Reverse cooling turbine one-dimensional uncertainty design optimization method and system

Abstract

The invention belongs to the field of uncertainty quantification and robustness design optimization of aero-engine air-cooled turbines, and particularly discloses a one-dimensional uncertainty design optimization method and system for a reverse cooling turbine based on a one-dimensional aerodynamic analysis method for the reverse cooling turbine. Forming an augmented space by the optimization variables and the uncertainty parameters, and generating a sample set; establishing a Kriging global agent model, and generating an uncertainty parameter sample set; an ASPC model is established, and one-dimensional uncertainty quantification of the reverse cooling turbine is completed; an NSGA-II multi-objective optimization algorithm is coupled, and one-dimensional robustness design optimization of the reverse cooling turbine is completed. The one-dimensional uncertainty design optimization method and system framework of the reverse cooling turbine are provided and established, aerodynamic performance analysis of the reverse cooling turbine can be completed through simple parameters, a geometric entity is not needed, and tasks such as one-dimensional uncertainty quantification and robustness design optimization of the reverse cooling turbine can be achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aero-engine air-cooled turbine uncertainty quantification and robust design optimization, and particularly relates to a one-dimensional uncertainty design optimization method and system for a reverse cooling turbine. BACKGROUND

[0002] The turbine is one of the three core components of an aero-engine, and is a turbomachinery that converts the energy of high-temperature and high-pressure gas into kinetic energy and mechanical energy. Rapid and accurate prediction of turbine performance is a prerequisite for developing high-performance turbines, and has always been the focus of the aero-engine field.

[0003] The flow inside the turbine is controlled by full three-dimensional N-S equations, and is a typical three-dimensional unsteady flow. Although modern CFD methods can obtain relatively accurate performance and flow field details, they require geometric entities and a large amount of time. In order to overcome this shortcoming, it is necessary to develop a high-precision one-dimensional aerodynamic analysis method. Considering that the gas flowing through the turbine will cause flow loss, accurate loss prediction is a prerequisite for accurate one-dimensional aerodynamic performance analysis. The flow inside the turbine is a typical unsteady three-dimensional viscous flow, and there are complex vortex systems such as passage vortex, corner vortex, and leakage vortex, and may be accompanied by shock waves, boundary layer separation, backflow and other flow phenomena and their mutual motion, which are very complex. There are many factors that affect turbine loss, such as geometric factors such as aspect ratio and air flow turning angle; aerodynamic factors such as incoming flow velocity, turbulence intensity and boundary layer thickness, so the understanding of the complex flow loss mechanism inside the turbine, the establishment and application of the loss model are constantly developing and improving, and are an important topic of one-dimensional aerodynamic analysis of turbines. In addition, the turbine components of modern aero-engines are mostly divided into high-pressure turbines and low-pressure turbines, and the rotation directions of the high-pressure turbines and the low-pressure turbines are opposite. In order to adapt to the development trend of gradually increasing turbine inlet temperature, the amount of turbine cooling gas is increasing, and the low-pressure turbine also needs to be cooled, resulting in more complex flow inside the turbine, which determines that the accurate prediction of reverse turbine loss is a difficult topic.

[0004] There are many uncertain factors in the design, processing and manufacturing and operation of the turbine, which affect the overall performance of the turbine. In order to fully grasp the transmission law of the uncertainty of the input parameters and reveal the influence law of the uncertainty on the overall performance, it is necessary to carry out uncertainty quantification research.

[0005] In addition, the traditional deterministic design optimization does not consider the influence of uncertain factors during optimization, and although an excellent design point can be obtained after optimization, the performance at the design point fluctuates greatly under the disturbance of uncertain factors, and the robustness is poor. As a kind of uncertain design optimization, robust design optimization can fully consider the uncertain factors affecting performance, and take the statistical information of design point performance as the optimization target, so that the design optimization solution with excellent average performance level and performance robustness under the disturbance of uncertain factors can be obtained.

[0006] In summary, the internal flow loss mechanism of the reverse cooling turbine is complex, and a high-precision loss model needs to be introduced to establish a robust and efficient one-dimensional aerodynamic analysis method for the reverse cooling turbine. SUMMARY

[0007] In order to solve the problems existing in the prior art, the present application provides a one-dimensional uncertain design optimization method and system for a reverse cooling turbine, which can realize technologies including one-dimensional aerodynamic analysis of a reverse cooling turbine, one-dimensional uncertainty quantification of a reverse cooling turbine, one-dimensional robust design optimization of a reverse cooling turbine, etc.

[0008] In order to achieve the above-mentioned purpose, in a first aspect, the present application provides a one-dimensional uncertain design optimization method and system for a reverse cooling turbine, comprising the following steps: S10, dividing the reverse cooling turbine into a plurality of calculation stations along the axial direction, solving the performance parameters of the reverse cooling turbine according to the actual outlet velocity of the cascade where the calculation station is located, and performing one-dimensional aerodynamic analysis; S11, according to the one-dimensional aerodynamic analysis results of the reference design of the reverse cooling turbine, dividing the input data into optimization variables and uncertainty parameters, and giving the range of the optimization variables and the probability distribution of the uncertainty parameters, and determining the target performance for carrying out uncertainty quantification and robust design optimization; S12, performing Latin hypercube sampling in the augmented space composed of the optimization variables and the uncertainty parameters, performing one-dimensional aerodynamic analysis on each sample, extracting the target performance, and generating a total sample set; S13, constructing a Kriging global surrogate model according to the total sample set and verifying the model accuracy; S14, randomly sampling the uncertainty parameters of each sample again, evaluating the target performance by using the Kriging model, and generating an uncertainty parameter sample set; S15, constructing an adaptive chaotic polynomial model according to the uncertainty parameter sample set, outputting the mean, variance, probability distribution and other information of the target performance, and completing the uncertainty quantification; S16, taking the mean and variance of the target performance as the objective function to carry out multi-objective optimization, obtaining the Pareto optimal front and solution set, and completing the robust design optimization.

[0009] Further, the counter-rotating cooling turbine is divided into multiple calculation stations along the axial direction, and the performance parameters of the counter-rotating cooling turbine are solved according to the outlet actual speed of the cascade at the calculation station, and the one-dimensional aerodynamic analysis includes: The differential evolution algorithm is used to optimize and solve the static pressure of each counter-rotating cooling turbine calculation station, the inlet total enthalpy, the inlet total pressure, the outlet static pressure, the rotational speed of each stage, the cold gas parameters and the blade geometric parameters are given, the one-dimensional aerodynamic analysis equation set is constructed according to the basic equation of one-dimensional flow, the inlet total temperature and the inlet total pressure after the cold gas mixing are calculated, the static cascade isentropic stagnation enthalpy drop, the static blade outlet ideal speed, the dynamic cascade isentropic enthalpy drop, the dynamic blade outlet ideal speed, then the cascade loss and the velocity coefficient are solved by the outlet flow angle initial value and the loss model, the outlet actual speed of the cascade at the calculation station is solved according to the velocity coefficient formula, the performance parameters of the counter-rotating cooling turbine are solved according to the outlet actual speed of the cascade at the calculation station, and the one-dimensional aerodynamic analysis is completed.

[0010] Further, the differential evolution algorithm is used to optimize and solve the static pressure of each counter-rotating cooling turbine calculation station, the inlet total enthalpy, the inlet total pressure, the outlet static pressure, the rotational speed of each stage, the cold gas parameters and the blade geometric parameters are given, the one-dimensional aerodynamic analysis equation set is constructed according to the basic equation of one-dimensional flow, the inlet total temperature and the inlet total pressure after the cold gas mixing are calculated, the static cascade isentropic stagnation enthalpy drop, the static blade outlet ideal speed, the dynamic cascade isentropic enthalpy drop, the dynamic blade outlet ideal speed, then the cascade loss and the velocity coefficient are solved by the outlet flow angle initial value and the loss model, the outlet actual speed of the cascade at the calculation station is solved according to the velocity coefficient formula, the performance parameters of the counter-rotating cooling turbine are solved according to the outlet actual speed of the cascade at the calculation station, and the one-dimensional aerodynamic analysis is completed. According to the meridian plane flow channel data of the counter-rotating cooling turbine, one calculation station is divided at the front end and the last end of the meridian plane flow channel, the relative positions of the blade leading edge and the trailing edge are drawn on the meridian plane diagram, and one calculation station is divided at the outlet position of each row of blades; For each calculation station, the average diameter, the blade height, the outlet geometric angle, the inlet geometric angle, the residual velocity utilization coefficient, the guessed pressure, and the distance from the previous row of blades are given; The solving of the static pressure is converted into an optimization problem, the static pressure of each calculation station is taken as a variable, the flow deviation is taken as an objective function, the differential evolution algorithm is used for optimization and solving, and the optimization solution is taken as the final static pressure result of each station.

[0011] Further, in S12, Latin hypercube sampling is performed in an augmented space composed of optimization variables and uncertain parameters, one-dimensional aerodynamic analysis is performed on each sample, target performance is extracted, and a total sample set is generated, which is specifically as follows: The 95% confidence interval of the uncertain parameters is calculated according to the probability distribution, which is taken as the sampling range of the uncertain parameters, then the variation range of the optimization variables and the sampling range of the uncertain parameters are subjected to tensor product operation to obtain an augmented space; Uniformly distributed random numbers are generated in each dimension of the augmented space, so that each dimension has enough sampling points to cover the entire range, and the sampling points in each dimension are grouped so that there is only one sampling point in each group; For each dimension, a permutation operation is performed to make each row and column contain only one sample point, convert the standardized sample points of the Latin hypercube to the actual value range, adjust according to the specific value range of each variable, complete the Latin hypercube sampling, and finally perform one-dimensional aerodynamic analysis on each Latin hypercube sampling sample to extract the target performance and generate the overall sample set.

[0012] Further, in S13, the Kriging global surrogate model is constructed using the overall sample set and the model accuracy is verified, as follows: The predicted value is regarded as a Gaussian random process , It is assumed that the prediction error of each point has correlation The hyperparameters are estimated by the maximum likelihood function estimation method, and the likelihood function is set to 0 for the partial derivatives of and , and the pattern search algorithm is used to solve , completing the Kriging modeling; the leave-one-out cross-validation is performed to evaluate the accuracy of the Kriging model.

[0013] Further, an adaptive chaotic polynomial model is constructed using the uncertainty parameter sample set, and the mean, variance, and probability distribution information of the target performance are output, completing the uncertainty quantification, including: The uncertainty parameter sample set is input; the initial order , the maximum order and the cross-validation threshold of the chaotic polynomial expansion are set; the orthogonal polynomial basis is constructed using the Stieltjes process according to the current order ; the expansion coefficients are solved using RVM regression, and cross-validation is carried out simultaneously to obtain the cross-validation error under the current order ; it is determined whether meets the set cross-validation threshold ; if yes, the chaotic polynomial model under the current order is output; if no, the chaotic polynomial order is incremented ; it is determined whether is less than the set maximum order ; if yes, the orthogonal polynomial basis constructed by the Stieltjes process and the expansion coefficients are updated, and iteration is performed; if no, the optimal model is selected as the final chaotic polynomial model ; after the chaotic polynomial model is established, the mean of the target performance is , and the variance is ; the probability distribution information is obtained through Monte Carlo simulation, and the uncertainty quantification is completed.

[0014] Further, the mean and variance of the target performance are used as the target function for multi-objective optimization, and the NSGA-II optimization algorithm is used to obtain the Pareto optimal front and solution set, and the robust design optimization is completed, as follows: Initialize a population in the design space composed of optimization variables, which contains a set number of individuals; for each individual, calculate its fitness value; according to the dominance relationship between individuals, divide the individuals in the population into different non-dominant levels; perform non-dominant sorting based on the Pareto dominance relationship of individuals in the target space; Calculate the distance between adjacent individuals in the comparison target for each individual and sum them up to obtain the crowding degree value of each individual; select individuals with higher crowding degree and individuals in the first few non-dominant levels as the parent population, generate offspring individuals through crossover and mutation operations, and thus generate a new population; Combine the parent and offspring individuals, and select the next generation population according to the non-dominant sorting and crowding degree and selection rules, first select individuals with high non-dominant levels, and then select according to the crowding degree; Repeat the above steps until the optimization termination condition is met, and after the optimization is terminated, the Pareto optimal front and Pareto optimal solution set are obtained, and the robust design optimization is completed.

[0015] In a second aspect, the present application provides a system for one-dimensional uncertainty quantification and robust design optimization of reverse cooling turbine, comprising a one-dimensional aerodynamic analysis module, a target performance determination module, a total sample set generation module, a global proxy model construction module, an uncertainty parameter sample set generation module, an uncertainty quantification module and a multi-objective optimization module; The one-dimensional aerodynamic analysis module is used to divide the reverse cooling turbine into multiple calculation stations along the axial direction, and to solve the performance parameters of the reverse cooling turbine according to the actual outlet velocity of the cascade where the calculation station is located, and to perform one-dimensional aerodynamic analysis; The target performance determination module is used to divide the input data into optimization variables and uncertainty parameters according to the one-dimensional aerodynamic analysis results of the reference design of the reverse cooling turbine, and to give the range of optimization variables and the probability distribution of uncertainty parameters, and to determine the target performance for uncertainty quantification and robust design optimization; The total sample set generation module is used to perform Latin hypercube sampling in the augmented space composed of optimization variables and uncertainty parameters, perform one-dimensional aerodynamic analysis on each sample, extract the target performance, and generate the total sample set; The global proxy model construction module is used to construct a Kriging global proxy model based on the total sample set and verify the model accuracy; The uncertainty parameter sample set generation module is used for re-sampling the uncertainty parameters of each sample, evaluating the target performance by using the Kriging model, and generating the uncertainty parameter sample set; The uncertainty quantification module is used for constructing an adaptive chaos polynomial model according to the uncertainty parameter sample set, outputting the mean value, variance, probability distribution and other information of the target performance, and completing the uncertainty quantification. The multi-objective optimization module is used for performing multi-objective optimization on the mean value and variance of the target performance as the objective function, obtaining the Pareto optimal front and solution set, and completing the robustness design optimization.

[0016] In a third aspect, the present application can also provide a computer device comprising a processor and a memory, the memory being used to store a computer executable program, the processor reading the computer executable program from the memory and executing, and the processor executing the computer executable program can realize the reverse cooling turbine one-dimensional uncertainty design optimization method and system.

[0017] Meanwhile, a computer readable storage medium is provided, and the computer readable storage medium stores a computer program, and the computer program can realize the reverse cooling turbine one-dimensional uncertainty design optimization method and system when executed by a processor.

[0018] Compared with the prior art, the present application has at least the following beneficial effects: the method can greatly reduce the time of reverse cooling turbine aerodynamic performance analysis, uncertainty quantification, robustness design optimization and other tasks; the present application can complete the aerodynamic performance analysis of the reverse cooling turbine through simple parameters without the need for geometric entities; the one-dimensional uncertainty quantification, robustness design optimization and other tasks of the reverse cooling turbine can be realized, the one-dimensional uncertainty quantification and robustness design optimization platform of the reverse cooling turbine is formed, the automatic robustness design optimization of the reverse cooling turbine is realized, the aerodynamic performance and performance robustness of the reverse cooling turbine are improved, and the process does not need human intervention. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The reverse cooling turbine one-dimensional uncertainty quantification and robustness design optimization framework established by the present application; Figure 2 The division diagram of a reverse cooling turbine one-dimensional analysis calculation station; Figure 3 The reverse cooling turbine one-dimensional analysis input parameter structure sample diagram; Figure 4 The reverse cooling turbine one-dimensional analysis output parameter structure sample diagram; Figure 5 The ASPC model flowchart; Figure 6The one-dimensional uncertainty quantification result total efficiency distribution diagram of a certain reverse cooling turbine; Figure 7 The one-dimensional robust design optimization result Pareto optimal front diagram of a certain reverse cooling turbine. DETAILED DESCRIPTION

[0020] For the purpose, technical scheme and advantages of the implementation of the present application, the technical scheme in the embodiments of the present application will be described in more detail below in combination with the drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions throughout. The described embodiments are part of the embodiments of the present application, not all. The embodiments described below by reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application. The structure and technical scheme of the present application will be further specifically described below in combination with the drawings, and an embodiment of the present application is given.

[0021] The present application introduces a one-dimensional aerodynamic analysis method of a reverse cooling turbine as a performance evaluator, couples an accurate and efficient uncertainty quantification method, a global surrogate model technology and an advanced multi-objective optimization algorithm, establishes a one-dimensional uncertainty design optimization method and system of a reverse cooling turbine, improves the overall performance and performance robustness of the reverse cooling turbine, and has important significance for designing and developing reverse cooling turbine components.

[0022] In combination with Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 explain the present embodiment method, in which, to realize one-dimensional uncertainty quantification and robust design optimization of a reverse cooling turbine, it is necessary to couple a one-dimensional aerodynamic analysis method of a reverse cooling turbine, a global surrogate model technology, an uncertainty quantification method and a multi-objective optimization algorithm module. The present application ingeniously combines the above technical methods, establishes a one-dimensional uncertainty quantification and robust design optimization framework of a reverse cooling turbine, and completes all processes of the entire framework through self-programming, as shown in Figure 1 .

[0023] The characters in the drawings are explained as follows: Kriging—Kriging surrogate model, NSGA-II—multi-objective optimization algorithm, ASPC—Adaptive Sparse Polynomial Chaos, English abbreviation, —current order of chaos polynomial, - initial degree of the chaotic polynomial, - maximum degree of the chaotic polynomial, - cross-validation discrimination threshold, - current chaotic polynomial cross-validation error, Stieltjes process, RVM - Relevance Vector Machine.

[0024] The steps of one-dimensional uncertainty quantification and robust design optimization of a counter-rotating cooled turbine are as follows: Step 1, divide the calculation station as shown in Figure 2 , organize the parameters required for one-dimensional aerodynamic analysis of the reference design of a counter-rotating cooled turbine, form a standardized input format, call the one-dimensional aerodynamic analysis module of the counter-rotating cooled turbine, and output the one-dimensional aerodynamic analysis results of the reference design of the counter-rotating cooled turbine. Specifically includes: S1, divide the counter-rotating cooled turbine into multiple calculation stations along the axial direction, the number of calculation stations is N+2, where N is the number of blade rows of the counter-rotating cooled turbine, the first and N+2 calculation stations are located at the axial positions of the turbine inlet and outlet respectively, the second to N+1 calculation stations are located at the axial positions of each row of blades respectively; According to the meridional flow data of the counter-rotating cooled turbine, divide one calculation station at the front and rear ends of the meridional flow passage, draw the relative positions of the blade leading edge and trailing edge on the meridional plane, and divide one calculation station at the outlet position of each row of blades; S2, for each row of blades, give the geometric parameters of the blade profile, including chord length, blade width, leading edge thickness, maximum thickness, trailing edge thickness; S3, for each row of blades, give the blade tip clearance, gas seal calculation control parameters, blade number, cold gas ratio, cold gas temperature and other parameters; S4, for each calculation station, give the average diameter, blade height, outlet geometric angle, inlet geometric angle, residual velocity utilization coefficient, guessed pressure, and distance from the previous row of blades; The straight line at the axial position of the calculation station intersects the hub and shroud lines respectively, and the intersection coordinates are calculated according to the plane curve intersection equation set and ; Calculate the average diameter , the blade height ; The residual velocity utilization coefficient of the last two calculation stations is 0, and the rest is 1; The guessed pressure is a series of pressure values approximately given between the inlet and outlet; The distance from the previous row of blades . In the above formula, are the calculation station numbers.

[0025] S5, give the turbine inlet total enthalpy, inlet total pressure, exhaust pressure, and rotational speed of each stage; S6, the differential evolution algorithm is used to optimize and solve the static pressure of each station; considering that the traditional iterative method is strongly dependent on the initial pressure value and is prone to divergence, especially in strong cold air conditions, the flow difference of each station is large, and this shortcoming is more prominent. The present application converts the solving of static pressure into an optimization problem, taking the static pressure of each calculation station as the variable and the flow deviation as the objective function, and uses the differential evolution algorithm to optimize and solve, which overcomes the dependence on the initial pressure value and has strong robustness. Specifically as follows: Given the total inlet enthalpy, total inlet pressure, speed and cold air parameters, the total inlet temperature and total inlet pressure of the cold air after mixing are solved, and the flow deviation is extracted as the objective function. The control parameters of the differential evolution algorithm are determined, including population size NP, scaling factor F and hybrid probability CR, and the flow deviation fitness function is determined; the initial population is randomly generated, and the initial population is evaluated, that is, the fitness value of each individual in the initial population is calculated; mutation and crossover operations are performed to obtain the intermediate population; select individuals from the original population and the intermediate population to obtain the next generation population, and the evolution number is increased by 1; determine whether the termination condition is reached or the evolution number reaches the maximum, if yes, terminate the evolution, and output the best individual as the optimal solution, if not, continue the iterative optimization process. After optimization, the optimized solution is taken as the final static pressure of each station, and the remaining performance parameters of each station are solved.

[0026] S7, according to the one-dimensional flow equation set, the isentropic stagnation enthalpy drop and the outlet ideal velocity of each station are solved, and the cascade loss and velocity coefficient are solved according to the initial value of the outlet flow angle; the one-dimensional flow equation set is used to solve the parameters of each calculation station, which includes the continuity equation , energy equation , state equation , process equation ; Specifically as follows: Given the total inlet enthalpy, total inlet pressure, outlet static pressure, speed of each stage, cold air parameters and blade geometry parameters, the one-dimensional aerodynamic analysis equation set is constructed according to the above one-dimensional flow basic equation, the total inlet temperature and total inlet pressure of the cold air after mixing are calculated first, then the isentropic stagnation enthalpy drop of the static cascade is calculated by formula , the static cascade outlet ideal velocity is calculated by formula , the dynamic cascade isentropic enthalpy drop is calculated by formula , the dynamic cascade outlet ideal velocity is calculated by formula , and then the cascade loss and velocity coefficient are solved according to the initial value of the outlet flow angle.

[0027] S8, determine whether the velocity coefficient meets the accuracy requirement, and iterate steps S6 and S7; S9, after completing the iteration, the outlet actual velocity of the cascade where the calculation station is located is solved according to the velocity coefficient formula and ; S10. Solve for parameters including total turbine efficiency, total turbine static efficiency, turbine power, ideal turbine enthalpy drop, and gas flow rate based on the actual exit velocity of the blade cascade where the calculation station is located, and complete the one-dimensional aerodynamic analysis. like Figure 3 As shown, the input parameters for the one-dimensional analysis of the reverse-flow cooling turbine required by this invention include turbine operating parameters (such as inlet total enthalpy, inlet total pressure, outlet static pressure, and speeds at each stage), geometric parameters (such as average diameter, blade height, inlet and outlet geometric angles, distance from the front blades, chord length, blade width, leading and trailing edge thickness, maximum thickness, and number of blades), cooling gas parameters (such as cooling gas percentage and cooling gas temperature), and physical property parameters (working fluid, air-fuel ratio, and gas constant). The specific process of the one-dimensional analysis is as follows: First, the differential evolution algorithm is used to optimize and solve the static pressure at each station. Given the inlet total enthalpy, inlet total pressure, outlet static pressure, speeds at each stage, cooling gas parameters, and blade geometric parameters, a one-dimensional aerodynamic analysis equation set is constructed based on the basic one-dimensional flow equations. The inlet total temperature and inlet total pressure after cooling gas mixing are calculated. Then, the formula... The isentropic hindrance enthalpy drop of the stationary cascade is calculated using the formula... The ideal exit velocity of the stator blade is calculated using the formula. The isentropic enthalpy drop of the moving blade cascade is calculated using the formula... Calculate the ideal velocity at the blade exit. Then, use the initial value of the exit airflow angle and the loss model formula. Solve for the blade cascade loss and velocity coefficient, where, For one-dimensional analysis of total loss, For leaf shape loss, These are correction factors related to the Reynolds number. For end secondary flow losses, For the loss of the wake, For the loss caused by leakage at the top of the leaf, To account for cold air mixing losses, determine whether the velocity coefficient meets the accuracy requirements. Iterate through the above steps, and after completing the iteration, apply the velocity coefficient formula. and The actual exit velocity of the blade cascade where the computing station is located is determined. Based on the actual exit velocity of the blade cascade where the computing station is located, other performance parameters are solved to complete the one-dimensional aerodynamic analysis. The output parameters of the one-dimensional aerodynamic analysis of the counter-rotating cooling turbine include the overall efficiency, overall static efficiency, power, reaction degree, velocity coefficient, and flow rate of the whole machine and each stage, such as... Figure 4 As shown.

[0028] Step 2: Determine the range of variation of the optimization variables and the probability distribution of the uncertainty parameters based on the parameters required for the one-dimensional aerodynamic analysis of the reference design. Perform Latin hypercube sampling within the augmented space composed of the optimization variables and uncertainty parameters. For each sample obtained from the Latin hypercube sampling, perform the calculations performed in Step 1 to obtain the one-dimensional analysis output results and generate a sample set.

[0029] First, the 95% confidence interval of the uncertainty parameter is calculated according to the probability distribution thereof, as the sampling range of the uncertainty parameter, then the variation range of the optimization variable is subjected to a tensor product operation with the sampling range of the uncertainty parameter to obtain an augmented space, then a uniformly distributed random number is generated in each dimension within the augmented space to ensure that there are enough sampling points in each dimension to cover the entire range, the sampling points in each dimension are grouped to ensure that there is only one sampling point in each group. For each dimension, a permutation operation is performed to ensure that each row and each column contains only one sampling point, the standardized sampling points of the Latin hypercube are converted to the actual value range, adjusted according to the specific value range of each variable, and the Latin hypercube sampling is completed. Finally, each Latin hypercube sampling sample is subjected to one-dimensional analysis of steps S1 to S10 to extract the target performance and generate the overall sample set.

[0030] Step 3, according to the sample set generated in step 2, a Kriging model is established, and the model accuracy is verified by leave-one-out cross-validation.

[0031] Each sample in the sample set is sequentially taken as a validation set, and the other samples are taken as a training set. In each iteration, the training set is used to train the model, and then the validation set is used to evaluate the model performance. The above process is repeated until each sample has served as a validation set. The average value of the performance indicators of all iterations is calculated as the final performance evaluation result of the model.

[0032] The predicted value is regarded as a Gaussian random process , It is assumed that the prediction error of each point has correlation The hyperparameters are estimated by maximum likelihood function estimation method, and the likelihood function is set to 0 for the partial derivatives of and , and the mode search algorithm is used to solve , completing Kriging modeling. Then, leave-one-out cross-validation is performed to evaluate the accuracy of the Kriging model.

[0033] Step 4, fixing the optimization variable, sampling the uncertainty variable, and using the Kriging model established in step 3 to evaluate the target performance to generate a sample set of uncertainty parameters.

[0034] Specifically, the optimization variable is fixed, and only the Latin hypercube sampling of the uncertainty parameter is carried out. Each Latin hypercube sampling sample is brought into the Kriging model to predict the target performance and generate a sample set of uncertainty parameters.

[0035] Step 5: Based on the uncertainty parameter sample set generated in Step 4, establish the ASPC model. The ASPC model outputs the mean and variance of the target performance, thus obtaining the uncertainty quantification result.

[0036] The process is as follows Figure 5 As shown, first, input the sample set of uncertain parameters and set the initial order of the chaotic polynomial expansion. Maximum order and cross-validation threshold Then, based on the current order An orthogonal polynomial basis is constructed using the Stieltjes process; then, the expansion coefficients are solved using RVM regression, and cross-validation is performed simultaneously to obtain the cross-validation error at the current order. ; Discrimination Does it meet the set cross-validation threshold? If yes, output the chaotic polynomial model of the current order; otherwise, increase the order of the chaotic polynomial. ; Discrimination Is it less than the set maximum order? If yes, then update the orthogonal polynomial basis and expansion coefficients constructed by the Stieltjes process, and perform iteration; if not, compare and select... The optimal model is taken as the final chaotic polynomial model. After the chaotic polynomial model is established, the mean performance of solving the objective problem is... The variance is Finally, the probability distribution information is obtained through Monte Carlo simulation, thus completing the uncertainty quantification, such as... Figure 6 As shown.

[0037] Step 6: Using the mean and variance results output in Step 5 as the objective function, perform multi-objective optimization. Employ the NSGA-II optimization algorithm to obtain the Pareto optimal front and solution set, thus completing the robust design optimization. Figure 7 As shown.

[0038] Initialize a population with a certain number of individuals in the design space of optimization variables; for each individual, calculate its fitness value using step S13; according to the dominance relationship between individuals, divide the individuals in the population into different non-dominated levels. Non-dominated sorting is based on the Pareto dominance relationship of individuals in the objective space. If the solution of an individual is better than that of another individual in all objective functions, it dominates the individual. The individuals in the population that are not dominated by any other individual constitute the first non-dominated level, the individuals with the least number of dominated individuals and relatively good individuals constitute the second level, and so on; in order to maintain the diversity and balance of the population, the crowding degree value of each individual is obtained by calculating the distance between adjacent individuals in the comparison target and summing up; select individuals with higher crowding degree and individuals in the first few non-dominated levels as the parent population. Generate offspring individuals through crossover and mutation operations to generate a new population; combine the parent and offspring individuals, and select the next generation population according to the non-dominated sorting and crowding degree and selection rules. The selection strategy aims to maintain diversity, that is, first select individuals with high non-dominated levels, and then select according to the crowding degree; repeat the above steps until the optimization termination condition is met. After optimization termination, the Pareto optimal front and Pareto optimal solution set are obtained, and the robust design optimization is completed.

[0039] So far, the one-dimensional uncertainty quantification and robust design optimization process of the reverse cooling turbine is completed.

[0040] In embodiment 2, the present application provides a one-dimensional uncertainty quantification and robust design optimization system for a reverse cooling turbine, which comprises a one-dimensional aerodynamic analysis module, a target performance determination module, a total sample set generation module, a global proxy model construction module, an uncertainty parameter sample set generation module, an uncertainty quantification module and a multi-objective optimization module. The one-dimensional aerodynamic analysis module is used to divide the reverse cooling turbine into multiple calculation stations along the axial direction, and to solve parameters including turbine total total efficiency, turbine total static efficiency, turbine power, turbine ideal enthalpy drop and gas flow according to the actual outlet velocity of the cascade where the calculation station is located, and to perform one-dimensional aerodynamic analysis; The target performance determination module is used to divide the input data into optimization variables and uncertainty parameters according to the one-dimensional aerodynamic analysis results of the reference design of the reverse cooling turbine, and to give the range of optimization variables and the probability distribution of uncertainty parameters, and to determine the target performance of uncertainty quantification and robust design optimization; The total sample set generation module is used to perform Latin hypercube sampling in the augmented space composed of optimization variables and uncertainty parameters, perform one-dimensional aerodynamic analysis on each sample, extract target performance, and generate a total sample set; The global proxy model construction module is configured to construct a Kriging global proxy model according to a total sample set and verify the model accuracy. The uncertainty parameter sample set generation module is configured to randomly sample the uncertainty parameters of each sample again, evaluate the target performance by using the Kriging model, and generate an uncertainty parameter sample set. The uncertainty quantification module is configured to construct an adaptive chaos polynomial model according to the uncertainty parameter sample set, output the mean value, variance, probability distribution and other information of the target performance, and complete the uncertainty quantification. The multi-objective optimization module is configured to perform multi-objective optimization on the mean value and variance of the target performance as objective functions, obtain a Pareto optimal front and a solution set, and complete the robust design optimization.

[0041] In another aspect, the present application provides a computer readable storage medium, and the computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the reverse cooling turbine one-dimensional uncertainty design optimization method and system.

[0042] The present application also provides a computer device, which comprises a processor and a memory, the memory is configured to store a computer executable program, and the processor reads the computer executable program from the memory and executes, and the processor executes the computer executable program to implement the reverse cooling turbine one-dimensional uncertainty design optimization method and system.

[0043] The computer device can be a notebook computer, a desktop computer or a workstation.

[0044] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC) or a ready programmable gate array (FPGA).

[0045] The memory of the present application can be an internal storage unit of a notebook computer, a desktop computer or a workstation, such as a memory or a hard disk, or an external storage unit, such as a mobile hard disk or a flash card.

[0046] The computer-readable storage medium can include a computer storage medium and a communication medium. The computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. The computer-readable storage medium can include read-only memory (ROM), random access memory (RAM), solid state disk (SSD), optical disk, etc. Among them, the random access memory can include resistance random access memory (ReRAM) and dynamic random access memory (DRAM).

[0047] The above is only to illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical scheme falls within the protection scope of the claims of the present application.

Claims

1. A one-dimensional uncertainty design optimization method for a reversible cooling turbine, characterized in that, Includes the following steps: S10. Divide the reverse cooling turbine into multiple calculation stations along the axial direction, and solve the performance parameters of the reverse cooling turbine based on the actual exit velocity of the blade cascade where the calculation station is located, and perform one-dimensional aerodynamic analysis. S11. Based on the one-dimensional aerodynamic analysis results of the reverse cooling turbine reference design, the input data is divided into optimization variables and uncertainty parameters. The range of optimization variables and the probability distribution of uncertainty parameters are given, and the target performance for uncertainty quantification and robust design optimization is determined. S12. Perform Latin hypercube sampling within the augmented space composed of optimization variables and uncertain parameters, conduct one-dimensional aerodynamic analysis on each sample, extract target performance, and generate the overall sample set; S13. Construct a Kriging global proxy model based on the overall sample set and verify the model accuracy; S14. For each sample, the uncertain parameters are randomly sampled again, and the Kriging model is used to evaluate the target performance to generate a sample set of uncertain parameters. S15. Construct an adaptive chaotic multinomial model based on the uncertainty parameter sample set, and output information such as the mean, variance, and probability distribution of the target performance to complete the uncertainty quantification. S16. Using the mean and variance of the target performance as the objective function, perform multi-objective optimization to obtain the Pareto optimal front and solution set, thus completing the robust design optimization.

2. The one-dimensional uncertainty design optimization method for reversing cooling turbines according to claim 1, characterized in that, The reverse-flow cooling turbine is divided into multiple calculation stations along the axial direction. The performance parameters of the reverse-flow cooling turbine are solved based on the actual exit velocity of the blade cascade where each calculation station is located. A one-dimensional aerodynamic analysis is then performed, including: The differential evolution algorithm is used to optimize the static pressure of each counter-rotating cooling turbine computing station. Given the total inlet enthalpy, total inlet pressure, outlet static pressure, speed of each stage, cooling gas parameters, and blade geometric parameters, a one-dimensional aerodynamic analysis equation set is constructed based on the basic equation of univariate flow. The total inlet temperature and total inlet pressure after cooling gas mixing are calculated. The isentropic stagnation enthalpy drop of the stationary blade cascade, the ideal velocity at the stationary blade outlet, the isentropic enthalpy drop of the moving blade cascade, and the ideal velocity at the moving blade outlet are calculated. Then, the blade cascade loss and velocity coefficient are solved using the initial value of the outlet airflow angle and the loss model. The actual outlet velocity of the blade cascade where the computing station is located is solved according to the velocity coefficient formula. The performance parameters of the counter-rotating cooling turbine are solved based on the actual outlet velocity of the blade cascade where the computing station is located, thus completing the one-dimensional aerodynamic analysis.

3. The one-dimensional uncertainty design optimization method for reversing cooling turbines according to claim 2, characterized in that, The differential evolution algorithm is used to optimize the static pressure of each reverse cooling turbine computing station, including: Based on the meridional flow channel data of the reverse cooling turbine, a calculation station is divided at the foremost and last ends of the meridional flow channel. The relative positions of the leading and trailing edges of the blades are plotted on the meridional diagram, and a calculation station is divided at the exit position of each row of blades. For each computing station, the following parameters are given: average diameter, blade height, outlet geometry, inlet geometry, residual velocity utilization factor, estimated pressure, and distance from the front row of blades. The static pressure problem is transformed into an optimization problem. The static pressure of each station is used as the variable, the flow deviation is used as the objective function, and the differential evolution algorithm is used to optimize the solution. The optimized solution is used as the final static pressure result of each station.

4. The one-dimensional uncertainty design optimization method for reversing cooling turbines according to claim 1, characterized in that, In S12, Latin hypercube sampling is performed within the augmented space composed of optimization variables and uncertain parameters. One-dimensional aerodynamic analysis is conducted on each sample to extract target performance and generate the overall sample set, as detailed below: The 95% confidence interval of the uncertainty parameter is calculated based on its probability distribution and used as the sampling range of the uncertainty parameter. Then, the range of variation of the optimization variable and the sampling range of the uncertainty parameter are subjected to tensor product operation to obtain the augmented space. Generate uniformly distributed random numbers in each dimension of the augmented space, ensuring that each dimension has enough sampling points to cover the entire range. Group the sampling points in each dimension so that each group contains only one sampling point. For each dimension, a permutation operation is performed so that each row and column contains only one sampling point. The standardized sampling points of the Latin hypercube are converted into the actual value range. Adjustments are made according to the specific value range of each variable to complete the Latin hypercube sampling. Finally, one-dimensional aerodynamic analysis is performed on each Latin hypercube sample to extract the target performance and generate the overall sample set.

5. The one-dimensional uncertainty design optimization method for a reversible cooling turbine according to claim 1, characterized in that, In S13, a Kriging global proxy model is constructed using the overall sample set, and the model accuracy is verified, as follows: Treat the predicted values ​​as Gaussian random processes , Assuming the prediction errors at each point are correlated The maximum likelihood function estimation method is used to estimate the hyperparameters. To make an estimate, let the likelihood function right and The partial derivatives are 0, and the solution is obtained using a pattern search algorithm. Complete the Kriging model; perform leave-one-out cross-validation to evaluate the accuracy of the Kriging model.

6. The one-dimensional uncertainty design optimization method for a reversible cooling turbine according to claim 1, characterized in that, An adaptive chaotic multinomial model is constructed using a sample set of uncertain parameters, outputting the mean, variance, and probability distribution information of the target performance. Uncertainty quantification includes: Input a sample set of uncertain parameters; set the initial order of the chaotic polynomial expansion. Maximum order and cross-validation threshold According to the current level An orthogonal polynomial basis is constructed using the Stieltjes process; the expansion coefficients are solved using RVM regression, and cross-validation is performed simultaneously to obtain the cross-validation error at the current order. ; Discrimination Does it meet the set cross-validation threshold? If yes, output the chaotic polynomial model of the current order; otherwise, increase the order of the chaotic polynomial. ; Discrimination Is it less than the set maximum order? If yes, then update the orthogonal polynomial basis and expansion coefficients constructed by the Stieltjes process, and perform iteration; if not, compare and select... The optimal model is taken as the final chaotic polynomial model; after the chaotic polynomial model is established, the mean performance of solving the objective is... The variance is The probability distribution information is obtained through Monte Carlo simulation, thus completing the quantification of uncertainty.

7. The one-dimensional uncertainty design optimization method for a reversible cooling turbine according to claim 1, characterized in that, Multi-objective optimization is carried out using the mean and variance of the target performance as the objective function. The NSGA-II optimization algorithm is used to obtain the Pareto optimal front and solution set, thus completing the robust design optimization, as follows: Initialize a population within the design space consisting of optimization variables, which contains a set number of individuals; for each individual, calculate its fitness value; and divide the individuals in the population into different non-dominant levels according to the dominance relationship between individuals. Non-dominated ranking is performed based on the Pareto dominance relationship of individuals in the target space; The crowding value of each individual is obtained by calculating and summing the distances between adjacent individuals on the comparison target; individuals with higher crowding values ​​and individuals in the top few non-dominant levels are selected as the parent population, and offspring individuals are generated through crossover and mutation operations, thereby generating a new population. The parent and offspring individuals are merged, and the next generation of the population is selected based on non-dominance ranking, crowding, and selection rules. Individuals with high non-dominance ranking are selected first, and then selected based on crowding. Repeat the above steps until the optimization termination condition is met. After optimization terminates, the Pareto optimal frontier and Pareto optimal solution set are obtained, thus completing the robust design optimization.

8. A one-dimensional uncertainty quantification and robust design optimization system for a reversible cooling turbine, characterized in that, It includes a one-dimensional aerodynamic analysis module, a target performance determination module, a total sample set generation module, a global proxy model construction module, an uncertainty parameter sample set generation module, an uncertainty quantification module, and a multi-objective optimization module; The one-dimensional aerodynamic analysis module is used to divide the reverse-rotation cooling turbine into multiple calculation stations along the axial direction, and solve the performance parameters of the reverse-rotation cooling turbine based on the actual exit velocity of the blade cascade where the calculation station is located, and perform one-dimensional aerodynamic analysis. The target performance determination module is used to divide the input data into optimization variables and uncertainty parameters based on the one-dimensional aerodynamic analysis results of the inverted cooling turbine reference design, and to determine the target performance for uncertainty quantification and robust design optimization by giving the range of optimization variables and the probability distribution of uncertainty parameters. The overall sample set generation module is used to perform Latin hypercube sampling within the augmented space composed of optimization variables and uncertain parameters, perform one-dimensional aerodynamic analysis on each sample, extract target performance, and generate the overall sample set; The global proxy model building module is used to build a Kriging global proxy model based on the overall sample set and verify the model accuracy. The uncertainty parameter sample set generation module is used to resample the uncertainty parameters of each sample, evaluate the target performance using the Kriging model, and generate the uncertainty parameter sample set. The uncertainty quantification module is used to construct an adaptive chaotic multinomial model based on the uncertainty parameter sample set, and output information such as the mean, variance, and probability distribution of the target performance to complete the uncertainty quantification. The multi-objective optimization module is used to perform multi-objective optimization by taking the mean and variance of the target performance as the objective function, obtaining the Pareto optimal frontier and solution set, and completing the robust design optimization.

9. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading part or all of the computer-executable program from the memory and executing it, and the processor executing part or all of the computed executable program is able to implement the one-dimensional uncertainty design optimization method and system for the reverse cooling turbine as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the one-dimensional uncertainty design optimization method and system for the reverse cooling turbine as described in any one of claims 1-7.

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