A data-driven robust design method for compressor blades

Abstract

The present application relates to a kind of robustness design optimization methods of data-driven compressor blade, using the way of middle camber line superposition thickness distribution to construct blade, using NURBS curve to parameterize middle camber line of blade.4-point 3-order data-driven non-embedded polynomial chaos method is used to quantify the uncertainty of sparse sampling data, and four blade configuration modes are obtained.Latin hypercube method is used to sample blade design space, and sampling set is used to train Gaussian process regression model under each blade configuration mode;GPR proxy model at each blade configuration mode is obtained respectively.After training, multi-objective optimization algorithm NSGA II is used to optimize search with the statistical mean and standard deviation of blade total pressure loss coefficient as target;Robust compressor blade with better performance and greatly reduced sensitivity to input uncertainty is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to a compressor blade optimization design method, in particular to a blade robustness optimization design method capable of quantifying the influence of sparse uncertainty input based on data-driven means. BACKGROUND

[0002] Advanced compressor blades not only require high performance, but also require high reliability under the influence of uncertain factors. Uncertain factors are inevitable and will cause the geometric profile or working point of the blade to deviate from the initial design, which has a non-negligible impact on aerodynamic performance. Blade robustness optimization design can eliminate the negative effects of uncertain factors and improve aerodynamic performance and reliability at the same time.

[0003] The core of robustness optimization design is uncertainty quantification technology. The reliability of uncertainty quantification depends on the distribution form of the model input parameters. In actual engineering, uncertain input data is usually sparse and cannot accurately describe the distribution form of the input parameters. At present, the distribution form of the input parameters is subjectively assumed in the optimization process, which will lead to a large error in the quantization result. Through the data-driven uncertainty quantification method, the probability information can be propagated through the statistical moment characteristics of the sampling data without the distribution form of the input parameters, which can avoid subjective assumptions and fitting errors.

[0004] For robustness optimization, direct use of CFD simulation will face the dilemma of excessive computation. Training a high-precision surrogate model to replace CFD simulation can greatly improve optimization efficiency. However, training a surrogate model itself also requires a large number of numerical simulations. Therefore, developing a surrogate model that only needs a small number of sampling points can further improve optimization efficiency and promote the transformation of robustness design methods to engineering practical applications. SUMMARY

[0005] Technical problems to be solved

[0006] In order to avoid the shortcomings of the prior art, the present application proposes a data-driven compressor blade robustness design method, which uses the statistical moments of sparse sampling data to propagate the probability information of input uncertainty, which can avoid subjective assumptions and fitting errors of the distribution form.

[0007] Technical scheme

[0008] A data-driven compressor blade robustness design method, characterized by the following steps:

[0009] Step 1: parameterize the camber line of the blade using NURBS curve; add the blade thickness distribution to the camber line to construct the blade;

[0010] Step 2: the influence of uncertain input parameters with sparse characteristics on the aerodynamic performance of the compressor blade is quantified by adopting the p-order DNIPC method, and the statistical mean and standard deviation of the aerodynamic parameters are obtained;

[0011] Step 3: the Latin hypercube method is used to sample the blade design space, and then CFD numerical simulation is carried out under each blade configuration mode in step 2; under each blade mode, a GPR proxy model is trained;

[0012] Step 4: the GPR model trained in step 3 is used to replace the CFD numerical simulation;

[0013] Step 5: the aerodynamic performance target function of the compressor blade is determined, and the NSGA II genetic algorithm is used for multi-objective search to obtain a set of Pareto front solutions that meet the target function.

[0014] Further technical solutions of the application: the uncertain quantification process in step 2 is: the first 2p-order statistical moments of the sparse sampling data are calculated, and the best orthogonal basis function is obtained by using the statistical moments; the zero point of the orthogonal basis function is the corresponding blade configuration mode; the numerical simulation calculation results of each blade configuration mode are statistically processed to obtain the uncertain quantification results of the aerodynamic parameters.

[0015] Further technical solutions of the application: the training process in step 3 is: based on the square exponential kernel function, the prior distribution of the training set and unknown points is obtained; then the prior information of the training points is used to obtain the prediction value at the unknown point.

[0016] Beneficial effects

[0017] The data-driven compressor blade robustness design method provided by the application adopts the method of superimposing the thickness distribution of the middle camber line to construct the blade, and uses the NURBS curve to parameterize the middle camber line of the blade. The 4-point 3-order data-driven non-embedded polynomial chaos method is used for uncertain quantification of sparse sampling data, and 4 blade configuration modes are obtained. The Latin hypercube method is used to sample the blade design space, and the sampling set is used to train the Gaussian process regression model under each blade configuration mode; the GPR proxy model at each blade configuration mode is obtained. After training, the multi-objective optimization algorithm NSGA II is used to optimize the search with the statistical mean and standard deviation of the blade total pressure loss coefficient as the target; thus, a robust compressor blade with better performance and greatly reduced sensitivity to input uncertainty is obtained. The application combines the DNIPC method for quantifying scarce sampling data with the GPR proxy model, improves the efficiency of blade robustness optimization design, and is easy to promote in engineering. The beneficial effects are as follows:

[0018] (1) In actual engineering, due to the lack of sufficient measurement or test data, the traditional uncertainty quantification method needs to make subjective assumptions about the distribution form of the input parameters, which may cause fitting errors of the distribution form of the input parameters. The data-driven non-intrusive polynomial chaos (DNIPC) method developed in step 2 does not need to make subjective assumptions and judgments about the distribution form of the input uncertainty parameters, but relies on the statistical moments of the input parameters to propagate the uncertainty information, which can avoid the fitting error of the distribution form of the input parameters.

[0019] (2) In the robustness optimization design process of the compressor blade, a large number of CFD numerical simulation calculations are involved for the blade samples, which faces the difficulty of unbearable calculation amount. In step 3, the Gaussian process regression (GPR) model is independently developed to replace the CFD numerical simulation calculation, which can greatly reduce the calculation burden and greatly improve the efficiency of the robustness optimization design of the compressor blade. BRIEF DESCRIPTION OF DRAWINGS

[0020] The accompanying drawings are included to provide a further understanding of the application, and are incorporated in and constitute a part of this specification, illustrate embodiments of the application, and together with the description serve to explain the principles of the application. In the drawings:

[0021] Figure 1 Arc line and control variable in NURBS parameterization

[0022] Figure 2 Uncertainty quantification result based on data driving

[0023] Figure 3 Prediction effect of unknown points by GPR surrogate model: (1) blade mode 1 prediction; (2) blade mode 2 prediction; (3) blade mode 3 prediction; (4) blade mode 4 prediction

[0024] Figure 4 Comparison chart of initial blade and optimized blade

[0025] Figure 5 Comparison chart of aerodynamic parameters of initial blade and optimized blade

[0026] Figure 6 Flow chart of the whole robustness optimization design of the blade DETAILED DESCRIPTION

[0027] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and not to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0028] The present application proposes a data-driven robust optimization design method for compressor blades, the steps are as follows:

[0029] Step 1: NURBS curve is used for parameterization of the camber line in the blade; the initial blade is constructed by superimposing the camber line and the inscribed circle, the camber line of the blade is parameterized by NURBS method to obtain the control points for describing the camber line, i.e. control variables. The control variables of the blade generated by NURBS method are less, which can reduce the optimization calculation amount.

[0030] Step 2: The influence of uncertain input parameters with sparse characteristics on the aerodynamic performance of the compressor blade is quantified by the p-order DNIPC method, and the statistical mean and standard deviation of the aerodynamic parameters are obtained. The uncertainty quantization process is: 1) calculate the first 2p-order statistical moments of the sparse sampling data, and obtain the best orthogonal basis function by using the statistical moments; 2) calculate the corresponding blade configuration mode by the zero point of the orthogonal basis function; 3) perform numerical simulation calculation on each blade configuration mode, and perform statistical post-processing on the calculation results to obtain the uncertainty quantization results of the aerodynamic parameters, i.e. mean and standard deviation.

[0031] Step 3: Latin hypercube method is used to sample the blade design space to obtain new blade samples. Then perform CFD numerical simulation calculation under the blade configuration mode obtained in step 2 to obtain the aerodynamic parameters of the blade samples. The aerodynamic parameters of the blade samples are used as a training set to train the GPR surrogate model. The training process of the GPR surrogate model is: first, based on the square exponential kernel function, the prior distribution of the training set and the unknown point is obtained; then the prior information of the training set is used to obtain the prediction value at the unknown point.

[0032] Step 4: The GPR model trained in step 3 is used to replace the CFD numerical simulation; the GPR surrogate model not only has high efficiency but also has high prediction accuracy, which solves the problem of excessive numerical simulation calculation amount in robust optimization.

[0033] Step 5: According to the design requirements of the compressor blade, the optimization objective function of the blade aerodynamic performance is determined, and the NSGAII genetic algorithm is used for multi-objective search to obtain a set of Pareto frontier solutions that meet the objective function.

[0034] The DNIPC in step 2 is the only method that can propagate sparse uncertainty; the method for determining the optimal squared exponential function in step 3 is to minimize the exponential likelihood function.

[0035] To address the uncertainty in compressor blade twist angle machining, this invention is further described with reference to the accompanying drawings, using the reduction of the mean and standard deviation of the total pressure loss coefficient of the blades as the objective function:

[0036] The blade mid-curve is parameterized using the NURBS method in step 1 to obtain c. i (x i ,y i The coordinates of control points i = 1, 2, ..., 5 are used, and the coordinates of the control points of the middle arc are used as control variables for optimization design.

[0037] Step 2 specifically includes: Due to manufacturing errors, the actual blade twist angle will always deviate from the design value. The actual twist angle can be expressed as: θ real =θ0 + Δθ, where θ0 is the design torsion angle and Δθ is the machining error disturbance. The torsion angles of N actual blades are measured to obtain the true torsion angle error. N is finite and insufficient to accurately describe the distribution of the input variables.

[0038] The statistical moments of N torsion angle error data are calculated using the following formula:

[0039]

[0040] In the formula, μ k ξ represents the k-th order statistical moment, and ξ represents the torsion angle error sampling data.

[0041] For a stochastic physical model Y = u(x, ξ), its output can be expressed as a linear combination of p-order orthogonal basis functions in physical space x, with the following expression:

[0042]

[0043] In the formula, Ψ i (ξ) is an orthogonal basis function, characterizing the random nature of the blade twist angle error. The core of the DNIPC method is to use the statistical moment matrix M of the sampled data to obtain the orthogonal basis functions. The expression for M is:

[0044]

[0045] Based on the orthogonality of the basis functions, we can obtain that...

[0046] In the formula, let the coefficient of the highest degree of the basis function be 1, and h be the coefficient of the orthogonal basis function. The zeros of the orthogonal basis function are the characteristic configuration modes of the blade twist angle machining error.

[0047] After obtaining the orthogonal basis function, the expression of the chaotic polynomial coefficient u i is as follows:

[0048]

[0049] After obtaining the chaotic polynomial u i and the orthogonal basis function Ψ i (ξ), the expression of the statistical mean μ Y and the standard deviation σ Y of the blade total pressure loss coefficient is as follows:

[0050] μ Y = u0

[0051]

[0052] The uncertainty quantification results of the twist angle machining error are shown in the accompanying Figure 2 Tables 1 and 2, and it can be seen that the mean value of the twist angle error is higher than the original design value, and the dispersion is large.

[0053] Step 3 specifically includes: the horizontal coordinates x i of the control points of the camber line in the blade remain unchanged, only the vertical coordinates y i are changed; the design space is [0.9y i , 1.1y i ]. The Latin hypercube method is used to select 100 sample points, and CFD numerical simulation calculation is performed under each configuration mode of the blade. For each configuration mode, 80 blade samples are selected to train the GPR surrogate model, and the other 20 are used as the test set.

[0054] The expression of the squared exponential kernel function is as follows:

[0055]

[0056] In the formula, Θ = (l, σ f ) T is the to-be-determined hyperparameter.

[0057] According to Bayesian estimation, the prior estimation of the unknown set y * and the observation point set y can be expressed as:

[0058]

[0059] In the formula, K(X,X) = (k(x i ,x j )) n is an n×n covariance matrix, and K(X,x * ) is an n×1 covariance matrix, representing the similarity between the unknown points and the observation points.

[0060] The optimal hyperparameter of the square exponential kernel function is determined by minimizing the exponential likelihood function; the minimum exponential likelihood function can be expressed as follows:

[0061]

[0062] The optimal hyperparameter of the kernel function can be determined by minimizing the exponential likelihood function.

[0063] The expression of the predicted value of the total pressure loss coefficient of the GPR surrogate model is as follows:

[0064] y * = K(x * , X) [K(X, X)] -1 y

[0065] In the formula, y * represents the total pressure loss coefficient of the blade to be predicted y represents the total pressure loss coefficient of the blade at the observation point.

[0066] The k-fold cross-validation method is used to verify the accuracy of the GPR surrogate model; the expression of the overall accuracy evaluation index of the GPR model is as follows:

[0067]

[0068] In the formula, E represents the average value; the closer E(R 2 ) is to 1, the higher the prediction accuracy of the GPR is.

[0069] The deviation evaluation index of the predicted value and the true value of the GPR model can be expressed as follows:

[0070]

[0071] In the formula, the closer E(RMSE) is to 0, the closer the predicted value of the GPR model is to the true value.

[0072] The prediction results of the surrogate model under four blade configuration modes are shown in Table 1. Figure 3 E(R 2 ) is higher than 98%; E(RMSE) is less than 0.6%; it can be seen that the GPR surrogate model has high prediction accuracy.

[0073] For the multi-objective problem of robust optimization design of the compressor blade, the NSGA II genetic algorithm is used for optimization; the number of design populations is 200, and the number of genetic generations is 100.

[0074] The robust optimization objective function can be expressed as follows:

[0075]

[0076] In the formula, Pr represents a compressor blade static pressure ratio; the method requires reducing the blade total pressure loss coefficient while ensuring that the blade pressure increasing capacity is not reduced.

[0077] After the optimization search, a set of Pareto solutions satisfying the objective function is obtained. The optimization sample OPT1 is selected for analysis.

[0078] The CFD software is called to verify the OPT1 optimized blade. If the OPT1 blade satisfies the optimization objective function, the robustness blade is output, as shown in the accompanying Figure 4 The figure gives the geometric comparison of the optimized blade and the original blade.

[0079] Under the influence of the blade torsion angle machining uncertainty, the robustness optimization result of the compressor blade is shown in the accompanying Figure 5 It can be seen that after optimization, the statistical mean and standard deviation of the blade total pressure loss coefficient are reduced, which indicates that the aerodynamic performance of the blade is improved, and the sensitivity to uncertain factors is greatly reduced.

[0080] Under the influence of the uncertain factors, the overall flow of the compressor blade is shown in the accompanying Figure 6 .

[0081] The above is a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. The above uncertain quantification result, the agent model prediction result and the blade optimization result show that the present application can effectively reduce the negative influence of the input uncertainty with sparse characteristics; the data-driven uncertain quantification method and the agent model can greatly reduce the calculation amount required for robustness optimization, have strong operability, and are very convenient for popularization in engineering practice.

[0082] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical range disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application.

Claims

1. A data-driven based robust design method for compressor blade, characterized in that The steps are as follows: Step 1: parameterize the camber line of the blade by using NURBS curve; construct the blade by superimposing the blade thickness distribution on the camber line; Step 2: Using p The influence of uncertain input parameters with sparse characteristics on the aerodynamic performance of a compressor blade was quantified using the DNIPC method, and the statistical mean and standard deviation of the aerodynamic parameters were obtained. Step 2 specifically includes: Due to manufacturing errors, the actual blade twist angle will always deviate from the design value; the actual twist angle can be expressed as: In the formula, is Design the torsion angle, To mitigate machining error disturbances; The actual twist angle of each blade was measured to obtain the true twist angle error; It is finite and insufficient to accurately describe the distribution of the input variables; Computing the statistical moments of the twist angle error data, given by: wherein representing k order statistical moments, representing twist angle error sample data; For a stochastic physical model whose output can be represented as a function in physical space x , p a linear combination of orthogonal basis functions of order n, expressed as: In the formula, is the orthogonal basis function, which represents the random property of the blade torsion angle error; the core of the DNIPC method is to use the statistical moment matrix of the sampling data The expression of the orthogonal basis function is: The expression of the orthogonal basis function is: According to the orthogonality of the basis functions, we have In the formula, the highest order coefficient of the base function is 1, h The coefficients of the orthogonal base function; the zero point of the orthogonal base function is the characteristic configuration mode of the blade torsion angle machining error; After obtaining the orthogonal basis functions, the expression of the chaotic polynomial coefficients is After obtaining the chaotic polynomial and the orthogonal basis function the statistical mean value and the standard deviation of the blade total pressure loss coefficient are as follows: Step 3: sample the blade design space by using Latin hypercube method, then perform CFD numerical simulation under each blade configuration mode in step 2; under each blade mode, train the GPR surrogate model; Step 3 specifically includes: blade in the arc control point horizontal coordinate unchanged, only change the longitudinal coordinate ; the design space is ; 100 sample points are selected by using a Latin hypercube method, and CFD numerical simulation calculation is performed under each blade configuration mode; for each configuration mode, 80 blade samples are selected to train the GPR proxy model, and the other 20 are used as a test set; The expression of the square exponential kernel function is as follows: In the formula, is a pending hyperparameter; According to the Bayesian estimation, the prior estimation of the unknown set and the observation set can be expressed as: wherein is covariance matrix, is covariance matrix, representing the similarity between unknown points and observation points; The optimal hyperparameter of the square exponential kernel function is determined by minimizing the exponential likelihood function; the minimum exponential likelihood function can be expressed as follows: By minimizing the exponential likelihood function, the optimal hyperparameter of the kernel function can be determined; The expression of the predicted value of the total pressure loss coefficient of the GPR surrogate model is as follows: wherein represents the total pressure loss coefficient of the blade to be predicted ; represents the total pressure loss coefficient of the blade at the observation point; use k The cross-validation method is used to verify the accuracy of the GPR surrogate model; the expression for the overall accuracy evaluation index of the GPR model is: In the formula, represent the average value; The closer to 1, the higher the GPR prediction accuracy. The deviation evaluation index of the predicted value of the GPR model from the true value can be expressed as follows: In the formula, The closer to 0, the closer the predicted value of the GPR model to the true value. Step 4: replace the CFD numerical simulation with the GPR model trained in step 3; Step 5: determine the target function of the aerodynamic performance of the compressor blade, perform multi-objective search by using NSGA II genetic algorithm, and obtain a set of Pareto front solutions satisfying the target function.

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