and mutation to obtain the candidate design variable set for the next iteration, and the execution of S2 to S7, non-dominated sorting and updating is performed in a loop until the preset termination condition is met.

[0053] When the preset termination condition is met, the optimized design variable set corresponding to the non-dominated solution set is output, and the fish-friendly design scheme of the axial flow pump is output based on the optimized design variable set.

[0054] The beneficial effects of this invention are:

[0055] 1. Achieve engineering and computability of fish injury assessment indicators: Extract key field quantities such as shear rate, pressure and pressure change rate through unsteady flow field, and integrate the over-threshold exposure on the trajectory over time to form the damage dose. Further, output the survival probability based on the multi-cause hazard rate survival model and construct fish-friendly evaluation indicators, thereby transforming the "risk of fish injury or death" into an objective function that can be directly used for optimization, which is convenient for implementation in the engineering design stage.

[0056] 2. Improve the statistical efficiency and convergence stability of risk assessment: By tracking the flow at the entrance to form a probability distribution of passage and determine the effective passage area for fish, fish trajectories are generated only within the effective area and sampled according to the release position weight. At the same time, the weights are updated based on the risk assessment results and the trajectory sampling of high-risk channels is adaptively encrypted, which can reduce invalid samples and computational overhead, and improve the convergence speed and result stability of evaluation indicators.

[0057] 3. Achieve synergistic optimization of fish-friendly and hydraulic performance: The fish-friendly evaluation index, efficiency index, and head index are used together to construct a multi-objective optimization problem. Under design constraints, the optimization design variable set is output through iterative solution. This enables the axial flow pump to significantly reduce the comprehensive risks of shearing, pressure drop, pressure change rate, and collision during the passage of fish while meeting the hydraulic performance requirements of the preset working conditions. Attached Figure Description

[0058] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0059] Figure 1 This is a flowchart of a fish-friendly design method for axial flow pumps based on multi-objective optimization proposed in this invention. Detailed Implementation

[0060] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0061] refer to Figure 1 A fish-friendly design method for axial flow pumps based on multi-objective optimization includes:

[0062] S1. Obtain the design variable set, design constraints, operating condition parameters, and target fish parameters for the axial flow pump. Target fish parameters include fish length, shear rate threshold, pressure threshold, pressure change rate threshold, and collision determination threshold. S2. Establish a three-dimensional geometric model of the axial flow pump based on the design variable set and generate a computational mesh. Perform unsteady computational fluid dynamics simulation under operating condition parameters to obtain the pressure field and velocity field. This yields the shear rate field and pressure change rate field for fish risk assessment, along with efficiency and head indices. S3. Based on the velocity field, at the axial flow pump inlet... S4. Set a set of release locations at the boundary and track them with the current to obtain the passage probability distribution, and determine the effective passage area for fish and its corresponding release location weights; S5. Generate fish trajectories based on release location weights within the effective passage area for fish, and conduct risk assessments on the fish trajectories based on shear rate field, pressure field, pressure change rate field and corresponding thresholds. Update the release location weights according to the risk assessment results and perform encrypted sampling to generate encrypted fish trajectories until the fish friendliness evaluation index meets the preset convergence conditions, and obtain the converged fish trajectories and updated release location weights; S6. For each converged fish trajectory... The trajectory is determined by the shear rate field, pressure field, and pressure change rate field, and the excess shear, pressure, and pressure change rate on the trajectory are integrated over time to obtain the shear damage dose, pressure damage dose, and pressure change rate damage dose. The collision event is determined based on the distance and relative velocity between the converged fish trajectory and the solid boundary of the axial flow pump's three-dimensional geometric model, and the collision event intensity is accumulated to obtain the collision damage dose. S6. Based on the shear damage dose, pressure damage dose, pressure change rate damage dose, and collision damage dose, a multi-cause hazard rate survival model is established to obtain the survival probability corresponding to each converged fish trajectory, and the fish-friendly evaluation index is calculated in combination with the updated release position weight. S7. Using the fish-friendly evaluation index as the fish-friendly objective function, and the efficiency index and head index as the hydraulic performance objective functions, a multi-objective optimization problem is formed under the design constraints. S8. The multi-objective optimization problem is solved iteratively. In each iteration, the candidate design variable set is updated, and S2 to S7 are executed based on the updated candidate design variable set to obtain the corresponding objective function values. When the preset termination condition is met, the optimized design variable set is output, and the fish-friendly design scheme of the axial flow pump is output accordingly.

[0063] In this specific embodiment, S1 includes:

[0064] Obtain the structural boundary conditions and installation boundary conditions corresponding to the axial flow pump to be designed. The structural boundary conditions are used to limit the flow channel shape and key flow dimensions, forming an insurmountable geometric boundary. The installation boundary conditions are used to limit the interface dimensions, axial available installation length, and connection position with the motor or transmission mechanism of the pump unit in the pump station or pipeline system. This determines the design variable set and its value range within the geometric boundaries. The design variable set consists of impeller blade geometric parameters, guide vane geometric parameters, hub geometric parameters, and tip clearance parameters. The impeller blade geometric parameters characterize the radial chord length distribution, installation angle distribution, curvature distribution, and thickness distribution of the blades, and are defined within the structural boundary conditions. The impeller outer diameter and hub outer diameter vary within the range defined by the component. The guide vane geometric parameters are used to characterize the radial chord length distribution, installation angle distribution, and thickness distribution of the guide vane, and vary within the range defined by the axial position and outer diameter of the guide vane stage. The hub geometric parameters are used to characterize the hub shape curve and hub ratio, and are consistent with the hub outer diameter and axial length in the structural boundary conditions. The blade tip clearance parameters are used to characterize the radial clearance between the impeller blade tip and the casing, and meet the upper and lower limit constraints required by manufacturing tolerances and structural safety. At the same time, the above geometric boundaries, manufacturing boundaries, and structural strength boundaries are solidified together as design constraints to ensure that any candidate design variable set can generate a manufacturable and installable three-dimensional geometric model.

[0065] Subsequently, the operating condition parameters corresponding to the axial flow pump to be designed are obtained. The operating condition parameters consist of flow rate parameters, speed parameters, inlet boundary condition parameters, and outlet boundary condition parameters. The flow rate parameters are used to determine the target flow capacity and are consistent with the subsequent head and efficiency calculations. The speed parameters are used to determine the motion conditions of the impeller rotation domain. The inlet boundary condition parameters are used to give the inlet total pressure or inlet velocity distribution and are consistent with the flow rate parameters. The outlet boundary condition parameters are used to give the outlet static pressure or mass flow conservation conditions to ensure the closure of the operating conditions.

[0066] Then, the species information and body length information of the target fish are obtained and the body length parameter is formed in the target fish parameters. The body length parameter is defined as follows: And let The total length of the fish body, consistent with the fish body length information, is taken as the unique length representation quantity for subsequent threshold retrieval and scale effect correction.

[0067] Finally, based on the pre-established correspondence between target fish parameters and thresholds, the shear rate threshold, pressure threshold, pressure change rate threshold, and collision determination threshold are determined, wherein the correspondence is expressed in a two-dimensional indexed threshold table. The data is stored in a fixed format and indexed by the target fish species information and fish length parameters. Each record in the threshold table consists of discrete length grading points for the same target fish species and their corresponding threshold groups, derived from injury or mortality test data of the target fish under shear exposure, low-pressure exposure, rapid pressure change exposure, and collision exposure conditions. When the fish falls between adjacent length division points, a threshold set is obtained by linear interpolation based on length. This ensures that the threshold changes continuously with the fish length and that the threshold is calculable and reproducible. The threshold set is given by the following formula:

[0068] ;

[0069] in Represents the shear rate threshold and its unit is . And it is used to limit the maximum shear rate level that the fish body can withstand. This represents the pressure threshold, expressed in Pa, and is used to define the minimum pressure level that a fish can withstand. Indicates the pressure change rate threshold and the unit is . And it is used to limit the maximum rate of pressure change that the fish body can withstand. This represents the collision detection threshold in meters (m) and is used to define the minimum distance threshold for determining a collision event. This represents the species index code corresponding to the target fish species information. The length parameter of the fish is represented in meters. This completes the determination of the design variable set, design constraints, operating condition parameters, and target fish parameters, and provides a consistent input data basis for subsequent steps such as 3D modeling, unsteady computational fluid dynamics simulation, trajectory sampling, and risk assessment.

[0070] In this specific embodiment, S2 includes:

[0071] A three-dimensional geometric model of the axial flow pump is constructed based on the design variable set, and the computational domain is divided based on the three-dimensional geometric model. The computational domain consists of an impeller rotation domain and a stationary domain connected to it. The impeller rotation domain includes the flow area corresponding to the impeller blades, hub, and tip clearance. The stationary domain includes the flow area of ​​the inlet section, guide vane section, and outlet section. A sliding mesh interface is set at the interface between the impeller rotation domain and the stationary domain to realize the transmission of unsteady information of rotation-stationary interference.

[0072] A computational mesh is generated within the computational domain. The computational mesh is a three-dimensional volume mesh and is locally refined in the leading edge, trailing edge, tip gap, guide vane passage, and near-wall boundary layer region. At the same time, a body-fitted boundary layer mesh is arranged on the solid wall to resolve the near-wall velocity gradient and to ensure that the first layer of the near-wall mesh meets the low Reynolds number wall resolution requirement to ensure the numerical stability of the shear rate calculation.

[0073] Boundary conditions are applied to the computational domain based on the operating parameters. The inlet boundary is given a velocity inlet or mass flow rate inlet consistent with the flow parameters, and the turbulence intensity and turbulence scale are given simultaneously to close the turbulence input. The outlet boundary is given a static pressure outlet and the outlet static pressure is used as the operating condition closure condition. The solid wall is given a no-slip wall condition and all solid walls in the impeller rotation domain move in the same way as the rotation coordinate system. The solid walls in the stationary domain remain stationary.

[0074] Under the above boundary conditions, the incompressible unsteady Reynolds-averaged Navier-Stokes equations are used as the governing equations, and shear stress transport is employed. The turbulence model is closed, and time-progression employs fixed-step long-term discretization, with the impeller rotating through a fixed angle at each time step to ensure analytical accuracy of the transition-to-stationary interference. Spatial discretization uses a second-order accurate convection scheme, and pressure-velocity coupling employs an iterative solution strategy based on pressure correction. Iteration continues within each time step until both the continuity residual and momentum residual are below preset thresholds, and the mass conservation errors at the inlet and outlet meet preset error limits. After completing multiple impeller rotation cycles, the flow field of subsequent consecutive cycles is taken as a statistical interval to output a stable unsteady pressure field and an unsteady velocity field. The unsteady pressure field is denoted as... The unsteady velocity field is denoted as ,in Represents a spatial location vector within the computational domain, with units of 1. Indicates the first Each time step corresponds to a physical time, and the unit is seconds (s).

[0075] Based on the above Within each grid cell, the velocity gradient is calculated and the strain rate tensor is constructed to obtain the shear rate field for fish risk assessment. And based on the adjacent time steps, Calculate the pressure change rate field Simultaneously, the head index is calculated based on the unsteady computational fluid dynamics simulation results. With efficiency indicators The shear rate field, pressure change rate field, head index, and efficiency index are determined according to the following formula:

[0076]

[0077] ;

[0078]

[0079] ;

[0080] in Represents the shear rate field and its unit is . Represents the components of the strain rate tensor and has units of . and Represents velocity vector In the With the The components in each coordinate direction, and the unit is and Represents spatial coordinate components and the unit is Represents the velocity gradient component and its unit is . Represents the pressure change rate field and the unit is Indicates the time step and the unit is and These represent the pressure values ​​at two adjacent time steps, with units of 1. Indicates head index and the unit is and These represent the pressures after averaging the area of ​​the outlet and inlet sections over time within the statistical interval, with units of [units missing]. Represents fluid density and its unit is Represents gravitational acceleration and its unit is . Represents flow rate parameters and the unit is Represents shaft power and the unit is It is obtained by multiplying the torque obtained by integrating the torque of the pressure and viscous force on the impeller surface within the impeller rotation domain with the angular velocity;

[0081] The outputs pressure field, velocity field, shear rate field, pressure change rate field, efficiency index, and head index are used for subsequent steps.

[0082] In this specific embodiment, S3 includes:

[0083] Based on unsteady velocity field Construct a set of release locations at the inlet boundary of the axial flow pump and calculate the passage probability distribution;

[0084] The inlet section of the inlet boundary is divided according to its actual cross-sectional shape in the three-dimensional geometric model. Each grid cell is a non-overlapping grid cell, and the boundary of each grid cell is enclosed by four adjacent dividing lines on the inlet section. The union of all grid cells covers the entire inlet section.

[0085] Set within each grid cell A set of release positions is formed by identifying several release positions. Take 9 and arrange the release positions in three rows and three columns with equal spacing within the grid cell and avoid the grid cell boundary to avoid numerical adhesion caused by the initial point falling near the wall;

[0086] Massless tracer particles are released from each release position as the initial position and then flow-tracked. The flow-tracking is performed using the Lagrange integral method and the velocity field. As the source of the tracer particle's instantaneous velocity, spatial interpolation uses trilinear interpolation to obtain the velocity at the tracer particle's location from the discrete grid node velocities. Temporal interpolation uses adjacent time-step linear interpolation to obtain the velocity at the tracer particle's instantaneous moment from the discrete time-step velocities. Trajectory integration uses the fourth-order Runge-Kutta method with a fixed integration step size. The Take as the time step of the unsteady computational fluid dynamics simulation. To ensure that the tracking and flow field time resolution are consistent;

[0087] Termination criteria are set for each tracer particle trajectory. Termination criteria include: successful passage when the tracer particle first crosses the axial flow pump outlet boundary and the axial velocity component at the instant of crossing points in the outlet direction; failure when the tracer particle comes into contact with any solid wall surface (i.e., the minimum distance from the tracer particle to the solid wall surface is less than or equal to 0); and the tracer particle's cumulative tracking time reaches the maximum tracking time. If the exit boundary is not reached before passage is deemed a failure, the maximum tracking time is... It is taken as 5 times the average residence time in the axial flow pump, and the average residence time is obtained by dividing the axial distance from the inlet to the outlet by the average axial velocity of the inlet section;

[0088] After tracking all release locations, the number of successfully traversed tracer particles is counted by grid cell, and the traversal probability is calculated to form a traversal probability distribution. Based on the traversal probability, the effective traversal area for fish and the weight of release locations are determined. The calculation relationship is given by the following formula:

[0089] ;

[0090] in Indicates the first The probability of passage for each grid cell is dimensionless. This represents the grid cell index, with values ​​ranging from 1 to... Indicates the first The number of tracer particles that successfully pass through each grid cell is an integer and satisfies the following condition: Indicates the number of release positions within each grid cell and takes... Indicates a preset passage probability threshold and takes This represents the set of grid cell indices corresponding to the valid area for fish passage. Indicates the first [number] fish in the effective fish passage area. The first grid cell of the first grid cell The release position weights are dimensionless. This indicates the release location index within the grid cell, with a value ranging from 1 to... This represents the normalization coefficient, which is the sum of the passage probabilities of all fish within the effective passage area, normalized by the number of their release locations.

[0091] The above calculations yield the traffic probability distribution, and... Limit the effective area for fish passage, and at the same time... This serves as the sole weight input for subsequent steps of extracting the release location and generating the trajectory.

[0092] In this specific embodiment, S4 includes:

[0093] Risk assessment-driven adaptive encrypted sampling is conducted based on the release location weights within the effective fish passage area to obtain converged fish trajectories and updated release location weights.

[0094] The motion of the fish within the pump is abstracted as the fish's center of mass moving with the flow, and the fish trajectory represents the time-varying position sequence of the fish's center of mass. The numerical generation of the fish trajectory and the tracking of the tracer particles with the flow adopt the same Lagrange integral framework, the same spatial and temporal interpolation strategies, and the same integration step size. And the same trajectory termination criterion is used to ensure consistency in the statistical caliber of passage;

[0095] The release position weight is used as the initial release position weight and denoted as . ,in This represents the grid cell index within the effective area for fish passage. Indicates the release position index within the grid cell;

[0096] The index set consists of all release location index pairs located within the effective fish passage area. ,in This represents the complete set of release locations used for sampling, satisfying the condition that each index pair... Each corresponds to a unique entry release position coordinate;

[0097] Setting the first The number of trajectory samples in the next adaptive encryption iteration is And let The maximum number of iterations is And using a fixed random seed Driven weighted sampling without replacement from Extraction The release position index pair is used to generate the first release position index pair. The initial set of fish body trajectories for the next iteration, the weighted sampling is based on... The sampling probability is determined by constructing a cumulative distribution function, ensuring that the initial position of each fish's trajectory is consistent with the coordinates of its sampled release position.

[0098] Regarding the first Each initial fish trajectory obtained in the next iteration is based on the shear rate field. Pressure field With pressure change rate field Interpolation was performed at the fish's centroid position at each time step of the trajectory to generate shear rate, pressure, and pressure change rate sequences, respectively. These sequences were then compared with shear rate thresholds. Pressure threshold With pressure change rate threshold A comparison was made to obtain three overthreshold sequences, where the shear rate overthreshold sequence was ordered according to... Calculation, pressure overthreshold sequence according to Calculation, pressure change rate exceeding threshold sequence Calculate and use The amplitude of the pressure change rate is used to cover two types of rapid changes: pressure increase and pressure decrease. Then, the three super-threshold sequences are integrated over time to obtain three types of super-threshold exposures, which are then divided by the corresponding thresholds for dimensionless conversion. Finally, the three dimensionless conversion results are added with the same coefficient to obtain the risk value corresponding to the initial fish trajectory. The larger the risk value, the higher the risk of the channel corresponding to the trajectory.

[0099] The first In the next iteration, the risk value of all initial fish body trajectories is indexed according to their initial position. Collection and union of the same The risk weight is obtained by taking the arithmetic average of the risk values. ,in Indicates the first In the next iteration, the release position is determined. The average risk value of the triggered fish trajectory and when the first A release position in the next iteration Not sampled by season To maintain the certainty of weight updates;

[0100] The release location weights are updated and normalized based on the risk weights to obtain the first... The updated release position weight used in the next iteration is updated using the following formula:

[0101] ;

[0102] in Indicates the first The release position weight in the next iteration is dimensionless. Indicates the first The risk weight of the next iteration is dimensionless. This represents a smoothing constant to prevent the denominator from being zero and to prevent the weights from being strictly zero, and takes... express Any release position index pair in the and Using the same indexing rules, This represents a summary normalization operation for all release locations within the effective area for fish passage;

[0103] After each weight update and generation of the corresponding encrypted fish trajectory set, steps S5 and S6 are called to calculate the fish-friendly evaluation index for this iteration and denoted as [index]. When satisfied Not greater than the convergence threshold and the convergence threshold is taken as The system determines when the fish-friendly evaluation index converges and outputs the converged fish trajectory corresponding to that iteration, along with the updated release position weights corresponding to that trajectory. If the maximum number of iterations is reached... If the convergence condition is not met, output the first... The fish trajectory and release position weights corresponding to the next iteration are used as the convergence output.

[0104] In this specific embodiment, S5 includes:

[0105] Each convergent fish trajectory in the set of convergent fish trajectories is processed step by step according to the time step of the unsteady computational fluid dynamics simulation.

[0106] The first The convergent fish trajectory is represented by the trajectory at discrete time... Fish body position sequence ,in The index for the convergent fish trajectory is 1, and its value ranges from the total number of convergent fish trajectories. It is a time step index with a value range from 0 to the last time step corresponding to the trajectory;

[0107] At each time step At this point, spatial trilinear interpolation and temporal linear interpolation, consistent with flow tracking, are used to obtain data from the shear rate field. Pressure field With pressure change rate field In the middle of the fish's body position Values ​​are taken at the specified locations and a shear rate sequence is formed. Pressure sequence With pressure change rate sequence The above sequences were then compared with shear rate thresholds. Pressure threshold With pressure change rate threshold The results are compared to obtain the overthreshold dose sequence, and the overthreshold dose sequence is numerically integrated to obtain the shear damage dose, pressure damage dose, and pressure change rate damage dose.

[0108] Simultaneously, collision events are determined based on the minimum distance between the fish's position and the solid boundary of the axial flow pump's three-dimensional geometric model, and the collision event intensity is accumulated to obtain the collision damage dose. The solid boundary includes the impeller blade surface, guide vane surface, hub surface, and inner casing surface, and its instantaneous boundary velocity is determined by the angular velocity of the rotating component and the zero velocity of the stationary component, specifically calculated using the following formula:

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] in Indicates the first The shear damage dose of the converging fish trajectory, in units of Indicates the first The pressure damage dose of the converging fish body trajectory is expressed in Pas. Indicates the first The rate of change of pressure on the converging fish body trajectory is the damage dose, and the unit is... Indicates the first The collision damage dose of the convergent fish trajectory, in units of Indicates at time From the shear rate field The interpolated shear rate is expressed in units of... , Indicates at time By pressure field The pressure obtained by interpolation and the unit is Indicates at time From the pressure change rate field The interpolated rate of change of pressure is expressed in units of , Represents the shear rate threshold and its unit is . Indicates the pressure threshold and the unit is Indicates the pressure change rate threshold and the unit is . This represents the time step consistent with unsteady computational fluid dynamics simulations, and the unit is 1. Indicates the first The index of the last time step of the converging fish trajectory is a non-negative integer. This represents the overthreshold extraction operator that truncates negative values ​​to zero. This indicates that the absolute value is used to characterize the magnitude of the rate of change of pressure. Indicates the first A set of time step indices for convergent fish trajectories and collision events, constructed according to the rule of calculating the fish position at each time step. The minimum distance to the solid boundary is denoted as . And if and only if At that time Included ,in Indicates the collision detection threshold and the unit is . Indicates the fish's body at a certain time. velocity vector and unit is And divided by the increment of the fish's body position during current tracking. get, This represents the solid boundary point corresponding to the minimum distance at time [time]. The boundary velocity vector and its unit is It can be obtained by cross product of the angular velocity in the impeller's rotational domain and the radial vector from the boundary point to the axis of rotation, or by taking zero in the stationary domain. The Euclidean norm is used to calculate the magnitude of relative velocity;

[0114] Shear damage dose, pressure damage dose, pressure change rate damage dose, and collision damage dose were obtained on each convergent fish trajectory.

[0115] In this specific embodiment, S6 includes:

[0116] Based on the Shear damage dose corresponding to the convergent fish trajectory Pressure injury dose Pressure change rate of injury dose and collision damage dosage Establish a survival model based on the causal harm rate and calculate fish-friendly evaluation indicators;

[0117] Shear, pressure, pressure change rate and collision are considered as independent competing risk causes. The total risk rate is constructed using an additive structure of sub-cause risk rates. Each sub-cause risk rate is obtained by mapping the corresponding damage dose through a monotonically increasing power function to reflect the dose accumulation effect. The model parameters of the power function are determined by the target fish parameters and solidified into a searchable parameter set.

[0118] Specifically, a parameter table for the hazard rate model is established in advance. The hazard rate model parameter table Encode the target fish species index in step S1 With fish body length parameters Used as an index key and output parameter group ,in It is a scale parameter and must be greater than 0 to ensure that the hazard does not decrease with increasing dose. The shape parameter is greater than 0 to describe the nonlinear sensitivity of risk to dose under different mechanisms;

[0119] The hazard rate model parameter table The parameter values ​​were determined by maximum likelihood estimation using single-mechanism exposure biological test data of the target fish. The single-mechanism exposure biological test data recorded the exposure dose and post-travel survival results for each test fish in four independent tests: shear, low pressure, rapid pressure change, and collision. During the fitting process, the survival result was used as a Bernoulli observation, and the survival probability was expressed as an exponential decay function of the total hazard rate, within the constraints... and The following numerical optimization of the parameters yields a unique solution, and when When located between adjacent length division points in the parameter table and Linear interpolation by length is used to obtain the results of linear interpolation with... A consistent set of parameters ensures the continuity of the model in the length dimension;

[0120] After obtaining the parameter set, the causal harm rate, total harm rate, and survival probability are calculated for each converged fish trajectory. The survival probability is then weighted and summarized based on the updated release position weights output after convergence in step S4 to obtain a fish-friendly evaluation index. The calculation relationship is as follows:

[0121] ;

[0122] in Indicates the first The survival probability corresponding to a convergent fish trajectory is dimensionless and ranges from 0 to... Represents an exponential function. and Let the scale parameter and shape parameter of the shear hazard rate model be respectively represented by the scale parameter and shape parameter. The search has been completed. and Represent the scale parameter and shape parameter of the pressure hazard rate model, respectively, and are given by... The search has been completed. and Represent the scale parameter and shape parameter of the pressure change rate hazard rate model, respectively, and are given by... The search has been completed. and Let the scale parameter and shape parameter of the collision hazard rate model be respectively represented by the following parameters: The search has been completed. Indicates shear damage dose, Indicates the dose of pressure injury. Indicates the rate of change of pressure and the resulting damage dose. Indicates the amount of damage caused by the impact. This represents a fish-friendly evaluation index that is dimensionless and ranges from 0 to 1, with higher values ​​indicating greater fish-friendliness. This represents the total number of convergent fish trajectories, which is a positive integer. Indicates the first The trajectory weights of the convergent fish body trajectory are determined by the updated release position weights corresponding to its initial release position and satisfy the following conditions: Specifically, the first order The initial release position index pair of the converging fish trajectory is And its corresponding updated release position weight is and order The initial release position in the convergent fish trajectory set is The number of trajectories, thus obtaining... This ensures that the weights at the release location level are consistently distributed to the corresponding trajectory level and avoids weighting bias introduced by differences in the number of samples due to adaptive encryption.

[0123] In this specific embodiment, S7 includes:

[0124] The design variable set is concatenated into a candidate design variable vector in a fixed order. The It includes the geometric parameters of the impeller blades, guide vanes, hub, and tip clearance. Each of the one-dimensional components has upper and lower bounds jointly defined by the structural boundary conditions and the installation boundary conditions, and together they constitute the feasible region. ;

[0125] For any given The efficiency index is obtained by performing step S2. With head index And fish-friendly evaluation indicators are obtained by performing steps S3 to S6. ,in The value ranges from 0 to 1, with higher values ​​indicating greater fish-friendliness. It is dimensionless, and the larger the value, the higher the hydraulic efficiency. The unit is m and it is used to characterize the energy lifting capacity of a pump under operating conditions;

[0126] The fish-friendly evaluation index is defined as the first objective function and is set to be maximized; the efficiency index is defined as the second objective function and is set to be maximized; and the head index is defined as the third objective function and is set to be maximized. Simultaneously, design constraints are used as constraints, and the head range requirement is solidified as an explicit constraint, thus forming a multi-objective optimization problem for iterative solution in step S8:

[0127] s. t. ;

[0128] in This represents a vector of candidate design variables, with each component corresponding one-to-one with the design variables in step S1. This represents the feasible region, which consists of the range of values ​​for each design variable. Indicators representing fish-friendly evaluation indicators, Indicates efficiency indicators. Indicates the head indicator. Indicates the first The constraint functions corresponding to the design constraints are used to express engineering feasibility requirements such as the inability to break geometric boundaries, the inability to conflict with installation interfaces, and the requirement that the blade tip clearance meets manufacturing and safety lower limits. Indicates a constraint index. This represents the total number of constraints and is a positive integer. Indicates the lower limit of the preset head range and the unit is This indicates the upper limit of the preset head range, and the unit is meters (m).

[0129] The above definition ensures that fish-friendly objectives and hydraulic performance objectives are calculated consistently within the same candidate design variable space and can be directly entered into the non-dominated ordination framework for trade-off solutions.

[0130] In this specific embodiment, S8 includes:

[0131] In the feasible region Multiple sets of candidate design variables are obtained through internal initialization, and the multi-objective optimization problem is solved iteratively.

[0132] A single set of candidate design variables is represented as a vector of candidate design variables. and set the group size Maximum number of iterations Crossover probability Probability of mutation Random seed ,in Represents the candidate design variable vector The dimension is a positive integer;

[0133] Rejection sampling is used during initialization. Endogenous generation A vector of candidate design variables that satisfy the design constraints is used to form the initial population. For each candidate design variable vector The fish-friendly evaluation index is obtained by sequentially performing steps S2 to S7. Efficiency indicators Head index And calculate constraint satisfaction;

[0134] Constraint satisfaction is expressed through constraint violation. The constraint violation degree is uniformly quantified and used for group screening and feasibility determination, and is defined as follows:

[0135] ;

[0136] in Represents the candidate design variable vector The constraint violation degree is dimensionless and satisfies This indicates that all constraints are met. Represents a vector of candidate design variables. Indicates the first The constraint functions corresponding to each design constraint condition. This indicates a constraint index with values ​​ranging from 1 to... This represents the total number of constraints and is a positive integer. Indicates head index and the unit is Indicates the lower limit of the preset head range and the unit is Indicates the upper limit of the preset head range and the unit is This represents an operator that truncates negative values ​​to zero.

[0137] In each iteration, only when the condition is met... Within the candidate design variable vector set, the non-dominated solution set is determined based on the non-dominated sorting, and the individual diversity measure is calculated based on the crowding distance. In the selection stage, a binary tournament is adopted, with the one with the lower non-dominated level winning, and the one with the larger crowding distance winning if the non-dominated levels are the same, to obtain the parent set used to generate the next generation.

[0138] The crossover phase uses a simulated binary crossover operator to reorganize the parent set and uses a distribution index. To control the distribution scale of offspring near their parents, a multinomial mutation operator is used during the mutation phase to perturb the crossover individuals and a distribution index is applied. The probability distribution of the variable time is controlled, and all design variable components obtained after crossover and mutation are restricted to a certain value through boundary truncation. Within the upper and lower bounds to ensure that geometric modeling is executable;

[0139] Parental group with offspring The merged result is of size Merge the groups and then perform steps S2 to S7 again for each individual in the merged group to obtain the corresponding... and Subsequently, after satisfying Individuals are filled sequentially from low to high non-dominated levels, and within the last non-dominated layer that needs to be truncated, individuals are selected from the crowding distance in descending order, thus forming the next generation of the population. And maintain the group size ;

[0140] When the iteration number reaches Stop iteration and output the final population that satisfies all conditions. The non-dominated solution set constituted by the non-dominated solution and output with Each set of candidate design variable vectors The corresponding fish-friendly design scheme for axial flow pumps.

[0141] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0142] This invention combines unsteady computational fluid dynamics simulation with flow tracking, overthreshold exposure dosing, and a causal hazard rate survival model. This transforms "fish-friendly" from an empirically difficult-to-engineer empirical criterion into a survival probability-based evaluation index that can be directly calculated from pressure and velocity fields. Key risk fields such as shear rate and pressure change rate are obtained from the unsteady flow field. Overthreshold exposure of each field is extracted along the fish's trajectory and integrated over time to form an accumulative and comparable damage dose. The causal hazard rate survival model then maps multiple mechanisms of damage, including shear, low pressure, rapid pressure changes, and collisions, into survival probabilities within a unified competitive risk framework. These probabilities are then weighted and aggregated according to the inlet release location to obtain a global fish-friendly evaluation index. Therefore, this evaluation index can be directly used as the objective function for multi-objective optimization, iteratively solved along with efficiency and head, achieving the technical effect of reducing the risk of fish passage damage while meeting the hydraulic performance constraints of the operating conditions.

[0143] The algorithm structure of this invention addresses the problems of "low trajectory statistics efficiency, non-convergence evaluation, and difficulty in incorporating indicators into optimization" during the engineering design stage. Firstly, it introduces a fish passage effective area determination and release position weight allocation based on passage probability distribution, generating fish trajectories only within effective areas, reducing invalid channel sampling and computational costs from the source. Secondly, it introduces a risk assessment-driven adaptive encrypted sampling mechanism, iteratively updating the release position weights based on trajectory risk and encrypting high-risk channels until the fish-friendly evaluation index meets the convergence condition, thereby improving statistical stability and result reproducibility. Thirdly, it improves the discrete determination of "recording upon exceeding the threshold" to time-integrated dose accumulation, and achieves additive and competitive characterization of multi-mechanism damage through a multi-causal hazard rate model, making the comprehensive index more sensitive and continuous to changes in structural parameters, and more suitable as an optimization objective function to participate in non-dominated sorting iterations, further enhancing the synergistic optimization effect of fish-friendly and hydraulic performance.

Claims

1. A fish-friendly design method for axial flow pumps based on multi-objective optimization, characterized in that, include: S1. Obtain the design variable set, design constraints, operating parameters, and target fish parameters for the axial flow pump. Target fish parameters include fish length, shear rate threshold, pressure threshold, pressure change rate threshold, and collision determination threshold. S2. Establish a three-dimensional geometric model of the axial flow pump based on the design variable set and generate a computational mesh. Perform unsteady computational fluid dynamics simulation under operating parameters to obtain the pressure field and velocity field. From this, obtain the shear rate field and pressure change rate field for fish risk assessment, and simultaneously obtain the efficiency index and head index. S3. Based on the velocity field, set a set of release positions at the axial flow pump inlet boundary and perform flow tracking to obtain the passage probability distribution, determining the effective passage area for fish and its corresponding release position weights. S4. Generate fish trajectories based on release location weights within the effective fish passage area, and conduct risk assessments on the fish trajectories based on shear rate field, pressure field, pressure change rate field and corresponding thresholds. Update the release location weights based on the risk assessment results and perform encrypted sampling to generate encrypted fish trajectories until the fish-friendly evaluation index meets the preset convergence conditions, and obtain the converged fish trajectories and updated release location weights. S5. For each convergent fish trajectory, determine the shear, pressure, and pressure change rate exceeding limits on the trajectory based on the shear rate field, pressure field, and pressure change rate field, and perform time integration to obtain the shear damage dose, pressure damage dose, and pressure change rate damage dose. Based on the distance and relative velocity between the convergent fish trajectory and the solid boundary of the axial flow pump's three-dimensional geometric model, determine the collision event and accumulate the collision event intensity to obtain the collision damage dose. S6. Based on the shear damage dose, pressure damage dose, pressure change rate damage dose, and collision damage dose, establish a multi-cause hazard rate survival model to obtain the survival probability corresponding to each convergent fish trajectory, and calculate the fish-friendly evaluation index in combination with the updated release position weight. S7. Using the fish-friendly evaluation index as the fish-friendly objective function, and the efficiency index and head index as the hydraulic performance objective functions, form a multi-objective optimization problem under design constraints. S8. Iteratively solve the multi-objective optimization problem, update the candidate design variable set in each iteration, and execute S2 to S7 based on the updated candidate design variable set to obtain the corresponding objective function value. When the preset termination condition is met, output the optimized design variable set, and output the fish-friendly design scheme of the axial flow pump accordingly.

2. The fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S1 includes: Obtain the structural boundary conditions and installation boundary conditions corresponding to the axial flow pump to be designed, and determine the design variable set and the value range of the design variable set based on the structural boundary conditions and installation boundary conditions. The design variable set includes impeller blade geometric parameters, guide vane geometric parameters, hub geometric parameters and blade tip clearance parameters. Obtain the operating condition parameters corresponding to the axial flow pump to be designed. The operating condition parameters include flow rate parameters, speed parameters, inlet boundary condition parameters, and outlet boundary condition parameters. Obtain the species information and body length information of the target fish, and determine the body length parameter based on the body length information; Based on the pre-established correspondence between target fish parameters and thresholds, the shear rate threshold, the pressure threshold, the pressure change rate threshold, and the collision determination threshold are determined according to the target fish species information and the fish body length parameter.

3. The fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S2 include: A three-dimensional geometric model of the axial flow pump is established based on the design variable set, and the computational domain is divided. The computational domain includes the impeller rotation domain and the stationary domain connected to the impeller rotation domain. A computational mesh is generated within the computational domain based on the three-dimensional geometric model of the axial flow pump. Based on the operating condition parameters, inlet and outlet boundary conditions are applied to the computational domain, and rotational speed parameters corresponding to the operating condition parameters are applied to the impeller rotation domain. Unsteady computational fluid dynamics simulation was used to solve the control equations in the computational domain by time-progression, and the pressure field and velocity field at each time step were obtained. The shear rate field is calculated based on the velocity gradient of the velocity field. Calculate the pressure rate of change field based on the pressure field of adjacent time steps; The head index is determined based on the shaft power, flow parameters, and pressure field obtained from the unsteady computational fluid dynamics simulation, and the efficiency index is determined based on the head index, the flow parameters, and the shaft power.

4. The fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S3 includes: The inlet section of the axial flow pump is divided into multiple grid cells at the inlet boundary, and a set of release positions is set in each grid cell; Using each release position in the set of release positions as the initial position, the massless tracer particle is tracked by the flow based on the velocity field to obtain the corresponding tracer particle trajectory. Based on the number of tracer particle trajectories that can reach the axial flow pump outlet boundary from the axial flow pump inlet boundary, the passage probability of each grid cell is calculated and a passage probability distribution is formed. Grid cells with a passage probability not less than a preset passage probability threshold are used as effective passage areas for fish. Based on the passage probability distribution, release position weights are assigned to each release position within the effective passage area for fish, and the release position weights are positively correlated with the passage probability of the corresponding grid cell.

5. The fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S4 includes: Within the effective area for fish passage, release positions are extracted from the set of release positions according to the weight of the release positions, and each extracted release position is used as the initial position. Based on the velocity field, the initial fish trajectory is obtained by following the flow. For each initial fish trajectory in the initial fish trajectory, the shear rate sequence, pressure sequence, and pressure change rate sequence on the initial fish trajectory are extracted based on the shear rate field, the pressure field, and the pressure change rate field, respectively. The shear rate sequence, pressure sequence, and pressure change rate sequence are then compared with the shear rate threshold, the pressure threshold, and the pressure change rate threshold, respectively. Based on the comparison results, the risk value corresponding to the initial fish trajectory is calculated. The risk values ​​of each initial fish trajectory are aggregated according to their initial positions to obtain the risk weight distribution corresponding to the set of release positions. The release position weights are then updated and normalized based on the risk weight distribution to obtain the updated release position weights. According to the updated release position weight, the release position is encrypted and extracted within the effective area for fish passage, and the encrypted fish trajectory is obtained by following the flow based on the velocity field. Based on the encrypted fish trajectory, S5 and S6 are executed to obtain the corresponding fish-friendly evaluation index. The change in the fish-friendly evaluation index obtained in two adjacent iterations is not greater than the convergence threshold as the convergence condition. The risk weight distribution calculation, release position weight update and encrypted extraction of release position are executed cyclically until the convergence condition is met, and the converged fish trajectory and the updated release position weight corresponding to the converged fish trajectory are obtained.

6. The fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S5 include: For each convergent fish trajectory in the set of convergent fish trajectories, the shear rate, pressure and pressure change rate values ​​are obtained by interpolation at the corresponding fish position at each time step of the unsteady computational fluid dynamics simulation, forming the shear rate sequence, the pressure sequence and the pressure change rate sequence respectively. The shear rate sequence is compared with the shear rate threshold to obtain the shear rate excess sequence, the pressure sequence is compared with the pressure threshold to obtain the pressure excess sequence, and the pressure change rate sequence is compared with the pressure change rate threshold to obtain the pressure change rate excess sequence. The shear rate excess sequence, the pressure excess sequence, and the pressure change rate excess sequence are numerically integrated at their respective time steps to obtain the shear damage dose, the pressure damage dose, and the pressure change rate damage dose, respectively. Simultaneously, collision events are determined based on the minimum distance between the fish position at each time step on the converged fish trajectory and the solid boundary of the three-dimensional geometric model of the axial flow pump. When the minimum distance is less than or equal to the collision determination threshold, a collision event is determined to have occurred. The collision event intensity is calculated based on the relative velocity between the fish velocity and the solid boundary at the time step where the collision event occurs and is accumulated to obtain the collision damage dose.

7. A fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S6 include: For each convergent fish trajectory in the set of convergent fish trajectories, the shear damage dose, pressure damage dose, pressure change rate damage dose, and collision damage dose corresponding to the convergent fish trajectory are used as independent variables, and the shear damage rate, pressure damage rate, pressure change rate damage rate, and collision damage rate are calculated according to a preset functional relationship. The model parameters of the preset functional relationship are determined or calibrated by the target fish parameters. The total hazard rate is obtained by adding the shear hazard rate, the pressure hazard rate, the pressure change rate hazard rate, and the collision hazard rate, and the survival probability corresponding to the convergent fish trajectory is calculated based on the total hazard rate. The survival probabilities corresponding to each convergent fish trajectory are weighted and summed according to the updated release position weights to obtain the fish-friendly evaluation index.

8. The fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S7 includes: The fish-friendly evaluation index is defined as the first objective function, the efficiency index is defined as the second objective function, the head index is defined as the third objective function, and the design constraints are used as constraints to form a multi-objective optimization problem. Wherein, the first objective function is to maximize the fish-friendly evaluation index, the second objective function is to maximize the efficiency index, and the third objective function is to make the head index meet the preset head range or maximize the head index.

9. A fish-friendly design method for axial flow pumps based on multi-objective optimization according to claim 1, characterized in that, S8 includes: Multiple sets of candidate design variables are initialized within the value range of the design variable set; For each set of candidate design variables, S2 to S7 are executed sequentially to obtain the corresponding fish-friendly evaluation index, efficiency index, head index, and constraint satisfaction. In the set of candidate design variables that satisfy the design constraints, the non-dominated solution set is determined according to the non-dominated sorting, and the set of candidate design variables for generating the next iteration is selected from the non-dominated solution set according to the crowding distance. The candidate design variable set used to generate the next iteration is updated by crossover and mutation to obtain the candidate design variable set for the next iteration, and the execution of S2 to S7, non-dominated sorting and updating is performed in a loop until the preset termination condition is met. When the preset termination condition is met, the optimized design variable set corresponding to the non-dominated solution set is output, and the fish-friendly design scheme of the axial flow pump is output based on the optimized design variable set.

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