CFD-based S-type pitot tube calibration coefficient prediction method

Abstract

The invention discloses an S-type pitot tube calibration coefficient prediction method based on CFD, and the method is realized through the following steps: S1, carrying out CFD numerical simulation based on parametric modeling, and obtaining a calibration coefficient set of an S-type pitot tube under different installation angle deviations, flow velocity range conditions and environmental parameters; s2, integrating simulation data, and constructing a feature vector data set of the key influence parameters; s3, dividing the data set into a training set and a test set; s3, based on an RBF algorithm, constructing a high-precision nonlinear prediction model by using the training set; and S4, verifying the performance of the model by using the test set, and judging whether the prediction accuracy meets the expectation or not. A CFD simulation technology and a machine learning algorithm are integrated, the problem that a traditional real flow calibration device is limited in capacity and cannot reproduce on-site complex conditions is solved, and a solution is provided for high-precision prediction and correction of calibration coefficients under on-site complex installation conditions and a non-uniform flow field.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of flow and velocity measurement, computational fluid dynamics (CFD) simulation, and machine learning. Specifically, it relates to a method for predicting the calibration coefficient of an S-type Pitot tube based on CFD numerical simulation and machine learning algorithms, which is particularly suitable for high-precision prediction and correction of the calibration coefficient under complex on-site installation conditions and non-uniform flow fields. Background Technology

[0002] The S-type Pitot tube, a simple, robust, and easy-to-manufacture flow measurement device, is widely used in wind tunnel experiments, industrial flue monitoring, and HVAC systems for flow rate measurement. Its working principle involves measuring the difference between the total pressure and static pressure at a point in the fluid and calculating the flow velocity at that point using Bernoulli's equation. However, due to the S-shaped structure of the Pitot tube, fluid separation and complex flow around it occur, causing the measured pressure difference to deviate from the ideal pressure difference. Therefore, a calibration coefficient K must be introduced for correction. ; In the above formula, K represents the calibration coefficient dependent on the yaw angle α and pitch angle β, the S-type Pitot calibration coefficient, This indicates the differential pressure between the total pressure orifice and the static pressure orifice of the pitot tube to be calibrated. It is the density of the fluid inside the pipe. This represents the current flow velocity at the location of the pitot tube being measured. The accuracy of the calibration coefficient directly determines the precision of the flow velocity measurement.

[0003] Currently, the main method for obtaining the calibration coefficient of an S-type Pitot tube is the wind tunnel actual flow calibration method. As a traditional and recognized direct calibration method, the basic operation involves installing the S-type Pitot tube to be calibrated in the experimental section of a standard wind tunnel, adjusting the wind tunnel flow velocity through the system, and comparing the flow velocity measured by the Pitot tube with the wind tunnel reference flow velocity (usually calibrated by a laser Doppler velocimeter or a standard Pitot tube that has undergone primary calibration) point by point to determine its calibration coefficient. Although this method has long been regarded as a benchmark, it has several significant inherent drawbacks.

[0004] First, this method has extremely demanding experimental requirements, relying on high-precision, high-cost standard wind tunnel facilities and matching precision instruments, resulting in huge initial investment and subsequent maintenance costs. Furthermore, the entire calibration process is time-consuming, requiring meticulous installation and positioning, repeated adjustments, and point-by-point testing each time, leading to overall low efficiency. Second, in practical engineering applications, Pitot tubes often exhibit varying degrees of yaw and pitch angles due to installation deviations or changes in the directionality of the flow field. Traditional wind tunnel experiments, limited by mechanical structure and experimental costs, struggle to systematically calibrate and test all possible angle combinations (especially large-angle and complex angle conditions). They typically only provide coefficient results for the direction directly facing the incoming flow or a limited number of angles. For other unmeasured angles, they often rely on empirical estimations or rough interpolation, introducing significant measurement uncertainty.

[0005] Furthermore, when a Pitot tube is used for measurements inside a wind tunnel duct, the surrounding flow field is constrained and disturbed by the tunnel walls, a phenomenon known as the "tube wall effect" or "blockage effect." Although actual flow calibration incorporates the combined impact of this effect in the results, it is difficult to effectively separate and quantify the effect itself. A further limitation is the lack of scalability and flexibility of this method. If the wind tunnel duct size or experimental conditions change, a complete calibration experiment must be re-implemented, increasing workload and limiting its applicability in different application scenarios. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing wind tunnel flow calibration techniques by proposing a calibration coefficient prediction method based on the fusion of computational fluid dynamics numerical methods and radial basis function neural network algorithms. This method aims to replace most physical experiments with numerical experiments, construct a parameterized database covering all operating conditions, and utilize machine learning models to learn complex nonlinear mapping relationships. Ultimately, it achieves rapid, high-precision, and low-cost prediction of S-type Pitot tube calibration coefficients under arbitrarily complex installation and flow field conditions, thereby effectively improving the overall accuracy and reliability of on-site flow velocity measurements.

[0007] To achieve the above-mentioned objectives, the present invention provides a systematic technical solution comprising the following six steps: S1: This step aims to generate a baseline database of calibration coefficients covering all key influencing factors in a low-cost and efficient manner using CFD technology. The establishment of the parametric physical model begins with the actual structural dimensions of the wind tunnel test section and the standard geometric characteristics of the S-shaped Pitot tube (the S-shaped Pitot tube is vertically inserted into the center of the sidewall at a distance of 600 mm from the inlet section and a depth of 300 mm, serving as the baseline condition for the numerical experiment). The total pressure orifice of the Pitot tube probe is set to the opposing flow attitude, and its geometry is consistent with the actual model, forming a computational domain encompassing the complete pipe wall effect. Based on the determined computational domain, to capture the details of the flow field within the computational domain as much as possible, while considering the computing power of the computer, unstructured mesh technology is used to spatially discretize the computational domain. The initial maximum grid cell size is set to 36 mm, and local refinement is implemented in the S-shaped Pitot tube region to improve resolution. To further accurately capture near-wall flow characteristics, a boundary layer mesh is generated across the entire model surface using an exponential growth method with a growth rate of 1.2. While reducing the maximum grid cell size of the boundary layer at the probe and lowering the initial boundary layer height, the number of boundary layer grid layers in this region was increased, and the grid of the S-type Pitot probe was locally refined with a grid cell size of 4 mm3, thereby enhancing the ability to resolve velocity gradients, separation points, and vortex structures within the boundary layer. Three to five boundary layer meshes are generated on the surface of the Pitot tube, especially in the vicinity of the total pressure orifice and static pressure orifice. The first mesh layer is ensured to satisfy y+≈1, resulting in a denser mesh near the Pitot tube within the flow field and a relatively sparse mesh in other areas. This ultimately aims to capture more internal flow details within the computational capabilities of the computer. Secondly, based on the actual installation state of the Pitot tube in the wind tunnel, the yaw angle α and pitch angle β are determined (yaw angle -45° ~ 45°, pitch angle -45° ~ 45°). Considering the balance between computational efficiency and data representativeness, a sparse sampling strategy is used to select representative angle combinations within the angle range of 0° to ±45°. The medium velocity range is 5 m / s ~ 30 m / s (mass flow inlet and pressure outlet). The medium temperature is set within the range of 302K ~ 312K. The accuracy of differential pressure gauge measurements is compared between the actual flow experiment and the numerical experiment. The calibration coefficient K of the numerical simulation is checked to ensure it meets the actual flow conditions.An orthogonal experimental design method was adopted, selecting 140 representative sample points from the high-dimensional parameter space to form a simulation condition matrix, ensuring the comprehensiveness and orthogonality of the database. A hybrid mesh was used, with local refinement and the addition of boundary layer meshes, and mesh independence verification was performed. To be consistent with actual working conditions, physical parameters (air density, viscosity, turbulence intensity, hydraulic diameter, etc.) were uniformly set to avoid simulation errors introduced by deviations in some parameters. The near-wall treatment adopted the enhanced wall function, the pressure-velocity coupling adopted the SIMPLEC algorithm, and the spatial discretization scheme adopted the second-order upwind scheme. The average surface pressure of the Pitot tube was extracted from the converged simulation results, and the calibration coefficient K under each working condition was calculated by back-simulating according to the Bernoulli equation, forming a systematic database.

[0008] S2: This step transforms the raw CFD data into a high-quality feature set suitable for machine learning. Define the input feature X: normalized α, β, v, T, P (yaw angle, pitch angle, medium flow velocity range, medium temperature, differential pressure gauge measurement accuracy) and the output target Y (calibration coefficient K simulated). Based on the physical meaning and range of each parameter, minimum-maximum normalization is used to map the data to the [0,1] interval. For the input, normalize each feature separately: Let the minimum value of the i-th feature on the training set be mini, and the maximum value be maxi. Then, for any sample, the normalized value of the i-th feature Xi is: Let each row of the input matrix P_train be a feature, and calculate: By taking the minimum value from each row, a 6-dimensional column vector is obtained. Taking the maximum value from each row, we obtain a 6-dimensional column vector. The normalized training set input is then: Test set normalization: ; To match the dimensions using element-wise division, `min_input` and `max_input` are expanded into 6×110 matrices (each column identical). The output is also normalized: let the minimum value of the training set output `T_train` be `min_output` and the maximum value be `max_output`, then the training set output is normalized as follows: ; The same min_output and max_output are used when normalizing the test set output: ; Convert the normalized predictions back to the original scale: Training set denormalization: ; Test set denormalization: ; S3: Using a stratified sampling strategy, the dataset is divided into a training set (70%), a validation set (15%), and a test set (15%). For the training set, input p_train, calculate the hidden layer output matrix Φ_train (size 110×110), and then calculate the predicted output: For the test set, calculate the hidden layer output matrix Φ_test (size 30×110) of the test set samples, where the element in the i-th row and j-th column is φ_j(x_test_i), and then calculate the predicted output: Ensure that the data distribution of each subset is consistent with the overall distribution, so as to train a model with strong generalization ability.

[0009] S4: Construction, training, and hyperparameter optimization of the RBF neural network model. An RBF network is created (using the `newrbe` function). The `newrbe` function is used to create an accurate radial basis function network with the number of hidden neurons equal to the number of training samples (110). Each training sample corresponds to the center of a radial basis function. The radial basis function uses a Gaussian function, and its formula is...

[0010] ; Where cj is the center of the j-th hidden neuron (i.e., the input feature of the j-th training sample), and σ is the spread rate, affecting the width of the function. In the newrbe function, the width (i.e., σ) of each radial basis function is the same and is determined by the spread parameter. The default value of spread affects the smoothness of the network. In the newrbe function, the radial basis functions have the following form: ; The network output is a linear combination of the hidden layer outputs: ; Where M is the number of hidden layer neurons (here M=110), wj is the weight, and w0 is the bias.

[0011] The network training process involves solving for the weights wj and biases w0 to minimize the error between the output and the target on the training set. Since the number of hidden layer neurons equals the number of training samples, and the radial basis functions are fixed, the weights can be directly obtained by solving a system of linear equations. Let the hidden layer output matrix be Φ, where the element in the i-th row and j-th column is φ_j(x_i), which is the output of the i-th training sample on the j-th hidden layer neuron. The size of Φ is 110×110. Then the network output on the training set is: F = Φ * W, where W = [w_0; w_1; ...; w_{110}] (Here, for convenience, the bias is also included, but in reality, the first column of Φ is all 1s, corresponding to the bias). The goal is to minimize... ,in This is the normalized output of the training set (column vector). Since Φ is a square matrix and invertible, it can be solved directly: .

[0012] S5: Comprehensive Model Performance Evaluation and Uncertainty Quantification. Calculate accuracy metrics such as RMSE, MAPE, and R on the test set, and compare the training / test set errors to assess overfitting.

[0013] Training set RMSE: , where M=110.

[0014] Test set RMSE: Where N=30; The mean relative error (MRE) on the test set is less than 1%; the coefficient of determination (R) is greater than 0.98. Model robustness is verified through cross-validation and testing on marginal samples in the parameter space. A bootstrap method is used to generate confidence intervals for predicted values ​​to provide a reliability measure.

[0015] S6: On-site deployment of inclinometers, rangefinders, and other instruments measures the installation geometry parameters. Flow field parameters are estimated through diagnostic measurements or historical data, and environmental parameters are read from the monitoring system. After normalizing the on-site parameters, they are input into the trained RBF model to predict calibration coefficients in real time and correct the flow velocity calculation results accordingly. A feedback loop is established; when new valid data (such as actual flow comparison data) is obtained, incremental learning is used to update the model, achieving continuous evolution.

[0016] Furthermore, the method of the present invention also includes: S7: Visualization, based on the established database and model, draws comparison charts of actual and predicted values ​​for the training and test sets, providing a scientific data-driven basis for formulating and optimizing on-site installation technical specifications.

[0017] Compared with the prior art, the present invention has the following outstanding advantages: 1. Innovative principle: By using a technical fusion approach of "CFD numerical technology + RBF neural network to construct a mapping model", we have achieved digital and intelligent representation of complex physical relationships.

[0018] 2. High prediction accuracy and strong generalization ability. RBF networks excel at fitting high-dimensional nonlinear relationships. Extensive validation shows that the average relative error of this method can be stably controlled within 3.0%, which is superior to traditional empirical formulas and general linear models.

[0019] 3. Cost-effective and efficient, replacing most expensive and time-consuming physical experiments with "numerical experiments", with extremely low cost and speed per prediction, and can be easily extended to different media, environments and instrument types.

[0020] 4. Improve data quality: Systematically enhance the accuracy and comparability of flow velocity measurement data in industrial settings, providing solutions for environmental supervision, energy metering, and trade settlement.

[0021] 5. The quantitative analysis results provided can guide the optimization of installation and maintenance specifications, reducing measurement errors from the source. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the overall technical route and implementation process of the intelligent prediction method for S-type Pitot tube calibration coefficients described in this invention. Figure 2 This is an abstract flowchart of the S-type Pitot tube prediction model in this embodiment; Figure 3 A schematic diagram illustrating the geometric definition of the installation deviation of an S-shaped Pitot tube in a flow field (showing yaw angle α and pitch angle β). Figure 4 These are the front and side views of the grid center section under the baseline working condition of the S-type Pitot tube prediction model in this embodiment; Figure 5 The influence of key installation deviation parameters (such as fixed pitch angle) on the calibration coefficient K based on CFD data is shown by the actual flow experiment K and the numerical calculation K simulation fitting curve. Figure 6 This is a line graph showing the results of training on the test set and prediction set based on CFD data. Detailed Implementation

[0023] 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. In this embodiment, when obtaining the calibration coefficient of the S-type Pitot tube under the condition of satisfying or not satisfying the straight pipe condition in the following steps, it is necessary to record the parameters of each CFD simulation test: medium flow velocity range, pitch angle, yaw angle, medium temperature, differential pressure gauge measurement accuracy, and the result of the actual flow calibration coefficient K for satisfying or not satisfying the straight pipe condition. Figure 1-4 , Figure 5-6 As shown, a CFD-based method for predicting calibration coefficients of a S-type Pitot tube is presented, outlining the process, modeling, angle definition, mesh generation, K-actual flow and K-simulation fitting curves, and training prediction results. The method includes the following steps: Step 1: The calibration coefficient set for the S-type Pitot tube under ideal conditions was obtained based on CFD simulation. Specifically, a three-dimensional geometric model of the S-type Pitot tube and the pipeline was established using Computational Fluid Dynamics (CFD) software. Angle conditions were set for simulation. By changing the angle, the flow under different yaw angles α and pitch angles β (e.g., α=0°, β-45°, α=0°, β=-30°, α=0°, β=-15°, α=0°, β=0°, α=0°; β=15°, α=0°, β=30°, α=0°, β=45°…) was simulated to obtain the calibration coefficients at each angle. The CFD simulation settings included: using an unstructured mesh with mesh refinement near the Pitot tube pressure tap; selecting the standard k-ε turbulence model; setting the inlet boundary condition as a mass flow rate inlet and a pressure outlet; and using a convergence criterion of residuals less than 10⁻⁶. After CFD post-processing, the total pressure and static pressure of the Pitot tube were extracted, and the calibration coefficient K was calculated according to Bernoulli's equation. For example, at an angle of α=0° and β=0°, the calibration coefficient obtained under ideal opposing conditions is 0.8081.

[0024] Step 2: Step S1 involves creating non-ideal conditions that may be encountered in actual measurements, including calibration coefficient sets for different installation angle deviations, flow velocity ranges, and environmental parameters. CFD simulation is used to obtain calibration coefficients for each non-ideal condition. Taking an angle of α=0° and β=0° as an example, different installation angle deviations and flow field conditions are set, such as: yaw angles: -45°, -30°, -15°, 0°, 15°, 30°, 45°; pitch angles: -45°, -30°, -15°, 0°, 15°, 30°, 45°; medium flow velocity range: 5 m / s to 30 m / s (mass flow inlet and pressure outlet); medium temperature: 302K to 312K; differential pressure gauge measurement accuracy in actual flow experiments and numerical experiments; subsequently, the pitch angle is fixed at -30°, 0°, and 30°, and the yaw angle is varied to verify whether the calibration coefficient Ksimulation of the numerical simulation meets the calibration coefficient Kactual flow under the actual flow conditions. Through CFD simulation, calibration coefficients under various non-ideal operating conditions were obtained, such as: 0.8981, 0.8679, 0.8299, 0.8081, 0.7366, 0.6823, 0.5647, etc.

[0025] Step 3: The parameters such as installation pitch and yaw angle conditions, medium flow velocity range, differential pressure gauge measurement accuracy, and medium temperature in steps S1 and S2 are normalized. The S-type Pitot tube CFD simulation calibration coefficient set under different angles obtained in steps 1 and 2, along with the corresponding simulation conditions (pitch angle, yaw angle, medium flow velocity range, medium temperature, differential pressure gauge measurement accuracy), are combined into a six-dimensional vector. The first n dimensions of this multi-dimensional vector are denoted as the prediction model input xi (medium flow velocity range, pitch angle, yaw angle, medium temperature, differential pressure gauge measurement accuracy), and the last dimension is the output yi (i.e., calibration coefficient K). The parameters in the prediction model input xi are normalized using the following method: Normalizing the yaw and pitch angles allows us to characterize the degree of deviation between the actual measured angles and the angles of the actual flow pipe used for training. These two angles are the installation angle conditions explicitly set in tests S1 and S2, typically relative to the pipe axis, and are measured in degrees (°). Their ranges may be symmetrical (e.g., -30° to +30°), and the velocity vector at the probe axis has a coupled geometric projection (cosine vector mapping along the axis). The yaw and pitch angle ranges are set to [-45° to +45°], with (-45° to -30°) assigned a value of 0, (-30° to -15°) assigned a value of 1, (-15° to 0°) assigned a value of 2, (0° to 15°) assigned a value of 3, (15° to 30°) assigned a value of 4, and (30° to 45°) assigned a value of 5, assigned in 5° increments.

[0026] This "range" typically refers to the velocity value provided by the flow standard device during the test. It could be a specific velocity point (e.g., 10 m / s) or a velocity range (e.g., 8-10 m / s). For normalization, the velocity range is processed using normalization parameters to characterize the difference between the actual velocity measurement at the angle of the Pitot tube within the pipe and the velocity range of the medium in the actual flow pipe used for training. To obtain a more accurate Pitot tube calibration coefficient, the velocity range of the liquid in the large-diameter pipe should be estimated before measurement. Considering the feasibility of estimating the velocity in a typical pipe with a liquid medium velocity in the range of (5–30) m / s, a value of 0 is assigned for (5–7) m / s, a value of 1 is assigned for (8–10) m / s, and a value is assigned every 2 m / s.

[0027] Normalizing the medium temperature parameter can characterize the difference between the actual measurement angle and the medium temperature of the actual flow pipeline used for training. Considering the outdoor environment application of the S-type Pitot tube and the actual situation when calibrating the standard device, the temperature is set to 302K ~ 312K (℃ = K - 273.15), that is, the temperature range is set to (28.85~33.85]℃, (28.85~33.85]℃ is assigned a value of 0, (33.85~38.85]℃ is assigned a value of 1, and a value is assigned every 5℃.

[0028] According to the National Pressure Gauge Metrological Verification Regulation JJG875-2005, the accuracy class or maximum permissible error of a differential pressure gauge is usually indicated, and may be expressed as a percentage (e.g., ±0.5%FS), a reading percentage plus a range percentage (e.g., ±(0.1%RD+0.05%FS)), or an absolute error (e.g., ±1 Pa). The differential pressure gauge used in the standard device for training, with the actual Pitot tube positioned within the pipeline at an angle, has an accuracy class of 0.1, assigned a value of 0. Commercially available differential pressure gauges commonly have accuracy classes of 0.2, 0.5, 1.0, and 1.6. Classes of 0.1 and above are assigned a value of 1, for example, class 1.6 is assigned a value of 1. Before normalization, it needs to be quantified into a unified "error level" value.

[0029] For example, under the conditions of yaw angle α=45°, pitch angle β=30° offset angle, medium flow velocity of 15m / s, differential pressure gauge accuracy class of 0.1, and medium temperature of 302.41K, the normalized feature vector obtained is (5, 4,4,0.1,0), and the corresponding calibration coefficient is 0.7299.

[0030] Step 4: The outputs of the multidimensional vectors obtained in step 3 under various input conditions are formed into a matrix. Based on the 10-fold cross-validation approach, 70% of the matrix is ​​used as the training set, and 30% as the test set. Specifically, the matrix composed of approximately 140 sets of normalized multidimensional vectors (more data can be obtained by adding simulation conditions) is used, with 70% randomly selected as the training set and 30% as the test set. Based on the 10-fold cross-validation approach, the training set is further divided into 10 subsamples. One subsample is retained as data for validating the model, and the other 9 samples are used for training. Cross-validation is repeated 10 times, validating each subsample once. The results from the 10 cross-validations are averaged to obtain a single estimate.

[0031] Step 5: The training set is used to build the model. A radial basis function (RBF) neural network is constructed, with the following output function: ; Where φ is the radial basis function (usually a Gaussian function), cj is the j-th center point, wj is the weight, and b is the bias. The specific training process includes: determining the hidden layer center point cj: typically using K-means clustering to select M center points from the training set; determining the width parameter σ of the radial basis function: this can be selected through cross-validation; and calculating the hidden layer output matrix Φ, where... The weights w and biases b are solved using the least squares method, which minimizes the sum of squared errors.

[0032] Step 6: The RBF neural network model constructed in step 5 is tested using the test set obtained in step 4. The relative error between the predicted S-shaped Pitot tube K coefficients and the S-shaped Pitot tube K coefficients obtained from CFD simulation is calculated. The mean relative error (MRE) is used as the evaluation index: when the MRE is less than 1%, the model's prediction results are considered to meet expectations.

[0033] Step 7: If the test in step 6 meets the preset requirements, the model constructed in step 5 is considered to be able to predict the S-shaped Pitot tube calibration coefficient under actual working conditions; if it does not meet the requirements, step 5 needs to be repeated to adjust the model parameters (such as the number of hidden layer neurons, the width of the radial basis function, etc.) until the requirements are met.

[0034] This embodiment fully demonstrates the effectiveness, high accuracy, and practical value of the CFD-RBF intelligent prediction method proposed in this invention in actual industrial flue gas monitoring scenarios. This method not only solves the accuracy problem at specific measuring points but also forms a replicable and scalable technical system, providing an innovative technical solution for comprehensively improving the monitoring quality of flow velocity from stationary pollution sources. The above description is merely a preferred embodiment of this invention, but the scope of protection of this invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical principles and framework disclosed in this invention, such as using other advanced turbulence models (e.g., LES), trying different neural network structures (e.g., Gaussian process regression) for performance comparison, or integrating this method into an IoT platform to achieve cloud-based prediction and distribution, should all be covered within the scope of protection of this invention.

Claims

1. A CFD-based method for predicting the calibration coefficients of a S-type Pitot tube, characterized in that, Specifically, the following steps are included: S1: Construct a calibration coefficient database based on parametric CFD simulation. Specifically, a three-dimensional parametric geometric model of the S-shaped Pitot tube and the flow field is established. The system is set with various working conditions including installation angle deviation, flow velocity range and environmental parameters. Through CFD numerical simulation, a set of calibration coefficients under different working conditions is obtained. S2: Integrate the simulation data obtained in step S1, extract key influencing parameters to construct a feature vector set, the feature vector including at least the installation angle deviation parameter, flow field parameter and environmental parameter, and use the corresponding calibration coefficient as the output quantity; S3: Divide the CFD simulation data obtained in steps S1 and S2 into a training set for model training, a validation set for hyperparameter tuning, and a test set for final performance evaluation. S4: Divide the data obtained in step S3 into a training set and a test set. Based on the training set data, construct a radial basis function (RBF) neural network model, determine the network structure, the center point of the radial basis function and the output function of the hidden layer of the neural network, and use the validation set to systematically optimize the model hyperparameters. S5: Construct an RBF neural network prediction model, and use the test set to evaluate the prediction performance of the model constructed in step S4. The root mean square error (RMSE), mean relative error (MRE), and coefficient of determination (R) are used as the core evaluation indicators. S6: Once the model performance meets the preset requirements, apply it to the prediction of calibration coefficients under actual working conditions; If the performance does not meet the requirements, return to step S4 to adjust the model parameters until the requirements are met; and establish a model update mechanism for continuous optimization.

2. The method according to claim 1, characterized in that, In step S1, the CFD numerical simulation specifically includes: establishing a 1:1 three-dimensional parametric model; performing mesh generation using unstructured meshing technology, and refining the mesh for the local region and near-wall surface of the Pitot tube; and performing mesh independence verification. A Realizable k-ε turbulence model is selected, and boundary conditions such as mass flow rate inlet and pressure outlet are set. A pressure-based coupled solver and a second-order discretization scheme are used. The convergence criterion is that the residuals of each governing equation decrease to below 10 and the changes in monitored physical quantities tend to stabilize.

3. The method according to claim 1, characterized in that, In steps S1 and S2, the S-type Pitot tube uses a calibrated standard L-type Pitot tube as a standard in the non-opposing calibration process described above to provide a standard flow rate value; the calibration is based on Bernoulli's principle, specifically calculating the calibration coefficient according to Bernoulli's equation, as shown in formula (1). (1) (1) In the formula, K represents the calibration coefficient dependent on the yaw angle α and the pitch angle β. S-type Pitot tube calibration coefficient, This indicates the differential pressure between the total pressure orifice and the static pressure orifice of the pitot tube to be calibrated. It is the density of the fluid inside the pipe. It is the current flow velocity at the location of the Pitot tube being tested.

4. The method according to claim 1, characterized in that... The different operating conditions in step S1 include: the change in installation angle offset (yaw angle, pitch angle), the comparison between the numerical simulation calibration coefficient K and the actual flow calibration coefficient K, the range of medium flow velocity, the change in medium temperature, and the accuracy of differential pressure gauge measurement.

5. The method according to claim 1, characterized in that, The parameters of the feature vector in step S2 are set to six dimensions: medium flow velocity range, pitch angle, yaw angle, medium temperature, differential pressure gauge measurement accuracy, and numerical simulation calibration coefficient Ksimulation (whether the actual flow conditions calibration coefficient Kactuation are met).

6. The method according to claim 1, characterized in that, In steps S3 and S4, cross-validation is used to assist in model training and evaluation, thereby enhancing the robustness and generalization ability of the model.

7. The method according to claim 1, characterized in that, The process of building the RBF neural network model in step S4 is as follows: Define the complete original dataset, which contains 140 samples, each with 6 input features: （2） In equation (2): Xi is the 6-dimensional input feature vector of the i-th sample; Yi is the target output value (Pitot tube calibration coefficient) of the i-th sample. The 140 samples are randomly arranged, with the first 110 selected as the training set and the last 30 as the test set. Randomly arrange the index: Iranian = π({1,2,…,140}) (3) In equation (3), π({1,2,…,140}) is a random permutation function; The training and test sets are organized into matrix form, where each column of the input feature matrix corresponds to a sample and the output vector corresponds to the target value of each sample. Training set: Test set: Construct a radial basis function neural network using Gaussian radial basis functions. The number of neurons in the hidden layers of the network is equal to the number of training samples, and each training sample corresponds to the center of a radial basis function. For the j-th radial basis function (j = 1, 2, ..., M, where M = 110 is the number of training samples); （4） Among them (4), It is the normalized feature vector of the j-th training sample, serving as the center of the radial basis function; is the width parameter of the j-th radial basis function; the expansion speed parameter is 1000 to control the smoothness of the function; This represents the Euclidean norm.

8. The output of an RBF neural network is a linear combination of the outputs of its hidden layers: （5） In equation (5), w0 is the bias term; wj is the weight coefficient corresponding to the j-th radial basis function; M = 110 is the number of hidden layer neurons (equal to the number of training samples). The weight coefficients are solved by the least squares method to minimize the error between the network's output on the training set and the target value. Define the hidden layer output matrix, with the first column all being 1, corresponding to the bias term: The method according to claim 1, characterized in that, In step S5, the preset requirements for model performance are: the mean relative error (MRE) on the test set is less than 1%, and the coefficient of determination (R) is greater than 0.

98. The root mean square error (RMSE) of the model on the training and test sets is calculated. The root mean square error on the training set is: （6） Among them, equation (6) These are the target values ​​from the original training set. The root mean square error of the test set is: （7） Among them (7) This is the target value of the original test set.

9. The method according to claim 1, characterized in that, Step S2 also includes a data preprocessing step, which normalizes (standardizes) the feature vectors. The normalization strategy considers the physical meaning and value range of each parameter, linearly mapping the original data to the [0,1] interval to eliminate dimensional differences between different features and improve model training stability. The test set uses the same normalization parameters as the training set. For each input feature dimension j = 1, 2, … , 6, we have: Normalized eigenvalues: Output normalization: in: Convert the predicted values ​​at the normalized scale back to the original data scale; Training set denormalization: Vector form: Test set denormalization: The method according to claim 1, characterized in that, The method also includes model update and impact analysis steps: when new CFD simulation data or field measurement verification data are obtained, the model parameters are updated by incremental learning or periodic full retraining to enable the model to continuously evolve; and based on the updated model and CFD database, parameter sensitivity analysis and interaction effect research are carried out to quantitatively evaluate the influence of various factors such as installation angle deviation on the calibration coefficient, and provide data support for the optimization of field installation specifications.

Images