Axial flow pump energy efficiency intelligent prediction and optimization control method and system

Abstract

This application relates to the field of axial flow pump technology, and in particular to a method and system for intelligent prediction and optimization control of axial flow pump energy efficiency. The method includes: acquiring the hydrodynamic differential algebraic equation model and initial operating parameters of the axial flow pump; setting multiple sets of control parameter combinations to be optimized as sample points; performing implicit integral solutions on each set of control parameter combinations to obtain steady-state energy efficiency; correlating the Jacobian matrix update with the rate of change of local truncation error; calculating the local truncation error based on the difference between high- and low-order numerical solutions; calculating the baseline step size using a proportional-integral controller in conjunction with historical errors; adjusting the step size using a condition number with an exponential decay function; solving until stability and recording the steady-state energy efficiency value; constructing a Gaussian process regression surrogate model to iteratively select control parameter combinations; and outputting control commands after convergence. This application can reduce the simulation computation overhead for axial flow pump energy efficiency prediction.

Description

Technical Field

[0001] This application relates to the field of axial flow pump technology, and in particular to a method and system for intelligent prediction and optimization control of axial flow pump energy efficiency. Background Technology

[0002] Axial flow pumps, as core water conveying equipment under high flow and low head conditions, are widely used in water conservancy projects such as urban drainage and agricultural irrigation. During operation, the configuration of control parameters such as impeller speed and guide vane angle directly affects the hydraulic efficiency of the pump unit; different parameter combinations can result in energy efficiency differences of several percentage points. To obtain the optimal combination of control parameters under given operating conditions, it is usually necessary to perform numerical simulation of the internal flow field of the axial flow pump and establish a quantitative mapping relationship between control parameters and energy efficiency.

[0003] The internal flow field of an axial flow pump exhibits three-dimensional unsteady characteristics, with dynamic and static interference between the impeller and guide vanes, and complex flow regimes such as vortex shedding and flow separation within the flow channel. Mathematical models describing this type of flow field behavior typically employ a system of differential-algebraic equations based on the Navier-Stokes equations. The numerical rigidity of this system makes explicit time integration methods prone to numerical instability. Implicit integration methods can handle rigid equation systems, but require solving a large-scale discrete system of equations using Newton's iteration method at each time step, with the assembly and decomposition of the Jacobian matrix accounting for the majority of the computational cost per step. When simulations are performed separately for multiple sets of control parameters to evaluate their respective steady-state energy efficiency, the accumulated computational overhead becomes a bottleneck restricting the efficiency of optimized control.

[0004] In the prior art, Chinese patent document CN111460379B discloses a method and system for performance prediction of multi-condition dynamic systems based on Gaussian process regression. This method collects conventional operating condition data to construct a training dataset, uses a Gaussian process regression model for performance prediction, and iteratively obtains new sampling points through a sequential sampling algorithm to expand the dataset and update the model. This method provides a technical path for constructing a performance prediction model with a small amount of data at the surrogate model level, but it does not address the optimization issues of the Jacobian matrix update strategy and time step control in the underlying numerical simulation solution process. When the underlying simulation system faces operating conditions with drastic changes in numerical rigidity, the efficiency of obtaining simulation samples is still limited by a fixed solution strategy.

[0005] In the underlying numerical integration stage, existing methods often trigger Jacobian matrix updates at fixed step intervals or based on preset empirical conditions, without establishing a correlation with the actual degree of change in the flow field state during the solution process. When the flow field is in a stable phase, fixed-frequency updates cause unnecessary matrix recalculations; when the flow field experiences abrupt changes, the update lag leads to difficulties in Newton iteration convergence. Regarding step size adjustment, single-step feedback control is performed only based on the error of the current time step, lacking utilization of historical error trends and failing to consider the constraints of the change in numerical stiffness of the equation system over time on step size selection. This results in a longer time consumption to obtain the steady-state energy efficiency corresponding to each set of control parameters, affecting the overall efficiency and convergence stability of the upper-level optimization iteration. Summary of the Invention

[0006] To address the technical problems of the Jacobian matrix update being disconnected from the flow field state, the lack of error trend in step size adjustment, and stiffness feedback when implicitly integrating to solve the axial flow pump flow field, this application provides solutions in the following aspects.

[0007] In a first aspect, this application provides a method for intelligent prediction and optimized control of axial flow pump energy efficiency, comprising: S1. Obtain the fluid dynamic differential algebraic equation model and initial operating parameters of the axial flow pump, and set multiple sets of control parameter combinations to be optimized as sample points; S2. Implicit integration is performed on each set of control parameters to obtain steady-state energy efficiency. The Newton-Raphson method is used to solve the discrete equations in each integral time step. The Jacobian matrix update is related to the rate of change of the local truncation error in the previous time step. When the rate of change of the local truncation error exceeds the preset threshold, the Jacobian matrix is ​​updated. The local truncation error is calculated based on the difference between the high-order and low-order numerical solutions. S3. Combine the local truncation error and historical error to calculate the reference next time step through the proportional-integral controller. When updating the Jacobian matrix, calculate the condition number as the numerical rigidity quantification index of the system. When the numerical rigidity quantification index of the system increases, reduce the reference next time step according to the exponential decay function to get the actual next time step. Repeat the implicit integration solution until the system state variables are stable and record the steady-state energy efficiency value. S4. Construct a Gaussian process regression surrogate model using sample points and steady-state energy efficiency values. Based on the posterior distribution, use the acquisition function criterion to iteratively select the next combination of control parameters. After convergence, output the energy-efficient optimal control parameter combination as the control instruction.

[0008] This application links the update timing of the Jacobian matrix to the rate of change of local truncation error. When the flow field changes gradually, the existing Jacobian matrix or its decomposition factor is reused, reducing the number of assembly and decomposition steps for large-scale sparse matrices. When drastic changes occur in the flow field, such as flow separation or vortex shedding, the matrix update is triggered in a timely manner to ensure the convergence reliability of Newton's iteration. At the step size control level, the proportional-integral controller incorporates current and historical error information to calculate the baseline step size. Based on this, the actual step size is obtained by exponentially decaying the condition number of the Jacobian matrix. Under the condition of increased stiffness, the time step size decreases as the relative increment of the condition number increases, thus suppressing the oscillation amplitude and iteration divergence risk during the step size adjustment process. At the surrogate model level, a small number of simulation samples are mapped to the posterior distribution between control parameters and energy efficiency through Gaussian process regression. Combined with the acquisition function criterion, directional sampling is performed in the parameter space, reducing the number of high-cost simulation calls and lowering the overall computational overhead of axial pump energy efficiency optimization and control.

[0009] Preferably, the acquisition of the fluid dynamics differential algebraic equation model and initial operating parameters of the axial flow pump includes: extracting the geometric model and boundary conditions of the axial flow pump; dividing the fluid domain from the inlet to the outlet of the axial flow pump into a structured or unstructured grid; constructing a fluid dynamics differential algebraic equation system containing the continuity equation and the momentum equation based on the incompressible Navier-Stokes equations; and setting the initial flow field velocity, pressure distribution, and boundary conditions as initial operating parameters.

[0010] The geometric model of the axial flow pump's flow components is transformed into a meshed fluid domain, and a set of differential-algebraic equations is constructed based on the incompressible Navier-Stokes equations. Subsequent implicit integration is performed using this set of differential-algebraic equations as input. The degree of matching between the energy efficiency prediction results and the actual pump operating performance depends on the accuracy of the equations in describing the physical behavior of the flow field.

[0011] Preferably, setting multiple sets of control parameter combinations to be optimized as sample points includes: determining the control parameters to be optimized, including the operating frequency and guide vane angle of the axial flow pump; determining the constraint range of each control parameter, with the operating frequency constrained from 42Hz to 55Hz and the guide vane angle constrained from -15° to +15°; and using the Latin hypercube sampling method to extract multiple sets of distinct control parameter combinations after deduplication within the constraint range to form an initial sample set, so that the combinations of control parameters are layered and covered in a multidimensional space.

[0012] Preferably, the local truncation error variation rate is calculated as follows: take the absolute value of the difference between the local truncation error of the previous time step and the local truncation error of the time step before that, and divide it by the local truncation error of the time step before that; when the local truncation error variation rate is greater than a preset variation threshold, the Jacobian matrix is ​​recalculated using the current system state variables; when the local truncation error variation rate is less than or equal to the preset variation threshold, the Jacobian matrix of the previous time step is kept in use, so that the frequency of matrix recalculation is related to the actual degree of change in the flow field.

[0013] Preferably, the step of calculating the local truncation error based on the difference between higher-order and lower-order numerical solutions includes: calculating the higher-order numerical solution of the current time step using the fourth-order implicit Runge-Kutta method, and calculating the lower-order numerical solution of the current time step using the third-order implicit Runge-Kutta method; calculating the difference between the higher-order and lower-order numerical solutions on each state variable and performing dimensionless processing; performing weighted root mean square calculation on the difference between each state variable after dimensionless processing, and using the weighted root mean square difference norm as the local truncation error of the current time step.

[0014] Preferably, the calculation of the reference next time step by the proportional-integral controller includes: using the ratio of the preset target truncation error to the local truncation error of the current time step as the basis for proportional adjustment, using the ratio of the target truncation error to the historical local truncation error as the basis for integral adjustment, multiplying the proportional adjustment basis and the integral adjustment basis by powers of the proportional gain and integral gain respectively to obtain the step size adjustment signal, and multiplying it by the current time step to obtain the reference next time step; using the singular value decomposition method to calculate the ratio of the maximum singular value to the minimum non-zero singular value of the updated Jacobian matrix as the system numerical rigidity quantification index; when the system numerical rigidity quantification index increases, multiplying the reference next time step by an exponential decay factor to obtain the actual next time step, where the exponential decay factor is a positive value obtained by mapping the increment of the system numerical rigidity quantification index by a negative exponential and taking the larger value of the preset minimum suppression coefficient.

[0015] The proportional and integral adjustments are applied to the current error and the historical error, respectively. The step size scaling factor is output through exponential transformation. The step size is reduced when the error is large and increased when the error is small. The step size shrinkage coefficient is calculated by using the relative increment of the condition number of the Jacobian matrix through an exponential decay function. The step size is further shrunk when the system stiffness increases, so that both the solution efficiency and the iteration stability are guaranteed.

[0016] Preferably, the construction of the Gaussian process regression surrogate model includes: using all tested control parameters as input feature vectors and the corresponding steady-state energy efficiency values ​​as output target values ​​to construct a training dataset; selecting the squared exponential kernel function or the Matrn kernel function as the covariance function of the Gaussian process; and using the training dataset to optimize the hyperparameters of the Gaussian process through the maximum likelihood estimation method to establish a mapping model from control parameters to system energy efficiency.

[0017] Preferably, the iterative selection of the next control parameter combination includes: calculating the acquisition function value at each point in the candidate parameter space based on the predicted mean and predicted variance output by the Gaussian process regression surrogate model; using a global optimization algorithm to find the control parameter combination that maximizes the acquisition function value as the next control parameter combination to be tested; inputting the next control parameter combination to be tested into the fluid dynamics differential algebraic equations model to obtain a new steady-state energy efficiency value; adding the new steady-state energy efficiency value to the training dataset and updating the Gaussian process regression surrogate model until the preset maximum number of iterations is reached or the energy efficiency improvement is lower than the convergence threshold, and outputting the control parameter combination that maximizes the steady-state energy efficiency value as the control instruction.

[0018] Preferably, the Jacobian matrix is ​​directly calculated and initialized in the first integration time step, the condition number calculated in the first integration time step is recorded as the initial value of the condition number, and the initial value of the local truncation error is set as the preset target truncation error in the first integration time step.

[0019] Secondly, this application provides an intelligent prediction and optimization control system for the energy efficiency of an axial flow pump, including a processor and a memory. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, the aforementioned intelligent prediction and optimization control method for the energy efficiency of an axial flow pump is implemented.

[0020] The computer program instructions corresponding to each step of the above-mentioned intelligent prediction and optimization control method for axial flow pump energy efficiency are stored in the memory, and the processor loads and executes the computer program instructions to implement the above method.

[0021] The beneficial effects of this application are as follows: At the implicit integral solution level, this application correlates the Jacobian matrix update strategy with the local truncation error variation rate. When the flow field is stable, existing matrices are reused to reduce the number of assembly and decomposition steps, while timely updates ensure convergence of the Newton iteration when the flow field changes drastically. A proportional-integral controller is used to calculate the baseline step size by combining current and historical error information, and then an exponential decay correction based on the condition number of the Jacobian matrix is ​​superimposed. When the numerical stiffness increases, the actual step size is reduced accordingly, reducing step size adjustment oscillations and improving integral stability. At the surrogate model level, a Gaussian process regression model is constructed with a small number of simulation samples and directional sampling is combined with the acquisition function criterion to reduce the number of high-cost simulation calls and accelerate convergence, thereby reducing the overall computational cost of axial flow pump energy efficiency optimization and control.

[0022] Furthermore, by using nested calculations of high- and low-order implicit Runge-Kutta methods for local truncation errors and then performing weighted root mean square dimensionless processing, the error metric covers state variables of different dimensions. Latin hypercube sampling is used to ensure that the initial sample set is uniformly and hierarchically distributed in the control parameter space, thereby improving the fitting accuracy of the surrogate model's initial training. Initial error values ​​and initial condition number values ​​are set in the first integration time step to ensure that the implicit integration process can proceed normally in the initial stage when there is no historical data. Attached Figure Description

[0023] Figure 1 A flowchart of a method for intelligent prediction and optimization control of energy efficiency of axial flow pumps; Figure 2 A scatter plot of the distribution of sample points for control parameter combinations obtained by Latin hypercube sampling; Figure 3 This is a line graph showing the trend of steady-state energy efficiency value as a function of the number of optimization iterations. Detailed Implementation

[0024] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0025] This application discloses a method for intelligent prediction and optimized control of axial flow pump energy efficiency, referring to... Figure 1 This includes steps S1-S4: S1. Establish fluid dynamics model and sampling.

[0026] The geometric model and boundary conditions of the axial flow pump are extracted, and the fluid domain from the pump inlet to the outlet is divided into structured or unstructured meshes. During geometric model extraction, the complete flow components, including the impeller, guide vanes, inlet pipe, and outlet pipe, are imported into the mesh generation software. The fluid domain is then divided into a hexahedral structured mesh with boundary layer refinement. The total number of meshes is controlled between 3 and 5 million, ensuring the dimensionless distance of the first layer mesh. Less than 5. The finite volume method is used to spatially discretize the Navier-Stokes continuity equation and the three-dimensional momentum equation based on the incompressibility assumption. The convection term adopts the second-order upwind scheme, and the diffusion term adopts the central difference scheme, thus constructing a set of differential-algebraic equations of fluid dynamics related to the pressure and velocity at the fluid nodes.

[0027] Initial flow field velocity, pressure distribution, and boundary conditions are set as initial operating parameters. Based on historical operating data, the three-dimensional initial velocity field within the flow field is set to a base velocity of 0.5 m / s along the main flow direction of the axial flow pump, while the remaining transverse velocity components are initially set to 0. No-slip boundary conditions are applied at the pipe wall. The inlet boundary condition is configured as a constant mass flow rate, set to 200 kg / s in this embodiment; the outlet boundary condition is set as a pressure outlet with an average static pressure reference value, set to standard atmospheric pressure (101325 Pa) in this embodiment. The SST turbulence model is selected. Model and configure the corresponding initial values ​​of turbulent kinetic energy. It is 0.01 Initial value of specific dissipation rate 1 .

[0028] The control parameters to be optimized were determined, including the operating frequency and guide vane angle of the axial flow pump. The operating frequency was constrained to a range of 42Hz to 55Hz, and the guide vane angle was constrained to a range of -15° to +15°. A Latin hypercube sampling method was used to extract multiple unique combinations of control parameters within the constraints to form an initial sample set.

[0029] The initial sample set contains 30 to 50 samples; in this embodiment, 40 samples are used. During Latin hypercube sampling, the operating frequency constraint range of 42Hz to 55Hz is divided into 40 equally probable sub-intervals, each with a span of 0.325Hz; the guide vane angle constraint range of -15° to +15° is also divided into 40 equally probable sub-intervals, each with a span of 0.75°. Within each of the 40 sub-intervals for operating frequency and guide vane angle, a specific value is randomly selected using a uniform distribution. The selected values ​​for the two parameters are then paired randomly to generate 40 distinct two-dimensional control parameter combination vectors. The sampled operating frequency values ​​are rounded to one decimal place according to the inverter's control resolution, and the guide vane angle values ​​are rounded to integer multiples of 0.5° according to the guide vane actuator's control resolution. If duplicate control parameter combinations appear after rounding, resampling or minor perturbation correction is performed within the corresponding sub-interval to ensure that each control parameter combination in the initial sample set is distinct. The distribution results of the control parameter combination sample points obtained by Latin hypercube sampling are referenced. Figure 2 .

[0030] S2. Implicit integration solution and error calculation.

[0031] Steady-state energy efficiency is obtained by implicitly integrating each set of control parameters. A diagonal implicit Runge-Kutta method family with L-stability is selected as the time-progression scheme, transforming the continuous differential-algebraic equations into a nonlinear algebraic equation system at each time step, which is then solved using Newton's iteration method. Newton's iteration constructs the residual function and its Jacobian matrix, repeatedly calculating the state variable corrections to gradually satisfy the equilibrium conditions of the discrete equation system for state variables such as pressure, flow rate, velocity, or rotational speed.

[0032] Calculate the local truncation error based on the difference between high-order and low-order numerical solutions. High-order numerical solutions The lower-order numerical solution was obtained using the fourth-order ESDIRK method. The numerical solutions are obtained synchronously through a nested third-order method. After obtaining two sets of numerical solutions, the three-dimensional velocity components of each mesh node are extracted. and static pressure State variables, etc., are then processed for differential quantization.

[0033] Calculate the differences between the higher-order and lower-order numerical solutions for each state variable and perform dimensionless processing. Utilize the absolute tolerance vector. and relative tolerance scalar After achieving dimensionless transformation, the absolute tolerance for velocity is set to... m / s, the absolute tolerance for pressure is set to 1 Pa, and the relative tolerance is uniformly set to [value missing]. For the th in the state variable vector Each component has a weight reference value calculated according to the following formula: ; In the formula, For the first The weight reference values ​​for each state variable, It is a relative tolerance scalar. For the first Higher-order numerical solutions for each state variable. For the first Low-order numerical solutions for each state variable. In order to be with the first Each state variable has an absolute tolerance of the same dimension. Dividing the difference by the corresponding weight yields the dimensionless difference.

[0034] The weighted root mean square (RMS) difference is calculated for the differences between the state variables after dimensionless processing, and the weighted RMS difference norm is used as the local truncation error of the current time step. The weighted RMS difference norm is calculated according to the following formula: ; In the formula, This represents the local truncation error at the current time step. This represents the total number of state variables. This norm value indicates the temporal discrepancy between high- and low-order schemes and can be used as a basis for subsequent step size control.

[0035] The Jacobian matrix update is related to the rate of change of the local truncation error from the previous time step. In the time step progression of the implicit integration process, let the current time step be... The previous step was The previous time step is The corresponding local truncation errors are recorded as follows: , and The rate of change of local truncation error is calculated according to the following formula: ; In the formula, This represents the dimensionless rate of change of the local truncation error. This is the local truncation error from the previous time step. For the local truncation error of the previous time step, when Below 10 -12 At 10 -12 This is an alternative to avoid numerical overflow caused by the denominator approaching zero.

[0036] Local truncation error variation rate This reflects the magnitude of changes in the flow field state and the local linear relationship of the residual function between two adjacent time steps. When the rate of change is large, the old Jacobian matrix is ​​difficult to accurately describe the current solution process. The preset change threshold is set between 0.15 and 0.25; in this embodiment, it is set to 0.2, which balances computational accuracy and cost. When the rate of change of the local truncation error is greater than the preset change threshold, the Jacobian matrix is ​​recalculated using the current system state variables. When the rate of change of the local truncation error is less than or equal to the preset change threshold, the Jacobian matrix of the previous time step is retained.

[0037] When encountering flow separation or vortex shedding conditions, When the value is greater than 0.2, based on the latest pressure and velocity state variable vectors, a first-order forward finite difference method with a relative perturbation step size matching the dimensions of each state variable is used to redifferentiate the residual function composed of the convection, diffusion, and source terms, and reassemble and update the sparse Jacobian matrix of a scale of millions. Following the standard perturbation strategy of the finite difference method, the [missing value] is then applied to the [missing value]. The finite difference perturbation is calculated for each state variable using the following relationship: ; In the formula, For the first Finite difference perturbation of a state variable, The relative disturbance coefficient. For the first The current value of each state variable. To serve as the reference scale for the corresponding state variables, 1 m / s is used for velocity-type state variables and 10 m / s for pressure-type state variables. 5 Pa. If the perturbation is too large, the truncation error will increase; if it is too small, the numerical accuracy will be insufficient. Take 10 -6 .

[0038] The relatively stable flow makes When less than or equal to 0.2, at the current time step In the Newton-Raphson iterative equations, the old Jacobian matrix or LU decomposition factor stored in memory is reused to solve the residual linear equation system.

[0039] In the first integration time step, the Jacobian matrix is ​​directly calculated and initialized, and the initial value of the local truncation error is set to the preset target truncation error. The time step size of the first integration time step. The convection timescale is determined based on the characteristic scale of the fluid domain and the initial velocity estimation; in this embodiment, it is taken as 10. -3 s.

[0040] S3, step size control and steady-state energy efficiency recording.

[0041] The proportional-integral controller calculates the next time step from the baseline. The ratio of the preset target truncation error to the local truncation error of the current time step is used as the basis for proportional adjustment, and the ratio of the target truncation error to the historical local truncation error is used as the basis for integral adjustment. The target truncation error of the controller is set. Assuming an ideal baseline value of 1, the local truncation error at the current time step is taken. Calculate the proportional deviation term. Proportional gain coefficient. The value ranges from 0.05 to 0.15, and in this embodiment, it is taken as 0.08; integral gain coefficient The value ranges from 0.2 to 0.4, and in this embodiment, it is 0.3.

[0042] To convert the deviation between the target error and the actual error into a step size scaling factor, a discrete PI control law is used to output the control signal. The dimensionless step size adjustment signal satisfies the following relationship: ; In the formula, This is a dimensionless step size adjustment signal. This is the proportional gain coefficient. This is the integral gain coefficient. For the target truncation error, This represents the local truncation error at the current time step. This represents the local truncation error from the previous time step. Less than When the ratio is greater than 1, After exponentiation If the value is greater than 1, the step size increases accordingly; conversely, if the value is less than 1, the step size decreases. The exponential transformation form ensures... It is always a positive value.

[0043] when or When the value is lower than the machine's accuracy limit, use a preset minimum positive number. Replacement Pick To avoid overflow in logarithmic operations, a dimensionless step size adjustment signal is obtained. Then, set the next time step of the reference. ,in This is the current time step. Set the upper limit for step size to avoid numerical oscillations; the single-step scaling ratio should not exceed 2, and the single-step scaling ratio should not be less than 0.5.

[0044] proportional gain coefficient If the step size is too small, the response of the step size to the current error change will be slow, and the convergence process will be slow. An excessively large step size will result in significant fluctuations in step size adjustment, easily causing numerical oscillations. A value of 0.08 is chosen as a compromise in engineering practice. Referring to engineering experience with similar fluid numerical integration systems, the integral gain coefficient... We set it to 0.3 to avoid excessive integration that could lead to cumulative step size shift, while ensuring the ability to correct historical errors.

[0045] Calculate the maximum singular value of the updated Jacobian matrix using singular value decomposition. and the smallest non-zero singular value The ratio of is used as a quantification index of the system's numerical rigidity. Condition number This can be expressed as follows: ; In the formula, For condition numbers, The largest singular value of the Jacobian matrix. Let be the smallest non-zero singular value of the Jacobian matrix. The maximum and minimum non-zero singular values ​​are approximated using the Krylov subspace iterative algorithm. During the first integration time step when calculating the Jacobian matrix, the condition number at that moment is recorded as the initial condition number. When comparing the number of conditions for the first triggering later, use As .

[0046] When the system's numerical quantification index increases, the baseline time step is reduced according to an exponential decay function to become the actual next time step. If the condition number at the current Jacobian matrix update time... The condition number is greater than the one at the last Jacobian matrix update time. As the numerical scale difference of the system's state equations increases, the solution stiffness increases. The condition number is taken from 10... 6 Increased to 5×10 6 For example, first calculate the relative increment of the condition number. : ; In the formula, The relative increment of the condition number. Let be the condition number at the current Jacobian matrix update time. This is the condition number at the time of the last Jacobian matrix update. When Value below 10 -10 At 10 -10 Substitute to avoid the denominator being close to zero.

[0047] Exponential decay factor Satisfying the relation: ; In the formula, It is an exponential decay factor. To preset the minimum suppression coefficient, This is the decay constant. The larger the relative increment of the condition number... The smaller the value, the greater the reduction in step size. Decay constant. The value ranges from 0.3 to 0.8, and in this embodiment, it is 0.5. When the value is 0.5, the step size reduction ratio corresponding to doubling the condition number is 0.61, which balances the suppression strength and the smoothness of the step size. The value range is from 0.3 to 0.7. In this embodiment, it is 0.5 to ensure that the step size reduction after a single stiffness correction does not exceed 50% of the original step size.

[0048] Determine the actual next time step If the Jacobian matrix has not been updated at the current time step, or if the current condition number is not greater than the condition number at the time of the last Jacobian matrix update, then let... It is 1, and with As the actual next time step.

[0049] The time is advanced using the actual next time step, and the implicit integration is repeated. After each solution, it is checked whether the relative change of the system state variables between the two time steps is less than 10. -5 If the value is less than 1, the system state variable is considered to have reached stability and the time integration is stopped. The steady-state energy efficiency value corresponding to the current control parameter combination is calculated and saved by dividing the product of the steady-state volumetric flow rate and the inlet / outlet pressure difference by the motor shaft power; when using mass flow rate, the mass flow rate is divided by the fluid density to convert it to volumetric flow rate before calculating the steady-state energy efficiency value.

[0050] S4, Agent Model Construction and Bayesian Optimization.

[0051] All tested control parameter combinations were used as input feature vectors, and the corresponding steady-state energy efficiency values ​​were used as output target values ​​to construct a training dataset. Before constructing the Gaussian process regression surrogate model, the input feature vectors consisting of operating frequencies of 42Hz to 55Hz and guide vane angles of -15° to +15° were uniformly mapped to the normalized interval [-1, 1] to eliminate the influence of inconsistent feature dimension units. The steady-state energy efficiency value obtained through implicit integration was used as the scalar output target value. The above control parameter combinations were paired with the steady-state energy efficiency values ​​to form an initial training dataset containing 40 sets of samples.

[0052] The Matrn kernel function is chosen as the covariance function for the Gaussian process. From an engineering application perspective, the smoothness of the Matrn 5 / 2 kernel function lies between that of the quadratic exponential kernel function and the absolute exponential kernel function, making it suitable for describing a smooth but not infinitely differentiable mapping relationship between axial flow pump control parameters and energy efficiency. The expression for the Matrn 5 / 2 kernel function is: ; In the formula, The value of the covariance function. The dimensionless distance in the normalized control parameter space after incorporating the length scale. Let V be the signal variance. Construct a marginal log-likelihood function with respect to the training dataset to determine the hyperparameter set, including the feature length scale and the standard deviation of Gaussian white noise. Perform multi-starting gradient descent optimization in the hyperparameter space with boundary constraints using the finite-memory quasi-Newton method L-BFGS-B algorithm to maximize the likelihood function, lock the optimal hyperparameters, and establish a mapping model from control parameters to system energy efficiency.

[0053] After obtaining the Gaussian process regression surrogate model, the next combination of control parameters is iteratively selected based on the posterior distribution and the acquisition function criterion. For any unexplored input point... The model outputs the predicted mean of energy efficiency at that point. and prediction variance In this embodiment, the upper confidence bound criterion is used as the acquisition function. The upper confidence bound function is calculated according to the following formula: ; In the formula, Candidate points The confidence upper bound function value, To predict the mean, To predict the standard deviation, To adjust the parameters. The larger the value, the more the search strategy will favor the unknown region with a large prediction variance. Set to vary with the number of iterations The increased logarithmic function. According to the Gaussian process confidence upper bound theory, in the confidence probability... Down, Calculate according to the following formula: ; In the formula, This represents the current iteration number. To explore the upper bound of the failure probability, this embodiment... Take 0.1. With... Increase Slow growth allows the optimization process to focus on development in the early stages and gradually increase exploration in the later stages.

[0054] Within a continuous normalized control parameter domain, a differential evolution global optimization algorithm with a population size of 100 and a maximum number of generations of 500 is invoked to locate the population that... The control parameter combination point that reaches the maximum value is identified. The parameter combination selected by the differential evolution algorithm is then denormalized again. In this embodiment, the operating frequency is 48.5Hz and the guide vane angle is -2.5°. This is used as a boundary condition and fed into the differential algebraic equation model of the axial flow pump to obtain a new round of implicit time integration to obtain the steady-state energy efficiency value.

[0055] It is worth noting that the population size and number of generations in the differential evolution algorithm need to strike a balance between search accuracy and computational time. A population size that is too small will cause the global search to miss local optima, while a population size that is too large will increase the number of function evaluations. In a two-dimensional control parameter space, 100 individuals can cover the main feature regions of the parameter domain. If the population has not converged after 500 generations of evolution, the current best individual is used as the output.

[0056] The actual operating data of this embodiment was used for verification: After obtaining the steady-state energy efficiency value through implicit integration of the initial 40 sets of samples, a surrogate model was constructed. The candidate point selected in the first iteration was an operating frequency of 48.5Hz and a guide vane angle of -2.5°, corresponding to a steady-state energy efficiency value of 0.872; the candidate point selected in the fifth iteration was an operating frequency of 49.8Hz and a guide vane angle of -1.0°, corresponding to a steady-state energy efficiency value of 0.891; by the 12th iteration, the absolute improvement in energy efficiency was less than 0.05% for three consecutive iterations, and the optimization process converged. The final output optimal control parameter combination for energy efficiency was an operating frequency of 50.2Hz and a guide vane angle of -0.5°, corresponding to a steady-state energy efficiency value of 0.896.

[0057] After obtaining the steady-state energy efficiency feedback from the new sampling points, it is paired with the input parameters and added to the training dataset, triggering the refitting and optimization of the Matrn kernel function hyperparameters to update the surrogate model. Iteration continues until the preset maximum number of additional samplings (30) is reached, or the absolute energy efficiency improvement brought by three consecutive iterations of new samples is less than the preset 0.05% convergence threshold. At this point, the loop stops, and the combination of control parameters that maximizes the steady-state energy efficiency value in the expanded dataset is read, converted into a standard industrial control current signal, and sent to the programmable logic controller as a control command output. The trend of energy efficiency change with the number of iterations is shown in the figure. Figure 3 .

[0058] This application also discloses an intelligent prediction and optimization control system for the energy efficiency of an axial flow pump, including a processor and a memory. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, an intelligent prediction and optimization control method for the energy efficiency of an axial flow pump according to this application is implemented.

[0059] The system also includes other components well known to those skilled in the art, such as communication buses and communication interfaces, the settings and functions of which are known in the art and will not be described in detail here.

[0060] In the description of this specification, "multiple" or "several" means at least two, such as two, three or more, unless otherwise expressly and specifically defined.

Claims

1. A method for intelligent prediction and optimized control of axial flow pump energy efficiency, characterized in that, include: S1. Obtain the fluid dynamic differential algebraic equation model and initial operating parameters of the axial flow pump, and set multiple sets of control parameter combinations to be optimized as sample points; S2. Implicit integration is performed on each set of control parameters to obtain steady-state energy efficiency. The Newton-Raphson method is used to solve the discrete equations in each integral time step. The Jacobian matrix update is related to the rate of change of the local truncation error in the previous time step. When the rate of change of the local truncation error exceeds the preset threshold, the Jacobian matrix is ​​updated. The local truncation error is calculated based on the difference between the high-order and low-order numerical solutions. S3. Combine the local truncation error and historical error to calculate the reference next time step through the proportional-integral controller. When updating the Jacobian matrix, calculate the condition number as the numerical rigidity quantification index of the system. When the numerical rigidity quantification index of the system increases, reduce the reference next time step according to the exponential decay function to get the actual next time step. Repeat the implicit integration solution until the system state variables are stable and record the steady-state energy efficiency value. S4. Construct a Gaussian process regression surrogate model using sample points and steady-state energy efficiency values. Based on the posterior distribution, use the acquisition function criterion to iteratively select the next combination of control parameters. After convergence, output the energy-efficient optimal control parameter combination as the control instruction.

2. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, The process of obtaining the fluid dynamics differential algebraic equation model and initial operating parameters of the axial flow pump includes: extracting the geometric model and boundary conditions of the axial flow pump; dividing the fluid domain from the inlet to the outlet of the axial flow pump into a structured or unstructured grid; constructing a fluid dynamics differential algebraic equation system containing the continuity equation and the momentum equation based on the incompressible Navier-Stokes equations; and setting the initial flow field velocity, pressure distribution, and boundary conditions as initial operating parameters.

3. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, The process of setting multiple sets of control parameter combinations to be optimized as sample points includes: determining the control parameters to be optimized, including the operating frequency and guide vane angle of the axial flow pump; determining the constraint range of each control parameter, with the operating frequency constrained from 42Hz to 55Hz and the guide vane angle constrained from -15° to +15°; and using the Latin hypercube sampling method to extract multiple sets of unique control parameter combinations within the constraint range after deduplication to form an initial sample set.

4. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, The local truncation error variation rate is calculated as follows: take the absolute value of the difference between the local truncation error of the previous time step and the local truncation error of the time step before that, and divide it by the local truncation error of the time step before that. When the local truncation error variation rate is greater than a preset variation threshold, the Jacobian matrix is ​​recalculated using the current system state variables. When the local truncation error variation rate is less than or equal to the preset variation threshold, the Jacobian matrix of the previous time step is used.

5. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, The method for calculating the local truncation error based on the difference between higher-order and lower-order numerical solutions includes: calculating the higher-order numerical solution of the current time step using the fourth-order implicit Runge-Kutta method, and calculating the lower-order numerical solution of the current time step using the third-order implicit Runge-Kutta method; calculating the difference between the higher-order and lower-order numerical solutions on each state variable and performing dimensionless processing; performing weighted root mean square calculation on the difference between each state variable after dimensionless processing, and using the weighted root mean square difference norm as the local truncation error of the current time step.

6. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, The next time step is calculated by the proportional-integral controller, including: using the ratio of the preset target truncation error to the local truncation error of the current time step as the basis for proportional adjustment, using the ratio of the target truncation error to the historical local truncation error as the basis for integral adjustment, multiplying the proportional adjustment basis and integral adjustment basis by powers of the proportional gain and integral gain respectively to obtain the step size adjustment signal, and multiplying it by the current time step to obtain the next time step; using the singular value decomposition method to calculate the ratio of the maximum singular value to the minimum non-zero singular value of the updated Jacobian matrix as the system numerical rigidity quantification index; when the system numerical rigidity quantification index increases, the next time step is multiplied by the exponential decay factor to obtain the actual next time step, where the exponential decay factor is the positive value obtained by mapping the increment of the system numerical rigidity quantification index to a negative exponential value and taking the larger value of the preset minimum suppression coefficient.

7. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, The construction of the Gaussian process regression surrogate model includes: using all tested control parameters as input feature vectors and the corresponding steady-state energy efficiency values ​​as output target values ​​to construct a training dataset; selecting the squared exponential kernel function or the Matrn kernel function as the covariance function of the Gaussian process; and using the training dataset to optimize the hyperparameters of the Gaussian process through the maximum likelihood estimation method to establish a mapping model from control parameters to system energy efficiency.

8. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, The iterative selection of the next control parameter combination includes: calculating the acquisition function value at each point in the candidate parameter space based on the predicted mean and predicted variance output by the Gaussian process regression surrogate model; using a global optimization algorithm to find the control parameter combination that maximizes the acquisition function value as the next control parameter combination to be tested; inputting the next control parameter combination to be tested into the fluid dynamics differential algebraic equations model to obtain a new steady-state energy efficiency value; adding the new steady-state energy efficiency value to the training dataset and updating the Gaussian process regression surrogate model until the preset maximum number of iterations is reached or the energy efficiency improvement is lower than the convergence threshold, and outputting the control parameter combination that maximizes the steady-state energy efficiency value as the control instruction.

9. The method for intelligent prediction and optimized control of axial flow pump energy efficiency according to claim 1, characterized in that, In the first integration time step, the Jacobian matrix is ​​directly calculated and initialized. The condition number calculated in the first integration time step is recorded as the initial value of the condition number. In the first integration time step, the initial value of the local truncation error is set as the preset target truncation error.

10. A smart prediction and optimization control system for the energy efficiency of an axial flow pump, characterized in that, include: The processor and memory, wherein the memory stores computer program instructions, which, when executed by the processor, implement the intelligent prediction and optimization control method for the energy efficiency of an axial flow pump according to any one of claims 1 to 9.

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