Laminate cooling structure performance optimization method adaptive to uncertainty analysis

Abstract

A laminate cooling structure performance optimization method adaptive to uncertainty analysis comprises the following steps: firstly, establishing a parameterized finite element model of a flame tube laminate cooling structure, and realizing flow heat exchange mechanism analysis of the laminate cooling structure by adopting a solid-thermal coupling mode; carrying out a DOE experiment by using Latin hypercube sampling LHS, generating a parameter set, importing the parameter set into a parameterized finite element model, obtaining a data set of a training proxy model BP-NN by combining a laminate cooling structure solid-heat coupling heat exchange method, and carrying out uncertainty quantification in a design space of the parameters of the laminate cooling structure by using an MC simulation method; using a Sobol sensitivity analysis method to analyze the uncertainty of the laminate cooling structure; the training agent model is combined with a multi-target particle swarm optimization algorithm to carry out multi-target optimization on the laminate cooling structure parameterization, and a laminate cooling ideal structure is found in the Pareto frontier; according to the method, the calculation cost and time of uncertainty analysis are reduced, and the calculation cost of laminate cooling uncertainty analysis is greatly reduced.

Description

Technical Field

[0001] This invention belongs to the field of gas turbine combustion chamber flame tube technology, specifically relating to a method for optimizing the performance of a laminated cooling structure adapted to uncertainty analysis. Background Technology

[0002] As the main heat-receiving component of the combustion chamber, the flame tube operates under high temperature and high pressure for extended periods. To extend its service life, efficient cooling of the flame tube wall is essential. Laminate cooling is a highly efficient cooling method integrating multiple cooling techniques such as impact, film cooling, and convection cooling. It boasts advantages such as high cooling efficiency and low cooling gas consumption, making it a major development direction for future gas turbine combustion chamber flame tubes and a current research hotspot. However, due to manufacturing tolerances and degradation during use, the geometry of the flame tube laminate cooling structure inevitably deviates from the designed geometry. With the development of refined design concepts, turbine design is gradually transitioning from deterministic to indeterminate design to achieve optimal aerodynamic and heat transfer performance.

[0003] Currently, methods for uncertainty analysis in turbine machinery include Monte Carlo (MC) simulation, sensitivity analysis, surrogate models, and Polynomial Chaos Expansion (PCE). However, MC simulation and PCE are computationally expensive and time-consuming in complex high-dimensional problems, and the sample size can affect the sensitivity analysis results. There are few methods for uncertainty analysis in laminated cooling systems, but the application of uncertainty analysis in turbine machinery can be referenced for uncertainty analysis of laminated cooling structures. Compared to PCE, surrogate models can use historical data to construct a nonlinear mapping relationship between laminated cooling structure parameters and cooling performance, enabling output value prediction and effectively reducing computational costs. Furthermore, using MC simulation to determine the sample size ensures the accuracy of sensitivity analysis results. Therefore, using surrogate models to predict the cooling performance of different laminated cooling structures, combined with MC simulation and sensitivity analysis to analyze laminated cooling uncertainty, significantly reduces the analysis cycle and cost, and further enhances the reliability of multi-objective particle swarm optimization results. Currently, no relevant literature has been published on this approach. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention aims to provide a performance optimization method for laminated cooling structures adapted to uncertainty analysis. This method utilizes a trained surrogate model BP-NN to reduce the computational cost and time of uncertainty analysis, uses MC simulation for uncertainty quantification, and combines Sobol sensitivity analysis to perform uncertainty analysis on laminated cooling. This method greatly reduces the computational cost of uncertainty analysis for laminated cooling, thereby meeting the needs of engineering applications.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A method for optimizing the performance of a laminated cooling structure adapted to uncertainty analysis includes the following steps:

[0007] Step (1): Establish a parametric finite element model of the flame tube cooling plate structure. When creating the geometric model, the cooling plate structure parameters are used as the three-dimensional model feature parameters. When the cooling plate structure parameters change in the design space, the cooling plate geometry will be automatically modeled accordingly.

[0008] Step (2): Combine the parameterized finite element model with the calculation conditions and use solid-thermal coupling to realize the flow heat transfer mechanism analysis of the plate cooling structure. At the same time, the calculation method is calibrated based on the experimental data.

[0009] Step (3): Within the parameter design space of the layered cooling structure, use Latin Hypercube Sampling (LHS) to design DOE experiments and establish the parameter set for training the surrogate model;

[0010] Step (4): Import the parameter set generated by the LHS method into the parameterized finite element model, and combine it with the solid-thermal coupling heat transfer method of the plate cooling structure in step (2) to obtain the plate cooling performance index set. The plate cooling performance index set and the parameter set together form the dataset for training the surrogate model BP-NN.

[0011] Step (5): Divide the dataset for training the agent model into a training set and a test set, train and verify the generalization ability of the BP-NN agent model to ensure the accuracy of the prediction ability of the agent model.

[0012] Step (6): Based on the training surrogate model, the uncertainty of the layer cooling structure parameters is quantified in the design space using the MC simulation method to determine the sample size; at the same time, the output value of the sample points is predicted by the training surrogate model to expand the sample set.

[0013] Step (7): Based on the expanded sample set, the uncertainty of the layer cooling structure is analyzed using the Sobol sensitivity analysis method.

[0014] Step (8) uses the trained surrogate model as a basis and combines the multi-objective particle swarm optimization algorithm to perform multi-objective optimization on the parameterization of the layered cooling structure established in step (1), while finding the ideal layered cooling structure in the Palito front.

[0015] The establishment of the parameterized finite element model in step (1) includes geometric parameterization of the plate cooling structure, mesh generation, setting of material property indices and boundary conditions.

[0016] In step (3), LHS sampling is a random sampling process. During sampling, the design parameters and the design range of the parameters need to be determined.

[0017] The cooling performance index of the intermediate layer in step (4) is the cooling efficiency. or and flow resistance coefficient C f ;

[0018]

[0019] In the formula m ∞ , m c , m w These are the weighted average temperatures of the main inlet, cold flow inlet, and study domain wall surface, respectively.

[0020]

[0021] In the formula: , These are the average total pressures at the coolant inlet and mains outlet surfaces, respectively. , These represent the mainstream density and flow velocity, respectively.

[0022] In step (5), the training set used to train the agent model accounts for 80% of the dataset. The metrics used to verify the training of the agent model include absolute error, relative error, mean percentage absolute error (MAPE), and goodness of fit (R²). 2 .

[0023]

[0024] In the formula: y i It is the actual value of the i-th data point; It is the model's prediction for the i-th data point.

[0025]

[0026] In the formula: The sum of squared residuals represents the degree of difference between the observed and predicted values; This represents the total sum of squares, reflecting the degree of dispersion of the observed values ​​relative to their mean.

[0027] In step (6), the standard deviation of the sample size is selected as the indicator for the sample size. With variance .

[0028]

[0029] In the formula: n The number of samples; y avg The mean of the sample; MAPE σ The standard deviation is the sample standard deviation. MAPE μ This represents the sample variance.

[0030] In step (7), the indicators used in Sobol sensitivity analysis to evaluate the uncertainty of the cooling structure of the analytical plate include: the first-order sensitivity index. S i Second-order sensitivity index S ij and total effect index S Ti .

[0031]

[0032] In the formula: S i The first-order sensitivity index; S ij It is a second-order sensitivity index; S Ti The total effect index; X i For the first i One input variable; X -i For all input variables except the i-th variable; Y Output variables for the model.

[0033] In step (8), the TOPSIS decision is used to select the ideal value from the Pareto frontier. Meanwhile, the multi-objective model is as follows:

[0034]

[0035] In the formula: F To optimize the objective; x i,min For the first i The lower bound of each variable; x i,maxFor the first i The upper limit of the number of variables.

[0036] Compared with existing technologies, the beneficial effects of this invention are as follows: In the face of manufacturing tolerances and degradation during use, the uncertainty caused by deviations in the geometry of the flame tube cooling structure on the cooling performance of the cooling plate is addressed. This invention provides a conceptual approach to uncertainty analysis of the cooling plate structure. By fully considering the influence of various parameters on the cooling performance of the cooling plate, and combining BP-NN training with MC simulation quantization and Sobol sensitivity analysis, the computation cycle and analysis cost of uncertainty analysis for cooling plate cooling are significantly reduced. Furthermore, a multi-objective particle swarm optimization algorithm is introduced to optimize the cooling plate structure under multi-objective problems, significantly reducing the flow resistance coefficient of the cooling plate structure while ensuring cooling efficiency. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0038] Figure 2(a) shows the structural unit of the physical model of the laminate cooling structure in an embodiment of the present invention; Figure 2(b) shows the calculated fluid domain of the physical model of the laminate cooling structure in an embodiment of the present invention.

[0039] Figure 3(a) shows the Monte Carlo simulations based on MC simulations with different sample sizes in the embodiments of the present invention. Values; Figure 3(b) shows the Monte Carlo simulations based on MC simulations under different sample sizes in the embodiments of the present invention. value.

[0040] Figure 4(a) is a sensitivity analysis diagram (influence) of Sobol analysis used in an embodiment of the present invention. or Parameters S i and S Ti Figure 4(b) is a sensitivity analysis diagram (influence) of the Sobol analysis used in the embodiment of the present invention. C f Parameters S i and S Ti Figure 4(c) is a sensitivity analysis diagram (influence) of the Sobol analysis used in the embodiment of the present invention. or Parameters S ij Figure 4(d) is a sensitivity analysis diagram (influence) of the Sobol analysis used in the embodiment of the present invention. C f Parameters S ij ).

[0041] Figure 5 This is a Palito solution set diagram for multi-objective optimization of the layered cooling structure according to an embodiment of the present invention. Detailed Implementation

[0042] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0043] Reference Figure 1 A method for optimizing the performance of a laminated cooling structure adapted to uncertainty analysis includes the following steps:

[0044] Step (1): Establish a parametric finite element model of the flame tube cooling structure. When creating the geometric model, the thickness of the impact plate is taken as the reference. H i Impact hole diameter D i , height of the turbulence column H r Diameter of the turbulence column D r Air film thickness H f Air film pore diameter D f air film pore inclination angle α The layer cooling structure parameters, such as the unit spacing P, are the feature parameters of the three-dimensional model. When the layer cooling structure parameters change in the design space, the layer cooling geometry will be automatically modeled accordingly.

[0045] Establishing a parametric finite element model includes geometric parameterization of the plate cooling structure, mesh generation, setting of material properties and boundary conditions, etc.

[0046] In this embodiment, the mesh is generated using a fluent mesh unstructured mesh, the plate material is 314 stainless steel, the fluid domain is air, and the mass flow rates of the main flow and coolant inlet are parameterized.

[0047] Step (2): Based on the parameterized set model established in step (1), and combined with the calculation conditions, the solid-thermal coupling method is used to analyze the effect of the plate cooling structure parameters in step (1) on the plate cooling efficiency. or and flow resistance coefficient C f The impact; at the same time, the calculation method is calibrated based on the experimental data;

[0048] Step (3): Within the design space of the layered cooling structure parameters, Latin Hypercube Sampling (LHS) is used to design DOE experiments and establish the parameter set used to train the surrogate model. LHS sampling is a random sampling process. When sampling, the design parameters and the design range of the parameters need to be determined. In this embodiment, 250 sets of sample data are collected to form an 8×250-dimensional input variable matrix.

[0049] Step (4): Import the parameter set generated by the LHS method into the parameterized finite element model, and combine it with the solid-thermal coupling heat transfer method of the plate cooling structure in step (2) to obtain the plate cooling performance index set. The plate cooling performance index set and the parameter set together form the dataset for training the proxy model.

[0050] The cooling performance index of the middle layer plate in step (4) is the cooling efficiency. or and flow resistance coefficient C f ;

[0051]

[0052] In the formula m ∞ , m c , m w These are the weighted average temperatures of the main inlet, cold flow inlet, and study domain wall surface, respectively.

[0053]

[0054] In the formula , These are the average total pressures at the coolant inlet and mains outlet surfaces, respectively. , These are the mainstream density and flow velocity, respectively.

[0055] In this embodiment, the input variable matrix generated by LHS is imported into the parametric finite element model, and the calculation method is used to obtain the results for each set of input samples. or and C f The output values ​​are constructed into a 2×250-dimensional output variable matrix, which together with the input variables forms the dataset for training the Proxy Model BP-NN.

[0056] Step (5): Divide the dataset for training the agent model into a training set and a test set, train and verify the generalization ability of the BP-NN agent model to ensure the accuracy of the prediction ability of the agent model.

[0057] The training set used to train the surrogate model comprises 80% of the dataset. Metrics used to validate the surrogate model include absolute error, relative error, mean percentage absolute error (MAPE), and goodness-of-fit R-squared. 2 .

[0058]

[0059] In the formula: y i It is the actual value of the i-th data point; It is the model's prediction for the i-th data point.

[0060]

[0061] In the formula: The sum of squared residuals represents the degree of difference between the observed and predicted values; This represents the total sum of squares, reflecting the degree of dispersion of the observed values ​​relative to their mean.

[0062] In this embodiment, 200 sets of data are randomly selected from the dataset constructed in step (4) for use. or and C f The training agent model BP-NN was used, and the remaining 50 sets of data were used to validate the generalization ability of the BP-NN training agent model. The absolute error, relative error, mean percentage absolute error (MAPE), and goodness-of-fit R-squared of the BP-NN training agent model were analyzed. 2 This ensures the fitting and generalization ability of the trained Proxy Model BP-NN, while also guaranteeing the accuracy of the trained Proxy Model's prediction capabilities.

[0063] Step (6): Based on the training agent model constructed in step (5), use the MC simulation method to quantify the uncertainty in the design space of the cooling structure parameters of the plate to determine the sample size. At the same time, use the training agent model in step (5) to predict the output value of the sample points to expand the sample set.

[0064] In step (6), the standard deviation under different sample sizes is selected as the indicator for the sample size. With variance ;

[0065]

[0066] In the formula: n The number of samples; y avg The mean of the sample; MAPE σ The standard deviation is the sample standard deviation. MAPE μ This represents the sample variance.

[0067] In this embodiment, when the sample set data size constructed using the trained proxy model is 20,000, and The sample size tends to stabilize; therefore, a sample size of 20,000 is chosen as the required sample size for Sobol analysis.

[0068] Step (7): Based on the expanded sample set in step (6), the uncertainty of the layer cooling structure is analyzed using the Sobol sensitivity analysis method.

[0069] In step (7), the Sobol sensitivity analysis is used to evaluate the uncertainty of the cooling structure of the analytical plate, including the first-order sensitivity index. S i Second-order sensitivity index S ij and total effect index S Ti ;

[0070]

[0071] In the formula: S i The first-order sensitivity index; S ij It is a second-order sensitivity index; S Ti The total effect index; X i For the first i One input variable; X -i For all input variables except the i-th variable; Y Output variables for the model.

[0072] This embodiment uses a sample size of 20,000 to analyze the main factors affecting the cooling efficiency and flow resistance coefficient of the shelf using the first-order sensitivity index and the total effect index; and uses the second-order sensitivity index to analyze the influence of the interaction between parameters on the cooling performance of the shelf.

[0073] Step (8): Based on the surrogate model trained in step (5), the multi-objective particle swarm optimization algorithm is combined to perform multi-objective optimization on the parameterization of the layered cooling structure established in step (1), and at the same time, the ideal layered cooling structure is found in the Palito front.

[0074] In step (8), the ideal value is selected from the Pareto frontier using TOPSIS decision-making. Meanwhile, the multi-objective model is as follows:

[0075]

[0076] In the formula: F To optimize the objective;x i,min For the first i The lower bound of each variable; x i,max For the first i The upper limit of the number of variables.

[0077] The principle of this embodiment is as follows: (1) Based on the flow heat transfer mechanism of the laminated cooling structure, the entire process of constructing the laminated cooling structure from geometric model parameterization to finite element modeling is realized; (2) Considering manufacturing tolerances and degradation during use, uncertainty analysis is performed on the laminated cooling structure based on uncertainty analysis theory; (3) In order to reduce the computational cost and time of uncertainty analysis, the uncertainty is quantified by MC simulation based on the constructed training surrogate model BP-NN to expand the dataset, and then the uncertainty analysis of the laminated cooling structure is performed by Sobol analysis; (4) Based on the training surrogate model BP-NN, the multi-objective optimization of the laminated cooling structure is realized with the goal of maximizing cooling efficiency and minimizing flow resistance coefficient. This embodiment minimizes the flow resistance coefficient as much as possible while ensuring cooling performance, thereby reducing the consumption of cooling air in the laminated structure.

[0078] To analyze the significant impact of small changes in geometric parameters on turbine performance under extreme operating conditions, this embodiment introduces a multi-objective optimization method with adaptive uncertainty analysis into the laminated cooling structure shown in Figure 2(a). Figure 2(a) is a unit diagram of the laminated cooling structure. H , D , P These represent the plate thickness, hole (column) diameter, and unit spacing, respectively. α The inclination angle of the film cooling hole is used. The entire computational domain consists of a solid domain and a fluid domain, with the coolant air domain and the mainstream high-temperature combustion gas domain on either side of the solid domain. To eliminate fully developed turbulence and the influence of the outlet, the inlet and outlet of the high-temperature combustion gas are extended outward by 50 mm, as shown in Figure 2(b). In this embodiment, the plate cooling structure parameters are used as design variables, and the plate cooling performance index is used as the design variable. or maximize, C f Minimization was adopted as the optimization objective, and a multi-objective prediction model for shelf cooling was established. The impact of small changes in shelf cooling structural parameters on turbine performance was analyzed, realizing multi-objective uncertainty analysis and optimization of shelf cooling. The design space range and initial values ​​of the parameters are shown in Table 1. The MSPE values ​​under different sample sizes based on MC simulations in the embodiment are shown in Figures 3(a) and 3(b). Figure 3(a) shows the MSPE values ​​under different sample sizes. or Monte Carlo simulation Values, Figure 3(b) shows the values ​​under different sample sizes. or Monte Carlo simulation The values ​​in the figure show that when the sample size is greater than 20,000, the MSPE fluctuates within a very small range. This means that choosing 20,000 as the sample size for uncertainty quantification can meet the analytical accuracy. The Sobol uncertainty analysis results are shown in Figures 4(a), 4(b), 4(c), and 4(d). Figure 4(a) shows the influence of... or Parameters S i and S Ti (b) is the influence C f Parameters S i and S Ti As can be seen from Figures 4(a) and (b) D i 、D r 、D f 、P right or The most important impact is D i , D f 、P right C f The impact is most pronounced; in Figure 4(c), the impact... or In the parameters D i and P , D f and P , H r and P , α and P , D i and α , D r and α , H r and α , D i and H r , D i and D r Between S ij >0.01, the interaction between parameters cannot be ignored; meanwhile, in Figure 4(d), the influence Cf In the parameters D i and P , D f and P Between S ij It is also greater than 0.01; the Palito solution set for laminate cooling optimization using the multi-objective particle swarm optimization algorithm is as follows: Figure 5 As shown in the figure, the solution set is obtained iteratively by the multi-objective particle swarm optimization algorithm. The blue circle represents the optimal solution selected using TOPSIS. In this case, the ideal value is selected from the Pareto front using TOPSIS decision-making, as shown in Table 2.

[0079] Table 1

[0080]

[0081] Table 2

[0082]

[0083] In summary, this invention proposes a performance optimization method for laminated cooling structures adapted to uncertainty analysis. This method uses the design parameters of the laminated cooling structure as design variables and cooling performance indicators as optimization objectives. A multi-objective prediction model for laminated cooling is established, analyzing the impact of small changes in laminated cooling parameters on turbine performance, thus achieving multi-objective uncertainty analysis and optimization of laminated cooling. Considering the high computational cost and long cycle of traditional uncertainty analysis methods, Monte Carlo simulation is used, and a surrogate model is employed to expand the sample size, ensuring it meets the requirements for uncertainty analysis. Based on this, Sobol analysis is used to perform uncertainty analysis on the laminated cooling performance, including the impact of single parameters on cooling performance, the impact of interactions between parameters on cooling performance, and the comprehensive impact of input variables on output. Furthermore, the uncertainty analysis method proposed in this invention can further enhance the reliability of the optimization results of the multi-objective particle swarm optimization algorithm.

[0084] The above are the specific implementation steps of the present invention and do not limit the scope of protection of the present invention. This method can be applied to the field of uncertainty analysis of plate cooling and multi-objective design optimization. Any technical solution formed by adopting equivalent or equivalent methods shall be included in the scope of protection of the present invention.

Claims

1. A method of performance optimization of a laminate cooling structure adapted for uncertainty analysis, characterized by, Comprising the following steps: Step (1), a parameterized finite element model of the flame tube layer plate cooling structure is established, and when creating the geometric model, the layer plate cooling structure parameters are taken as the characteristic parameters of the three-dimensional model. When the layer plate cooling structure parameters change in the design space, the layer plate cooling geometric structure will be automatically modeled; Step (2), the parameterized finite element model is combined with the calculation condition, and the heat conduction coupling method is used to realize the flow and heat transfer mechanism analysis of the layer plate cooling structure. At the same time, the calculation method is calibrated based on the test data; Step (3), in the parameter design space of the layer plate cooling structure, Latin Hypercube Sampling (LHS) is used for DOE experimental design to establish the parameter set for training the proxy model; Step (4), the parameter set generated by the LHS method is imported into the parameterized finite element model, and the layer plate cooling performance index set is obtained by combining the heat transfer method of the layer plate cooling structure in step (2). The layer plate cooling performance index set and the parameter set together constitute the data set of the training proxy model BP-NN; Step (5), the data set of the training proxy model is divided into a training set and a test set, and the generalization ability of the training proxy model BP-NN is trained and verified to ensure the accuracy of the prediction ability of the training proxy model; Step (6), based on the training proxy model, the MC simulation method is used to quantify the uncertainty in the design space of the layer plate cooling structure parameters to determine the size of the sample size; at the same time, the training proxy model is used to predict the output value of the sample point to expand the sample set; Step (7), based on the expanded sample set, the Sobol sensitivity analysis method is used to analyze the uncertainty of the layer plate cooling structure; Step (8), based on the training proxy model, the multi-objective particle swarm optimization algorithm is combined to perform multi-objective optimization on the layer plate cooling structure parameterization established in step (1), and the ideal structure of the layer plate cooling is found in the Pareto front.

2. The optimization method of claim 1, wherein: The step (1) of establishing the parameterized finite element model includes layer plate cooling structure geometric parameterization, mesh division, material property index setting and boundary condition setting.

3. The optimization method of claim 1, wherein: The LHS sampling in step (3) is a random sampling process, and the design parameters and the design range of the parameters need to be determined during sampling.

4. The optimization method of claim 1, wherein: The performance index of the cooling of the layer plate in the step (4) is cooling efficiency η and a flow resistance coefficient C f ; wherein m ∞ , m c , m w are the bulk inlet, cold stream inlet, and wall face weighted average temperature of the research domain, respectively. where , are the average total pressure at the coolant inlet and primary flow outlet face, respectively; , are the primary flow density and velocity, respectively.

5. The optimization method of claim 1, wherein: The training set used for training the proxy model in the step (5) accounts for 80% of the data set, and the indicators for verifying the trained proxy model include absolute error, relative error, mean percentage absolute error (MAPE), and goodness of fit R 2 ; wherein: y i is the actual value of the i-th data point; is the predicted value of the i-th data point by the model. where: is the sum of squared residuals, indicating the degree of difference between the observed and predicted values; is the total sum of squares, reflecting the degree of dispersion of the observed values relative to their mean.

6. The optimization method of claim 1, wherein: The index for selecting sample size in the step (6) is the standard deviation under different sample sizes and variance ; where: n is the sample size; y avg is the sample mean; MAPE σ is the sample standard deviation; MAPE μ is the sample variance.

7. The optimization method of claim 1, wherein: The index for evaluating the uncertainty of the cooling structure of the analysis layer plate in step (7) is the first-order sensitivity index S i the second-order sensitivity index S ij and the total effect index S Ti ; wherein: S i is the first order sensitivity index; S ij is the second order sensitivity index; S Ti is the total effect index; X i is the i-th input variable; i X -i is all input variables except the i-th variable; Y is the model output variable.​ 8. The optimization method of claim 1, wherein: In step (8), the ideal value is selected from the Pareto front by using the TOPSIS decision, and at the same time, the multi-objective model is as follows: wherein: F is an optimization target; x i,min is the lower limit of the i th variable. x i,max is the upper limit for the i th variable.

Images