Centrifugal compressor map fitting method based on reference-residual hybrid architecture

Abstract

The application discloses a centrifugal compressor map fitting method based on a benchmark-residual hybrid architecture, belongs to the technical field of compressor performance map fitting, and solves the problems of long modeling period and small sample prone to overfitting. The method comprises the following steps: obtaining performance data, dividing the performance data into a source model data set and a target model data set, and further dividing the target model data set into a target model context reference set and a target model to-be-reconstructed working condition point set; constructing and standardizing a physical derived feature set; training a Gaussian process regression benchmark model by using the standardized source model data set, and obtaining benchmark prediction values of the two; calculating prediction residuals of the target model context reference set, learning a residual mapping relationship by using a pre-trained cross-domain table context reasoner, and correcting the prediction values; after being inversely standardized, monotonically decreasing constraints are applied to pressure ratios, and unimodal smoothing constraints are applied to isentropic efficiencies, so that the reconstructed pressure ratio and isentropic efficiency are obtained, the centrifugal compressor map fitting is completed, and full-working-condition map high-precision reconstruction under sparse data is realized.

Description

Technical Field

[0001] This invention relates to the field of centrifugal compressor performance map fitting and data expansion technology, specifically to a centrifugal compressor map fitting method based on a Gaussian process regression benchmark model, tabular context reasoning residual correction, and hierarchical physical constraint post-processing. This method can be used to reconstruct the pressure ratio, isentropic efficiency, and volumetric flow rate characteristic curves of centrifugal compressors in marine diesel engine turbochargers under sparse test data conditions. Background Technology

[0002] In the aerodynamic design and overall matching process of marine diesel engine turbochargers, the full-condition performance profile of the centrifugal compressor is the core foundational data supporting power system simulation, control strategy development, and fault diagnosis. This profile, using engine speed as a parameter, comprehensively describes the nonlinear mapping relationship between pressure ratio, isentropic efficiency, and volumetric flow rate. Its accuracy directly determines the matching effect between the turbocharger and the diesel engine, the overall fuel economy, and the dynamic response characteristics under varying operating conditions. Especially in high-power marine power plants, the coverage and fidelity of the compressor performance profile are crucial for evaluating the system's operational stability under extreme conditions and predicting surge and blockage risks.

[0003] The traditional main approach to obtaining complete performance profiles is bench testing, but this method suffers from insurmountable engineering bottlenecks. To obtain continuous characteristic curves, tests require point-by-point flow rate adjustments and stable operation at dozens of speed settings to collect data. A complete test cycle for a single compressor typically lasts several weeks, and places extremely high demands on the measurement and control accuracy of the test bench and equipment wear and tear. Due to limitations in testing costs and time, in practice, only 3-5 typical speed profiles can be tested, and each speed profile can only yield 5-8 discrete operating points, resulting in extremely sparse data that cannot directly meet the needs of full-condition simulation and optimization design.

[0004] To fill the gaps in experimental data, the industry commonly employs engineering techniques such as interpolation and similarity theory scaling for data expansion. However, these methods all have significant limitations: linear and spline interpolation can only achieve local smoothing and cannot capture global nonlinear correlations across rotational speeds, easily generating non-physical results that violate fluid dynamics laws; similarity theory scaling, based on the assumption of perfect geometric and flow similarity, struggles to accurately reflect the changing patterns of flow losses at different rotational speeds, with particularly significant errors in efficiency prediction. While traditional machine learning methods can handle nonlinear problems, they require rebuilding models and optimizing parameters for each compressor, resulting in long modeling cycles and a high risk of overfitting and insufficient generalization ability in scenarios with small, sparse data. Summary of the Invention

[0005] To address the issues of long modeling cycles for fitting centrifugal compressor Map diagrams and the tendency for overfitting in scenarios with small, sparse data, this invention provides a centrifugal compressor Map diagram fitting method based on a baseline-residual hybrid architecture.

[0006] The present invention provides a method for fitting a centrifugal compressor map based on a baseline-residual hybrid architecture, comprising:

[0007] The centrifugal compressor's rotational speed, volumetric flow rate, pressure ratio, and isentropic efficiency are acquired as raw performance data. This raw performance data is divided into a source model dataset and a target model dataset. The target model dataset is further divided into a target model context reference set and a target model operating point set to be reconstructed. The target model context reference set includes rotational speed, volumetric flow rate, pressure ratio, and isentropic efficiency, while the target model operating point set to be reconstructed includes rotational speed and volumetric flow rate. A physically derived feature set is constructed based on the rotational speed and volumetric flow rate, and the source model dataset, target model dataset, and physically derived feature set are then standardized.

[0008] Using the standardized source model dataset's rotational speed, volumetric flow rate, and physical derived features as inputs, and the standardized pressure ratio and isentropic efficiency as outputs, a Gaussian process regression benchmark model is trained. The standardized target model context reference set and the target model's reconstructed operating point set's rotational speed, volumetric flow rate, and physical derived features are input into the Gaussian process regression benchmark model to obtain the target model context reference set's benchmark predicted values ​​and the target model's reconstructed operating point set's benchmark predicted values.

[0009] Calculate the prediction residuals of the target aircraft context reference set, where the prediction residuals are the differences between the normalized true values ​​of pressure ratio and isentropic efficiency in the target aircraft context reference set and the baseline prediction values ​​of the target aircraft context reference set. Using the rotational speed, volumetric flow rate, and physical derived features in the normalized target aircraft context reference set as input features and the prediction residuals as output features, a pre-trained cross-domain table context inferencer is used to learn the residual mapping relationship. The inferencer does not perform parameter gradient updates. The baseline prediction values ​​of the target aircraft reconstructed operating point set are corrected using the residual mapping relationship to obtain the corrected prediction values ​​of the target aircraft reconstructed operating point set.

[0010] After destandardizing the predicted values ​​of the target compressor's operating point set to be reconfigured, a monotonically decreasing order-preserving regression constraint is applied to the pressure ratio prediction sequence in ascending order of volumetric flow rate. After smoothing the isentropic efficiency prediction sequence, the peak value is located. Using the peak value as the boundary, monotonically increasing order-preserving regression constraints before the peak and monotonically decreasing order-preserving regression constraints after the peak are applied respectively to obtain the reconfigured pressure ratio and isentropic efficiency. The centrifugal compressor Map is then fitted using the original performance data.

[0011] Preferably, the physical derived feature set includes at least the rotational speed secondary feature, the flow rate-rotational speed ratio feature, the flow rate-rotational speed interaction feature, and the flow rate deviation feature;

[0012] The second-order characteristic of rotational speed is:

[0013] ;

[0014] in, This represents the normalized rotational speed characteristic.

[0015] The flow-to-speed ratio is characterized as follows:

[0016] ;

[0017] in, To normalize the volumetric flow rate characteristics, It is the minimum value;

[0018] The flow-speed interaction characteristics are as follows:

[0019] ;

[0020] The flow deviation characteristics are:

[0021] ;

[0022] The input features are:

[0023] .

[0024] Preferably, when the source model dataset contains multiple speed lines, representative data points are selected on each speed line at equal flow intervals to participate in the training of the Gaussian process regression benchmark model; when the number of data points on a single speed line is greater than or equal to 15, 15 data points at equal flow intervals are selected; when the number of data points on a single speed line is less than 15, all valid data points of that speed line are retained to participate in the training of the benchmark model.

[0025] Preferably, the cross-domain table context inferencer is a Transformer model pre-trained on massive synthetic table data.

[0026] As a preferred approach, the Gaussian process regression model employs a composite kernel function that combines radial basis functions with a white noise kernel.

[0027] As a preferred approach, the pre-training dataset, transfer dataset, and physically derived feature set are standardized, resulting in:

[0028] ;

[0029] in The feature values ​​of the source model dataset, the target model dataset, or the physically derived feature set; This is the mean of the feature value across the source model dataset, the target model dataset, and the physically derived feature set; The standard deviation of the feature value is defined on the source model dataset, the target model dataset, and the physically derived feature set.

[0030] Preferably, if the target model's set of reconfigurable operating conditions has a true pressure ratio and isentropic efficiency, then the reconfigured pressure ratio and isentropic efficiency are compared with the true pressure ratio and isentropic efficiency, the root mean square error and mean absolute error are calculated, and the reconfigured pressure ratio and isentropic efficiency, the true pressure ratio and isentropic efficiency, and the corresponding root mean square error and mean absolute error are output.

[0031] The beneficial effects of this invention lie in leveraging the unique advantages of cross-domain table context inference in mining relationships within small-sample table data. This enables high-precision, high-fidelity fitting of sparse performance data and full-condition expansion of the Map graph. The inference, pre-trained on massive amounts of multi-domain synthetic table data, internalizes general data distribution prediction logic, allowing direct application to fitting tasks using sparse test data from centrifugal compressors. Its core advantage lies in eliminating the need for complex parameter tuning and retraining for specific aircraft models, possessing extremely high inference speed, prediction accuracy, and numerical robustness, and accurately capturing complex nonlinear relationships between small-sample features. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the centrifugal compressor Map fitting method based on source model-target model residual migration correction according to the present invention;

[0033] Figure 2 The diagram shows the performance data of two models, where (a) is the source model volumetric flow rate-pressure ratio centrifugal compressor map and (b) is the target model sparse volumetric flow rate-pressure ratio centrifugal compressor map.

[0034] Figure 3 A comparison chart of volumetric flow rate-compression ratio map between the original sparse data and the reconstructed data for the target model;

[0035] Figure 4 A comparison chart of volume flow rate-isoentropy efficiency map of the original sparse data and reconstructed data for the target model;

[0036] Figure 5 The volumetric flow rate-isentropic efficiency performance comparison curves are shown for two representative speed lines for the target model. Detailed Implementation

[0037] The technical solutions of 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.

[0038] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0039] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0040] This embodiment provides a centrifugal compressor map fitting method based on a benchmark-residual hybrid architecture. This method addresses the problem that traditional methods struggle to reconstruct centrifugal compressor maps within the target operating range with high accuracy and physical consistency under sparse experimental data conditions. The overall process includes: data acquisition and partitioning, physical feature construction and standardization, Gaussian process regression benchmark model training and prediction, cross-domain table context inference engine residual learning and correction, hierarchical physical constraint post-processing, and finally outputting reconstructed performance data and completing map fitting. The following detailed description of the specific operational steps demonstrates this application; those skilled in the art can fully reproduce this embodiment without creative effort.

[0041] S1. Data acquisition, segmentation, and feature construction, including:

[0042] S101. Raw Data Acquisition

[0043] Raw performance data for two different centrifugal compressor models were obtained from bench tests or historical databases, and denoted as the source model dataset and the target model dataset, respectively. Each data record includes four core parameters: rotational speed N (unit: rpm), volumetric flow rate, and so on. (Unit: m³ / s), pressure ratio (Dimensionless) and isentropic efficiency (Dimensionless). The source compressor is a centrifugal compressor with an existing, relatively complete centrifugal compressor map, used to establish a Gaussian process regression baseline model; the target compressor is a centrifugal compressor whose centrifugal compressor map needs to be completed, used to construct contextual reference information and reconstruct the target compressor's centrifugal compressor map. Preferably, the source and target compressors belong to the same series, or are similar in at least two of the following: impeller type, diffuser structure, design pressure ratio, design flow range, and speed range, with overlap in the normalized speed range and normalized flow range.

[0044] The source model dataset is represented as follows: The target model dataset is represented as follows: .

[0045] In the formula, the subscript (s) represents the source model and the subscript (t) represents the target model.

[0046] S102, Data Reading and Preprocessing

[0047] Define a main program function that reads the source model performance data file and the target model performance data file (in Excel format) respectively, and reads the data from the Excel file using the pandas library.

[0048] Import the Python libraries required for data processing, model building, numerical computation, and visualization, including the pandas library for data reading and processing, the numpy library for numerical computation and root mean square error calculation, and the matplotlib library for plotting performance comparison curves, to ensure that each function works correctly.

[0049] S103, Source Model Dataset Construction

[0050] Source machine model dataset This benchmark training set is used to train a Gaussian process regression benchmark model. The benchmark training set includes complete input and output parameters, namely, rotational speed. Volumetric flow rate Pressure ratio and isentropic efficiency .

[0051] When the source model data includes multiple speed lines, select several representative data points at equal flow intervals on each speed line to reduce the bias impact of local dense sampling on model training. When the number of data points for each speed line of the source model is sufficient, it is preferable to select 15 data points at equal flow intervals on each speed line; when a single speed line has fewer than 15 data points, retain all valid data points for that speed line to participate in the baseline model training.

[0052] S104, Target Model Sparse Dataset Partitioning

[0053] Target model dataset The system is divided into a target aircraft context reference set and a target aircraft reconfigurable operating condition point set. The target aircraft context reference set is used to calculate the prediction residual of the target aircraft relative to the source aircraft baseline model and serves as the context input for the cross-domain table context inferencer. The target aircraft reconfigurable operating condition point set is used to output the pressure ratio and isentropic efficiency prediction results of the target aircraft under unknown operating conditions.

[0054] The target model context reference set is represented as follows: The target model's set of reconfigurable operating conditions is represented as follows: .

[0055] In the formula, the subscript (c) represents the context reference point, and the subscript (q) represents the query point to be reconstructed.

[0056] Each sample in the target aircraft context reference set includes data on engine speed, volumetric flow rate, pressure ratio, and isentropic efficiency. The target aircraft operating point set to be reconstructed only includes engine speed and volumetric flow rate; the corresponding pressure ratio and isentropic efficiency are obtained through subsequent baseline model prediction, residual correction, and physical constraint post-processing. If real experimental values ​​exist for the target aircraft operating points to be reconstructed, these real values ​​are only used for subsequent error verification and do not participate in baseline model training, residual learning, or physical constraint processing.

[0057] S105, Target model's reconfigurable operating point is generated.

[0058] Based on the reconstruction requirements of the known speed lines of the target aircraft and the target centrifugal compressor map, the volumetric flow rate range to be reconstructed is determined on each target speed line. The volumetric flow rate range can be determined by the minimum and maximum volumetric flow rates at existing test points of the target aircraft, or it can be determined by combining known surge boundaries, blockage boundaries, or the engineering allowable operating range.

[0059] After determining the volumetric flow rate range, operating points for the target model to be reconfigured are generated at equal flow rate intervals. Fifteen operating points at equal flow rate intervals are generated on each target speed line to form continuous and smooth volumetric flow rate-pressure ratio characteristic curves and volumetric flow rate-isentropic efficiency characteristic curves for the target model. The volumetric flow rate-pressure ratio characteristic MAPs for the source and target models are shown below. Figure 2 As shown;

[0060] S106, Construction of Basic Input Features

[0061] Basic input features are extracted from the source model dataset, the target model context reference set, and the target model operating point set to be reconstructed, respectively. The basic input features include at least engine speed. and volumetric flow rate Basic output parameters include pressure ratio and isentropic efficiency .

[0062] S2, Construction of Physically Derived Feature Set

[0063] To avoid misrepresenting empirical features as strictly dimensionless parameters, this implementation method uniformly refers to the derived features constructed from rotational speed and volumetric flow rate as "physical derived features." These features do not replace the strict compressor similarity criterion parameters, but are used to enhance the model's ability to characterize rotational speed effects, flow rate effects, and their coupling relationships.

[0064] Rotational speed N and volumetric flow rate are respectively based on the source model dataset, the target model context reference set, and the target model's reconstructed operating point set. A physical derivative feature set is constructed. Considering the inherent differences between the source and target models in terms of speed range, flow range, and geometry, this application adopts a model-independent normalization strategy to eliminate baseline deviations between different models and improve the comparability and universality of operating condition characteristics.

[0065] Independent reference parameters are set for the source and target models respectively: reference speed of the source model. Source model reference volumetric flow rate Target model reference speed Target model reference volumetric flow rate The benchmark parameters are preferably selected from the design speed and design volumetric flow rate of the corresponding model; if the design parameters are not available, the average speed and flow rate of all valid samples of the model are selected as the benchmark values.

[0066] Based on the aircraft model baseline parameters, normalized operating condition characteristics for the source and target aircraft models are constructed respectively:

[0067] Source model normalized speed and normalized volumetric flow rate:

[0068]

[0069]

[0070] Normalized rotational speed and normalized volumetric flow rate of the target model:

[0071]

[0072]

[0073] Based on the normalized operating condition parameters, four types of physically derived characteristics are constructed, namely, the second-order characteristics of rotational speed. Flow rate-speed ratio characteristics Flow rate-speed interaction characteristics and flow deviation characteristics .

[0074] (1) This is used to characterize the trend of pressure rise capability of a centrifugal compressor as a function of the square of the impeller circumferential velocity. Since the impeller circumferential velocity is approximately proportional to the rotational speed, there is usually a strong correlation between pressure rise capability and the square of the rotational speed. Therefore, this feature can be used to enhance the model's ability to characterize the nonlinear variation of pressure ratio with rotational speed. The formula is:

[0075]

[0076] To normalize the speed characteristics, the speeds of the source and target engines are respectively... and ;

[0077] (2) It describes the relative magnitude of volumetric flow rate at different speed levels and can be used as an approximate representation of the compressor's operating condition. Its formula is:

[0078]

[0079] in, To normalize the volumetric flow rate characteristics, the normalized volumetric flow rate characteristics of the source and target models are as follows: and , To prevent extremely small positive numbers with a denominator of zero, it should be noted that... The flow-speed ratio characteristic, constructed based on input rotational speed and volumetric flow rate, is not a compressor flow coefficient in the strict sense; therefore, it is not referred to as a dimensionless flow coefficient in this embodiment. When the compressor's geometric parameters are known, a geometrically related approximate flow-speed ratio characteristic can also be constructed using the following formula. :

[0080]

[0081] in The effective flow area at the impeller outlet. Let be the impeller outlet circumferential velocity, and satisfy:

[0082]

[0083] In the formula Where is the impeller outlet diameter. If the geometric parameters are not available, then use . As an alternative feature.

[0084] (3) This feature describes the coupling effect between volumetric flow rate and rotational speed. It helps the model capture performance differences caused by variations in flow rate levels across different rotational speeds, and is particularly suitable for local corrections of pressure ratio and efficiency in cross-rotational speed fitting. The formula is:

[0085]

[0086] (4) For the same rotational speed line, the deviation of the volumetric flow rate within that rotational speed line from the average flow rate of that rotational speed line can be calculated. :

[0087]

[0088] in This is the average value of the known volumetric flow rate within the same speed range. This feature is used to characterize the relative position of the operating point on the single-speed characteristic curve, which helps the model identify the performance differences in the near-surge region, the intermediate high-efficiency region, and the near-blocking region.

[0089] In summary, the input feature vector in this embodiment can be expressed as:

[0090]

[0091] When there are too few data points on a single speed line, stable calculation is not possible. In this case, a simplified feature vector can also be used:

[0092]

[0093] S3. Standardization processing, including:

[0094] Standardized parameter fitting: For input features, standardized parameters are calculated solely based on input features from the source aircraft benchmark training set; for output parameters, standardized parameters are calculated solely based on the true pressure ratio and true isentropic efficiency from the source aircraft benchmark training set. The target aircraft context reference set and the target aircraft reconstructed operating point set do not participate in the standardized parameter fitting and both reuse standardized parameters obtained from the source aircraft benchmark training set. The StandardScaler method is used for data processing, with the following formula:

[0095]

[0096] Taking the benchmark training set as an example, The feature values ​​of the benchmark training set; This is the mean of the feature value on the benchmark training set; This represents the standard deviation of the feature value on the benchmark training set.

[0097] Standardization Transformation: The input features of the source model dataset, the target model context reference set, and the target model's reconstructed operating point set are standardized using the mean and standard deviation of the input features obtained from the source model benchmark training set. The true pressure ratio and true isentropic efficiency of the source model output labels and the target model context reference set are standardized using the mean and standard deviation of the output parameters obtained from the source model benchmark training set. The target model's reconstructed operating point sets do not contain true output parameters, therefore their output parameters are not standardized.

[0098] S4. Training and Prediction of Gaussian Process Regression Benchmark Model:

[0099] Gaussian Process Regression (GPR) serves as the foundational modeling layer of this application's method. It establishes global performance response surfaces for pressure ratio and isentropic efficiency with respect to engine speed, volumetric flow rate, and the previously constructed physical derivative feature set, based on the complete performance dataset of the source aircraft. This baseline model is used to fit the overall variation trend of the source aircraft's compressor performance map, providing initial estimates for cross-aircraft migration in performance prediction within the target aircraft's reconfiguration range.

[0100] S401, Training Process of Gaussian Process Regression Benchmark Model

[0101] The input features are composed of rotational speed, volumetric flow rate, and physically derived features from the source model dataset. As model inputs, the standardized source model pressure ratio labels are respectively used. Isoentropy efficiency label As independent regression outputs, two Gaussian process regression models are trained separately, corresponding to the pressure ratio and isentropic efficiency prediction tasks, respectively. The mapping relationship is defined as follows:

[0102]

[0103] In the formula: The baseline model for the regression of the pressure ratio Gaussian process; This is the baseline regression model for isentropic efficient Gaussian processes.

[0104] This application uses a radial basis function (RBF) kernel and a Gaussian white noise kernel to form a composite covariance kernel function for Gaussian process regression. At the same time, it limits the optimization search boundary of the hyperparameters of each kernel function to avoid problems such as hyperparameter divergence and overfitting during training, thereby improving the stability and generalization ability of global response surface fitting.

[0105] S402, Gaussian process regression benchmark model cross-domain prediction

[0106] After completing the training of the Gaussian process regression benchmark model for the source aircraft model, cross-aircraft benchmark predictions were performed using two classes of samples:

[0107] (1) Target model context reference set baseline prediction

[0108] The input features are composed of rotational speed, volumetric flow rate, and physically derived features from the standardized target model context reference set. Input the pre-trained Gaussian process regression baseline model and output the baseline predicted value of the context reference point:

[0109]

[0110] (2) Prediction of the target model's reconfigurable operating point

[0111] The input features are composed of the speed, volumetric flow rate, and physically derived characteristics of the standardized target model's set of operating points to be reconstructed. By inputting the same Gaussian process regression baseline model for the source aircraft model, the baseline predicted values ​​of the target aircraft model's set of operating point values ​​to be reconfigured are obtained:

[0112]

[0113] The aforementioned benchmark prediction essentially involves directly transferring the performance response surface of the source model to the target model for estimation. However, the source and target models generally have structural differences such as impeller outer diameter, diffuser structure, flow cross-sectional area, number of blades, and internal flow loss distribution. Relying solely on the global response surface of the source model for direct prediction will result in fixed systematic biases. Therefore, a residual correction module is introduced to compensate for and correct the inherent biases of the model through a cross-domain table context inferencer.

[0114] S5, Residual Calculation and Cross-Domain Table Context Inferencer Correction

[0115] The cross-domain table context inferencer, as a residual correction layer, plays a core role in learning the local performance deviation mapping law of the target aircraft relative to the source aircraft Gaussian process regression benchmark model by using a small number of target aircraft context reference samples, thereby achieving adaptive compensation for the benchmark prediction results.

[0116] S501, Target Model Context Sample Residual Calculation

[0117] For each known operating condition sample in the target aircraft context reference set, the pressure ratio residual and isentropic efficiency residual are calculated by combining the actual performance parameters with the baseline prediction values ​​of the target aircraft context reference set from the Gaussian process regression benchmark model.

[0118]

[0119] In the formula: , To standardize the true pressure ratio and the true isentropic efficiency of the target model by transforming the standardized parameters of the source model output; , This represents the baseline predicted value output by the Gaussian process regression baseline model in the standardized space. , These are the pressure ratio residual and the isentropic efficiency residual in the standardized space, respectively.

[0120] S502, Residual Inference Sample Construction

[0121] Input features are composed of rotational speed, volumetric flow rate, and physically derived features from the standardized target model context reference set. As input to the inference model, the residuals calculated within the standard space , As the regression output, a residual learning dataset is constructed.

[0122] S503, Gradient-free update of context residual mapping inference

[0123] Input features and residual labels are paired and fed into a pre-trained cross-domain tabular context inference engine. The inference process does not perform parameter gradient updates or retrain the network; it only infers the target model residual mapping relationship based on a small amount of contextual reference information, thus obtaining the mapping relationship from operating condition features to performance residuals.

[0124]

[0125] The target model's reconfigurable operating conditions Input the residual mapping function, and output the compensated residual estimate for each working condition point to be predicted:

[0126]

[0127] S504, Performance Prediction Result Residual Compensation Overlay

[0128] The operating condition residuals obtained from the inference are linearly superimposed with the initial predicted values ​​of the Gaussian process regression benchmark model to complete the systematic bias correction, thus obtaining the corrected predicted values ​​of the target aircraft model's reconfigurable operating condition point set:

[0129]

[0130] This completes the entire prediction process: a global GPR baseline response surface is trained based on the complete dataset of the source model; a model-specific residual field is fitted through a cross-domain inference engine using a small number of context samples of the target model; and after superimposed compensation, the pressure ratio and isentropic efficiency prediction results within the reconstruction range of the target model are obtained.

[0131] S6. Post-processing of hierarchical physical constraints and output of the map graph, including:

[0132] The corrected predicted values ​​for pressure ratio and isentropic efficiency after residual compensation correction are still in the standardized numerical space and cannot directly correspond to the real physical dimensions. Therefore, the predicted values ​​are first corrected for the set of operating points to be reconfigured for the target aircraft model. , Perform an inverse standardization transform to map the result to the original physical quantity space, and obtain performance prediction results with real physical meaning.

[0133] S601, Correcting Predicted Values ​​and Inverse Standardization

[0134] The inverse normalization transform reduction formula is defined as follows:

[0135]

[0136] In the formula: These are the model predictions after residual correction in the standardized space; The predicted performance values ​​at the original physical scale after inverse standardization transformation; , The standard deviation and mean of the corresponding output parameters calculated and saved in S3 based on the source model benchmark training set are reused in the destandardization process.

[0137] S602, Post-processing strategy for hierarchical physical constraints

[0138] First, the performance prediction results after destandardization are corrected for their basic value range. Within the normal operating range of the centrifugal compressor, the predicted pressure ratio is ensured to be no less than 1, and the predicted isentropic efficiency is ensured to be within the range of 0-1.

[0139] The corrected prediction sequence directly output by the model is susceptible to modeling errors and sample sparsity, resulting in local non-physical fluctuations that violate the inherent performance variation law of centrifugal compressors. This application designs a hierarchical physical constraint post-processing method based on the characteristics of the linear performance curve at the same rotational speed to correct unreasonable predictions and improve the consistency between the prediction curve and the aerodynamic characteristics of the compressor.

[0140] (1) Monotonically decreasing pressure ratio constraint

[0141] For any constant-speed, stable operating condition line, within the normal operating range without surge or blockage, the pressure ratio generally decreases with increasing volumetric flow rate. Based on this aerodynamic constraint, all operating points at the same target speed are arranged in ascending order of volumetric flow rate. When there are local upward fluctuations in the pressure ratio prediction sequence exceeding the preset tolerance, monotonically non-increased order regression is used to correct the pressure ratio prediction sequence; when the local fluctuations do not exceed the preset tolerance, the original prediction results are retained. The preset tolerance can be determined based on the pressure ratio test measurement uncertainty or a pre-set allowable relative deviation, expressed as follows:

[0142]

[0143] In the formula: The corrected pressure ratio sequence after applying a monotonically decreasing physical constraint; It is a monotonically decreasing order-preserving regression operator.

[0144] (2) Isoentropy efficiency single-peak piecewise monotonic constraint

[0145] The linear isentropic efficiency of a centrifugal compressor at single speed typically exhibits an approximately unimodal distribution characteristic, first increasing and then decreasing with volumetric flow rate, with the curve usually containing a main high-efficiency peak region. This application employs a processing flow of "smoothing and noise reduction + piecewise order preservation constraints":

[0146] 1. Perform sliding smoothing on all isentropic efficiency prediction sequences under the same rotational speed line to eliminate local random jitter;

[0147] 2. Locate the peak operating point of the smoothed efficiency curve; when the efficiency curve has a clear main peak, divide the sequence into a low flow range before the peak and a high flow range after the peak, using the main peak operating point as the boundary.

[0148] 3. Apply a monotonically increasing order-preserving constraint to the pre-peak interval:

[0149]

[0150] 4. Apply a monotonically decreasing order-preserving constraint to the interval after the peak:

[0151]

[0152] 5. By splicing the two constrained sequences, an isentropic efficiency correction sequence that satisfies the unimodal variation law is obtained:

[0153]

[0154] If the number of operating points to be reconstructed on a single speed line is too small, or if the smoothed efficiency curve does not have a clear main peak, then only smoothing and noise reduction and reasonable value range truncation will be performed, and segmented single-peak constraints will not be enabled.

[0155] S603, Centrifugal Compressor Map Reconstruction Output

[0156] After completing the hierarchical physical constraint correction, the corrected pressure ratio of the target model is... Corrected isentropic efficiency Speed ​​corresponding to operating conditions Volumetric flow rate By matching and merging them one by one, the reconstructed pressure ratio and isentropic efficiency can be obtained, and a complete target model reconstructed performance data table can be constructed.

[0157] The reconstructed full-condition prediction data and the target model context reference measured samples are grouped and sorted according to the isotropic speed line. Volumetric flow rate-pressure ratio centrifugal compressor map and volumetric flow rate-isentropic efficiency centrifugal compressor map are plotted respectively to intuitively compare the degree of fit between the measured points and the model reconstruction curve.

[0158] For sparse raw performance data, a basic response surface is established by constructing a Gaussian process regression benchmark model. A cross-domain table context inference engine is then used to refine the prediction residuals, and a hierarchical physical constraint post-processing module is overlaid. This directly fits high-precision, high-fidelity centrifugal compressor performance data, expanding to obtain a centrifugal compressor map covering the target reconstruction range. This invention aims to solve the problems of fitting distortion, inconsistent physical laws, and large errors in existing fitting methods under sparse data. By leveraging the synergistic effect of the benchmark model capturing global trends and the inference engine correcting local details, prediction accuracy and physical consistency are significantly improved.

[0159] In a preferred embodiment, the cross-domain table context inferencer of this implementation specifically employs a Transformer model pre-trained on massive synthetic table data. This type of model can be pre-trained through numerous synthetic table tasks to develop context inference capabilities suitable for prediction using small-sample table data, learning nonlinear mapping relationships in general table data and context inference rules under small-sample conditions. In this application, the inference interface of this model is directly called, without any fine-tuning or retraining for centrifugal compressor data. During use, the number of context reference samples does not exceed the maximum supported length of the corresponding version of the selected cross-domain table context inference model. When the number of context reference samples for the target aircraft exceeds the maximum supported length, representative samples are selected according to speed stratification and volumetric flow rate interval stratification, with priority given to retaining samples close to surge boundaries, efficiency peak regions, and blockage boundaries, until the number of context reference samples does not exceed the maximum supported length.

[0160] In a preferred embodiment, the composite kernel function is specifically implemented as follows:

[0161]

[0162] The kernel of the radial basis functions, The kernel of white noise;

[0163] A combined kernel function of radial basis function and white noise kernel is adopted, and the hyperparameters of the kernel function are determined by marginal likelihood optimization within the preset search boundary to reduce the risk of hyperparameter divergence and overfitting, improve the training stability of Gaussian process regression model, establish the basic response surface of centrifugal compressor performance parameters as a function of speed and flow rate, and capture the global trend of performance data.

[0164] In a preferred embodiment, the method of this implementation further includes:

[0165] S7. Result Validation and Data Export. After the model training is completed, construct a prediction result table, calculate and statistically analyze the root mean square error (RMSE) and mean absolute error (MAE) of the target aircraft model's reconstructed operating condition point set (including actual experimental values), and export and save the result table with the file name "Benchmark-Residual Hybrid Architecture Prediction Results.xlsx". This table includes the target aircraft model's reconstructed operating condition point set, the reconstructed data of the prediction set, the actual values, the root mean square error, the mean absolute error, and a summary of error indicators, facilitating subsequent data review and validation.

[0166] The formulas for RMSE and MAE are shown below:

[0167]

[0168]

[0169] The RMSE and MAE of the reconstructed data relative to the true values ​​based on the pressure ratio and isentropic efficiency are shown in the table below.

[0170]

[0171] MAE and RMSE were used to evaluate the error of the reconstructed fitting results. After error calculation, the fitted extended data and the original measured data were merged in an orderly manner according to rotational speed and volumetric flow rate. The complete dataset was then output in a standardized Excel file format.

[0172] Based on the fused high-quality extended data, the centrifugal compressor map is refined and reconstructed. The focus is on achieving high-precision drawing and optimization of two core centrifugal compressor maps: volumetric flow rate-pressure ratio and volumetric flow rate-isentropic efficiency. This significantly improves the completeness, detail, and practicality of the performance map.

[0173] The performance data corresponding to the fitted target speed is then visualized. A comparison chart of the volumetric flow rate-pressure ratio of the original sparse data and the reconstructed data for the target model is plotted, such as... Figure 3 As shown.

[0174] A volume flow-isotropy efficiency map comparing the original sparse data and reconstructed data of the target model is plotted, such as... Figure 4 As shown;

[0175] Further, select two target rotational speed lines and plot the volumetric flow rate-isentropic efficiency performance comparison curves, such as... Figure 5 As shown;

[0176] This application employs a hybrid architecture combining a Gaussian process regression baseline layer and a cross-domain table context inference residual correction layer. A baseline response surface is established using performance data from the source aircraft, and cross-aircraft residual biases are learned using a small number of measured data points from the target aircraft, thereby reconstructing the centrifugal compressor map of the target aircraft. By leveraging the synergistic effect of the baseline layer capturing global aerodynamic trends and the inferencer correcting local nonlinear biases, the application effectively overcomes the shortcomings of traditional mathematical interpolation methods, which are prone to non-physical distortions when handling large-scale nonlinearities. This significantly improves the fitting accuracy and numerical reliability of the centrifugal compressor map.

[0177] This application leverages the small-sample feature mining capabilities of a cross-domain table context inference engine to further characterize local aerodynamic performance deviations that are difficult for benchmark models to fully represent. In data scenarios where a single speed line contains only a small number of discrete measurement points, this model can be used to characterize the location and amplitude variations of efficiency peaks at different speeds, as well as the changing trends of performance curves near surge and blockage boundaries, which helps improve the fidelity and stability of aerodynamic parameter prediction results.

[0178] This application constructs a dual constraint mechanism combining general table priors and explicit hierarchical physical constraints to improve the consistency between the output results and the basic laws of fluid mechanics. The cross-domain table context inferencer learns the nonlinear mapping relationships and small sample inference rules in the general table data during the pre-training stage; this application further improves the consistency between the prediction results and the performance variation law of the centrifugal compressor by constructing a physical derivative feature set and performing hierarchical physical constraint post-processing.

[0179] This application significantly reduces the reliance on single-aircraft intensive test data for constructing a complete centrifugal compressor map by leveraging the cross-aircraft reuse capability of the benchmark model and the zero-retraining characteristic of the inference engine. The benchmark model trained based on existing source aircraft performance data can serve as the initial response surface for target aircraft of the same series or similar structures; after residual correction using a small number of measured points on the target aircraft, the performance map of the target aircraft can be reconstructed. While maintaining accuracy for engineering applications, this reduces the number of intensive test points required for the target aircraft, significantly shortening the product development cycle and demonstrating extremely high engineering practical value.

[0180] While specific embodiments of the invention have been described herein, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for fitting centrifugal compressor Map diagrams based on a baseline-residual hybrid architecture, characterized in that, include: The centrifugal compressor's rotational speed, volumetric flow rate, pressure ratio, and isentropic efficiency are acquired as raw performance data. This raw performance data is divided into a source model dataset and a target model dataset. The target model dataset is further divided into a target model context reference set and a target model operating point set to be reconstructed. The target model context reference set includes rotational speed, volumetric flow rate, pressure ratio, and isentropic efficiency, while the target model operating point set to be reconstructed includes rotational speed and volumetric flow rate. A physically derived feature set is constructed based on the rotational speed and volumetric flow rate, and the source model dataset, target model dataset, and physically derived feature set are then standardized. Using the standardized source model dataset's rotational speed, volumetric flow rate, and physical derived features as inputs, and the standardized pressure ratio and isentropic efficiency as outputs, a Gaussian process regression benchmark model is trained. The standardized target model context reference set and the target model's reconstructed operating point set's rotational speed, volumetric flow rate, and physical derived features are input into the Gaussian process regression benchmark model to obtain the target model context reference set's benchmark predicted values ​​and the target model's reconstructed operating point set's benchmark predicted values. Calculate the prediction residuals of the target aircraft context reference set, where the prediction residuals are the differences between the normalized true values ​​of pressure ratio and isentropic efficiency in the target aircraft context reference set and the baseline prediction values ​​of the target aircraft context reference set. Using the rotational speed, volumetric flow rate, and physical derived features in the normalized target aircraft context reference set as input features and the prediction residuals as output features, a pre-trained cross-domain table context inferencer is used to learn the residual mapping relationship. The inferencer does not perform parameter gradient updates. The baseline prediction values ​​of the target aircraft reconstructed operating point set are corrected using the residual mapping relationship to obtain the corrected prediction values ​​of the target aircraft reconstructed operating point set. After destandardizing the predicted values ​​of the target compressor's operating point set to be reconfigured, a monotonically decreasing order-preserving regression constraint is applied to the pressure ratio prediction sequence in ascending order of volumetric flow rate. After smoothing the isentropic efficiency prediction sequence, the peak value is located. Using the peak value as the boundary, monotonically increasing order-preserving regression constraints before the peak and monotonically decreasing order-preserving regression constraints after the peak are applied respectively to obtain the reconfigured pressure ratio and isentropic efficiency. The centrifugal compressor Map is then fitted using the original performance data.

2. The centrifugal compressor Map fitting method based on a baseline-residual hybrid architecture according to claim 1, characterized in that, The physical derived feature set includes at least the rotational speed secondary feature, the flow rate-rotational speed ratio feature, the flow rate-rotational speed interaction feature, and the flow rate deviation feature; The second-order characteristic of rotational speed is: ； in, This represents the normalized rotational speed characteristic. The flow-to-speed ratio is characterized as follows: ； in, To normalize the volumetric flow rate characteristics, It is the minimum value; The flow-speed interaction characteristics are as follows: ； The flow deviation characteristics are: ； The input features are: 。 3. The centrifugal compressor Map fitting method based on a baseline-residual hybrid architecture according to claim 1, characterized in that, When the source model dataset contains multiple speed lines, representative data points are selected on each speed line according to equal flow intervals to participate in the training of the Gaussian process regression benchmark model; when the number of data points on a single speed line is greater than or equal to 15, 15 data points with equal flow intervals are selected; when the number of data points on a single speed line is less than 15, all valid data points of that speed line are retained to participate in the training of the benchmark model.

4. The centrifugal compressor Map fitting method based on a baseline-residual hybrid architecture according to claim 1, characterized in that, The cross-domain table context inferencer is a Transformer model pre-trained on massive synthetic table data.

5. The centrifugal compressor Map fitting method based on a baseline-residual hybrid architecture according to claim 1, characterized in that, The Gaussian process regression model uses a composite kernel function that combines radial basis functions with a white noise kernel.

6. The centrifugal compressor Map fitting method based on a baseline-residual hybrid architecture according to claim 1, characterized in that, The pre-training dataset, transfer dataset, and physically derived feature set are standardized. The standardized result is: ； in The feature values ​​of the source model dataset, the target model dataset, or the physically derived feature set; This is the mean of the feature value across the source model dataset, the target model dataset, and the physically derived feature set; The standard deviation of the feature value is defined on the source model dataset, the target model dataset, and the physically derived feature set.

7. The centrifugal compressor Map fitting method based on a baseline-residual hybrid architecture according to claim 1, characterized in that, If the target model's set of working conditions to be reconstructed has a true pressure ratio and isentropic efficiency, then the reconstructed pressure ratio and isentropic efficiency are compared with the true pressure ratio and isentropic efficiency. The root mean square error and mean absolute error are calculated, and the reconstructed pressure ratio and isentropic efficiency, the true pressure ratio and isentropic efficiency, and the corresponding root mean square error and mean absolute error are output.

8. A computer-readable storage device storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the centrifugal compressor map fitting method based on the benchmark-residual hybrid architecture as described in any one of claims 1 to 7.

9. A centrifugal compressor map fitting device based on a baseline-residual hybrid model, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the centrifugal compressor map fitting method based on the benchmark-residual hybrid architecture as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the centrifugal compressor map fitting method based on the benchmark-residual hybrid architecture as described in any one of claims 1 to 7.

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