A method for quantifying aerodynamic performance uncertainty of compressor blade fouling geometric deviation

Abstract

This invention relates to the field of turbomachinery technology and discloses a method for quantifying the uncertainty of aerodynamic performance due to geometric deviations caused by fouling on compressor blades. The method includes defining a sampling space for fouling variables and operating condition variables and obtaining an initial parameter sample set; generating a three-dimensional geometric model of the fouled blade based on the sample set; performing computational fluid dynamics simulation to extract flow rate, pressure ratio, and efficiency parameters to construct a sample database; training three independent fully connected neural network surrogate models to predict flow rate, pressure ratio, and efficiency using the database; sampling within the operating condition variable sampling space, inputting the flow rate surrogate model to obtain the predicted flow rate, and comparing the error with the target flow rate under a benchmark operating condition to obtain the optimal operating condition variable; inputting the parameter combination containing the optimal operating condition variable into the pressure ratio and efficiency surrogate models to output the predicted distribution, and completing the quantification of aerodynamic performance uncertainty through statistical processing. This invention reduces the computational cost of large-scale evaluations and improves the efficiency of quantifying aerodynamic performance degradation under complex fouling conditions.

Description

Technical Field

[0001] This invention relates to the field of turbomachinery technology, specifically to a method for quantifying the uncertainty of aerodynamic performance due to geometric deviations caused by fouling on compressor blades. Background Technology

[0002] The compressor is a core component of energy conversion devices such as aero engines, gas turbines, turbochargers, and industrial compressors. Its aerodynamic performance directly affects the energy conversion efficiency and reliability of the entire device. In actual service environments, compressor blades are prone to fouling due to factors such as dust, salt spray, oil mist, and humid heat in the intake air. Fouling causes the blade profile to deviate from the initial design, leading to increased flow losses, decreased stability margin, and degraded operating efficiency. Because the formation and evolution of fouling have inherent randomness, compressor performance degradation exhibits uncertainty, posing a challenge to accurately assessing the aerodynamic performance of blades under operating conditions during the design phase.

[0003] Currently, methods relying on physical experiments struggle to realistically reproduce the fouling process under complex operating conditions in a laboratory environment, while numerical simulation-based evaluation methods face several technical bottlenecks when addressing blade fouling issues. Regarding the geometric reconstruction of fouled blade profiles, conventional parametric methods employ the theoretical assumption of uniform thickness increases, failing to fully reflect the non-uniform adhesion characteristics of fouling under real physical conditions. These methods, lacking reasonable geometric constraints on the closed regions with equal curvature at the leading and trailing edges of the blade, easily lead to geometric distortion in the three-dimensional reconstruction model, directly resulting in a decrease in the objectivity and accuracy of the aerodynamic performance degradation assessment conclusions for fouled blades.

[0004] Meanwhile, the quantification of aerodynamic performance uncertainties relies on large-scale sample analysis. Existing methods for parameterizing fouling deposits are typically high-dimensional, and directly performing three-dimensional computational fluid dynamics numerical simulations on massive fouling geometry samples would consume excessive computational resources. This computational approach results in an excessively long evaluation cycle for performance uncertainty quantification, making it difficult to support the rapid iteration of solutions and multi-condition verification requirements during the compressor blade design phase in practical engineering.

[0005] Furthermore, after completing the macroscopic aerodynamic performance degradation assessment, existing technologies lack quantitative attribution methods that delve into the local spatial characteristic dimension. Because they cannot effectively extract the primary and secondary influences of fouling characteristics at different spatial spans on changes in overall aerodynamic performance (such as flow rate, pressure ratio, and efficiency), existing methods cannot complete the sensitivity assessment of contamination variables. This lack of attribution analysis makes it difficult to translate the assessment results into effective information to guide actual engineering operations, and fails to provide a solid data basis for subsequent targeted cleaning and maintenance of equipment and the anti-fouling and desensitization design of blades. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for quantifying the uncertainty of aerodynamic performance due to geometric deviations of compressor blade fouling. This method solves the problems of three-dimensional reconstruction geometric distortion, excessive resource consumption in numerical simulation of massive samples, and lack of quantitative attribution of aerodynamic performance degradation based on local fouling characteristics in existing compressor blade fouling assessments.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] This invention provides a method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation, comprising the following steps:

[0009] First, the parameter variation ranges of pollution variables and operating condition variables are defined as the sampling space, and an initial parameter sample set is extracted from it.

[0010] Subsequently, the three-dimensional blade geometric model with fouling characteristics is reconstructed by combining the parameter sample set, and the model is subjected to computational fluid dynamics numerical simulation to obtain the corresponding aerodynamic performance indicators such as flow rate, pressure ratio and efficiency, thereby establishing a sample database containing geometric input and performance output.

[0011] Based on this, three structurally independent fully connected neural network proxy models were established and trained for traffic, pressure ratio, and efficiency, respectively.

[0012] When performing performance evaluation, the sampling space of operating condition variables is sampled to generate input variables, the predicted flow rate is calculated using the flow proxy model, and the target flow rate under the baseline operating condition is set. The optimal operating condition variable that conforms to the actual operating state is determined by comparing the error between the two.

[0013] Finally, the characteristic parameter set containing the optimal operating condition variable is input into the pressure ratio surrogate model and the efficiency surrogate model respectively to obtain the predicted results of the pressure ratio distribution and efficiency distribution under the fouling state. Statistical analysis is performed on the predicted distribution to realize the quantification of the uncertainty of aerodynamic performance.

[0014] Preferably, the specific method for obtaining the initial parameter sample set is as follows: set the starting position of blade pollution and the intensity of pollution thickening to form a pollution variable sampling space, set the outlet static pressure to form a working condition variable sampling space, and use Latin hypercube sampling technology to explore the parameter space within the above space and obtain the initial sample points.

[0015] Preferably, the reconstruction process for generating a three-dimensional fouled blade geometric model is as follows: The contour coordinates of the original two-dimensional blade profile are extracted and rotated for alignment. A continuous basic blade profile curve is generated using a cubic spline fitting method, and the unit tangential vector and unit outward normal vector at each data point on the curve are calculated. A functional relationship describing the tangential fouling distribution thickness is established by combining the extracted fouling initiation position and fouling thickening intensity. The dot product of this thickening function value and the unit outward normal vector is performed to calculate the spatial geometric offset of the blade surface. After superimposing the original coordinates, the fouled blade profile coordinates of the current section are obtained. Finally, surface skinning is performed on the coordinates of different height sections distributed along the span to generate a three-dimensional solid model.

[0016] Preferably, the mathematical construction logic of the aforementioned chordal thickening function is as follows: The effective length of fouling coverage along the blade surface is determined by introducing geometric constraint coefficients, and a local normalized coordinate system for the fouling region is established by combining the fouling initiation position and the effective length. A cubic interpolation algorithm is used to fit the spatial thickening curve between the absolute initiation position and the extreme point of fouling thickness. Simultaneously, to ensure the physical consistency of the aerodynamic shape, the calculated value of the thickening function is forcibly limited to zero at the geometrically closed junction of the equal curvature of the leading and trailing edges of the blade.

[0017] Preferably, the fluid simulation evaluation process for extracting aerodynamic performance parameters is as follows: conduct mesh independence analysis on the reconstructed three-dimensional fouling geometry model to determine the benchmark mesh scale scheme, divide the spatial computational mesh according to the benchmark scheme and start the iterative solution of the fluid control equations, and output the flow rate, pressure ratio and efficiency index corresponding to the effective data sample after the flow field calculation residuals meet the convergence requirements.

[0018] The preferred network topology configuration for the fully connected neural network proxy model is as follows: a feedforward network architecture consisting of a single input layer, two connected hidden layers, and a single output layer. The input layer is configured with three neurons to receive input features, each of the two hidden layers is configured with eight neurons to extract nonlinear correlation features between variables, and the output layer is configured with one neuron to output the predicted value. Furthermore, network weights are updated using a supervised learning mechanism based on a sample database.

[0019] Preferably, the supervised learning training for network topology includes a model performance feedback and evaluation mechanism: during the training phase, the determination coefficient between the predicted values ​​of the surrogate model and the actual values ​​of the samples is calculated simultaneously, with a threshold of 0.99 for the determination coefficient. If the calculated determination coefficient is lower than the threshold, a closed-loop parameter tuning process is triggered to adjust hyperparameters such as the learning rate and retraining is performed; if the determination coefficient is greater than the threshold, the trained surrogate model for traffic, pressure ratio, and efficiency is output.

[0020] Preferably, the logic for performing error comparison to select the optimal operating condition variable is as follows: The actual physical flow rate generated by the original pollution-free design blade operating under the baseline design point condition is set as the target flow rate. The percentage error of each predicted flow rate relative to the target flow rate within the sample space is calculated. Abnormal sample points with error percentages exceeding the specified range are eliminated. From the remaining candidate samples that meet the conditions, specific samples with absolute relative error values ​​at their minimum are extracted, and the outlet static pressure parameter associated with this sample is confirmed as the optimal operating condition variable.

[0021] Preferably, the statistical processing method for quantifying aerodynamic performance uncertainty is as follows: The frequency of sample landing points within different numerical intervals of the predicted pressure ratio and efficiency distributions is statistically predicted, and a frequency histogram is generated accordingly. Then, data fitting is used to generate a density distribution curve reflecting the probability fluctuations of performance parameters. The expected values ​​of the total pressure ratio and efficiency after the impact of fouling degradation are calculated, and the difference between these and the design total pressure ratio and efficiency at the design point under the original uncontaminated state is calculated to clearly define the range of performance degradation.

[0022] Preferably, after obtaining the quantification results of aerodynamic performance uncertainty, an attribution analysis mechanism for pollution variables is further introduced: the SHAP analytical method is applied to calculate the marginal contribution of fouling characteristic parameters during performance prediction and extrapolation using a fully connected neural network. Sensitivity values ​​reflecting fouling characteristics at different spanwise height locations are extracted, and based on these values, the primary and secondary influences of fouling phenomena at different spatial distribution locations on the aerodynamic performance degradation trend are determined.

[0023] This invention provides a method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation. It offers the following advantages:

[0024] 1. This invention constructs a parameter sample set containing pollution variables and operating condition variables, and uses fluid simulation data to train three independent fully connected neural network surrogate models for predicting flow rate, pressure ratio, and efficiency. In the training phase, a parameter tuning closed loop triggered by the determination coefficient threshold is configured. The surrogate models that meet the convergence criteria replace the process of directly performing three-dimensional fluid numerical calculations on massive fouling samples. While ensuring the accuracy of aerodynamic performance prediction results, this invention reduces the computational resource consumption required for large-scale uncertainty quantification analysis and shortens the evaluation cycle.

[0025] 2. In the stage of generating the three-dimensional fouled blade geometric model, this invention extracts the original two-dimensional blade profile data, combines the unit outward normal vector with the fouling features to construct a chordal thickening function to calculate the geometric offset, and forcibly sets the thickening function value of the high curvature closed region of the leading and trailing edges of the blade to a constant of zero. This parametric modeling mechanism fits the non-uniform fouling adhesion law of compressor blades in the actual physical environment, overcomes the geometric distortion defects caused by the conventional assumption of uniform thickness increase, and improves the objectivity of the aerodynamic performance degradation assessment conclusion of fouled blades.

[0026] 3. After statistically predicting the pressure ratio distribution and efficiency distribution to quantify aerodynamic performance, this invention introduces the SHAP method to calculate the marginal contribution of input feature variables in the fully connected neural network surrogate model and extracts the sensitivity values ​​of contamination features at different spanwise locations. This step degrades the macroscopic aerodynamic performance degradation phenomenon to the local spatial feature dimension, realizes the quantitative attribution of performance degradation, clarifies the primary and secondary influence of fouling at different spanwise locations on the overall aerodynamic performance change, and provides data basis for subsequent targeted cleaning and maintenance operations of equipment. Attached Figure Description

[0027] Figure 1 A flowchart outlining the overall steps of a method for quantifying the uncertainty of aerodynamic performance due to fouling geometric deviations in compressor blades, provided in an embodiment of the present invention.

[0028] Figure 2 A comparison image of the thickened blade profile due to scale buildup and the original blade profile generated by the script provided in this embodiment of the invention;

[0029] Figure 3 This is a schematic diagram illustrating the verification of blade mesh independence provided in an embodiment of the present invention;

[0030] Figure 4 A schematic diagram of a fully connected neural network structure involved in the quantification of pollution uncertainty in polluted leaves provided in an embodiment of the present invention;

[0031] Figure 5 This is a total pressure ratio frequency distribution diagram of a fan blade under fouling conditions provided in an embodiment of the present invention.

[0032] Figure 6 This is a frequency distribution diagram of the efficiency of a fan blade under fouling conditions provided in an embodiment of the present invention.

[0033] Figure 7 This is a schematic diagram showing the SHAP sensitivity analysis results of different pollution variables under fouling conditions on a fan blade provided in an embodiment of the present invention.

[0034] Figure 8 A chordal distribution diagram of the geometric offset of compressor blade fouling provided in an embodiment of the present invention;

[0035] Figure 9 A flowchart illustrating the generation process of a three-dimensional fouling blade geometric model provided in an embodiment of the present invention. Detailed Implementation

[0036] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] See attached document Figure 1 This invention provides a method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation, comprising the following steps:

[0038] Define a sampling space for pollution variables and a sampling space for operating conditions. The parameters of the pollution variable sampling space include the blade pollution initiation location and pollution thickening intensity, while the parameters of the operating condition variable sampling space include the outlet static pressure.

[0039] Latin hypercube sampling is performed within the aforementioned variable sampling space to obtain an initial parameter sample set. A three-dimensional fouling blade geometric model is generated based on the fouling variable parameters in the parameter sample set. Computational fluid dynamics (CFD) simulation is performed on the generated three-dimensional geometric model. The corresponding aerodynamic performance parameters, including flow rate, pressure ratio, and efficiency, are extracted from the simulation results to construct a sample database.

[0040] Three independent fully connected neural network surrogate models are trained using a constructed sample database. These three models are a traffic surrogate model for predicting traffic volume, a pressure ratio surrogate model for predicting pressure ratio, and an efficiency surrogate model for predicting efficiency. The determination coefficients of these surrogate models are calculated, and it is determined whether the determination coefficients are greater than a set threshold. If the determination coefficient is less than or equal to the set threshold, the model parameters are adjusted and training is re-executed. If the determination coefficient is greater than the set threshold, the trained surrogate model is output. The set threshold is 0.99.

[0041] Monte Carlo sampling is performed within the variable sampling space to generate input variable samples. These samples are then input into the output flow proxy model to obtain the calculated predicted flow. The predicted flow is compared with the set target flow based on the error. Based on the comparison result, a condition filtering operation is performed to obtain the optimal condition variables that match the set target flow.

[0042] The parameter combinations containing the optimal operating condition variables are input into the pressure ratio surrogate model and the efficiency surrogate model, respectively. The predicted pressure ratio distribution and predicted efficiency distribution of the compressor blades at the target flow rate are output. Based on the obtained predicted distribution results, statistical processing is performed to quantify the uncertainty of aerodynamic performance. The SHAP method is executed to calculate the sensitivity parameters of the pollution variables, obtaining the degree of influence of pollution variables on aerodynamic performance changes at different spanwise locations.

[0043] To avoid excessively high computational dimensionality caused by using high-dimensional control points to represent three-dimensional geometric distortion when defining the sampling spaces for pollution variables and operating conditions, low-dimensional dimensionless parameters are extracted to characterize the geometric features of fouling. The parameters for establishing the sampling space for pollution variables include the blade fouling initiation location and fouling thickening intensity. The blade fouling initiation location defines the relative coordinate position of the fouling phenomenon at the starting point in the chordal direction of the blade, and the fouling thickening intensity defines the maximum relative thickness scale reached by the fouling layer. The parameters for establishing the sampling space for operating conditions include the outlet static pressure, which characterizes the aerodynamic boundary constraints of the compressor blades during service.

[0044] See attached document Figure 9 After defining the variable sampling space, a parameter sample set is obtained within the variable sampling space, and a three-dimensional fouling blade geometric model is generated based on the pollution variable parameters in the parameter sample set. During the generation of the geometric model, the original three-dimensional compressor blade geometric model is obtained, and the model is sliced ​​along the spanwise direction to extract two-dimensional original blade profile data points at different spanwise height sections. The extracted two-dimensional original blade profile data points are distributed in different spatial coordinate systems. To facilitate the unified establishment of a parameterized model, a rotation and alignment operation is performed on the extracted two-dimensional original blade profile data points so that the chord of the section coincides with the set coordinate reference axis. For the coordinate system transformation and rotation and alignment operations of the blade profile data points, those skilled in the art can use conventional affine transformation matrices; the specific algorithms are well-known in the field and will not be elaborated here.

[0045] Based on the rotated and aligned two-dimensional original airfoil profile data points, a continuous mathematical function is constructed using a cubic spline fitting method to generate the basic airfoil curve. For the cubic spline fitting calculation process of discrete data points, those skilled in the art can utilize standard numerical analysis algorithms; the interpolation and fitting principles are well-known techniques in the field and will not be elaborated upon here.

[0046] Based on the fitted basic airfoil curve, the unit tangential vector and unit outward normal vector at any position on the curve are calculated to provide a directional reference for the superposition of fouling layer thickness. The formula for calculating the unit tangential vector of the basic airfoil curve is:

[0047] ;

[0048] in, The x-axis of the basic air profile curve is... The unit tangent vector at that point; Represents the abscissa on the basic air profile curve; The basic air profile curve is represented on the horizontal axis as... The derivative at point . The x-coordinate is The unnormalized tangent vector at the x-axis, where the constant 1 represents the unit increment of the x-axis; This represents the magnitude of the unnormalized tangent vector; This represents the x-coordinate component of the normalized unit tangent vector; This represents the ordinate component of the normalized unit tangent vector.

[0049] Based on the obtained unit tangent vector, the unit outward normal vector of the basic airfoil curve is defined through orthogonal transformation. This unit outward normal vector is perpendicular to the tangent direction of the basic airfoil curve, and its direction points to the outer boundary of the blade entity. The formula for calculating the unit outward normal vector is:

[0050] ;

[0051] in, The x-axis of the basic air profile curve is... The unit outward normal vector at that location; This represents the x-coordinate component of the unit outward normal vector, and its value is the opposite of the y-coordinate component of the unit tangent vector. This represents the ordinate component of the unit outward normal vector, whose value is equal to the abscissa component of the unit tangent vector.

[0052] After extracting and preprocessing the basic airfoil data, it is necessary to construct the low-dimensional parameterization of the fouling geometry. Real compressor blade fouling manifests as irregular deposits on the blade surface. Directly subjecting a large number of surface mesh nodes in three-dimensional space to random perturbations would result in excessively high dimensionality of the geometric features, leading to the curse of dimensionality in the subsequent quantification of aerodynamic performance uncertainties. Therefore, this method extracts two dimensionless feature parameters: the initial location of blade fouling and the intensity of fouling thickening, to achieve global control of the fouling shape using a low-dimensional parameterization model.

[0053] The blade fouling initiation position is used to determine the initial coordinates of fouling on the basic blade airfoil profile. This parameter is a dimensionless quantity, defined as the ratio of the arc length from the initiation point to the total arc length or chord length of the blade cross-section. Based on actual engineering measurements and statistics of fouled compressor blades using coordinate measuring machines, the value range for this blade fouling initiation position is set to 0.4 to 0.8. Based on the determined blade fouling initiation position, it is converted into absolute initiation coordinates on the basic airfoil profile. The formula for calculating the absolute initiation coordinates is:

[0054] ;

[0055] in, This indicates the absolute starting coordinates of the fouling initiation point on the basic air profile curve; This indicates the starting position of leaf contamination, with a value range of [0.4, 0.8]. This represents the chord length of the base airfoil curve at the current spanwise height section.

[0056] The fouling thickening intensity is used to characterize the maximum relative thickness of the fouling layer at the corresponding spanwise section. This parameter is also dimensionless. Based on measured fouling data from engineering studies, the value of this fouling thickening intensity is set to range from 0.005 to 0.3, corresponding to a maximum thickening thickness of 0.5% to 30% of the maximum thickness of the base airfoil. The absolute thickening scale in actual geometric space can be obtained by multiplying the fouling thickening intensity by the chord length at the current section.

[0057] By defining the above, the complex fouling morphology is reduced in dimension and unified within a two-dimensional variable space consisting of the blade fouling initiation location and fouling thickening intensity. This provides a definite mathematical boundary and data input for subsequently constructing a continuous chordal thickening function and generating a three-dimensional fouling blade model.

[0058] Based on the obtained blade fouling initiation location and fouling thickening intensity, a thickening function along the chord direction is constructed. The actual physical process of fouling accumulation involves the thickness gradually increasing from zero to its maximum value, followed by a smooth transition towards the blade trailing edge. To ensure that the fouling thickening process ends before reaching the blade trailing edge, geometric constraints are introduced to define the fouling thickening effect length. The formula for calculating the fouling thickening effect length is:

[0059] ;

[0060] in, It indicates the length of the thickening effect of dirt buildup and is used to define the physical span of the thickness increase segment; Indicates the starting location of leaf contamination; This represents the geometric constraint coefficient, and its value range is... This is used to allocate the proportion of the thickness-lifting section and the smooth transition section in the remaining chord length. In this embodiment, the geometric constraint coefficient... The preferred value is 0.5, which means that the thickness rise section and the smooth transition section at the tail edge each occupy half of the total length of the fouling action area; This represents the chord length of the basic airfoil curve.

[0061] To facilitate the construction of a smooth curve equation, the abscissa within the length affected by the buildup of dirt is converted into locally normalized coordinates. The formula for calculating the locally normalized coordinates is as follows:

[0062] ;

[0063] in, This represents locally normalized coordinates, whose values ​​are constrained to be between 0 and 1. Represents the current x-coordinate of the basic air profile curve; This indicates the absolute starting coordinates of the fouling initiation point on the basic air profile curve; Indicates the length of the thickening effect of scale buildup.

[0064] To ensure the continuity of the function values ​​and their first derivatives at both the starting point and the target amplitude point of the thickness rise segment, a cubic Hermite interpolation method is used to construct the curve shape of the thickening interval. For polynomial interpolation calculations within a given interval, those skilled in the art can employ conventional numerical approximation algorithms; the interpolation derivation is well-known in the field and will not be elaborated upon here. Based on locally normalized coordinates, a chordal thickening function is constructed from the absolute starting coordinates to the peak position of the fouling accumulation. The formula for calculating this chordal thickening function is as follows:

[0065] ;

[0066] in, Indicates the current x-coordinate is The chord-direction thickening function at that location; , , and The four basis functions represent cubic Hermite interpolation; This represents the normalized initial thickness reference value at the beginning of the thickness rise segment; This indicates the target slope at the beginning of the thickness rise segment; Indicates the length of the thickening effect of the deposits; This represents the normalized maximum thickness value at the peak position at the end of the thickness rise segment; This indicates the target slope at the end of the thickness rise segment.

[0067] The formulas for calculating the four basis functions are as follows:

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] The Hermite interpolation method is chosen because it can directly constrain the curve shape of the uplift segment using endpoint values ​​and endpoint derivatives. Specifically, this manifests in locally normalized coordinates. Place, satisfy and In locally normalized coordinates Place, satisfy and In practice, to ensure that the blade thickness increases gradually at the beginning, the target slope at the starting point of the thickness increase segment is... The value range is set to 0 to 0.05. To ensure a smooth transition when the thickness increase reaches the target value, the target slope at the end of the thickness rise segment is... The value range is set to -0.05 to 0. When the horizontal coordinate exceeds the thickness increase range, the chordal thickening function follows the same logic as... A consistent slope is used for a linear transition, allowing the value to fall smoothly back down. In the high-curvature geometrically closed region near the leading and trailing edges of the blade, the chordal thickening function is forcibly set to a constant of 0 to avoid introducing geometric abrupt changes and to ensure the smoothness of the curve and the quality of the subsequent mesh generation.

[0073] After obtaining the smooth and continuous chordal thickening function, the specific geometric offset of each chordal sampling point is calculated. The formula for calculating the geometric offset is:

[0074] ;

[0075] in, The x-axis of the basic air profile curve is... The geometric offset vector that extends outward along the outer normal of the point; This indicates the intensity of pollution thickening and is used to convert normalized parameters into a physical length scale. Indicates the chord length of the basic air profile curve; This indicates that the location depends on the initiation point of leaf contamination. and the intensity of pollution thickening The chordal thickening function, whose value is equal to the calculated value. ; The x-axis of the basic air profile curve is... The unit outward normal vector at that location is used to determine the orientation of the thickened space.

[0076] Based on the geometric offset obtained above, the blade coordinates after contamination are obtained. The formula for calculating the blade coordinates after contamination is:

[0077] ;

[0078] in, The horizontal axis of the leaf shape curve after pollution is... The three-dimensional coordinate vector at the location; This indicates that the corresponding x-axis on the basic air profile curve is The original three-dimensional coordinate vector at the location; This represents the calculated geometric offset vector.

[0079] In the above coordinate superposition and transformation process, the product term Transform the normalized pollution intensity into a true physical length scale. (Chord-direction thickening function) Determine the location of the thickening and the rate of thickening up to the target amplitude. Unit outward normal vector. This determines the direction of thickening. Furthermore, a forced setting is applied near the leading and trailing edges of the blade. This is to avoid introducing sharp corners at high curvature or geometrically closed points, ensuring the smoothness of the curve and the quality of the subsequent mesh generation.

[0080] See attached document Figure 2 After completing the extraction and reconstruction of the geometric features of the leaf-shaped fouling in the two-dimensional plane, it is necessary to extend the obtained geometric changes in the two-dimensional plane to three-dimensional space.

[0081] Appendix Figure 2 This demonstrates the spatial geometric relationship between the polluted blade profile generated using different combinations of pollution characteristic parameters and the original blade profile within a specific spanwise height section. (See appendix...) Figure 2 The nine sub-figures contain an axial axis representing the projected position of the blade section along the compressor's rotation axis, and a circumferential axis representing the projected position of the blade section along the compressor's circumference. The solid lines in the figures are of two types: red solid lines represent the uncontaminated original blade profile, and blue solid lines represent the contaminated blade profile after the geometric offset vector has been superimposed.

[0082] Appendix Figure 2 The diagram specifically illustrates nine parameter control states resulting from the cross-combination of leaf contamination initiation location and contamination thickening intensity. Specifically, according to the subgraph arrangement, the leaf contamination initiation location is set to values ​​of 0.4, 0.6, and 0.8; the contamination thickening intensity is set to values ​​of 0.01, 0.02, and 0.03. (See attached diagram.) Figure 2The distribution of the lines reveals that the original blade profile and the contaminated blade profile completely overlap in the axial region from near the origin of the coordinate system (i.e., the leading edge of the blade) to the designated contamination initiation position. This overlap occurs because the chordal thickening function, as constructed earlier, is always zero within this axial region, resulting in a zero-vector geometric offset. Therefore, the superimposed coordinates of the contaminated blade profile are completely consistent with the original three-dimensional coordinate vector. This phenomenon, at the physical geometry level, ensures that the original aerodynamic shape of the blade leading edge does not undergo unintended distortion.

[0083] As the horizontal axis crosses the blade contamination initiation position set by parameters, the trend of the lines changes significantly. The blue line representing the contaminated blade shape begins to separate from the red line representing the original blade shape and shifts outward along the outer normal of the original blade shape curve. As the horizontal axis moves further backward along the axis, the normal distance between the blue and red lines gradually increases. When the maximum thickness position determined by the intensity of contamination thickening is reached, the normal offset distance between the two reaches its peak, forming the highest point of the protrusion in the fouling geometry.

[0084] After surpassing the aforementioned peak, the lines converge in the axial region near the blade trailing edge. Constrained by the linear transition and forced zero-value boundary set at the end of the chordal thickening function, the blue lines gradually recede inward, the normal distance between them continuously decreases, and they eventually completely overlap again at the blade trailing edge. This closed-loop trend avoids generating non-physical faults or sharp angles at the generated three-dimensional geometric trailing edge.

[0085] Comparison Appendix Figure 2 Subplots with different parameter combinations further illustrate the control of geometric features by low-dimensional parameters. In subplots on the same horizontal row, when the blade fouling initiation position remains fixed, as the fouling thickening intensity increases from 0.01 to 0.03, the convexity of the blue line in the normal direction gradually increases, directly reflecting the physical increase in the relative thickness of the fouling layer. In subplots on the same vertical column, when the fouling thickening intensity remains constant, as the value of the blade fouling initiation position increases from 0.4 to 0.8, the axial distance between the blue and red lines gradually lengthens, and the geometric convex shape caused by fouling is compressed and pushed towards the rear of the blade axis.

[0086] Based on the coordinate reconstruction rules of the two-dimensional plane explained above, the generation of a three-dimensional geometric model is performed. Along the spanwise height of the compressor blade, the corresponding two-dimensional fouling blade shape coordinates are calculated at multiple discrete cross-sections. The obtained two-dimensional fouling blade shape curves at multiple cross-sections are stacked according to their respective spatial positions. Using three-dimensional modeling methods, these discrete two-dimensional fouling cross-sections are surface-skinned along the spanwise direction to generate continuous and closed three-dimensional surface entities, thereby outputting the final three-dimensional fouling blade geometric model. For the three-dimensional surface skinning and lofting fitting operations of discrete two-dimensional cross-sections, those skilled in the art can use conventional computer-aided design algorithms. Surface fitting and solid topology generation are well-known techniques in this field and will not be elaborated further here. The output three-dimensional fouling blade geometric model will serve as the physical boundary input for subsequent computational fluid dynamics mesh generation and aerodynamic simulation.

[0087] After defining the variable sampling space and constructing the parametric reconstruction method for the three-dimensional fouled blade geometric model, the following steps are performed: mesh generation and numerical simulation calculation of the three-dimensional fouled blade geometric model to construct a sample database containing geometric feature parameters, operating condition parameters, and corresponding aerodynamic performance indicators. To construct a mapping relationship between geometric deviations and performance covering the actual service environment, sampling operations are conducted within the measured range of fouling geometric deviation variables, and the aerodynamic performance of the obtained blade samples is evaluated using numerical analysis methods.

[0088] In the sampling phase of acquiring the parameter sample set, a Latin hypercube sampling strategy is employed to obtain statistically representative data with a limited number of samples within a multi-dimensional variable sampling space. The specific sampling operations are performed within a pollution variable sampling space comprised of the leaf contamination initiation location and contamination thickening intensity, and a working condition variable sampling space comprised of outlet static pressure. During sampling, the range of values ​​for each defined variable is divided into several equal non-overlapping intervals according to the principle of equal probability. Subsequently, a value is randomly selected from each interval of each variable, and the extracted values ​​from different variables are randomly combined to form a multi-dimensional parameter vector sample. This sampling strategy ensures that each parameter is selected uniformly and without repetition throughout its defined value range, avoiding the dimensionality explosion problem caused by full-factor sampling. The specific multi-dimensional matrix generation and orthogonalization processing for Latin hypercube sampling can be implemented using conventional statistical algorithms by those skilled in the art; its stratified sampling and space-filling principles are well-known techniques in the field and will not be elaborated upon here.

[0089] Based on the multidimensional parameter vector samples obtained above, the parameters of the blade contamination initiation position and contamination thickening intensity are extracted and substituted into the previously constructed geometric feature reconstruction model of the fouled blade to calculate the corresponding geometric offset, thereby generating the corresponding three-dimensional fouled blade solid models in batches and constructing a sample library of fouled blade deviations.

[0090] Before conducting specific numerical simulations of the aerodynamic performance of the deviated airfoil, a mesh independence analysis was performed on the baseline three-dimensional fouled blade geometry model to eliminate the interference of computational mesh density on the accuracy of the flow field solution. In the mesh generation stage, multiple mesh schemes with a sparse to dense distribution were constructed by progressively increasing the number of mesh nodes in the flow field along the flow direction, circumferential direction, and radial direction. Subsequently, while maintaining complete consistency in the numerical solution method and boundary condition settings, aerodynamic simulations of the flow field were performed using these multiple mesh schemes. After the calculations, the flow rate, pressure ratio, and efficiency of the blade computational domain were extracted as key aerodynamic performance indicators. The sensitivity of the flow field calculation results to mesh spatial resolution was analyzed using the changing trends of these key aerodynamic performance indicators with the increase of the total number of mesh nodes. The verification analysis results show that as the mesh density increases, the physical details captured in the flow field gradually become richer, and the variation amplitude of the values ​​of each key aerodynamic performance indicator gradually decreases and tends to stabilize. Taking into account the computational time cost required for subsequent simulation of large-scale sample libraries and the accuracy requirements of flow field analysis, a grid topology and node distribution scheme that can guarantee the convergence accuracy of the results and consume relatively few computational resources is selected and set as the benchmark grid scheme for subsequent uncertainty quantification and batch simulation.

[0091] After determining the baseline mesh scheme, large-scale batch simulation calculations using a sample library were conducted. A Python script interface was used to call the NUMECA Fine / Turbo aerodynamic simulation software component to achieve batch data transfer and execution. The script sequentially imported the 3D solid models from the fouled blade deviation airfoil sample library and generated spatial meshes for the computational domain of each sample according to the baseline mesh scheme. Simultaneously, operating condition variables such as outlet static pressure were read from the parameter vector samples, and the solver numerical format selection, turbulence model settings, and inlet / outlet boundary condition parameter assignments were completed in batches. After the above settings were completed, independent computational project files were generated and submitted to the solver for iterative flow field solving.

[0092] After all samples have been solved, the script extracts and organizes the valid samples that meet the residual convergence criteria. The input geometric feature parameters, operating condition parameters, and corresponding aerodynamic performance indicators from the simulation output are aligned and stored to generate a sample database containing geometric deviations, airfoils, service conditions, and their corresponding performance indicators. This database establishes a physical mapping from low-dimensional fouling characteristics to the compressor's macroscopic aerodynamic response, providing a complete data foundation for subsequent training of surrogate models and performance prediction verification.

[0093] See attached document Figure 3 Before conducting specific numerical simulations of the aerodynamic performance of the deviated airfoil, it is necessary to perform a mesh independence analysis on the baseline three-dimensional fouled blade geometry model to eliminate the interference of computational mesh density on the accuracy of the flow field solution. Specifically, the mesh nodes are progressively refined in the three spatial directions of the flow field—flow direction, circumferential direction, and radial direction—constructing multiple mesh generation schemes with a distribution from sparse to dense. While maintaining complete consistency between the numerical solution method and boundary condition settings, aerodynamic simulation calculations of the flow field are performed using each of the aforementioned mesh schemes.

[0094] Using the changing trends of key aerodynamic performance indicators of the blades as a criterion, the sensitivity of flow field calculation results to grid spatial resolution is analyzed. (Combined with attached...) Figure 3 As shown, the horizontal axis represents the number of grids in the computational domain, in units of ten thousand. The figure shows five grid number nodes: 130, 140, 150, 160, and 170. The vertical axis represents the flow rate of the blade mass, a key aerodynamic performance indicator, in kg / s. The figure shows a value range from 122.8 to 123.6. Observation Figure 3 The trend of the black square data points and the connected dashed lines shows that when the number of grid points is 1.3 million, the calculated flow rate is relatively low, approximately 122.8 kg / s. As the number of grid points increases from 1.3 million to 1.6 million, the calculated flow rate shows a significant upward trend. With further increases in grid density, i.e., from 1.6 million to 1.7 million grid points, the fluctuation range of the flow rate gradually decreases and stabilizes, remaining around 123.6 kg / s. The verification results indicate that when the grid density reaches a certain scale, the sensitivity of key performance indicators to the grid decreases, and the flow field solution tends to converge.

[0095] In practical engineering applications, performance prediction using large-scale sample databases requires enormous computational resources. Therefore, considering both the time cost of subsequent large-scale sample calculations and the accuracy requirements of flow field analysis, a compromise solution needs to be selected. (See attached diagram) Figure 3The red circle and arrow indicate the "finally selected grid," indicating a grid scheme with approximately 1.5 million grid cells. The flow rate calculations using this grid scheme are close to the final stable value, ensuring the accuracy of the flow field solution. Furthermore, compared to grid schemes with 1.6 or 1.7 million grid cells, its single-calculation cost is relatively low. Besides the flow rate indicators shown in the figure, those skilled in the art can also use other key aerodynamic performance indicators such as pressure ratio and efficiency to conduct similar grid independence verifications. Therefore, this 1.5 million grid cell division scheme is used as the benchmark grid scheme for subsequent uncertainty quantification and batch simulation, balancing the efficiency of computational database generation with flow field fidelity.

[0096] After determining the baseline mesh generation scheme, it is necessary to conduct batch computational fluid dynamics numerical simulations and data extraction based on the fouled blade deviation airfoil sample library constructed using the aforementioned Latin hypercube sampling strategy. Since Latin hypercube sampling generates a large number of data pairs consisting of geometric deviation variables and operating condition variables, manually creating computational engineering files one by one would be extremely costly. Therefore, automated scripting technology is introduced to establish a high-fidelity batch evaluation mechanism for aerodynamic performance.

[0097] By utilizing a written Python script in conjunction with the NUMECA Fine / Turbo aerodynamic simulation software component, batch transfer and automated execution of the calculation process are achieved. The script commands iteratively read data files from various 3D blade solid models in the sample library of blade deviations due to fouling. The corresponding blade geometry models are imported into the mesh generation module, and the previously selected baseline mesh topology and node distribution pattern, verified for independence, are forcibly applied to generate the spatial mesh for the blade's computational domain. This fixed mesh generation strategy not only ensures the consistency of spatial discretization errors among different geometric deviation samples but also meets the efficiency requirements of large-scale computation.

[0098] After the mesh is generated, the script automatically jumps to the solver settings module to assign parameters for the numerical method and boundary conditions. For the selection of the turbulence model, due to the strong adverse pressure gradient and boundary layer separation phenomenon inside the compressor, the Spalart-Allmaras single-equation turbulence model or the k-omega SST two-equation turbulence model, suitable for analyzing the internal flow field of aero-engines, can be selected. For the setting of inlet and outlet boundary conditions, total pressure, total temperature, and absolute airflow deflection angle are given at the inlet of the computational domain, and adiabatic no-slip solid wall conditions are set at the blade surface, hub, and casing wall. Specifically, at the outlet of the computational domain, the script reads the outlet static pressure variable value generated during the sampling process and assigns it as the outlet back pressure boundary condition. This change in the outlet static pressure parameter simulates the actual service conditions of the compressor under different throttling states. For the specific derivation of the flow field spatial discretization scheme and the setting of the time step, those skilled in the art can use conventional numerical analysis methods for configuration; the internal solution algorithm is a well-known technology in the field and will not be elaborated here.

[0099] After configuring all calculation parameters, the script control software generates an independent calculation project file and submits it to the fluid solver for iterative calculation of three-dimensional steady flow. During the solution process, the convergence status of the flow field is monitored in real time. The criteria for valid convergence samples include: the calculation residuals of the continuity equation, momentum equation, and energy equation all decrease to below the set convergence order of magnitude; the mass flow rate error at the inlet and outlet of the computational domain tends to zero; and the key aerodynamic performance indicators of the blades no longer exhibit significant periodic oscillations or divergences with increasing iteration steps.

[0100] After the computational engineering for all samples is completed, batch extraction of performance data is performed. A post-processing script reads the result files of valid samples that meet the aforementioned residual convergence criteria and extracts the integral values ​​of macroscopic aerodynamic parameters of the flow field cross-section. The key aerodynamic performance indicators extracted mainly include flow rate, pressure ratio, and efficiency. Flow rate reflects the flow capacity of the compressor blades under current operating conditions; pressure ratio is obtained by the ratio of the mass-average total pressure at the outlet cross-section to the mass-average total pressure at the inlet cross-section, used to characterize the blades' work capacity for the airflow; efficiency combines the total temperature ratio and total pressure ratio at the airflow inlet and outlet, used to quantify the degree of aerodynamic losses caused by fouling and viscous dissipation in the flow field. The definitions and calculation formulas of the above conventional performance indicators are common knowledge in this field; their physical characterization meaning is disclosed here to ensure the complete support of the technical solution.

[0101] After data extraction, the input geometric feature parameters such as the blade fouling initiation location and fouling thickening intensity, as well as operating condition parameters such as outlet static pressure, were matched one-to-one with the aerodynamic performance indicators such as flow rate, pressure ratio, and efficiency output from the simulation. The cleaned and integrated data points were compiled and summarized to generate a database of geometric deviation blade profiles, operating conditions, and their corresponding performance. This database establishes a high-fidelity physical mapping relationship between low-dimensional fouling characteristics, service conditions, and the macroscopic aerodynamic response of the compressor within a multidimensional variable space. It comprehensively covers the performance degradation range of blades after fouling, providing a complete and reliable data foundation for subsequent training of surrogate models and performance prediction verification.

[0102] See attached document Figure 4 To establish a nonlinear mapping relationship between the geometric deviation variables of the contaminated blade shape, operating condition variables, and the aerodynamic performance of the blade, a fully connected neural network is used to construct a surrogate model of the aerodynamic performance. Combined with... Figure 4 The network topology shown is a neural network consisting of an input layer, hidden layer 1, hidden layer 2, and output layer from left to right. The input layer has three neurons, each corresponding to an independent input feature in one of the three dimensions. Figure 4 The two yellow circular nodes at the top center represent the input pollution characteristic deviation variables, namely the previously extracted blade pollution initiation position and pollution intensity; the blue-green circular node at the bottom represents the input operating condition variable, namely the outlet static pressure reflecting the compressor throttling state.

[0103] Following the input layer, two consecutive hidden layers are configured within the network to extract the complex nonlinear coupling features between the input variables and the aerodynamic response. Both hidden layer 1 and hidden layer 2 contain eight neurons. Figure 4 The black vertical dots inside the hidden layer nodes represent other neurons in the same layer that are omitted. Network layers are fully connected by solid lines with arrows, indicating that each neuron in the previous layer transmits its forward output signal to each neuron node in the next layer, multiplying it by the corresponding weight matrix and adding a bias vector during signal transmission. The output layer has one neuron unit, used to output a single predicted aerodynamic performance index.

[0104] Based on the aforementioned geometric deviation and performance sample database, supervised learning training was performed on the fully connected neural network. According to the sample simulation results, three surrogate models with independent weight parameters were trained in parallel using the same network topology. Specifically, a surrogate model predicting traffic flow using pollution and operating condition variables as inputs was constructed, denoted as the traffic flow surrogate model (Net_Mass); a surrogate model predicting pressure ratio using pollution and operating condition variables as inputs was constructed, denoted as the pressure ratio surrogate model (Net_TPR); and a surrogate model predicting efficiency using pollution and operating condition variables as inputs was constructed, denoted as the efficiency surrogate model (Net_Eta). During the parameter iterative optimization of each surrogate model, the backpropagation solution of the specific loss function can be implemented using conventional gradient descent algorithms, and its network convergence logic is a well-known technique in this field, which will not be elaborated here. After the three surrogate models were trained, the coefficient of determination (COP) was used for each model. The accuracy of the model is verified using this as a core indicator to quantitatively evaluate the goodness of fit of the model to the nonlinear mapping of the flow field.

[0105] After training the multi-objective surrogate model, an operating condition screening strategy is introduced to equivalently match the aerodynamic performance of contaminated blades. To objectively compare the aerodynamic performance degradation of blades with different contamination deviations, it is necessary to ensure that the performance of blades with different contamination deviations is compared under a unified benchmark operating condition with equal rotational speed and mass flow rate. The trained Net_Mass surrogate model is used to optimize the forward operating condition parameters. For a given combination of extracted fixed contamination feature parameters, Monte Carlo random sampling is performed within the physical value range of the operating condition variables to generate input variable samples. These input variable samples, along with the fixed contamination feature parameters, are then batch-input into Net_Mass to quickly calculate the corresponding predicted flow rate set.

[0106] The calculated prediction results are extracted and compared with a pre-defined target flow rate to locate and filter the optimal operating condition variable that makes the predicted flow rate closest to the target flow rate. This location and filtering mechanism is limited by a preset error threshold criterion. The formula for determining the relative error of the flow rate is:

[0107] ;

[0108] in, This represents the calculated percentage of relative error, which is strictly constrained to be no greater than 0.5% in the screening strategy. This represents the predicted flow rate calculated by the Net_Mass proxy model based on Monte Carlo sampling points. This represents a pre-defined unified baseline target flow rate. The actual physical flow rate of the compressor blades under baseline operating conditions, extracted from their original design state without fouling, is used to ensure the positive scalar characteristics of the error assessment.

[0109] After successfully locating the optimal operating condition variable that meets the aforementioned error threshold, this optimal operating condition variable is used to drive the other two surrogate models for aerodynamic performance prediction. Specifically, the optimal operating condition variable, along with the corresponding blade contamination initiation location and contamination intensity, is combined into an input vector and input into Net_TPR and Net_Eta, respectively. The Net_TPR model predicts and outputs the predicted pressure ratio distribution under the corresponding uniform inflow condition, while the Net_Eta model predicts and outputs the predicted efficiency distribution under the corresponding uniform inflow condition. This joint driving and operating condition selection strategy satisfies the requirement of obtaining the performance distribution under different fouling conditions under consistent inflow conditions, while avoiding the resource consumption of repeatedly calling the fluid dynamics solver for trial and error, thus balancing the rigor of the performance uncertainty quantification benchmark with computational efficiency.

[0110] To ensure high confidence in the actual performance predictions of the three surrogate models, Net_Mass, Net_TPR, and Net_Eta, a closed-loop mechanism for accuracy verification and parameter tuning is introduced simultaneously during the model training phase. Before training using the aforementioned geometric bias and performance sample database, this database is randomly divided into training, validation, and test sets according to a specific ratio. The training set is used for gradient update calculations of the network's internal weights and bias parameters; the validation set is used to monitor the model's generalization ability in real time during training to prevent overfitting; and the test set is used to independently and objectively quantitatively evaluate the prediction accuracy of the final model parameters after the entire training process is completed.

[0111] In the quantitative evaluation phase, the coefficient of determination is used as the core accuracy verification index to quantitatively characterize the degree of agreement between the predicted values ​​output by the surrogate model and the actual values ​​calculated by high-fidelity fluid dynamics numerical simulation. The formula for calculating the coefficient of determination is:

[0112] ;

[0113] in, The coefficient of determination is the closest the value is to a constant of 1, indicating that the surrogate model has a higher accuracy in fitting nonlinear data. The summation operator is used to calculate summation values. From 1 to The continuous values ​​of each item are accumulated and calculated; This represents the total number of samples participating in the accuracy verification. Indicates the current sample number being calculated; The first value obtained from computational fluid dynamics numerical simulation is... The actual aerodynamic performance indicators of each sample correspond to the calculated values ​​of mass flow rate, total pressure ratio, or equivalent efficiency in the database. This indicates that the output of the corresponding proxy model is calculated forward based on the input variables. Predicted aerodynamic performance indices for each sample; Indicates all The arithmetic mean of the actual aerodynamic performance indicators of each sample.

[0114] Based on the calculation results of the determination coefficients mentioned above, a closed-loop system for model training parameter tuning is constructed. At the end of the set training period, the determination coefficients of the three surrogate models on the validation set are calculated and compared with a preset accuracy threshold. When the calculated determination coefficient is lower than the preset threshold of 0.99, it indicates that the currently set network topology or training parameters have failed to fully capture the deep mapping relationship between blade fouling variables, operating condition variables, and aerodynamic response. At this time, the system triggers the parameter tuning closed-loop operation.

[0115] In the closed-loop hyperparameter tuning process, the model architecture and learning process are optimized by adjusting the hyperparameters of the fully connected neural network. Specific adjustments include increasing or decreasing the number of neurons in the hidden layers, adjusting the batch size of input samples, and modifying the optimizer's initial learning rate and its decay strategy. For the specific iterative optimization of the network hyperparameters and the regularization configuration to prevent overfitting, those skilled in the art can use conventional deep learning tuning algorithms. The weight update and internal backpropagation mechanisms are well-known techniques in the field and will not be elaborated upon here.

[0116] After multiple rounds of closed-loop parameter tuning iterations, when the determination coefficients of the three surrogate models—Net_Mass, Net_TPR, and Net_Eta—on the independent test set all reach or exceed the preset accuracy threshold, the parameter tuning loop is stopped, and the weight matrices and bias vectors within each neural network are solidified. At this point, the final surrogate model components with high-fidelity flow field prediction capabilities are obtained. These three surrogate models, verified by closed-loop accuracy, will serve as the underlying computing engine. Combined with the aforementioned Monte Carlo sampling-based operating condition selection and equivalent matching strategy, they will provide accurate data support for the performance degradation assessment and uncertainty quantification of the compressor under uniform inflow conditions, while ensuring computational efficiency.

[0117] In the actual operational evaluation of aero-engine compressors, to objectively measure the degree of aerodynamic performance degradation caused by blade surface fouling, performance comparisons need to be conducted under a unified benchmark operating condition with constant speed and mass flow rate. Directly employing computational fluid dynamics numerical simulations to approximate a unified target flow rate by continuously adjusting the outlet back pressure boundary conditions presents engineering challenges, including excessive computational resource consumption and difficulty in achieving rapid flow field convergence. Therefore, an equivalent matching mechanism based on Monte Carlo mass sampling and target flow rate comparison and screening is constructed.

[0118] In practice, for a given geometric deviation state of fouling accumulation—the initial location of blade fouling and the intensity of fouling thickening—Monte Carlo sampling is performed within the effective physical range of the operating variable, namely, the outlet static pressure. By introducing a pseudo-random number generation sequence, a massive number of candidate outlet static pressure sample points are generated within the set upper and lower limit intervals. The specific random distribution function call and discrete point generation operations for this Monte Carlo sampling can be implemented using conventional statistical algorithms by those skilled in the art; the principle of random number generation and the probability density distribution model are well-known techniques in this field and will not be elaborated upon here.

[0119] After obtaining a massive number of candidate outlet static pressure sample points, these are combined with the given pollution variables to construct a large-scale query parameter matrix. This query parameter matrix (i.e., the input variable samples) is then batch-input into the Net_Mass surrogate model, which has undergone closed-loop accuracy verification. The Net_Mass surrogate model performs forward calculations based on its internally fixed nonlinear weight relationships, quickly outputting the predicted flow rate corresponding to each candidate sample point. Based on this, a target flow rate comparison and filtering operation is performed. A target flow rate value representing a specific operating state of the compressor is set as the comparison benchmark. The massive set of predicted flow rates output by the network is traversed, and the relative error between each predicted flow rate and the target flow rate value is calculated.

[0120] As constrained by the aforementioned relative error formula, the goal of the comparison and screening is to locate sample points with a relative error of no more than 0.5%. When multiple calculation results satisfy this threshold exist in a massive sample set, the sample with the smallest absolute value of relative error is further extracted, and its corresponding candidate outlet static pressure is used as the optimal operating condition variable for final matching. This operation precisely locks the specific throttling back pressure condition that maintains a constant compressor flow rate in a multidimensional variable space.

[0121] After accurately locating the equivalent operating point, the matched outlet static pressure value is extracted and recombined with the initially given blade contamination initiation location and contamination thickening intensity to form a target input vector representing a unified inflow condition. This target input vector is then used to jointly drive the other two surrogate models for performance parameter prediction. The target input vector is input into the Net_TPR surrogate model, directly outputting the predicted pressure ratio distribution under the unified baseline condition; simultaneously, it is input into the Net_Eta surrogate model, outputting the predicted efficiency distribution under the unified baseline condition.

[0122] Through the aforementioned execution logic based on operating condition screening, rapid location and matching of uniform incoming flow conditions is achieved in a massive random sample space. This mechanism relies on the millisecond-level forward computation capability of a neural network surrogate model to replace the time-consuming iterative solution of the three-dimensional flow field. This not only ensures the rigor of the aerodynamic performance comparison benchmark at the physical level, but also obtains the true performance distribution of blades affected by different degrees of fouling at a relatively low computational cost, providing a reliable technical approach for subsequent quantitative analysis of compressor performance uncertainties.

[0123] See attached document Figure 5 After obtaining a large amount of total pressure ratio prediction data of compressors under a unified reference operating condition under different fouling conditions using the aforementioned proxy model and operating condition screening strategy, statistical analysis is performed on these discrete prediction results to carry out uncertainty quantification of aerodynamic performance. Figure 5 This figure illustrates the probability distribution of the total pressure ratio from the evaluation output. The horizontal axis represents the compressor's total pressure ratio, and the vertical axis represents the frequency of that total pressure ratio value in a large sample of predictions. The green bars in the figure are frequency histograms generated by dividing the predicted data into numerical intervals and counting the corresponding sample sizes. The black solid line in the figure is a probability density distribution curve generated by fitting data from the green bar chart. The red vertical dashed line in the figure marks the position of the "design total pressure ratio" of the compressor in its original, uncontaminated state. The black vertical dashed line in the figure marks the position of the statistically calculated "mean total pressure ratio under contamination uncertainty."

[0124] contrast Figure 5 The positional relationship between the red and black dashed lines shows that the design total pressure ratio is in the higher range of the horizontal axis, while the average total pressure ratio affected by fouling shifts to the left, meaning the value decreases. This shift quantifies the weakening effect of blade surface fouling on the compressor's work capacity. The black solid line in the figure exhibits a bell-shaped distribution, high in the middle and low on both sides, covering a specific width of the horizontal axis. This reflects that randomly combined geometric deviations in fouling cause fluctuations in the total pressure ratio output within a certain range, demonstrating the nonlinearity and uncertainty of the transfer of fouling characteristics to aerodynamic performance.

[0125] See attached document Figure 6The same statistical evaluation method as the total pressure ratio is used to quantify the uncertainty of the massive efficiency prediction data obtained. Figure 6 The horizontal axis represents the compressor efficiency, and the vertical axis represents the frequency of the corresponding efficiency value in the massive predicted sample. The yellow bars in the figure are statistically generated efficiency frequency distribution histograms. The black solid line in the figure is the probability density distribution curve generated by fitting. The red vertical dashed line in the figure marks the position of the compressor's "design point efficiency" under the original uncontaminated state. The black vertical dashed line in the figure marks the position of the "mean efficiency under fouling uncertainty".

[0126] observe Figure 6 The relative positional distribution of the data shows that the design point efficiency is located in the high-value region on the right side of the distribution interval, while the mean efficiency affected by fouling uncertainty shifts significantly to the left. This bias phenomenon confirms that fouling increases viscous dissipation within the flow field, resulting in aerodynamic efficiency penalties. Furthermore, the width of the distribution interval occupied by the yellow bars further indicates that different degrees of fouling geometric deformation can cause large-scale dispersion in efficiency indicators.

[0127] By generating the aforementioned probability density distribution and statistical indicators, a mapping between uncertain fouling geometric deviations and compressor performance degradation intervals was established. For the frequency statistical interval division and probability density curve fitting calculation of massive data samples, those skilled in the art can use conventional statistical algorithms. The kernel density estimation model and the solution of mathematical expectation and variance are well-known techniques in this field and will not be elaborated upon here.

[0128] See attached document Figure 7 After predicting the aerodynamic performance distribution, to quantify the impact of fouling geometric deviations at different spanwise locations on the compressor's aerodynamic performance, the SHAP method was introduced to conduct feature sensitivity analysis. Based on game theory, the SHAP method calculates the marginal contribution of each input variable in the surrogate model's prediction to assess the importance of the variable to aerodynamic performance.

[0129] Combination Figure 7 As shown, the horizontal axis represents the SHAP value, which reflects the contribution or sensitivity of the corresponding variable to the aerodynamic performance prediction results. A larger SHAP value indicates a more significant impact of the variable on performance. The vertical axis represents the input variable names, covering ten fouling geometric deviation parameters of the compressor blades at five spanwise positions. These five spanwise positions, from the blade hub to the blade tip, are: 10% spanwise position, 30% spanwise position, 50% spanwise position, 70% spanwise position, and 90% spanwise position. At each spanwise position, two variables are included: "starting position," representing the initiation of fouling distribution, and "fouling intensity," representing fouling thickness. Specifically, Figure 7The vertical axis lists the starting position of the 10% spanning position, the pollution intensity of the 10% spanning position, the starting position of the 30% spanning position, the pollution intensity of the 30% spanning position, the starting position of the 50% spanning position, the pollution intensity of the 50% spanning position, the starting position of the 70% spanning position, the pollution intensity of the 70% spanning position, the starting position of the 90% spanning position, and the pollution intensity of the 90% spanning position from top to bottom.

[0130] observe Figure 7 The length distribution of the blue horizontal bars shows that the longest bar corresponds to the 90% spanwise contamination intensity, with the largest SHAP value. This indicates that the contamination thickening characteristics near the blade tip have the strongest influence on compressor aerodynamic performance changes. Since the compressor rotor blade tip region typically experiences complex gap leakage flow, geometric changes in this region easily trigger drastic changes in the flow field structure, thus exhibiting the highest aerodynamic sensitivity. The SHAP value for contamination intensity at the 10% spanwise position is the second highest, indicating that the fouling intensity near the hub region also has a significant impact on performance, consistent with the flow physics characteristic of boundary layer separation easily occurring in the hub corner region. The SHAP value is smallest at the 50% spanwise starting position in the middle of the blade, indicating that changes in the fouling initiation location in this region have a relatively low sensitivity to overall performance.

[0131] Comparing the differences in variables at the same spanwise position, at all five spanwise positions (10%, 30%, 50%, 70%, and 90%), the SHAP value of the "fouling intensity" variable, representing the characteristics of fouling thickness, was greater than the SHAP value of the "starting position" variable, representing the distribution start point at the same position. This comparison confirms that the degree of fouling thickness on the blade surface has a more direct impact on the compressor's macroscopic aerodynamic response than the fouling initiation position.

[0132] For the specific solution of the aforementioned SHAP value and the construction of the summation interpretation model, those skilled in the art can use conventional machine learning interpretive algorithms for calculation and implementation. The logic for local attribution and global feature importance assessment is well-known in the field and will not be elaborated upon here. This spanwise geometry sensitivity analysis clearly identifies the key fouling regions and key geometric parameters affecting the compressor's aerodynamic performance, providing data support for subsequent targeted maintenance cleaning and anti-fouling modification design of compressor blades.

[0133] Specific application examples:

[0134] To more intuitively demonstrate the execution process of low-dimensional parameterization construction of fouling geometry and equivalent matching working condition positioning, a 50% spanwise section of a compressor rotor blade of a certain type of aero-engine is selected as a specific application object for illustration.

[0135] The chord length of the basic airfoil curve at this cross-section is known. Under this operating condition, a uniform reference target flow rate is set when the compressor is uncontaminated. .

[0136] In Latin hypercube sampling or subsequent random testing, it is assumed that a specific set of fouling characteristic parameters is extracted: the initiation location of leaf fouling. Pollution thickening intensity At the same time, set the geometric constraint coefficients. The target slope at the beginning of the thickness rise segment The target slope at the end of the thickness rise segment .

[0137] According to the formula for absolute starting coordinates:

[0138] ;

[0139] This indicates that the physical protrusions of the scale buildup begin to appear from the blade chord toward the center point.

[0140] According to the formula for the length of the thickening effect of scale buildup:

[0141] ;

[0142] This indicates that the physical span of the thickness gradually increasing from zero to the target maximum is 25mm. Therefore, the absolute starting coordinates for the product to reach the target maximum thickness extreme value are... .

[0143] Within this thickness increase range (i.e.) Using locally normalized coordinates Calculation of chordal thickening function using cubic Hermite interpolation When the target maximum value is reached ( )hour, ,at this time .

[0144] According to the formula for calculating geometric offset, the maximum absolute thickness of the target at this cross-section, controlled by parameters, is:

[0145] ;

[0146] When the horizontal axis exceeds the rising range (i.e.) After mm), the chordal thickening function is compared with A linear transition is achieved with a consistent slope. The blade reaches its trailing edge after an axial distance of 25 mm. When ), the value exactly drops back to: This calculation result perfectly matches the setting that "in the high curvature geometrically closed region near the leading and trailing edges of the blade, the value of the chordal thickening function should be set to a constant of 0 to avoid introducing geometric abrupt changes and to ensure the smoothness of the curve and the quality of the subsequent mesh generation".

[0147] To visually verify the above calculation results, in conjunction with the appendix... Figure 8 Perform the corresponding analysis:

[0148] Coordinate axis definition: The horizontal axis in the figure is labeled "absolute chordal coordinate / mm", with a value range from 0 to 100mm of the blade's basic chord length; the vertical axis is labeled "geometric offset of scale / mm", with a value range from 0 to 12mm, reflecting the absolute thickness of the scale protruding along the outer normal direction of the blade surface.

[0149] The initial fouling zone (0-50mm on the horizontal axis): Within this range, the solid black line completely adheres to and remains on the horizontal line with a vertical axis of 0. This corresponds to a physically uncontaminated, original surface, and the calculated absolute starting coordinates. A perfect match.

[0150] The starting point of scale buildup is located at 50mm on the horizontal axis and 0mm on the vertical axis of the curve. This point visually demonstrates the physical boundary where the thickness rise function calculated above takes effect.

[0151] The raised area and maximum thickness extreme: After exceeding 50mm, driven by a cubic Hermite polynomial, the curve exhibits a smooth upward bulge. At a position approximately 73mm on the horizontal axis and 10mm on the vertical axis, a black square data point is marked on the curve, representing the maximum thickness extreme. This point corresponds precisely to the target position calculated by the formula. and the intensity of pollution thickening The maximum controlled thickness is 10 mm.

[0152] Trailing edge retreat zone (horizontal coordinate 75-100mm): After passing the extreme point of the black square, the black line shows a straight linear downward trend along the slope of −0.04, and finally converges to zero precisely at the right boundary of the horizontal coordinate (100mm), demonstrating the forced closure constraint result of the fouling on the trailing edge of the blade.

[0153] After completing the aforementioned three-dimensional geometric reconstruction and computational mesh generation, the system needs to locate the fouling blade at the target flow rate. The aerodynamic performance of the device.

[0154] In this embodiment, Monte Carlo random sampling is performed within the outlet static pressure variable space (e.g., 100 kPa-150 kPa) to generate 100,000 candidate outlet static pressure points. These are then compared with the aforementioned fixed fouling variable. The data is then input into the pre-trained Net_Mass proxy model in batches.

[0155] The system completed 100,000 forward calculations in just 1.2 seconds. A review of the prediction results revealed that when the candidate outlet static pressure was 128.5 kPa, the predicted flow rate was... .

[0156] Based on the formula for determining relative flow error:

[0157] ;

[0158] The relative error percentage The convergence threshold set by the screening criteria was met. Therefore, 128.5 kPa was accurately identified as the equivalent operating point, which was then input into Net_TPR and Net_Eta for pressure ratio and efficiency prediction.

[0159] To verify the fidelity and efficiency advantages of the above method, a rigorous CFD numerical calculation comparison experiment was conducted:

[0160] Traditional CFD trial-and-error optimization method: Engineers manually adjusted the outlet back pressure boundary conditions to approximate a flow rate of 20.0 kg / s, performing six back pressure adjustments and three-flow-field recalculations. This process took approximately 12.5 hours, ultimately locking the back pressure at 128.45 kPa, and calculating the true total pressure ratio to be 1.845.

[0161] The surrogate matching method of this invention: using Monte Carlo and surrogate models, the optimal equivalent back pressure of 128.5 kPa is locked within 1.2 seconds, and the total pressure ratio predicted by Net_TPR is 1.848.

[0162] The relative error between the total pressure ratio of the output results of this invention and the actual CFD results is only [percentage missing]. This demonstrates that, while maintaining extremely high prediction accuracy (error < 0.2%), this method drastically reduces the time cost of single-point aerodynamic performance matching and evaluation from tens of hours to seconds. It achieves both complex nonlinear geometric reconstruction and overcomes the computational bottleneck of massive aerodynamic attenuation analysis under complex geometric deviations.

Claims

1. A method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation, characterized in that, Includes the following steps: Define the sampling space for pollution variables and the sampling space for operating condition variables, and perform sampling operations to obtain the initial parameter sample set; A three-dimensional fouling blade geometric model is generated based on the parameter sample set. Computational fluid dynamics simulation is performed on the three-dimensional fouling blade geometric model to extract aerodynamic performance parameters including flow rate, pressure ratio and efficiency, and a sample database is constructed. Three independent fully connected neural network proxy models were trained using the sample database. These three independent fully connected neural network proxy models were a traffic proxy model, a pressure ratio proxy model, and an efficiency proxy model. Within the operating condition variable sampling space, sampling is performed to generate input variable samples. The input variable samples are then input into the traffic proxy model to obtain predicted traffic. The target traffic under the baseline operating condition is obtained, and the predicted traffic and the target traffic are compared by error to obtain the optimal operating condition variable. The parameter combination containing the optimal operating condition variables is input into the pressure ratio proxy model and the efficiency proxy model respectively to output the predicted pressure ratio distribution and the predicted efficiency distribution; The uncertainty of aerodynamic performance is quantified by performing statistical processing on the predicted pressure ratio distribution and the predicted efficiency distribution.

2. The method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation according to claim 1, characterized in that, The steps of defining the pollution variable sampling space and the operating condition variable sampling space, and performing sampling operations to obtain the initial parameter sample set specifically include: The sampling space for pollution variables is defined by using the initiation location of blade pollution and the intensity of pollution thickening as parameters, and the sampling space for operating condition variables is defined by using the outlet static pressure as a parameter. Latin hypercube sampling is performed within the pollution variable sampling space and the operating condition variable sampling space to obtain the initial parameter sample set.

3. The method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation according to claim 2, characterized in that, The steps for generating a three-dimensional geometric model of the fouling blade based on the parameter sample set specifically include: Extract two-dimensional original blade profile data points, perform rotation and alignment operations on the two-dimensional original blade profile data points, generate a basic blade profile curve using a cubic spline fitting method based on the rotated and aligned two-dimensional original blade profile data points, and calculate the unit tangential vector and unit outward normal vector based on the basic blade profile curve. Extract the initial location of the leaf contamination and the intensity of the contamination thickening to construct a chordal thickening function. Combine the chordal thickening function with the unit outward normal vector to calculate the geometric offset. Obtain the leaf shape coordinates after contamination based on the geometric offset. The three-dimensional geometric model of the fouled blade is generated by performing surface skinning operation on the contaminated blade coordinates at different spanwise height sections.

4. The method for quantifying the uncertainty of aerodynamic performance due to geometric deviation of compressor blade fouling according to claim 3, characterized in that, The steps for extracting the leaf contamination initiation location and the contamination thickening intensity to construct a chordal thickening function specifically include: Geometric constraint coefficients are introduced to calculate the length of fouling thickening effect, and local normalized coordinates are calculated by combining the blade fouling initiation position and the fouling thickening effect length. The chordal thickening function is constructed using a cubic interpolation method, ranging from the absolute starting coordinates to the peak position of fouling. In the high curvature geometrically closed region near the leading and trailing edges of the blade, the value of the chordal thickening function is forcibly set to 0.

5. The method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation according to claim 1, characterized in that, The specific steps for performing computational fluid dynamics simulation on the three-dimensional fouling blade geometry model to extract aerodynamic performance parameters including flow rate, pressure ratio, and efficiency include: A mesh independence analysis was performed on the three-dimensional fouling blade geometric model to select a reference mesh scheme. A spatial mesh was generated according to the reference mesh scheme, and the flow field was iteratively solved. The key aerodynamic performance indicators of the valid samples that meet the residual convergence criteria are extracted as the flow rate, the pressure ratio, and the efficiency.

6. The method for quantifying the aerodynamic performance uncertainty of compressor blade fouling geometric deviation according to claim 1, characterized in that, The specific steps for training three independent fully connected neural network proxy models using the aforementioned sample database include: Construct a fully connected neural network topology that includes an input layer, two consecutive hidden layers, and an output layer. Set three neuron units for the input layer, configure eight neuron units for each of the two consecutive hidden layers, and set one neuron unit for the output layer. The fully connected neural network topology is trained using the sample database in a supervised manner.

7. The method for quantifying the uncertainty of aerodynamic performance due to geometric deviation of compressor blade fouling according to claim 6, characterized in that, The steps of supervising the training of the fully connected neural network topology using the sample database specifically include: During supervised learning training, the decision coefficient of the fully connected neural network surrogate model is calculated. When the decision coefficient is lower than a set threshold, a parameter tuning closed-loop operation is triggered to adjust the model hyperparameters and supervised learning training is re-executed. When the determination coefficient is greater than the set threshold, the trained traffic proxy model, pressure ratio proxy model, and efficiency proxy model are output. The set threshold is 0.

99.

8. The method for quantifying the uncertainty of aerodynamic performance due to geometric deviation of compressor blade fouling according to claim 1, characterized in that, The step of obtaining the target flow rate under the baseline operating condition and comparing the predicted flow rate with the target flow rate to obtain the optimal operating condition variable specifically includes: The actual physical flow rate of the compressor blades under the original design condition without fouling is extracted as the target flow rate, and the percentage error between each predicted flow rate and the target flow rate is calculated. Candidate sample points whose relative error percentage is not greater than a limit value are located. Among the multiple candidate sample points that meet the conditions, the sample with the smallest absolute value of relative error is extracted. The candidate parameter corresponding to the sample with the smallest absolute value of relative error is taken as the optimal operating condition variable.

9. The method for quantifying the uncertainty of aerodynamic performance due to geometric deviation of compressor blade fouling according to claim 1, characterized in that, The specific steps for quantifying the uncertainty of aerodynamic performance by statistically processing the predicted pressure ratio distribution and the predicted efficiency distribution include: The predicted samples of the predicted pressure ratio distribution and the predicted efficiency distribution are divided into numerical intervals and the number of samples is counted to generate a frequency histogram. The probability density distribution curve is then generated by fitting the frequency histogram data. Calculate the average total pressure ratio and average efficiency after the impact of fouling, and compare them with the design total pressure ratio and design point efficiency under the original unpolluted state to quantify the performance degradation range.

10. The method for quantifying the uncertainty of aerodynamic performance due to geometric deviation of compressor blade fouling according to claim 1, characterized in that, After completing the uncertainty quantification of aerodynamic performance, the method further includes calculating the sensitivity parameters of pollution variables. The specific steps for calculating the sensitivity parameters of pollution variables include: The SHAP method is used to calculate the marginal contribution of the input feature variables in the prediction of the fully connected neural network surrogate model, and the sensitivity values ​​of the contamination feature variables at different spanning positions are extracted respectively. The magnitude of the sensitivity value is used to assess the degree of influence of the pollution variable at the corresponding spanwise location on the aerodynamic performance change.

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