A method for quantitatively evaluating uncertainty of performance deviation of blade geometry deviation

Abstract

This invention relates to the field of compressor aerodynamic performance evaluation technology, and discloses a method for quantitatively evaluating the uncertainty of blade geometric deviation performance. The method includes: acquiring the original design geometry of a multi-stage compressor and performing CFD simulation to determine the target reference flow rate; extracting deviation parameters to generate a deviation geometry sample set; performing multi-row CFD simulations on the samples; dynamically adjusting the outlet back pressure to constrain each sample to converge under the target reference flow rate; acquiring aerodynamic response data; training a surrogate model using the deviation parameters and aerodynamic response data; using the surrogate model for random sampling inference to obtain the probability distribution characteristics of the aerodynamic response data; combining a sensitivity analysis algorithm to calculate the global feature importance of each geometric deviation parameter and outputting core sensitive parameters; and determining the aerodynamic performance boundary and stall risk threshold of the compressor blade under operating conditions. This invention solves the problem of simulation condition deviation, reduces the computational cost of evaluation, and provides an engineering quantitative basis for stall risk early warning.

Description

Technical Field

[0001] This invention relates to the field of compressor aerodynamic performance evaluation technology, specifically to a method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation. Background Technology

[0002] During the manufacturing and actual service of multi-stage compressors, compressor blades will exhibit geometric deviations due to limitations in machining accuracy, material wear, and surface fouling. These microscopic geometric variations alter the flow area and local aerodynamic boundaries of the flow channels, leading to degradation of macroscopic aerodynamic performance such as the compressor's overall pressure ratio, isentropic efficiency, and available surge margin. To understand the probabilistic characteristics of performance degradation during the design and operation phases, engineering approaches are needed to quantify uncertainties.

[0003] Current aerodynamic performance evaluation primarily relies on three-dimensional computational fluid dynamics simulations. When dealing with high-fidelity numerical solutions involving multi-stage solid computational domains, single computation times are lengthy, and uncertainty quantification typically requires repeated calculations on a large number of geometric samples. Conventional simulation methods struggle to balance computational cost with the accuracy of multi-stage aerodynamic predictions. Furthermore, because flow capacity varies among samples with different geometric deviations, using a fixed outlet back pressure as a boundary condition during simulation evaluation leads to deviations in the actual operating mass flow rates of each sample. The aerodynamic response data of different samples will fall at different flow rate operating points, resulting in a lack of a unified physical benchmark for performance comparison.

[0004] In existing solutions that introduce surrogate models and statistical algorithms to reduce computational overhead, the underlying division operation for mapping high-dimensional geometric features and nonlinear aerodynamic responses often lacks amplitude constraint protection against data anomalies. This can easily trigger numerical division-to-zero overflow when processing highly aggregated engineering sampling data, affecting the continuity of the evaluation process. Furthermore, existing technologies often focus on outputting probability density distribution charts of aerodynamic performance, lacking systematic quantitative methods for reverse analysis of performance degradation results back to the input. This evaluation model struggles to calculate the core sensitive variables that drive performance degradation from numerous geometric deviation parameters, resulting in evaluation results remaining at the statistical observation level. It fails to provide quantitative engineering physical input for confirming the aerodynamic performance boundaries and setting stall risk thresholds for multi-stage compressors under actual operating conditions. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation. The technical problem it solves is that multi-stage compressors will generate blade geometric deviations during manufacturing and actual service. Existing aerodynamic performance evaluation methods are difficult to balance between high computational costs and the accuracy of multi-stage three-dimensional aerodynamic simulation. At the same time, after introducing geometric deviations, the flow channel capacity changes, and conventional simulation methods are difficult to ensure the alignment of actual operating conditions between different geometric samples.

[0006] Furthermore, existing technologies lack systematic quantitative methods to map microscopic geometric deviations to macroscopic aerodynamic performance boundaries and extract core sensitive parameters, which makes it impossible to provide engineering physical basis for the aerodynamic robustness design and stall risk warning of compressors.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation, comprising the following steps:

[0008] Obtain the original design geometry of the multi-stage compressor, perform CFD simulation calculations to determine the target reference flow rate; extract geometric deviation parameters and sample them to generate a deviation geometry sample set containing multiple deviation geometry samples;

[0009] For each deviation geometry sample, CFD simulation calculations are performed in a multi-stage environment. By dynamically adjusting the outlet back pressure constraint, each deviation geometry sample converges under the target reference flow rate, and the corresponding aerodynamic response data is obtained.

[0010] The surrogate model is trained by using geometric deviation parameters as input features and aerodynamic response data as output labels.

[0011] The trained surrogate model is used for random sampling and performance inference to obtain the probability distribution characteristics of aerodynamic response data; the global feature importance of various geometric deviation parameters is calculated by combining sensitivity analysis algorithm to output core sensitive parameters; and the aerodynamic performance boundary and stall risk threshold of multi-stage compressor blades under operating conditions are determined based on the core sensitive parameters.

[0012] The steps for obtaining the original design geometry of a multi-stage compressor and generating a deviation geometry sample set include: establishing an unbiased computational domain model of the original design geometry, performing CFD simulation calculations under rated operating conditions, and extracting the converged mass flow rate as the target reference flow rate; extracting the geometric deviation features of the multi-stage compressor blades, using the thickening initiation position and maximum thickening intensity as geometric deviation parameters, and setting the geometric deviation boundary by combining the spanwise reference distribution function and the preset floating range; using the Latin hypercube sampling algorithm to generate an initial geometric feature vector set in a multidimensional continuous parameter space, and removing abnormal vectors that trigger channel closure singularities, outputting a geometric deviation parameter sample space matrix without collinearity redundancy; based on the geometric deviation parameter sample space matrix, reconstructing two-dimensional airfoils with geometric deviations at each spanwise position, and generating three-dimensional geometric deviation blades by lofting along the stacking line; assembling the three-dimensional geometric deviation blades with the inlet guide vanes and downstream stator blades to construct a multi-stage solid computational domain model containing real geometric deviation features, thus forming a deviation geometry sample set.

[0013] When performing CFD simulations in a multi-row environment for various deviation geometric samples, a spatial mesh deformation algorithm is used to generate the computational domain mesh required for the simulation: the mesh generated by the original design geometry is set as the reference mesh topology; for the constructed multi-row solid computational domain model, a spatial mesh deformation algorithm based on radial basis functions is called, and the displacement of the blade surface wall before and after geometric reconstruction is used as boundary constraints to solve the linear displacement interpolation equation in the flow field; while keeping the total number of mesh nodes and the connection topology of the reference mesh topology unchanged, the spatial mesh nodes are made to smoothly migrate in accordance with the deformation of the blade surface to generate the computational domain mesh required for the simulation, and CFD simulations in a multi-row environment are performed based on the computational domain mesh.

[0014] The steps for dynamically adjusting the outlet backpressure constraint to converge each deviation geometric sample under the target reference flow rate include: updating the outlet backpressure during the iterative solution of the CFD simulation calculation and simultaneously performing the operating condition alignment check; extracting the actual flow rate in the current iteration step of the CFD simulation calculation and determining the deviation state between the actual flow rate and the target reference flow rate; eliminating invalid waste points where the actual flow rate deviates from the target reference flow rate by more than a predetermined tolerance due to convergence oscillations; constraining each deviation geometric sample to converge under the target reference flow rate, extracting the aerodynamic features corresponding to the deviation geometric samples that meet the convergence conditions to construct a column vector, and using this column vector as the corresponding aerodynamic response data. In this process, a joint judgment logic based on flow deviation and back pressure fluctuation rate is constructed: based on the mass flow spatial integral value of the outlet and inlet sections of the computational domain, the global mass conservation deviation rate, which includes the comparison logic of the maximum value of the denominator excluding zero, is extracted; the absolute flow error rate and the root mean square value of the outlet back pressure fluctuation are extracted in the current iteration step; when the global mass conservation deviation rate is lower than the first set threshold, the absolute flow error rate is lower than the second set threshold, the root mean square value of the outlet back pressure fluctuation is lower than the third set threshold, and the interstage characteristic parameters of the static-to-static interface do not undergo monotonically drift, the current deviation geometric sample is comprehensively judged to be aligned to the target reference flow and converged.

[0015] Aerodynamic response data includes total pressure ratio, isentropic efficiency, and available surge margin. The steps for acquiring aerodynamic response data include: extracting the total pressure ratio and isentropic efficiency of the compressor for the deviation geometry sample that converges at the target reference flow rate; triggering a back pressure incremental approximation program to gradually increase the outlet back pressure according to a preset pressure step until a numerical stall point is detected, extracting the total pressure ratio and mass flow rate corresponding to the numerical stall point, and calculating the available surge margin of the current deviation geometry sample in combination with the target reference flow rate data; scaling the extracted total pressure ratio, isentropic efficiency, and available surge margin using a standardization algorithm to obtain dimensionless aerodynamic response characteristics, and inserting a constant tolerance constraint to prevent singularities into the standard deviation of the denominator in the mapping calculation of the standardization algorithm.

[0016] The steps for training the surrogate model include: constructing the surrogate model using a deep residual network based on a fully connected topology; introducing skip connection paths with linear projection transformations between adjacent hidden layers and performing identity mapping; inputting geometric deviation parameters into the surrogate model to obtain prediction vectors; calculating the mean square error (MSE) of the squared absolute deviation of the prediction vectors using aerodynamic response data; configuring the joint loss function, which consists of the MSE and a model complexity penalty term representing the product of the sum of squared trainable weights and the weight decay coefficient; updating the network computation parameters of the surrogate model using an adaptive moment estimation algorithm, and adding a constant fine-tuning factor to the denominator of the square root of the second-order moment of the gradient history used to calculate the update step size; and triggering an early stop truncation command and freezing the network computation parameters of the surrogate model when the joint loss function on the validation set no longer decreases within a preset number of consecutive rounds and the isentropic efficiency prediction error falls back to within a preset engineering tolerance band.

[0017] The steps for obtaining the probability distribution characteristics of aerodynamic response data include: performing random sampling on the distribution interval of geometric deviation parameters to generate a random geometric parameter matrix; inputting the random geometric parameter matrix into the trained surrogate model to obtain dimensionless prediction labels; calling the feature statistical mean and standard deviation in the standardization algorithm to perform a reverse algebraic mapping operation on the dimensionless prediction labels to restore them to aerodynamic response data with real physical dimensions; constructing a continuous probability density function for the aerodynamic response data with real physical dimensions based on the kernel density estimation algorithm; in the probability weight cumulative average division operation of the kernel density estimation algorithm, replacing the denominator bandwidth parameter with a maximum value boundary constraint function composed of the actual bandwidth and a preset positive definite small tolerance to obtain the probability distribution characteristics of the aerodynamic response data.

[0018] The steps for calculating the global feature importance of each geometric deviation parameter include: using an approximate Shapley and interpretation algorithm optimized for deep neural networks to extract the local marginal contribution scalar values ​​of the geometric deviation parameters for the predicted samples; performing data validation at the algorithm interface, setting the lower bound of the dimension of the input feature tensor to be absolutely greater than or equal to 2; performing global expectation aggregation on the local marginal contribution scalar values ​​based on multi-source predicted samples; taking the absolute value of the local marginal contribution scalar values ​​of each geometric deviation parameter and performing algebraic accumulation, dividing the accumulated result by the maximum value limiting constraint term composed of the total number of test samples and a preset positive definite constant, and outputting the global feature importance.

[0019] The steps for outputting core sensitive parameters include: obtaining the global feature importance of the output; sorting the global feature importance corresponding to each geometric deviation parameter in descending order of numerical value to construct a one-dimensional feature importance sequence; calculating the cumulative contribution rate of the local importance corresponding to the current geometric deviation parameter in the total importance of all features along the descending direction of the feature importance sequence; when the cumulative contribution rate first reaches a preset truncation ratio threshold, extracting the top-ranked geometric deviation parameters covered by the truncation ratio threshold, confirming them as core sensitive parameters, and outputting them; and determining the aerodynamic performance boundary and stall risk threshold of the multi-stage compressor blades under operating conditions based on the core sensitive parameters.

[0020] This invention provides a method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation. It has the following beneficial effects:

[0021] 1. This invention introduces dynamic outlet back pressure adjustment during the iterative process of multi-row CFD simulation calculation, and a joint judgment logic based on flow deviation and back pressure fluctuation rate to constrain the convergence of samples with different geometric deviations under the same target reference flow rate. This solves the problem of deviation of actual operating flow rate caused by the change of flow channel area after the introduction of geometric deviation, ensures the consistency of the aerodynamic response data extraction conditions of each sample, and improves the objectivity of aerodynamic performance comparison and evaluation.

[0022] 2. This invention employs a deep residual network to construct a surrogate model to replace the traditional three-dimensional flow field numerical solution. Furthermore, it incorporates amplitude constraints based on constant tolerance into the underlying division operations of data standardization, network parameter updates, and kernel density estimation. The surrogate model reduces the significant computational overhead required for uncertainty quantification assessment, and the underlying anti-singularity constraints prevent numerical division-to-zero overflow when processing engineering calculation data, ensuring the continuity and numerical stability of large-scale sampling inference and probability distribution calculation processes.

[0023] 3. This invention combines the approximate Shapley algorithm and the interpretation algorithm to calculate the global feature importance of geometric deviation parameters, and extracts core sensitive parameters based on the cutoff ratio threshold of the cumulative contribution rate. It transforms high-dimensional random geometric sample data into the dominant variables affecting aerodynamic performance degradation, separates key factors from multi-dimensional coupling features, and directly provides a quantitative engineering physical basis for determining the aerodynamic performance boundary and stall risk threshold of multi-stage compressor blades under actual operating conditions. Attached Figure Description

[0024] Figure 1 This is a schematic diagram illustrating the degradation of the fan or compressor caused by uncertainties in this invention.

[0025] Figure 2 This is a schematic diagram of the thickening initiation position and the thickening intensity distribution function along the span direction in this invention;

[0026] Figure 3 This is a schematic diagram of the thickened blade profile and multi-stage compressor model construction of the present invention;

[0027] Figure 4 This is a schematic diagram of the 1.5-stage compressor model of the inlet guide vane-rotor-stator of the present invention;

[0028] Figure 5 This is a schematic diagram of the process for constructing a high-fidelity mapping database of geometric deviation and aerodynamic performance according to the present invention;

[0029] Figure 6 This is a schematic diagram of the efficiency dispersion under the condition of rotor blade geometric deviation in this invention;

[0030] Figure 7 This is a schematic diagram of the pressure ratio dispersion obtained by a 1.5-stage compressor under geometric deviations according to the present invention;

[0031] Figure 8 This is a comparative schematic diagram showing the results of sensitivity analysis of geometric deviation characteristics of the rotor blades of the 1.5-stage compressor of the present invention;

[0032] Figure 9 This is a schematic diagram showing the predicted and comparative curves of the surge margin of a multi-stage compressor under long-term service conditions according to the present invention. Detailed Implementation

[0033] 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.

[0034] See attached document Figure 1 Turbomachinery is subject to various geometric deviations during manufacturing, assembly, and service, causing its actual operating performance to exhibit a specific probability distribution. Due to uncertainties, the actual performance deviates from the design performance, with some performance characteristics falling below the required performance threshold, creating substandard performance areas and leading to decreased overall efficiency and reliability. Traditional deterministic design methods struggle to account for the performance degradation caused by these geometric deviations. Existing methods for quantifying the uncertainty of blade aerodynamic performance typically rely on simulation analysis based on a three-dimensional single-row blade model. However, single-row blade analysis ignores the multi-row operating environment of turbomachinery and neglects the coupling effects of blade geometric deviations on upstream and downstream blade matching and the interference of potential flow wakes between blade rows.

[0035] See attached document Figure 5This invention provides a method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation based on environmental conditions, comprising the following steps:

[0036] S1. Obtain the original design geometry of the multi-stage compressor, perform CFD simulation to obtain the characteristic curve at the design speed, determine the flow rate corresponding to the highest efficiency point, and conduct geometric deviation sampling based on the multi-stage compressor model to generate a deviation geometric sample set containing multiple individuals with different parameters.

[0037] S2, perform CFD simulation calculations for each deviation geometric sample. During the calculation process, the flow rate at the highest efficiency point determined by the original design geometry is used as the target benchmark. By dynamically adjusting the outlet back pressure of each sample model, all deviation geometric samples are constrained to operate at the same flow rate to eliminate the interference of operating condition fluctuations on performance evaluation.

[0038] S3, extract the efficiency and pressure ratio data corresponding to each deviation geometric sample, match the input deviation geometric samples with the output efficiency and pressure ratio, construct a high-fidelity mapping database, use this database to train the surrogate model, take the geometric deviation parameters as the input layer and the efficiency and pressure ratio as the output layer, establish the mapping relationship through internal parameter iterative optimization, and replace the physical flow field simulation calculation;

[0039] S4 utilizes the trained surrogate model to conduct random sampling and performance prediction within a given geometric deviation parameter space. Based on the statistical probability distribution characteristics of the predicted efficiency and pressure ratio results, it obtains the aerodynamic performance dispersion under multi-bladed coupling environment. Combined with the sensitivity analysis algorithm, it calculates the contribution ratio of each geometric deviation parameter to the overall performance and outputs the core sensitive parameters to guide subsequent robust design and maintenance strategies.

[0040] See attached document Figure 2 The process of extracting and parameterizing the true geometric deviation features specifically includes the following steps:

[0041] S101, In this embodiment, the geometric deviation characteristics of the turbomachinery blades during the manufacturing, assembly, or service environments are obtained. From a physical causal relationship analysis, specific geometric deviation types include blade surface fouling, wear, erosion, blade profile machining contour errors, installation angle errors, and tip clearance changes. These deviations directly alter the actual flow area and airflow turning angle within the blade channel, thereby inducing aerodynamic performance degradation. As a preferred method, the blade profile deviation data and its distribution range are obtained by measuring the actual deviation blade profile under specific conditions. Taking the geometric deviation caused by blade surface fouling as an example, measured data shows that fouling leads to thickening of the blade's suction surface. To accurately quantify this phenomenon, the starting position and intensity of fouling thickening are extracted from the measured data as the main geometric deviation characteristic parameters. The starting position of thickening is defined as the normalized position along the blade chord length. Its calculation involves the ratio of the current chord coordinate to the actual chord length. The system must have amplitude limiting protection logic during calculation to ensure that the actual chord length, as the denominator, is always greater than zero. The intensity of thickening is defined as the maximum relative thickness at the location of fouling.

[0042] S102, Based on the key deviation parameters extracted above, the extracted geometric deviation features are parametrically modeled. Before mathematical derivation, the general technical principle of this step is to transform the complex discrete point cloud geometric deviation into a continuous function space controlled by a few independent variables. Specifically, the surface geometric coordinates of the original design blade profile are set as the calculation reference, and the geometric deviation features caused by fouling are defined as feature vectors. The feature vectors contain parameters of the thickening initiation position and the maximum thickening intensity. For a specific spanwise section of the blade, the actual deviation blade profile geometry is composed of the superposition of the design geometry and the geometric deviation function. The physical meaning of this superposition mapping process is to reconstruct the ideal design state and the actual deviation, as shown in the following formula:

[0043] ;

[0044] In the formula, Representatives at the exhibition height The actual deviation of the airfoil geometric coordinates at the location; Representatives at the exhibition height The original design blade geometry coordinates at the location, with its subscript... and These correspond to the actual service status and the theoretical design status, respectively. Represents the geometric deviation function; Representatives at the exhibition height The parameters of the initial position of the thickening at that location; Representatives at the exhibition height The maximum thickening strength parameter at this location. (Variable here) The range of values ​​is defined as the effective aerodynamic radial span from the blade root to the blade tip.

[0045] S103. To further define the evolution boundaries of the above parameters in three-dimensional space, it is necessary to determine the spanwise distribution law of the geometric deviation characteristic parameters and set the parameter floating range. The actual fouling distribution along the blade height has specific spatial variation characteristics. This spatial non-uniformity is usually dominated by the centrifugal force caused by rotor rotation and the spanwise migration of the secondary flow field. Based on the measured geometric deviation data of the blade along the spanwise direction, the baseline distribution function of the thickening intensity along the spanwise direction is determined, and the range of thickening intensity variation at different relative blade height positions is clarified. At the same time, the baseline distribution function of the thickening initiation position along the spanwise direction is determined, and the thickening starting point at the corresponding blade height is obtained. Based on the baseline distribution function, a unified floating boundary is set for the characteristic parameters of each section to completely cover the space of uncertain parameters, thereby ensuring the completeness of the subsequent robustness evaluation samples. The corresponding formula is as follows:

[0046]

[0047] In the formula, Representing the The actual values ​​of the geometric deviation parameters are variables. Refers to the starting position of the thickening or the maximum thickening intensity; The first term is determined by the spanwise distribution function. The reference value of each geometric deviation parameter, the subscript of which is... Characterizes the central tendency of its measured fit; This represents the defined uniform floating range boundary ratio. In this embodiment, The value range needs to be comprehensively calibrated in combination with engineering processing tolerances and actual measurement errors. As a preferred setting, it can be set to fluctuate by 5% above and below the benchmark value, that is, a value of 0.05. This value takes into account both the effective coverage of the random sample space and the physical rationality of the occurrence of extreme working condition parameters.

[0048] For the specific reconstruction process of three-dimensional blade modeling using parametric methods within a given geometric deviation range, those skilled in the art can use general blade parametric modeling software modules or self-written programs based on spline interpolation to complete it. The principles of blade parametric modeling and surface generation are well-known technologies in this field and will not be elaborated here.

[0049] Based on the geometric deviation characteristic parameters and their fluctuation range determined above, the foundation for constructing a high-dimensional parameter sample space lies in clarifying the probability distribution characteristics of each dimension parameter.

[0050] S104, in this embodiment, a joint probability distribution model is established for the thickening initiation position and the maximum thickening intensity parameter. Analyzing the sources of randomness accumulated from physical processing or service environment, if there is a lack of prior statistical data on the massive long-term operation of this type of compressor, based on the maximum entropy principle, the geometric deviation parameters within the set boundary can be considered to follow a uniform distribution. To ensure the independence of parameter space sampling and the physical rationality of subsequent flow field evolution, the system needs to decouple the extracted parameter matrix based on correlation. Specifically, in implementation, the first... Geometric deviation parameters In a given interval The probability density within the range is a constant, and this probability density value is numerically equal to the upper bound of the parameter floating. and lower boundary The reciprocal of the difference. To prevent division by zero anomalies caused by overlapping upper and lower boundaries, the system applies tolerance check logic before performing calculations. Approaching zero (e.g., the absolute value of the difference is less than 10) −6 When this is the case, a fixed, small, discrete constant is forcibly assigned to that dimension to maintain algorithm stability. The general technical principle of the above uniform distribution setting is to provide an unbiased initial evaluation benchmark for all deviations, ensuring that every local deformation region in the parameter space has an equal probability of being sampled, and avoiding over-focusing on the center point while missing edge extreme cases.

[0051] After establishing the marginal distribution model of parameters in each dimension, in order to cope with the curse of dimensionality brought about by the high-dimensional parameter space, it is necessary to introduce a sampling strategy with strong space filling ability and controllable computational cost to discretize the continuous geometric deviation space.

[0052] S105, as a preferred method, employs the Latin hypercube sampling algorithm to generate the initial geometric feature vector set. The general principle of this algorithm is to force samples to be uniformly projected onto the edge distribution of each dimension in the multidimensional space through stratified sampling, overcoming the problems of local sample clustering or missing edges in high-dimensional space that easily occur in traditional pure random Monte Carlo algorithms with limited sample sizes. When performing multidimensional parameter sampling, the algorithm will... The range of the cumulative distribution function of each deviation parameter is divided into: There are n equally probable disjoint subintervals. For the nth... The first sample point The sampling calculation logic for the 3D feature is as follows:

[0053] ;

[0054] In the formula, Representing the The th generated sample The specific values ​​of each geometric deviation characteristic; superscript This represents the sample number, and its value ranges from 1 to... Integers; Representing the The inverse mapping function of the cumulative distribution function with one parameter; Represents a sequence A random permutation function, through the orthogonal design of this function, can shuffle the sample matching order between different dimensions, aiming to reduce the singularity risk of the spurious correlation matrix between dimensions and ensure that the generated global sample matrix has full rank characteristics; This represents a standard uniform random variable that is independent and identically distributed in the interval (0,1); This represents the set total sample size. In this embodiment, The value of is limited by the computational cost of high-fidelity calculation of the three-dimensional flow field and the convergence requirements of subsequent surrogate model training; its value is usually determined based on the number of feature dimensions. Perform proportional calibration, with an optimal range of 10. Up to 50 The range of values ​​is determined by balancing the physical time consumption of CFD flow field solution with the data abundance required to construct a high-precision response surface.

[0055] After obtaining the initial set of geometric feature vectors, considering that random combinations in a purely mathematical sense may cause interference or mesh distortion in physical space, it is necessary to perform a physical domain validity check on the generated vector set.

[0056] S106 establishes a multi-dimensional sample filtering criterion that includes mesh topology constraints and flow channel geometric limits. The verification logic of this criterion mainly focuses on the absolute flow throat area between two adjacent blades, the smoothness of the blade surface, and the aerodynamic constraints of the maximum thickness section. The system performs virtual reconstruction detection on each sample vector containing the coordinates of the thickening start position and thickening intensity. During the comprehensive judgment process, if the local radius of curvature after the maximum thickening intensity is detected to be less than the preset CNC machining tool radius limit, or the minimum normal distance between adjacent blade surfaces approaches zero, or the extracted relative throat area reduction exceeds the design margin threshold (e.g., exceeding 15% of the design flow area), then the sample is determined to have caused a non-physical flow channel closure singularity. At this time, the system will trigger an error-prevention resampling mechanism, discarding the abnormal vector and regenerating a replacement value using the aforementioned layered intervals. All individual row vectors after legality verification... The rows will be arranged and combined to output the complete dimensions. Geometric deviation parameter sample space matrix The physical significance of this matrix integration lies in combining independent single-sample states into a structured feature flow that can be directly invoked by the CFD solver. The resulting sample space matrix thus encompasses typical combinations of random variables such as fouling, manufacturing tolerances, etc. Provided the system confirms that the parameter matrix is ​​non-singular and free from collinearity and redundancy, this matrix will directly serve as the basic input command for the next step of batch reconstruction of the multi-row blade solid model and updating the flow field mesh.

[0057] See attached document Figure 3 After outputting the geometric deviation parameter sample space matrix in the aforementioned steps, the core task of this stage is to transform the abstract mathematical parameter vector into a three-dimensional solid model with a physical topological structure, and then construct a multi-row computational domain that can reflect the real inter-level coupling effect. This process strictly follows the geometric evolution logic from two-dimensional cross-section reconstruction, three-dimensional solid volume superposition to multi-level environment assembly.

[0058] S107, in this embodiment, a two-dimensional airfoil with geometric deviation is reconstructed at each blade height position according to the set spanwise distribution law. Specifically, during execution, the system reads the parameter vectors in the sample matrix line by line, extracts the corresponding thickening start position and maximum thickening intensity for a specific relative spanwise height, and applies these as input boundary conditions to the thickness distribution curve of the original airfoil design. For example... Figure 3 As shown, the solid line represents the original airfoil profile, and the dashed line represents the airfoil profile after superimposed fouling deviation. The normal distance between the two is the geometric deviation. To ensure the continuity and smoothness of the airfoil surface and avoid non-physical mesh distortion or flow field pseudo-entropy increase caused by small surface protrusions in subsequent CFD calculations, the system uses a cubic spline interpolation function to construct the thickness increment curve. Since this step belongs to the core deformation mapping logic, the mathematical description of the corresponding two-dimensional thickness superposition needs to be clarified as follows:

[0059] ;

[0060] In the formula, The reconstructed representation is located at the span height. Normalized chord length The actual leaf thickness of the distribution; This represents the original design blade thickness at the corresponding location; This represents a smooth spline function controlled by a deviation parameter. In this calculation, to prevent excessive thickness from causing the suction and pressure surfaces to intersect (i.e., negative thickness anomalies), the system sets a non-negativity constraint on thickness: when a non-negativity constraint is detected... If this occurs, it will be forcibly set to a minimum positive value or trigger a geometric error. After obtaining the actual blade thickness, the system uses the original mid-curve of the cross-section as a reference and spatially distributes the thickness scalar along the normal vector direction of each corresponding point on the mid-curve, thereby calculating the deviation blade profile coordinate vector in the two-dimensional local coordinate system. .

[0061] S108, after completing the two-dimensional reconstruction and coordinate system transformation of each discrete spanwise section, the discrete two-dimensional deviation airfoil is lofted along the preset stacking line to generate a continuous three-dimensional geometric deviation airfoil. The physical significance of this operation lies in integrating isolated section thickness variations into a complete three-dimensional aerodynamic interactive surface, providing a closed physical boundary for the subsequent generation of the three-dimensional spatial mesh. In this process, the system, according to the turbomachinery geometric modeling specifications, uses the airfoil centroid or leading edge point as the stacking reference point and utilizes a spatial coordinate transformation algorithm to map each section to three-dimensional space. This step involves cross-dimensional rigid body assembly and is the core control logic for three-dimensional modeling. The corresponding formula for the reconstructed three-dimensional surface coordinate set is as follows:

[0062] ;

[0063] In the formula, The absolute three-dimensional coordinate column vector representing the discrete points on the surface of the generated three-dimensional true deviation blade. ; This represents the deviation airfoil profile coordinate vector in the two-dimensional local coordinate system obtained from the aforementioned steps. ; Representative exhibition to a high level The spatial rotation transformation matrix at the location is uniquely determined by geometric parameters such as the blade's installation angle and sweep angle, and must satisfy the orthogonality condition. This is to ensure that the blade cross-section does not undergo non-physical stretching or deformation during rotation; This represents the coordinate translation vector of the superposition line in three-dimensional space.

[0064] S109, to realistically reproduce the multi-row coupling effect and support performance evaluation in a multi-stage environment, the generated three-dimensional geometrically biased blades need to be assembled into the multi-row stage environmental geometry model. In this embodiment, the single-row rotor blade model with fouling bias generated in the above steps is extracted and spatially aligned and assembled with the inlet guide vanes and downstream stator blades that maintain their original design geometry. The assembly process strictly follows the axial clearance design specifications of multi-stage compressors, keeping the design axial distance between each blade row unchanged. The technical purpose of this multi-row assembly logic is to retain the unsteady interference of the upstream stator wake on the rotor in the real operating environment, as well as the impact of the flow field distortion in the rotor channel on the stator matching characteristics when it is transmitted downstream, thereby overcoming the fundamental defect of traditional single-row models that cannot perceive system-level potential flow fluctuations and wake transport. Finally, the system outputs a topologically closed multi-row stage solid computational domain model containing the characteristics of the specified geometrically biased sample. This model will be directly used as an input source for subsequent high-fidelity computational fluid dynamics mesh generation.

[0065] For the underlying operations of performing specific surface skinning, periodic boundary arrays of adjacent leaf cascade channels, and exporting solid models in standard format in three-dimensional space, those skilled in the art can call the general geometric kernel of existing computer-aided design tools to complete them. The rules for three-dimensional solid encapsulation and coordinate system alignment are well-known technologies in this field and will not be elaborated here.

[0066] See attached document Figure 4 Based on the multi-row solid computational domain model containing real geometric deviation characteristics constructed above, it needs to be imported into a fluid simulation environment and discretized to establish a high-fidelity CFD computational model that can accurately capture the microstructure of the flow field. This process specifically includes three related steps: computational grid discretization, boundary condition configuration, and multidimensional convergence determination.

[0067] S201, In this embodiment, a high-quality three-dimensional mesh is generated for the computational domain of the multi-stage compressor. Considering the complex viscous shear and flow separation phenomena in the near-wall region of the blades, as a preferred approach, a structured O-type or C-type boundary layer mesh is constructed on the blade surface and near the hub and casing wall.

[0068] Before proceeding to specific mesh size allocation, the general technical principle of this step is to constrain the absolute physical scale of the boundary layer mesh using a dimensionless wall distance parameter, thereby ensuring that the selected turbulence model can resolve the viscous dissipation at the bottom of the boundary layer without bias. Specifically, the dimensionless wall distance... In numerical calculation logic, it is defined as: local wall friction velocity. Absolute physical height of the first layer mesh The product of the two, divided by the kinematic viscosity of the fluid. From the perspective of thermodynamic properties of fluid media, specifically for the air medium inside the compressor, the kinematic viscosity... Constrained by absolute temperature, the value remains positive; therefore, the system's underlying computation is not protected against zero-limiting. In this embodiment, based on the two-equation turbulence model (such as...), The solution requirements for the SST model The value of needs to be dynamically adjusted during the mesh generation stage to keep the y+y+ value range on the blade surface around 1.0 (preferably within the range of 0.5 to 2.0). The technical purpose of this parameter configuration is to accurately define the analytical resolution of numerical calculations for the momentum exchange characteristics of the boundary layer's bottom layer, avoiding flow separation prediction distortion caused by excessively sparse meshes. For regions with obvious geometric scales, such as the main flow region and the tip gap, a hexahedral structured mesh is used for spatial filling to ensure the computational accuracy and orthogonality of spatial discretization.

[0069] To avoid introducing spurious numerical noise due to abrupt changes in node topology during mesh refactoring of different samples, the system, as a preferred approach, sets the generated unbiased design geometric mesh as the baseline mesh topology. For subsequent batches of computational domain models with geometric deviations, the system no longer performs mesh refactoring but instead invokes a spatial mesh deformation algorithm based on Radial Basis Function (RBF). This algorithm uses the wall displacements before and after geometric reconstruction as boundary constraints. By solving the linear displacement interpolation equations within the flow field, it ensures that the spatial mesh nodes smoothly migrate in accordance with the deformation of the blade surface, while maintaining the absolute invariance of the total number of mesh nodes and the connection topology. This ensures that subtle degradations in aerodynamic performance can be attributed with high fidelity to pure physical geometric deviations, rather than mesh discretization errors.

[0070] After the spatial discretization of the computational domain is completed, in order to drive the solution of the numerical equations, the model needs to be given boundary conditions and physical constraints that reflect the real physical service environment.

[0071] S202, configuration-level environment, multi-row rotor-stator interface and inlet / outlet aerodynamic conditions. Since the configuration-level environment includes rotating rotor rows and stationary stator rows, with relative motion between them, a hybrid plane model is introduced at the rotor-stator interface to achieve cross-scale flux transfer within a steady-state calculation framework. The physical purpose of this model is to transform the unsteady wake parameters upstream into uniform steady boundaries downstream by circumferential flux averaging, thereby achieving forced alignment logic of multi-source flow field data across time and operational scales.

[0072] The logic for averaging the circumferential area of ​​any conserved variable at the interface is as follows:

[0073] Radial position in polar coordinate system above the interface Circumferential angle Local flow field instantaneous variables The integrand is the parameter along the circumferential direction (the integration interval is 0 to 2). Perform area integral and divide the result by the physical area of ​​the corresponding radial infinitesimal ring. This allows us to obtain the average value of the steady-state conserved variables after the mixed-plane processing. This set of variables encompasses the total pressure, total temperature, and velocity components of the flow field. During the integral transfer operation, the system incorporates geometric area verification logic to ensure the physical area of ​​the radial micro-element. Greater than the system tolerance threshold (e.g., set to 10) −8The calculation is performed in square meters to strictly avoid the risk of flux calculation divergence caused by dividing by zero. At the same time, the total temperature, total pressure and inlet airflow angle based on experimental measurements are given at the inlet boundary of the computational domain, and the average static pressure or mass flow rate is given at the outlet boundary, thereby constructing a complete well-posed partial differential equation solution boundary.

[0074] After establishing the boundary model, it is necessary to reasonably set the discretization format and convergence criteria of the numerical solver in order to monitor the physical evolution trajectory of the flow field iteration.

[0075] S203 employs a density-based implicitly coupled solver and uses a second-order upwind scheme to spatially discretize the convection and dissipation terms, reducing the interference of numerical viscosity on shock wave and wake capture within the channel. To avoid spurious convergence caused by a single residual extremum-based criterion, the system constructs a multi-dimensional joint convergence criterion based on residual and macroscopic physical quantity fluctuations. Specifically, in addition to requiring the root mean square residuals of the continuity equation, momentum equation, and energy equation to decrease to a preset threshold (e.g., 10), the criterion also includes... −5 Below, the global mass conservation deviation rate is forcibly introduced as a core monitoring variable to reflect the macroscopic intake and exhaust balance of the flow field. Since this decision logic directly relates to the algorithm's anti-divergence capability under extreme conditions, its global mass conservation deviation rate... The specific corresponding determination formula is as follows:

[0076] ;

[0077] In the formula, Represents the global mass conservation deviation rate; The spatial integral value of mass flow rate representing the inlet section of the multi-stage computational domain; The spatial integral value of mass flow rate at the outlet section; This represents a preset non-zero reference mass flow rate (which can be set to 10% of the design point rated flow rate in this embodiment). Because the flow field is prone to violent oscillations or even local backflow during the initial transient phase of CFD calculations, the instantaneous inlet flow rate's mass flow rate spatial integral value... There is a risk of singularity when the denominator approaches zero. This can be addressed by introducing a logic for comparing the maximum value of the denominator. The system can truncate this risk of division by zero, ensuring the underlying robustness of the algorithm framework. Based on this logic, when the system detects... When the efficiency of the CFD simulation model stabilizes within 0.1% for multiple consecutive iterations (e.g., 100 consecutive steps), and the overall isentropic efficiency and total pressure ratio parameter fluctuation rate of the compressor are both less than 0.05%, the current CFD simulation model can be comprehensively judged to have reached a stable convergence state. The technical purpose of this joint judgment is to ensure that the acquired flow field data not only converges at the numerical mathematical level, but also possesses a high degree of physical realism at the macroscopic aerodynamic conservation level.

[0078] For low-level operations such as assigning specific fluid domain material property parameters, calling low-level constants of turbulence models, and hardware communication mechanisms for multi-threaded parallel computing in simulation software, those skilled in the art can use commercial fluid dynamics simulation software. The basic preprocessing and solver configuration principles are well-known technologies in this field and will not be elaborated here.

[0079] After completing the construction of the high-fidelity CFD calculation model and setting the initial physical boundaries, in order to ensure the physical comparability of samples with different geometric deviations during the performance evaluation stage, it is necessary to introduce an operating condition consistency control strategy. The core technical task of this stage focuses on eliminating the interference caused by the flow channel blockage effect due to geometric deformation on the operating point offset, so that all samples carry out flow field evolution under aligned aerodynamic conditions.

[0080] S204, in this embodiment, an operating condition alignment reference based on equivalent mass flow rate is established. Before specific pressure field adjustment, the corresponding general technical principle is that actual geometric deviations (such as thickening of blade fouling or profile manufacturing errors) will inevitably reduce the flow throat area of ​​the blade passage. If a constant physical outlet back pressure is maintained for all reconstructed samples, the calculated actual flow rate will inevitably deviate significantly from the original design operating point according to the gas dynamic flow characteristics, causing the shock wave structure and boundary layer separation characteristics inside the flow field to lose the lateral comparison reference. Based on the above physical causal relationship, the system extracts the mass flow rate converged under rated operating conditions of the unbiased original design model and defines this value as the target reference flow rate. The physical reason for selecting a specific macroscopic aerodynamic parameter as the locking reference is that the mass flow rate directly determines the inlet velocity triangle and blade leading edge angle of attack state of the multi-stage compressor. This parameter is the most core invariant characterizing the matching relationship between the actual working load and the airflow inside the compressor.

[0081] After establishing the equal flow rate alignment benchmark, the system needs to establish a dynamic feedback adjustment mechanism for the outlet static pressure, thereby forcing the CFD solver to approach the target operating point.

[0082] S205, as a preferred approach, employs a proportional-integral (PI) control algorithm to update the outlet backpressure boundary conditions in real time during the iterative solution process. The physical meaning of the corresponding control logic is: treating the current flow rate deviation as a system error signal, dynamically changing the downstream flow resistance to reshape the reverse pressure gradient of the entire flow channel, and thus adjusting the flow capacity to match the preset target. For each iteration step, the system initially extracts the current actual outlet mass flow rate. With target mass flow The absolute difference, and divide it by The term is used to calculate and obtain the dimensionless normalized flow error signal. The division term is subject to an underlying maximum value function limiting logic (where...). It is a preset non-zero reference lower limit protection value, used to ensure the absolute safety of division operations when the flow field is violently oscillating.

[0083] After obtaining the error signal, the back pressure update for the next iteration is calculated using a PI feedback mechanism. To avoid accumulated deviations from compromising the well-posedness of the flow field boundary, the corresponding control action output formula is as follows:

[0084] ;

[0085] In the above formula, Representing the Normalized mass flow error for each iteration step, superscript Represents the current iteration number of the numerical solution; Representing the The physical outlet static pressure updated after each iteration step; Representing the The current outlet static pressure in each iteration step; This represents the minimum absolute physical back pressure threshold preset by the system. and These represent the dimensionless proportional control coefficient and integral control coefficient, respectively.

[0086] To address the numerical divergence problem unique to aerodynamics, the aforementioned boundary update action is supplemented with an output limiting algorithm at its underlying level. This is because the purely mathematical integral term... During the initial oscillation phase, integral saturation may occur. Excessive negative errors can cause the calculated backpressure to become negative, leading to a non-physical collapse of the partial differential equations. The system incorporates maximum value comparison logic during computation; if the iterative backpressure is determined to be below the design lower limit, the outlet static pressure is forcibly reset to [the specified value]. This is used to maintain a positive pressure state within the fluid domain. In this embodiment, The preferred value range is between 1000 and 5000. The optimal value range for this parameter is between 10 and 100. The determination of these parameter values ​​is based on balancing the dynamic response tracking speed of back pressure regulation with the numerical stability of the flow field partial differential equation calculation, to avoid non-physical pressure fluctuations in the flow field caused by sudden changes in back pressure or to cause the solver to diverge.

[0087] After dynamic back pressure regulation is performed, the system must perform multi-dimensional convergence determination of the operating condition approximation state to confirm that the flow field is indeed stable within the target aerodynamic constraint environment.

[0088] S206, constructing a joint judgment logic based on flow deviation and back pressure fluctuation rate. Considering that a single step's transient flow rate compliance cannot confirm the establishment of a stable aerodynamic equilibrium in the entire fluid computation domain, the system's judgment output refuses to rely solely on instantaneous extreme values. In specific execution, the system not only requires the absolute flow error rate of the current iteration step to decrease to a set threshold (e.g., no higher than 0.1%), but also continuously monitors the relative change rate of the outlet back pressure within a consecutive preset window number of steps (e.g., 200 consecutive steps). Only when the root mean square value of the determined outlet back pressure fluctuation decays to below 0.05%, and the interstage characteristic parameters of the transition-stator interface (e.g., the total pressure recovery coefficient) no longer exhibit monotonically drift, can the system comprehensively determine that the current sample has successfully aligned to the target operating condition. The technical purpose of the above multi-dimensional weighted judgment logic is to eliminate local limit cycle oscillations occurring during PI control adjustment, ensuring that the extracted steady-state flow field data strictly corresponds to the same aerodynamic operating line, thereby providing a clean data source for subsequent performance degradation evaluation.

[0089] For the low-level operations of dynamically updating pressure boundaries in numerical solvers using user-defined functions or built-in macro instructions, those skilled in the art can accomplish this using the secondary development interfaces of conventional commercial CFD software. The corresponding control loop mounting and iterative communication mechanisms are well-known technologies in this field and will not be elaborated upon here.

[0090] After confirming that all geometric deviation samples have reached physical convergence under the target reference flow rate, the system enters the stage of extracting and building a database of aerodynamic response data. The core technical objective of this stage is to transform the discrete three-dimensional flow field solution results into a structured set of macroscopic performance and microscopic flow field features, thereby providing high-quality training samples with physical causal relationships for subsequent construction of data-driven models.

[0091] S207, In this embodiment, macroscopic aerodynamic performance parameters and local flow field microscopic features are extracted simultaneously from the fluid computational domain. The extraction of local flow field microscopic features specifically refers to extracting the Mach number distribution, static pressure distribution, and entropy increase distribution fields of key spanwise sections (e.g., 10%, 50%, and 90% relative blade height). The technical purpose is to provide downstream models with a quantitative characterization of the shock wave location and boundary layer separation intensity within the blade passage. The corresponding general technical principle for extracting macroscopic aerodynamic parameters is that geometric fouling of compressor blades not only leads to a decrease in overall work capacity, but the resulting boundary layer thickening and intensified wake mixing also leave specific spatial distribution characteristics within the three-dimensional flow channel.

[0092] Based on the aforementioned physical causal mapping, the system extracts the compressor's total pressure ratio and isentropic efficiency as macroscopic response labels for each converged sample. Simultaneously, to support robustness assessment of the entire envelope, the system automatically triggers a backpressure incremental approximation program for each geometric sample after convergence at the target reference flow rate. This program gradually increases the outlet static pressure with preset small pressure steps (e.g., 500 Pa) until the numerical solver detects low-frequency oscillations in the global mass conservation deviation rate and a sharp drop in efficiency. This point is marked as the numerical stall point. The system extracts the total pressure ratio and mass flow rate corresponding to this stall point and, combined with the data from the aforementioned target reference point, calculates the available surge margin for that sample geometry, simultaneously storing it as a macroscopic aerodynamic response label in the database. The physical rationale for choosing total pressure ratio, isentropic efficiency, and available surge margin as core output parameters is that they directly characterize the compressor's effectiveness in doing work on the airflow and the degree of irreversible energy dissipation in the energy conversion process.

[0093] Given that isentropic efficiency is a well-known parameter in gas dynamics, its extraction logic is directly and formally defined as follows: The ratio of the area-weighted average absolute total pressure of the outlet and inlet sections of the computational domain is calculated by performing an isentropic exponent power operation (specifically, subtracting one from the isentropic exponent and then dividing by the isentropic exponent), and subtracting a constant of one, yields the ideal work numerator. Simultaneously, the ratio of the absolute total temperature of the corresponding sections is subtracted from the constant of one to obtain the actual work consumption denominator. Dividing the two yields the overall isentropic efficiency of the sample under the corresponding operating conditions. Considering the physical nature of the compressor as a work-consuming machine, the airflow is compressed and dissipated by viscous friction during actual operation, and the outlet total temperature is usually greater than the inlet total temperature under normal operating conditions. However, in the underlying logic of automatic data extraction, to prevent singularities caused by non-converged divergent samples, the system forcibly introduces non-isothermal verification logic: when the detected absolute total temperature difference is less than a preset small positive threshold, the sample is automatically marked as invalid and removed, thereby preventing division-by-zero overflow errors at the algorithm level.

[0094] After the extraction of the original feature data is completed, in order to avoid gradient interference from different physical dimensions to downstream algorithms, the multi-source flow field data must be standardized.

[0095] S208, as a preferred approach, employs a standardization algorithm to scale the feature dataset. The physical significance of data cleaning and scaling lies in the fact that aerodynamic variables often span multiple orders of magnitude (e.g., total absolute pressure reaches the order of hundreds of thousands of Pascals, while isentropic efficiency is between 0 and 1). If the original dimensions are directly used for joint evaluation, parameters with large numerical scales will completely mask the influence weights of small changes on model evolution. Regarding the first... For each aerodynamic response feature, the system performs a normalization mapping based on the global sample distribution. Since this mapping operation contains underlying singularity protection constraints and constitutes core security logic in data processing, its corresponding feature scaling formula is as follows:

[0096] ;

[0097] In the above mathematical operations, Representing the The sample after scaling Dimensionless response eigenvalues; This represents the corresponding original atmospheric physical quantity measurement value; and These represent the statistical mean and standard deviation of this feature across the entire sample set, respectively. To overcome the division-to-zero overflow caused by a small standard deviation due to the high concentration of the sample set, a maximum value boundary constraint function is forcibly introduced at the system's underlying level. ,in This represents a preset small constant tolerance for preventing singularities (preferably set to 10 in this embodiment). −6 The implementation of this protection logic ensures the numerical robustness of matrix operations.

[0098] After data cleaning and feature scaling, the system enters the assembly stage of the structured dataset.

[0099] S209 establishes the mapping alignment logic between multidimensional geometric parameter features and the normalized aerodynamic response matrix. During the specific assembly and execution, the system strictly adheres to the simulation task's timestamp and unique identifier, horizontally concatenating the previously verified compliant geometric deviation parameter row vectors with the aerodynamic response feature column vectors extracted in the preceding steps. In this data fusion process, the system simultaneously performs operational condition alignment verification, eliminating invalid data points where the actual flow rate deviates from the target reference flow rate by more than a predetermined tolerance (e.g., 0.5%) due to convergence oscillations. Through the above alignment and filtering mechanisms, the system ultimately outputs a structured database matrix. This database fully defines the mapping relationship for supervised learning: using multidimensional parameter vectors covering the thickening start positions and maximum thickening intensity of each spanwise section as input features. The corresponding macroscopic aerodynamic decay index and microscopic flow field distortion characteristics are used as output labels. This explicit definition of data dimensions has the direct technical purpose of serving as a training data foundation for the subsequent construction of deep neural network models, providing a high-fidelity mapping basis from multidimensional geometric deformation to complex aerodynamic responses.

[0100] For the underlying operations of encapsulating specific data tables, scheduling parallel read and write operations, and automatically imputing missing values ​​in the backend server or distributed storage cluster using structured query language, those skilled in the art can call conventional database management systems and data science toolkits to complete these tasks. The corresponding data flow tracking and heterogeneous storage media mounting are well-known technologies in this field and will not be elaborated here.

[0101] Based on the structured high-fidelity aerodynamic response database constructed in the aforementioned steps, the system enters the architecture design and parameter configuration stage of the data-driven proxy model. The technical objective of this stage is to use deep neural networks to replace the computationally expensive traditional CFD solver, establishing a direct nonlinear mapping relationship from multidimensional geometric deviations at the input end to aerodynamic performance degradation at the output end, thereby providing a predictive tool with engineering real-time capabilities for subsequent rapid performance evaluation and uncertainty quantification.

[0102] S301, in this embodiment, the overall structure type and input / output interface mapping definition of the proxy model are established. Considering the high-dimensional nonlinearity and parameter coupling properties of aerodynamic flow field characteristics, as a preferred approach, the system adopts a deep residual network based on a fully connected topology to construct the main architecture. Before configuring specific data interfaces, the corresponding general technical principle is that neural networks require clearly defined perception boundaries to extract physical laws. The system directly reads the normalized database matrix generated in the previous stage and divides the row vectors representing the geometric parameters characterizing the blade thickening position and intensity into the model's input feature vectors. (For example, the dimension is set as) Simultaneously, the total pressure ratio, isentropic efficiency, and key cross-section flow field distribution feature column vectors, which are strictly aligned with these parameters, are divided into output target labels for the model. (For example, the dimension is set as) The purpose of this end-to-end mapping configuration is to enable hidden nodes within the neural network to autonomously extract the hidden fluid dynamics laws governing aerodynamic losses induced by geometric deformation during training, thereby reducing reliance on manual empirical formulas.

[0103] After defining the model interface, it is necessary to design the hierarchical connections and forward propagation mechanism within the network to ensure the depth of feature extraction and the stability of gradient signals.

[0104] S302, constructing a residual block structure containing multi-layer perceptual units and cross-layer identity mappings. Conventional deep feedforward networks are prone to gradient vanishing during backpropagation, leading to ineffective parameter updates near the input layer. To overcome this algorithmic limitation, the system introduces skip connection paths between adjacent hidden layers. Considering the feature extraction and dimensionality reduction operations in deep networks, direct addition would cause dimension mismatch errors in matrix operations; therefore, the system embeds a linear projection transformation in the identity mapping. Since this transformation determines the reconstructing path of the feature matrix, its corresponding... The core mathematical transfer logic of each residual feature extraction unit is as follows:

[0105] ;

[0106] In the formula expression, Representing the The feature column vectors output by each residual block; This represents the input feature column vector of the previous layer; This represents the neuron connection weight matrix of the current layer; This represents the corresponding bias vector; Represents a non-linear activation function; The representative dimension-matching projection matrix degenerates into an identity matrix when the input and output dimensions are the same, performing a pure identity mapping. In the feature matrix multiplication operations described above, to prevent the feature variance from exponentially diverging or shrinking with increasing layer number during network initialization, the system adjusts the neuron connection weight matrix... A He normal distribution initialization strategy based on adaptive adjustment of the number of input and output neurons is adopted to ensure the approximate orthogonality and full rank of the initial parameter matrix.

[0107] For nonlinear activation functions The system incorporates a modified linear unit with leakage parameters. This function maintains a relatively small positive slope (e.g., set to 0.01) when handling negative inputs. Its underlying technical purpose is to prevent neuron inactivation caused by nonlinear truncation and maintain consistent update activity of the entire network parameters under the dynamic distribution of multiple flow field conditions.

[0108] After completing the network topology construction, the error measurement benchmark and weight optimization iterative algorithm for supervised learning are set.

[0109] S303 configures a joint loss function with regularization constraints and initiates adaptive training based on historical gradient momentum. Due to the high cost of acquiring high-fidelity CFD samples and the limited size of available training datasets, optimizing solely based on prediction errors can easily lead to overfitting to specific discrete samples. Therefore, the system constructs an overall loss function with a penalty mechanism. The loss function is logically defined as: for the data contained in a single training batch... For the nth sample, first calculate the model for the nth sample. Aerodynamic response prediction vector obtained from forward inference of samples With the corresponding real physical label vector The L2 norm squared of the absolute deviation between the values ​​is calculated, and the mean squared error of the batch is obtained. Subsequently, a model complexity penalty term is forcibly concatenated, which constitutes the set of neural network parameters. All trainable weights The sum of squares and the weight decay coefficient The product of. In this configuration, the weight decay coefficient. (In this embodiment, it is preferably set to 10) −4 It controls the strength of the penalty term and forcibly limits the absolute magnitude of the hidden layer weights, thereby improving the physical generalization ability of the surrogate model when facing unseen geometric deviations.

[0110] The gradient is calculated based on the aforementioned loss function, and the neural network parameter set is updated. At this time, the system employs the Adam adaptive moment estimation algorithm. This algorithm requires dividing by the square root of the second moment of the gradient history when calculating the update step size. To strictly prevent the division-to-zero overflow crash path caused by the gradual flattening of the gradient region in the later stages of training, a constant fine-tuning factor is forcibly added to the denominator of the underlying division. (Set to 10) −8 To ensure the comprehensiveness of model evaluation, the convergence determination of the output results avoids relying solely on a single extreme value. When the system detects the overall loss function on the validation set... When the training of the surrogate model stops decreasing after a series of preset rounds (e.g., 50 iterations) and the average absolute error of the predicted isentropic efficiency falls back to within the engineering tolerance zone (e.g., 0.2%), the training can be considered to have converged. Then the network weight structure file is frozen and exported.

[0111] For the underlying operations of calling the underlying tensor computation graph, configuring the backpropagation chained differentiation algorithm, and performing large-scale parallel matrix multiplication using a graphics processing unit cluster in a deep learning computing framework, those skilled in the art can use existing open-source deep learning platform libraries to complete them. The specific software environment depends on the hardware-driven communication mechanism, which is a well-known technology in the field and will not be elaborated here.

[0112] After determining the basic network architecture and loss function configuration of the surrogate model, the system enters the model training and hyperparameter dynamic optimization phase. The technical task of this phase is to locate the optimal network computational parameter configuration through an adaptive search algorithm, driven by a limited number of high-fidelity aerodynamic samples, to avoid overfitting and local minima during deep training.

[0113] S304, in this embodiment, the dataset is independently partitioned and preloaded in micro-batches. Before implementing specific batch data feeding, the general technical principle is that the generalization ability of a neural network needs to be unbiasedly evaluated on a data distribution independent of the training phase; mixed and overlapping samples will lead to distorted model performance evaluation. The system reads the normalized aerodynamic response database matrix and uses a proportionally randomized non-reset sampling algorithm to divide the full set of samples into training, validation, and test sets (e.g., allocated in an empirical ratio of 7:2:1). To alleviate the pressure on computing devices and ensure the random exploration capability of gradient descent trajectories, the system establishes a micro-batch data encapsulation mechanism. High-dimensional geometric input features and aerodynamic response labels are synchronously sliced ​​and packaged into data blocks of fixed sample size (e.g., 64 samples), which are then injected into the model input interface in tensor form.

[0114] After defining the data flow channels, the prediction accuracy of the proxy model is highly dependent on the joint configuration space of the model hyperparameters.

[0115] S305, as a preferred approach, employs a Bayesian optimization algorithm to adaptively optimize the initial learning rate, the number of hidden layer nodes, and the regularization decay coefficient. For the hyperparameter search space configuration, the system predefines clear optimization boundaries; for example, the initial learning rate range is set to

[10] . −5 10 −2 The number of hidden nodes in a single layer is set to [32, 512], and the regularization decay coefficient is set to

[10] . −6 10 −3 The physical significance of this algorithm in engineering dimensions lies in: using Gaussian processes to model the posterior probability of the unknown target loss function, and reducing the ineffective computational cost in high-dimensional space by balancing the exploration of unexplored parameter regions with the utilization of known high-potential regions. The system sets the Bayesian optimization decision acquisition function as a confidence upper bound. Since this function directly constrains the sampling coordinates of the next hyperparameter combination, and given that confidence upper bound calculation is a routine operation in the field of Bayesian optimization, the system solidifies its core logic as follows: for a specific hyperparameter combination vector... Extract the expected mean of the Gaussian process model's predicted loss value for the validation set under this combination. and compared with the prediction standard deviation and dimensionless confidence weighting coefficient The product of these products is summed to obtain the evaluation scalar value of the acquisition function. .

[0116] In the above logical mapping, the prediction standard deviation It is mainly used to quantify the cognitive uncertainty of the current parameter space region. In this embodiment, The optimal value range for this parameter is between 1.5 and 2.5, determined by balancing the optimization accuracy in local regions with the probability of escaping local optima. To address the matrix singularity collapse risk inherent in Gaussian process inference, when dense sampling leads to a high degree of overlap in local hyperparameter sample points, the internal covariance matrix tends to be ill-conditioned. The system forcibly introduces anti-singularity correction logic during the underlying kernel matrix operation, i.e., adding a small positive definite jitter noise term (e.g., set to 10) to the diagonal of the covariance matrix. −6 ), which is used to ensure that the inversion operation has strict full-rank non-singularity.

[0117] After locking in a better combination of hyperparameters using Bayesian optimization, the system starts formal deep learning iterative computation.

[0118] S306, Constructing a dynamic learning rate annealing and multi-dimensional sliding window-based early stopping control strategy. A fixed learning step size can easily lead to high-frequency pulsation of network weights near their optimum in the later stages of training. Based on the aforementioned numerical optimization principles, the system configures a cosine annealing learning rate decay mechanism to smoothly reduce the weight update step size over the iteration cycle. Simultaneously, the system monitors the mean squared error trend of the surrogate model on the validation set in real time. Considering the random fluctuations in single validation errors caused by small perturbations in the flow field characteristics under various operating conditions, the output result determination avoids relying on the extreme value of a single validation cycle. Specifically, the system establishes a historical sliding window containing a preset number of steps and dynamically calculates the moving average of the validation set error within this window. When the moving average no longer shows a decreasing trend, or the L2 norm of the current weight gradient decays to a preset zero-point tolerance boundary (e.g., below 10), the system stops the error. −7 Only when the system can trigger the early stop truncation command comprehensively. The technical purpose of this multi-dimensional joint truncation logic is to avoid overfitting the model to the inherent data noise of the training set, and to ensure the engineering generalization effectiveness of the derived weights, while ensuring that the network nodes fully absorb the mapping law of geometric deformation and aerodynamic decay.

[0119] For the underlying operations of deploying distributed computing containers in cloud computing nodes, configuring hyperparameter search space dimensional boundaries, and saving model breakpoint training state, those skilled in the art can accomplish these tasks using mature automated machine learning hyperparameter tuning frameworks. The corresponding computing resource scheduling protocols and parallel communication mechanisms are well-known technologies in this field and will not be elaborated upon here.

[0120] See attached document Figure 6 With appendix Figure 7 After completing the architecture construction and weight parameter solidification of the proxy model, the system enters the stage of large-scale performance uncertainty quantification evaluation. The technical objective of this stage is to use the trained and converged deep neural network to map the random geometric uncertainty of upstream manufacturing tolerances or operational fouling into the probability distribution characteristics of downstream macroscopic aerodynamic performance degradation, with the computing power overhead of engineering real-time performance.

[0121] S401, in this embodiment, a random geometric deviation input matrix covering the entire design space is constructed. Before generating specific samples, the corresponding general technical principle is that the actual geometric variation of compressor blades usually follows a specific statistical distribution (e.g., normal distribution or Weiber distribution), and relying solely on a small number of marginal extreme conditions cannot reflect the overall performance degradation probability of mass production or long-term service. As a preferred method, the system uses the Latin hypercube sampling algorithm to generate a preset size (e.g., 10) based on preset mean and variance parameters. 5 A geometric parameter row vector (on the order of magnitude of...). To avoid the sampling algorithm generating out-of-bounds anomalous samples that deviate from the actual physical reality of fluid dynamics in the tail region, the system introduces a layer based on... The criterion employs a boundary truncation mechanism. When the generated random parameters deviate from the mean by more than three standard deviations, they are automatically mapped back to the truncation boundary, thereby ensuring the physical validity of the multidimensional input tensor.

[0122] After defining the boundaries of the random parameters, the system enters the batch prediction stage of performance parameters.

[0123] S402, perform forward inference based on the deep proxy model. The system directly injects the previously generated large-scale random geometric parameter matrix into the fixed neural network interface. Utilizing the large-scale parallel matrix multiplication operations of the graphics processor, the system can output the corresponding dimensionless isentropic efficiency and total pressure ratio prediction label column vectors. To ensure the prediction results can be aligned with subsequent engineering physics judgment thresholds, the system calls the statistical averages of the aerodynamic characteristics in each dimension saved during the data preprocessing stage (S208). The aforementioned dimensionless prediction vector is subjected to a reverse algebraic mapping operation (i.e., the predicted value is multiplied by the standard deviation and then averaged) to accurately restore it to physical parameters such as isentropic efficiency, total pressure ratio, and surge margin with real thermodynamic dimensions. Compared with traditional numerical solutions for three-dimensional viscous flow fields, this end-to-end data-driven inference mode bypasses the complex grid space discretization and partial differential equation iteration process. Its direct technical purpose is to provide a large data source with physical mapping basis for subsequent probabilistic statistical analysis.

[0124] After obtaining the batch prediction results, a continuous probability distribution model must be established to extract robust reliability indicators.

[0125] S403, based on the kernel density estimation algorithm, constructs the probability density function for aerodynamic performance degradation. The corresponding statistical distribution visualization results are shown in the attached figure. Figure 6 With appendix Figure 7 As shown. Specifically, attached Figure 6 The figure shows the statistical distribution of isentropic efficiency, where the horizontal axis represents efficiency and the vertical axis represents frequency. and These represent the distribution mean of the actual isentropic efficiency of the 1.5-stage compressor and the distribution mean of the actual isentropic efficiency of the blades, respectively. and These represent the deviations between the design point efficiency of the 1.5-stage compressor and its corresponding distribution mean, and the deviations between the design point efficiency of the blade and its corresponding distribution mean, respectively. Similarly, see Appendix... Figure 7 The graph shows the statistical distribution of total pressure ratio, with the horizontal axis representing pressure ratio and the vertical axis representing frequency. and These represent the average distribution of the actual total pressure ratio of the 1.5-stage compressor and the average distribution of the actual total pressure ratio of the blades, respectively. and These represent the deviations between the design total pressure ratio of the 1.5-stage compressor and its corresponding distribution mean, and the deviations between the design total pressure ratio of the blades and their corresponding distribution mean, respectively. Considering that discrete prediction scatter points cannot intuitively reflect the degradation trend and aggregation trend of performance parameters, the system performs a continuous smoothing mapping on the output aerodynamic labels. The core mathematical logic of this mapping operation is: for specific aerodynamic performance indicators... (e.g., isentropic efficiency assessment value), its probability density scalar value The process of obtaining the total number of samples in the Monte Carlo sampling is as follows: For each sample, calculate specific aerodynamic performance indicators. Predicted label corresponding to this sample The algebraic difference between them; divide this difference by the bandwidth parameter. Then, input a non-negative smoothing kernel function. (In this embodiment, a standard Gaussian kernel function is preferred) calculate the single-point probability weight; then, sum the probability weights of all samples and divide the sum by the total number of samples. With bandwidth parameters The product of these factors is used to obtain the smoothed probability density value.

[0126] In the aforementioned underlying division operation and kernel function mapping, to prevent bandwidth parameters If the value is too small, a division-by-zero overflow and divergence crash will be triggered, and the system will forcibly remove all bandwidth parameters used as the denominator. Replace with maximum boundary constraint function ,in This represents a preset positive definite small tolerance (e.g., set to 10). −5 This bandwidth limiting protection logic rigorously ensures the numerical stability of the algorithm when processing highly concentrated data clusters. Simultaneously, it addresses bandwidth parameters. The determination of the metric is based on the fact that setting it too large will mask the local characteristics of the distribution, while setting it too small will lead to non-physical spurious oscillations in the curve. As a preferred approach, the system uses the Silverman rule for adaptive solution, which is based on the minimum value of the standard deviation of the sample set and the interquartile range, combined with the total number of samples. The optimal smoothing scale was calculated.

[0127] Based on the constructed continuous probability density function, the system further extracts multi-dimensional statistical characteristic indicators of aerodynamic performance degradation. Specifically, the system determines the one-sided confidence lower bound of performance at a preset probability level (e.g., 95%) through inverse function integration, used to quantitatively assess the compressor's performance baseline under harsh service conditions. Given that statistical mean and variance are known characteristic parameters, their extraction logic is directly formalized as follows: algebraically sum the predicted performance labels of all Monte Carlo samples and divide by the total number of samples to obtain the expected mean of performance degradation; simultaneously, calculate the sum of squares of the differences between each sample's predicted value and the expected mean, and then divide by the total number of samples to obtain the variance parameter reflecting the dispersion of performance fluctuations. In the final engineering judgment stage, the system comprehensively considers the degradation magnitude of the expected mean, the expansion ratio of the variance, and the shift of the confidence lower bound to perform a multi-dimensional joint judgment on the compressor's aerodynamic robustness. This joint judgment mechanism overcomes the one-sidedness of traditional engineering design that relies solely on single sample extreme values ​​or a single nominal model for evaluation, providing a comprehensive quantitative basis for the compressor's structural optimization design.

[0128] The low-level operations of calling statistical analysis toolkits, configuring sampling pseudo-random number generator seeds, and outputting visualized probability distribution cloud maps in engineering calculation software can be accomplished by those skilled in the art using conventional reliability analysis platform frameworks. The mechanisms for mounting library files and allocating video memory for the corresponding basic statistical functions are well-known technologies in the field and will not be elaborated upon here.

[0129] See attached document Figure 8 After completing the large-scale aerodynamic performance uncertainty quantification, the system enters the sensitivity analysis and key feature extraction stage. The technical objective of this stage is to analyze the input-output dependency relationship in the nonlinear mapping process of the deep neural network, quantify and decompose the overall performance degradation and attribute it to independent input geometric deviation variables, thereby providing clear optimization directions for the anti-fouling or anti-deformation structural design of compressor blades.

[0130] S404, In this embodiment, a local sensitivity attribution architecture based on feature marginal contributions is constructed. Before conducting specific attribution calculations, the corresponding general technical principle is: multidimensional geometric parameters (such as the thickening initiation position, maximum contamination intensity, etc.) have complex physical coupling effects when influencing the three-dimensional flow field, and conventional single-variable control methods cannot isolate the interaction weights between parameters. As a preferred approach, the system introduces the Shapley and interpretation algorithms to rigorously decompose the output deviation of the surrogate model for a specific sample into the algebraic sum of the independent contributions of each input feature. Its core mathematical mapping logic is as follows:

[0131] ;

[0132] In the above joint calculation formula, Representing the The geometric feature variable for the first The local marginal contribution scalar value generated by the aerodynamic performance (such as isentropic efficiency) of each predicted sample; The set representing the geometric feature variables of the entire input. This represents the total number of feature dimensions contained in the set; This represents removing the first feature from the full set of features. Any subset formed after considering a feature This represents the number of feature dimensions for that subset. This represents the predicted output function of the deep proxy model given a subset of features as input. Considering that high-dimensional input features lead to an exponential increase in computational complexity for the aforementioned permutation subset traversal, the system employs the DeepSHAP approximation algorithm optimized for deep learning networks as a specific lower-level feature implementation. This algorithm, combined with the backpropagation rules within the network, approximates the theoretical marginal contribution value in polynomial time by comparing the differences in neuron activation between the input sample and the reference baseline sample, thus ensuring the computational feasibility of high-dimensional feature attribution in engineering.

[0133] In the above factorial division operation and approximate solution, the denominator term The value of is directly determined by the system's preset input feature dimension. To avoid division by zero overflow, the system sets a lower bound on the dimension of the input tensor during the interface data verification process, i.e., prohibiting the input of completely empty or single-dimensional feature matrices (ensuring...). This ensures the strict computability of the combined weight coefficients. The physical meaning of this formula is that by traversing the feature combination benchmark, the sequential dependency when the model extracts patterns is eliminated, thus achieving unbiased allocation of feature weights.

[0134] After obtaining the local sensitivity mapping of a single sample, the system initiates global importance fusion extraction across operating conditions.

[0135] S405 performs global expectation aggregation on the discrete local sensitivity values ​​of multi-source samples. Since the sensitivity of a single sample only reflects the flow field response under a specific combination of geometric deformations and cannot support macroscopic engineering design guidance, the system targets the full range of test samples (scale set to...). Extracting global feature importance Given that global feature aggregation is a well-known statistical operation, the core mathematical logic of this aggregation operation is directly and explicitly stated as: traverse all features in the test sample set. Extracting the nth predicted sample respectively The local marginal contribution scalar values ​​corresponding to each geometric feature variable Then calculate its absolute value; after algebraically summing the above absolute values, divide the whole by the maximum value limiting term. This allows us to derive the global feature importance of that feature. .

[0136] In the aforementioned division mechanism, the purpose of introducing absolute value operations is to prevent the physical cancellation of positive and negative aerodynamic effects (e.g., one deformation leading to efficiency improvement while another leads to efficiency decrease) during algebraic accumulation. Simultaneously, to prevent zero-division without samples errors caused by abnormal test set slicing, a maximum value limiting constraint is forcibly implanted in the denominator. middle, The preset positive definite tolerance parameter (preferably set to a constant 1 in this embodiment) ensures that the aggregation algorithm maintains the non-singular state of the underlying values ​​even in extreme data loss situations.

[0137] Based on the above quantitative attribution, the system synchronously establishes verification alignment logic with the experimental testing system.

[0138] S406, combined with appendix Figure 8 The comparison chart showing the analysis results demonstrates how the system comprehensively assesses the output sensitivity indicators from an engineering perspective. Specifically, during execution, the system extracts the marginal contribution values ​​of core features, including pollution intensity and initiation location, and compares them with the results of single-blade aerodynamic blowing experiments and real-world bench experiments with a 1.5-stage compressor. Figure 8 As can be seen from the two sets of column distributions, whether in the blade experiment results where the rotor-stator interference effect is weak or in the 1.5-level experiment results where the multi-row interference is strong, the global importance corresponding to the pollution intensity shows the main numerical order.

[0139] Based on the selection and judgment criteria of the above output results, the system establishes an explanation mechanism based on physical causality to avoid simply relying on data extreme values. The contamination intensity on the compressor blade surface directly changes the effective flow area of ​​the blade channel and causes the shock wave structure to move forward, resulting in a nonlinear amplification of the aerodynamic blocking effect. In contrast, the initial position only determines the development length of boundary layer thickening, and its excitation effect on wake mixing and dissipation is a secondary influence. Based on this multi-dimensional correlation logic, the system finally outputs a joint judgment conclusion: in the subsequent compressor robustness modification design and maintenance cleaning cycle scheduling, higher dimensional and positional tolerance control weight and monitoring priority must be given to the region with the highest contamination intensity.

[0140] For the underlying execution logic of rendering distribution maps by calling drawing libraries, configuring multi-threaded call mechanisms for test cases, and mounting physical experiment result verification databases in data visualization terminals, those skilled in the art can implement it using conventional data science analysis toolkits. The corresponding underlying driver mounting and distributed scheduling thread synchronization are well-known technologies in this field and will not be elaborated upon here.

[0141] In conjunction with the aforementioned appendix Figure 8 The compressor geometric deviation parameter sensitivity analysis results shown indicate that after key feature extraction, the system enters the engineering guidance and strategy feedback stage. The technical objective of this stage is to transform the performance uncertainty and local sensitivity attribution conclusions quantified by the deep proxy model into specific engineering constraint commands for compressor manufacturing, operation, maintenance, and modification design, thereby achieving aerodynamically robust closed-loop control.

[0142] To achieve the above closed-loop control, in this embodiment, S407, a non-uniform distribution mechanism for manufacturing tolerances based on feature importance is constructed.

[0143] Before implementing specific tolerance allocation, the general technical principle is that traditional uniform tolerance allocation strategies can lead to excessive manufacturing costs due to imposing excessively high processing requirements on non-sensitive geometric areas, while simultaneously resulting in insufficient tolerance constraints in highly sensitive areas. As a preferred approach, this allocation mechanism uses minimizing manufacturing costs as the constraint optimization objective. Considering the positive correlation between cost and the reciprocal of tolerance, the system establishes an algebraic mapping function that is inversely proportional to the corresponding geometric tolerance values, and embeds the aforementioned extracted global feature importance as a penalty weighting coefficient into this function. To prevent the tolerance value from approaching zero during theoretical optimization, which could cause the cost function to diverge and collapse, the system forcibly embeds a positive definite lower bound constraint based on the processing limits of the equipment at the bottom layer (for example, setting the minimum geometric profile tolerance lower limit to 0.01mm based on the processing accuracy of existing CNC machine tools). After the above non-uniform distribution, the system ensures that the lower confidence limit of the overall aerodynamic performance of the compressor meets the design baseline, while appropriately relaxing the machining tolerance of less sensitive geometric areas (such as the starting position of fouling) and strictly tightening the manufacturing boundary of highly sensitive areas (such as the location where the maximum contamination intensity occurs).

[0144] After defining the tolerance boundaries at the manufacturing end, the system synchronously deploys the proxy model to the health management node at the actual operating end. S408 establishes a predictive cleaning and maintenance cycle planning strategy based on multi-dimensional performance degradation trajectories. Addressing performance degradation during compressor service, the system abandons the judgment logic relying solely on a single aerodynamic extreme value and instead adopts a multi-dimensional joint evaluation. Specifically, the system extracts multi-source aerodynamic monitoring time-series data under actual operating conditions. Before data input, considering the inherent differences in physical sampling frequencies among sensors such as speed, pressure ratio, and flow rate, the system performs frequency alignment and linear interpolation preprocessing based on historical time windows to ensure physical synchronization of multi-source input tensors under the same sampling cycle.

[0145] After data synchronization, the system inputs the aligned operating parameter matrix and nominal geometric parameters into the aforementioned deep proxy model with solidified weights to obtain the performance degradation prediction value under the current service state. When executing the cleaning work order trigger judgment, the system comprehensively evaluates the degradation bias of isentropic efficiency and the reduction ratio of available surge margin. As a preferred approach, when the predicted isentropic efficiency decreases relative to the initial baseline by more than a preset efficiency tolerance threshold (e.g., 1.5%), or when the current available surge margin approaches a preset stall margin threshold (e.g., below 12%), the system comprehensively triggers a predictive cleaning and maintenance command. The implementation of this joint judgment mechanism shields against false alarms caused by single-parameter transient measurement noise, ensuring the physical rationality of the cleaning cycle.

[0146] In addition to guiding manufacturing and operation, the system further implements aerodynamic reverse profile modification design for robust anti-fouling. S409, based on the physical causal relationship between local geometric features derived from sensitivity attribution and flow field blockage effects, the system reverse maps high-sensitivity fouling characteristics to the initial airfoil parameter space. As a specific lower-level feature implementation, the system introduces a thickness distribution compensation mechanism in the compressor blade centerline design stage. For the aforementioned sensitive region that has a major impact on flow field blockage effects (i.e., the area from the blade leading edge to the maximum thickness section), the system appropriately reduces the basic design thickness along the centerline normal and reconstructs the curvature transition spline parameters. The physical significance of this operation is to pre-allocate a flow area margin in the geometric space to accommodate the development of fouling during service. The technical objective of the above strategy is to introduce a controllable, small nominal performance degradation in the early stages of blade service in exchange for a reduction in the expected average aerodynamic performance degradation under severe operating conditions throughout the entire life cycle.

[0147] For the underlying operations of configuring non-uniform tolerance parameters in an enterprise resource planning system, issuing cleaning work order instructions in an equipment maintenance management platform, and updating spline curve control points in computer-aided design software, those skilled in the art can implement these operations by calling conventional industrial production management software and 3D modeling interfaces. The corresponding underlying database read / write and application programming interface communication are well-known technologies in this field and will not be elaborated upon here.

[0148] In one embodiment, Figure 9 This is a schematic diagram illustrating the decrease in available surge margin and changes in flow field stability recorded by the system described in this invention under a specific scenario where a multi-stage compressor experiences prolonged and harsh service conditions (such as continuous fouling buildup on the blade surface). The diagram is a two-dimensional coordinate graph, with the horizontal axis representing the cumulative service time of the compressor. The vertical axis represents the core parameter characterizing the global aerodynamic stability of the flow field, which can be expressed as surge margin. .

[0149] Reference Figure 9 The diagram contains the following elements:

[0150] A horizontal line segment is marked as the stall margin baseline. This line segment represents a preset stall margin baseline that ensures the compressor will not experience rotating stall or deep surge. (For example, it is set at 12% according to engineering specifications).

[0151] A dashed line represents the traditional isolation assessment method. This curve illustrates the change in the predicted available surge margin in a system that does not employ the level-environment coupling mapping algorithm described in this invention, but only performs uncertainty quantification based on a single-row isolated rotor domain. In the early stages of the service life, the value of this dashed line decreases gradually. Even after the geometric deformation parameters accumulate to a high level, its value still evolves with an approximately linear, fixed slope, remaining at the stall margin baseline for a considerable period. The above presents a falsely optimistic expectation that fails to reflect the deterioration of the real three-dimensional flow field.

[0152] A solid line marks the use of the coupled evaluation method of this invention. This curve represents the actual predicted change in available surge margin in a system using the deep surrogate model described in this invention and aligned with multi-row environmental aerodynamic characteristics. In the early stages of service, the numerical evolution trajectories of the solid and dashed lines largely overlap. Near and after time point, accompanied by geometric deviation characteristic parameters (such as maximum thickening intensity) As the sum of these factors increases, the curve exhibits a non-linear, accelerating downward trend, reaching and breaching the stall margin threshold significantly faster than the traditional dashed trajectory. .

[0153] Figure 9 The document also marks two specific time points:

[0154] Time point This indicates that the compressor is at its nominal design service starting point without geometric deviation, meaning the actual airfoil thickness on each spanwise section is equal to the original design airfoil thickness (satisfying...). And the local geometric deviation function The method described in this invention is at the time of [the event / time]. The initial available surge margin recorded at each moment reaches the global maximum value, and this is used as a benchmark to initiate dynamic monitoring of the multidimensional aerodynamic performance degradation trajectory.

[0155] Time point This represents the physical critical moment when the unsteady wake fluctuation of the flow field caused by the accumulated geometric deformation of the upstream rotor blades crosses the rotor-stator mixing interface and undergoes strong aerodynamic interference with the inherent potential flow field of the downstream stator blades. The method described in this invention, after capturing the dramatic change in microscopic local entropy caused by the strong coupling of multiple rows, accurately maps the step-like decay of the macroscopically available surge margin at this moment.

[0156] The figure illustrates that, when addressing the same technical problem of random deviations in blade geometry caused by long-term service, the traditional isolation assessment method (shown by the dashed line) lacks system-level modeling of unsteady interference and error propagation channels between stages. This is particularly problematic after the geometric deviation crosses a critical state. Subsequently, the output was a flat prediction that deviated significantly from physical reality, which could easily lead to sudden and fatal aerodynamic stalls in actual equipment during operation. In contrast, the method of this invention, shown by the solid line, constructs a rigorous multi-row coupling mapping relationship and joint feature importance aggregation in three-dimensional space (i.e., based on global importance scalar values). By identifying core sensitive deformations, the system can accurately capture the global aerodynamic blockage effect amplified by local geometric deviations. When the true margin trajectory (solid line) approaches the safety threshold, the system can issue predictive cleaning and maintenance commands in advance based on accurate time anchors, thereby solving the technical problem that existing technologies cannot quantify the risk of multi-level environmental cascade failures and cause maintenance delays.

Claims

1. A method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation, characterized in that, Includes the following steps: Obtain the original design geometry of the multi-stage compressor, perform CFD simulation calculations to determine the target reference flow rate, extract geometric deviation parameters and sample them to generate a deviation geometry sample set containing multiple deviation geometry samples; For each of the aforementioned deviation geometric samples, CFD simulation calculations are performed in a multi-row environment. By dynamically adjusting the outlet back pressure constraint, each of the aforementioned deviation geometric samples converges under the target reference flow rate, and the corresponding aerodynamic response data is obtained. The geometric deviation parameters are used as input features, and the aerodynamic response data are used as output labels to train the surrogate model. By using the trained surrogate model for random sampling and performance inference, the probability distribution characteristics of the aerodynamic response data are obtained. The global feature importance of each geometric deviation parameter is calculated by combining the sensitivity analysis algorithm, and the core sensitive parameters are output. Based on the core sensitive parameters, the aerodynamic performance boundary and stall risk threshold of the multi-stage compressor blade under operating conditions are determined, thereby realizing the uncertainty quantification evaluation method of blade geometric deviation performance deviation.

2. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 1, characterized in that, The specific steps of obtaining the original design geometry of a multi-stage compressor, performing CFD simulation to determine the target reference flow rate, extracting and sampling geometric deviation parameters, and generating a deviation geometry sample set containing multiple deviation geometry samples include: Establish an unbiased computational domain model of the original design geometry, perform CFD simulation calculations under rated operating conditions, and extract the converged mass flow rate as the target reference flow rate; The geometric deviation characteristics of the blades of the multi-stage compressor are extracted, and the thickening start position and the maximum thickening intensity are used as the geometric deviation parameters. The geometric deviation boundary is set by combining the reference distribution function along the span and the preset floating range. The Latin hypercube sampling algorithm is used to generate an initial set of geometric feature vectors in a multidimensional continuous parameter space, and to remove the abnormal vectors that trigger the singularity of the flow channel blockage, and output a geometric deviation parameter sample space matrix without collinearity redundancy. Based on the geometric deviation parameter sample space matrix, a two-dimensional airfoil with geometric deviation is reconstructed at each spanwise position, and a three-dimensional geometric deviation airfoil is generated by lofting along the stacking line. The three-dimensional geometric deviation airfoil is then assembled with the inlet guide vane and the downstream stator blade to construct a multi-row level solid computational domain model containing real geometric deviation features, thus forming the deviation geometric sample set.

3. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 2, characterized in that, Before performing CFD simulation calculations in a multi-row environment for each of the aforementioned deviation geometric samples, the process also includes a step of generating the computational domain mesh required for the simulation using a spatial mesh deformation algorithm, specifically including: Set the mesh generated from the original design geometry as the baseline mesh topology; For the constructed multi-row level entity computational domain model, the spatial mesh deformation algorithm based on radial basis function is called to use the displacement of the blade surface wall before and after geometric reconstruction as boundary constraints to solve the linear displacement interpolation equation in the flow field domain. While keeping the total number of grid nodes and the connection topology of the reference grid unchanged, the spatial grid nodes are made to migrate smoothly in accordance with the deformation of the blade surface to generate the computational domain grid required for the simulation, and the CFD simulation calculation in the multi-row environment is performed based on the computational domain grid.

4. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 1, characterized in that, The step of obtaining the corresponding aerodynamic response data by dynamically adjusting the geometric samples of each deviation under the target reference flow rate to converge is specifically as follows: During the iterative solution process of the CFD simulation calculation, the outlet back pressure is updated, and the operating condition alignment verification is performed simultaneously. Extract the actual flow rate calculated in the current iteration step of the CFD simulation, and determine the deviation status of the actual flow rate from the target reference flow rate; Remove invalid points where the actual flow rate deviates from the target reference flow rate by more than a predetermined tolerance due to convergence oscillations; Through the above alignment and filtering mechanism, each deviation geometric sample is constrained to converge under the target reference flow rate. The aerodynamic features corresponding to the deviation geometric samples that meet the convergence conditions are extracted and constructed into a column vector, and the column vector is used as the corresponding aerodynamic response data.

5. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 4, characterized in that, The step of constraining the convergence of each of the aforementioned deviation geometric samples under the target reference flow rate further includes constructing a joint determination logic based on flow deviation and back pressure volatility: Based on the spatial integral values ​​of mass flow rate at the outlet and inlet sections of the computational domain, the global mass conservation deviation rate, which includes the maximum value of the denominator and the zero-limiting comparison logic, is extracted. Extract the absolute flow error rate and the root mean square value of the outlet back pressure fluctuation for the current iteration step; When the global mass conservation deviation rate is lower than the first set threshold within a consecutive preset window number of steps, the absolute flow error rate is lower than the second set threshold, the root mean square value of the outlet back pressure fluctuation is lower than the third set threshold, and the interstage characteristic parameters of the transition-static interface do not undergo monotonically drift, it is comprehensively determined that the current deviation geometric sample is aligned to the target reference flow and converges.

6. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 1, characterized in that, The aerodynamic response data includes total pressure ratio, isentropic efficiency, and available surge margin. The specific steps for obtaining the corresponding aerodynamic response data include: For the deviation geometry sample that converges under the target reference flow rate, the total pressure ratio and isentropic efficiency of the compressor are extracted; Trigger the back pressure incremental approximation program, gradually increase the outlet back pressure according to the preset pressure step amount until the numerical stall point is detected, extract the total pressure ratio and mass flow rate corresponding to the numerical stall point, and calculate the available surge margin of the current deviation geometry sample in combination with the target reference flow rate data. The extracted total pressure ratio, isentropic efficiency, and available surge margin are scaled using a standardization algorithm to obtain dimensionless aerodynamic response characteristics. A constant tolerance limit to prevent singularity is inserted into the standard deviation of the denominator in the mapping calculation of the standardization algorithm to complete the acquisition of the aerodynamic response data.

7. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 1, characterized in that, The steps for training the surrogate model, using the geometric deviation parameters as input features and the aerodynamic response data as output labels, specifically include: The proxy model is constructed using a deep residual network based on a fully connected topology. Skip connection paths with linear projection transformation are introduced between adjacent hidden layers to perform identity mapping. The geometric deviation parameters are input into the surrogate model to obtain the prediction vector, and the mean square error of the square of the absolute deviation of the prediction vector is calculated by combining the aerodynamic response data. Configure a joint loss function, which consists of the mean squared error base term and a model complexity penalty term representing the product of the sum of squared trainable weights and the weight decay coefficient, concatenated together. The network computation parameters of the surrogate model are updated using an adaptive moment estimation algorithm, and a constant fine-tuning factor is added to the denominator of the square root of the second moment of the gradient history when calculating the update step size. When it is detected that the joint loss function on the validation set no longer decreases within a preset number of consecutive rounds, and the isentropic efficiency prediction error falls back to the preset engineering tolerance band, an early stop truncation instruction is triggered and the network calculation parameters of the proxy model are frozen, thus completing the training of the proxy model.

8. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 6, characterized in that, The steps of obtaining the probability distribution characteristics of the aerodynamic response data by performing random sampling and performance inference using the trained surrogate model specifically include: Random sampling is performed on the distribution range of the geometric deviation parameters to generate a random geometric parameter matrix; Input the random geometric parameter matrix into the trained surrogate model to obtain dimensionless prediction labels; The feature statistical mean and standard deviation in the standardization algorithm are called to perform a reverse algebraic mapping operation on the dimensionless prediction label to restore it to the aerodynamic response data with real physical dimensions; Based on the kernel density estimation algorithm, a continuous probability density function is constructed for the aerodynamic response data with real physical dimensions. In the probability weight cumulative average division operation of the kernel density estimation algorithm, the denominator bandwidth parameter is replaced with a maximum value boundary constraint function composed of the actual bandwidth and a preset positive definite small tolerance, so as to obtain the probability distribution characteristics of the aerodynamic response data.

9. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 1, characterized in that, The steps for calculating the global feature importance of each of the geometric deviation parameters using the sensitivity analysis algorithm specifically include: An approximate Shapley sum interpretation algorithm optimized for deep neural networks is used to extract the local marginal contribution scalar value of the geometric deviation parameter for the predicted sample; Perform data validation at the algorithm interface, and set the lower bound of the dimension of the input feature tensor to be absolutely greater than or equal to 2. Global expectation aggregation is performed on the local marginal contribution scalar values ​​based on multi-source prediction samples; The absolute values ​​of the local marginal contribution scalar values ​​of each of the geometric deviation parameters are taken and algebraically accumulated. The accumulated result is divided by the maximum value limiting constraint term composed of the total number of test samples and a preset positive definite constant, and the global feature importance is output.

10. The method for quantitatively evaluating the uncertainty of blade geometric deviation performance deviation according to claim 1, characterized in that, The specific steps for outputting core sensitive parameters include: Obtain the output global feature importance, sort the global feature importance corresponding to each geometric deviation parameter in descending order of numerical value, and construct a one-dimensional feature importance sequence; Along the descending direction of the feature importance sequence, calculate the cumulative contribution rate of the local importance corresponding to the current geometric deviation parameter in the total importance of all features; When the cumulative contribution rate reaches the preset cutoff ratio threshold for the first time, the top-ranked multiple geometric deviation parameters covered by the cutoff ratio threshold are extracted, and the multiple geometric deviation parameters are identified as the core sensitive parameters and output. Based on the core sensitive parameters, the aerodynamic performance boundary and stall risk threshold of the multi-stage compressor blade under operating conditions are determined, and finally the uncertainty quantification assessment method of blade geometric deviation performance deviation is completed.

Images