A hollow turbine blade casting wall thickness size prediction method based on machine learning

Abstract

This invention discloses a machine learning-based method for predicting the wall thickness of hollow turbine blade castings, belonging to the field of precision casting technology for hollow turbine blades for aero-engines. The method includes the following steps: constructing a set of points for predicting wall thickness; designing wax patterns and tooling for marking wall thickness measurement points on the casting; constructing a raw machine learning database; preprocessing the raw wall thickness data; establishing a size prediction model using a machine learning regression model algorithm and a training / test set partitioning strategy; verifying the prediction performance of the trained model; if the model's prediction accuracy does not meet the requirements, adjusting the basic parameters of the machine learning model until a suitable prediction accuracy is achieved; using the trained machine learning model to predict the wall thickness of other batches of turbine blades, and selecting wax patterns for hollow turbine blades that do not meet the requirements. This invention improves the dimensional pass rate and production efficiency of blades, increases the utilization rate of production line equipment resources, and reduces production costs.

Description

Technical Field

[0001] This invention belongs to the field of precision casting technology for hollow turbine blades for aero-engines, specifically involving a method for predicting the wall thickness of hollow turbine blade castings based on machine learning. Background Technology

[0002] Turbine blades are critical hot-end components of aero engines, and their manufacturing reliability has a profound impact on the engine's service performance and lifespan. To meet the harsh service conditions of turbine inlet temperatures exceeding 1500K, advanced aero engines both domestically and internationally design turbine blades as hollow structures with complex internal and external cavities, and manufacture them using investment casting technology.

[0003] Investment casting mainly includes three important steps: investment pattern preparation, shell preparation, and casting pouring. In the whole process, multiple nonlinear physical processes are coupled with each other and accompanied by the type and phase transformation of the material medium. The geometric dimensions of the blades change continuously as the investment casting process progresses, resulting in the final casting dimensions deviating from the design dimensions, which is difficult to characterize using traditional fitting methods.

[0004] Predicting and evaluating the wall thickness qualification status of hollow turbine blade castings is a quantitative analysis problem involving multi-dimensional data. The core issue lies in accurately predicting the numerical changes in casting wall thickness accuracy during the investment casting process. Existing technical literature highlights the crucial role of precise shape control of the hollow turbine blade wax pattern in improving the final manufacturing accuracy and performance of the blade. It analyzes the main factors affecting blade profile deformation during the investment casting process from wax pattern to casting. However, the literature's analysis of the wall thickness accuracy error of hollow turbine blades is limited to qualitative analysis or simulation of deformation, without establishing a numerical relationship suitable for predicting the wall thickness accuracy of hollow turbine blades. Existing technologies include methods for predicting casting wall thickness deviation using mesh feature data from CAD reference models, but these methods are limited to predicting wall thickness accuracy during secondary finishing after investment casting and cannot predict wall thickness dimensions during the investment casting process. Currently, no effective solution has been proposed to address these issues. Summary of the Invention

[0005] The technical problem to be solved:

[0006] To overcome the shortcomings of existing technologies, this invention provides a machine learning-based method for predicting the wall thickness of hollow turbine blade castings. The aim is to address the problem of excessive wall thickness in hollow turbine blades produced by investment casting due to complex physical processes and human uncertainties. This method can identify unqualified wax patterns that may cause excessive wall thickness during investment casting, thereby improving the dimensional pass rate and production efficiency of the blades, increasing the utilization rate of production line equipment resources, and reducing production costs.

[0007] The technical solution of this invention is: a method for predicting the wall thickness of hollow turbine blade castings based on machine learning, characterized by the following specific steps:

[0008] Step 1: Based on the internal structure and dimensional design requirements of the hollow turbine blade, construct a set of points with wall thickness to be predicted;

[0009] Step 2: Based on the distribution of wall thickness points and the shrinkage coefficient, design the wax pattern and the tooling for marking the wall thickness measuring points on the casting;

[0010] Step 3: Obtain the measured values ​​of wax pattern wall thickness and casting wall thickness from multiple production batches to build a raw database for machine learning;

[0011] Step 4: Perform data preprocessing on the raw wall thickness data;

[0012] Step 5: Using the preprocessed wax pattern wall thickness data as input and the preprocessed casting wall thickness data as output, a size prediction model is established through machine learning regression model algorithm and training set / test set partitioning strategy.

[0013] Step 6: Validate the prediction performance of the trained model. If the prediction accuracy does not meet the requirements, adjust the basic parameters of the machine learning model until a suitable prediction accuracy is achieved.

[0014] Step 7: Use the trained machine learning model to predict the wall thickness of other batches of turbine blades and screen out the hollow turbine blade wax patterns of unqualified blades.

[0015] A further technical solution of the present invention is: in step 1, the distribution positions of the casting wall thickness points are determined by the cross-sectional height H (H1, H2, H3, ...) of the aero-engine rotation center and the position of the internal cavity structural features K (K0, K1, K2, ...).

[0016] A further technical solution of the present invention is as follows: In step 2, the wax pattern / casting wall thickness measuring point marking fixture includes a blade basin template and a blade back template. The blade basin template and the blade back template are connected by a rotating shaft sleeve structure. The contour shape of the inner surface of the blade basin and blade back templates is adapted to the casting to be measured and the wax pattern. The specific dimensions are obtained by three-dimensional non-uniform scaling based on the theoretical casting model. After determining the template shape, a fixing structure is set to ensure the relative positional relationship between the wall thickness marking fixture and the wax pattern and casting to be measured. Several conical holes are machined along the normal direction of the curved surface at all measuring point positions of the fixture for marking the wall thickness measuring points of the wax pattern or casting.

[0017] A further technical solution of the present invention is: the three-dimensional scaling ratio of the wax pattern wall thickness measuring point marking fixture is: 1.032 in the X direction, 1.032 in the Y direction, and 1.028 in the Z direction; the three-dimensional scaling ratio of the casting wall thickness measuring point fixture is: 1.016 in the X direction, 1.016 in the Y direction, and 1.014 in the Z direction.

[0018] A further technical solution of the present invention is: a boss is provided on the positioning surface, and the wax pattern / casting wall thickness measuring point marking fixture contacts the edge plate surface of the blade to be measured through the boss to ensure accurate positioning.

[0019] A further technical solution of the present invention is as follows: In step 3, the wall thickness measurement value is obtained through the ultrasonic thickness measurement principle. First, the wall thickness measurement point position is determined on the wax pattern or casting surface by using a wall thickness measurement point marking fixture. Then, the wall thickness data at each position is measured using an ultrasonic measuring device. The wall thickness data of each point needs to be measured three times and the average value is recorded. The format of the wall thickness dimension dataset for each blade is as follows:

[0020]

[0021]

[0022] Where, θ w Includes all wall thickness measurement data of the wax model. This refers to the set of parameters of a wax model at section H1, composed of data from various wall thickness measurement points; θ c Includes all wall thickness measurements of the casting corresponding to the wax pattern. This refers to the set of parameters for the casting at section H1, composed of data from various wall thickness measurement points.

[0023] A further technical solution of the present invention is: in step 4, Z-Score standardization is used to preprocess the wall thickness data at the same measuring point of all blade samples. After standardization, all wax pattern wall thickness data and casting wall thickness data are within the dimensionless numerical range of [-1,1].

[0024] A further technical solution of the present invention is: in step 5, machine learning regression algorithm code is written based on the Scikit-learn algorithm library functions in the Python programming language, and the input data of all models is uniformly the preprocessed wall thickness data of the i-th cross-section of the wax model sample, i.e. The output data of all models are unified as the preprocessed wall thickness data of the i-th cross-section of the casting sample, i.e. After setting the model's parameters to default values, the machine learning model was trained, and the goodness-of-fit R-squared was used to compare the models. 2 The value is used as a performance evaluation index for the model, and the goodness of fit R is selected. 2The largest machine learning regression algorithm was used as the base regression model for predicting casting wall thickness. Further, cross-validation was employed to adjust the input data sample size of the training model. The complete dataset was divided into training / test sets at ratios of 50% / 50%, 60% / 40%, 70% / 30%, 80% / 20%, and 90% / 10% to conduct comparative experiments on the base regression model, verifying the model's goodness of fit (R²) on the training and test sets. 2 The value is used to further optimize the dataset partitioning strategy.

[0025] A further technical solution of the present invention is as follows: In step 6, the prediction requirement is that the size deviation between the predicted value and the actual value is within ±0.10mm; a BP artificial neural network model is selected, and if the prediction accuracy of the model does not meet the requirements, the number of hidden layers, the number of nodes in a single hidden layer, and the learning rate of the artificial neural network are adjusted until the prediction accuracy meets the requirements.

[0026] A further technical solution of the present invention is as follows: In step 7, for the blades produced subsequently, after the wax pattern pressing process, the measured value of the wax pattern wall thickness is input into the trained prediction model to obtain the casting wall thickness. If the predicted size is out of tolerance, it is marked as an unqualified wax pattern. If the predicted size is within the qualified range, the subsequent processes are continued.

[0027] A machine learning-based system for measuring the wall thickness of hollow turbine blade castings includes a dedicated wax pattern wall thickness measuring fixture, a dedicated casting wall thickness measuring fixture, a Novascope 6000 ultrasonic thickness gauge, and a PC with a Python programming environment. It should be noted that equipment used in the hollow turbine blade investment casting production line is not within the scope of this invention; such equipment is only used to provide raw data for training and validating the machine learning model.

[0028] Beneficial effects

[0029] The beneficial effects of this invention are as follows: By selecting and optimizing the machine learning regression model and the training / test set partitioning strategy, this invention establishes a BP artificial neural network model for predicting the wall thickness of turbine blades. The specific parameters of the model are: 8 neurons in the input layer, 25 neurons in the hidden layer, 1 neuron in the output layer, and 3 layers in the hidden layer. This prediction model can predict the wall thickness of the finished casting formed after the investment casting process based on the measured wall thickness of the wax pattern of the turbine blade at the same cross section. The results of the verification experiment show that the absolute error range between the predicted value and the actual measured value is -0.09 to 0.06 mm. Compared with the traditional linear fitting method (-0.26 to 0.10 mm), the average prediction error of the wall thickness value is reduced by 0.09625 mm.

[0030] This invention can very effectively predict the changes in the wall thickness of castings during the investment casting process of hollow turbine blades for aero engines. It helps to identify unqualified wax patterns in advance during the production process, thereby reducing the formation of castings with excessive wall thickness and improving the pass rate of investment casting products.

[0031] By using an artificial neural network model, an accurate dimensional transfer relationship with spatiotemporal correspondence is established between the wall thickness of the wax pattern obtained from wax pattern pressing and the wall thickness of the casting obtained from melting and pouring. This enables accurate prediction of the casting wall thickness. Subsequently, the established artificial neural network prediction model can be used to quickly identify and eliminate unqualified wax patterns that are prone to wall thickness deviations. This can greatly improve the wall thickness compliance of blade castings in the subsequent wax pattern pressing process, reduce production costs, and increase the pass rate of blade wall thickness dimensions. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the method for establishing a prediction model for the wall thickness of hollow turbine blades in an example of the present invention.

[0033] Figure 2 This is a schematic diagram of the regression prediction results of different machine learning models in the examples of this invention;

[0034] Figure 3 This is a schematic diagram of the training set / test set partitioning strategy of the artificial neural network prediction model in an example of the present invention.

[0035] Figure 4 This is a diagram showing the distribution of the cross section of a hollow turbine guide vane of a certain type and the location of the wall thickness measurement points in an example of the present invention.

[0036] Figure 5 This is a schematic diagram of the structure of the guide vane wax pattern wall thickness measuring point marking fixture in an example of the present invention. Since the casting wall thickness measuring point marking fixture has the same structure and only differs slightly in size, it will not be shown again here. Detailed Implementation

[0037] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0038] This embodiment provides a machine learning-based method for predicting the wall thickness of hollow turbine blade castings. The purpose is to address the problem of excessive wall thickness in hollow turbine blades produced by investment casting due to complex physical processes and human uncertainties. It can screen out unqualified wax patterns that may cause excessive wall thickness during investment casting, thereby improving the dimensional pass rate and production efficiency of the blades, increasing the utilization rate of production line equipment resources, and reducing production costs.

[0039] This embodiment presents a machine learning-based method for predicting the wall thickness of hollow turbine blade castings, referring to... Figure 1 The steps shown are as follows:

[0040] (1) Determine the set of points with wall thickness to be predicted based on the internal structure and size design requirements of the hollow turbine blade;

[0041] (2) Design wax pattern and casting wall thickness measuring point marking fixtures according to the distribution location of wall thickness points and shrinkage coefficient;

[0042] (3) Use an ultrasonic measuring instrument to detect the wall thickness of wax patterns and castings in multiple production batches to build a raw database for machine learning;

[0043] (4) Preprocess the original data of turbine blade wax patterns and casting wall thickness;

[0044] (5) Using the wax pattern wall thickness data after data processing as the input and the casting wall thickness data after data processing as the output, the machine learning regression prediction model is selected, a suitable training set and test set partitioning strategy is set, the model parameters are adjusted, and a size prediction model is established.

[0045] (6) Test the prediction performance of the trained model. If the prediction accuracy of the model does not meet the prediction requirements, then adjust the basic parameters of the machine learning model to correct it until a suitable prediction accuracy is achieved.

[0046] (7) Use the trained machine learning model to predict the wall thickness of other batches of turbine blades and select the wax pattern of blades that are prone to exceeding the tolerance.

[0047] Preferably, the distribution of casting wall thickness points in step (1) is determined by the cross-sectional height H (H1, H2, H3, ...) of the aero-engine rotation center and the location of internal cavity structural features K (K0, K1, K2, ...).

[0048] Preferably, the shrinkage coefficient value of the wax pattern wall thickness measuring point marking fixture in step (2) is based on the scaling ratio given in the turbine blade outer mold design, and the reverse-enlarged casting model serves as the basis for the inner surface shape design of the wall thickness measuring point marking fixture; the casting wall thickness measuring point marking fixture is directly based on the final casting model for inner surface design. In addition, a boss needs to be set at the end face to contact the edge plate surface of the blade to be measured to ensure accurate positioning; and tapered holes of the same size are machined along the normal direction of the curved surface at all measuring point positions of the fixture for marking.

[0049] Reference Figure 5As shown, the prototype design of the wax pattern / casting wall thickness measuring point marking fixture includes a blade basin template and a blade back template. The blade basin template and the blade back template are connected by a rotating shaft sleeve structure. The contour shape of the inner surface of the blade basin and blade back templates is adapted to the casting to be measured and the wax pattern. The specific dimensions can be obtained by three-dimensional non-uniform scaling based on the theoretical casting model. The three-dimensional scaling rate of the wax pattern wall thickness measuring point marking fixture is: 1.032 in the X direction, 1.032 in the Y direction, and 1.028 in the Z direction; the three-dimensional scaling rate of the casting wall thickness measuring point fixture is: 1.016 in the X direction, 1.016 in the Y direction, and 1.014 in the Z direction. After determining the shape of the professional template, a fixing structure needs to be set to ensure the relative positional relationship between the wall thickness marking fixture and the wax pattern and casting to be measured.

[0050] Preferably, the wall thickness measurement value in step (3) is obtained through ultrasonic thickness measurement. First, the wall thickness measurement point positions are determined on the wax pattern or casting surface using a wall thickness measurement point marking fixture. Then, the wall thickness data at each position is measured using an ultrasonic measuring device. The wall thickness data for each point needs to be measured three times, and the average value is recorded. The format of the wall thickness dimension dataset for each blade is as follows:

[0051]

[0052]

[0053] Where, θ w Includes all wall thickness measurement data of the wax model. This refers to the set of parameters for a wax model at section H1, composed of data from various wall thickness measurement points. θ c Includes all wall thickness measurements of the casting corresponding to the wax pattern. This refers to the set of parameters for the casting at section H1, composed of data from various wall thickness measurement points.

[0054] Preferably, in step (4), the data preprocessing adopts the Z-Score standardization method to preprocess the wall thickness data at the same measuring point of all blade samples. After standardization, all wax pattern wall thickness data and casting wall thickness data are in the dimensionless numerical range of [-1,1]. It should be noted that in order to ensure the accuracy of the prediction model, the sample size of the database should not be less than 100.

[0055] Preferably, in step (5), the preprocessed database is compared to other models to assess their fitting performance on the test set and select the best model. It should be noted that, for the database in this embodiment, the BP artificial neural network model exhibits the best fitting performance. Subsequently, the preprocessed sample data is used to train artificial neural network models with the same parameters using different training / test set ratios, and the goodness of fit R of the artificial neural network model on the training and test sets is verified.2 Values ​​are used to avoid overfitting or underfitting of the model.

[0056] Preferably, the model prediction requirement in step (6) is that the size deviation between the predicted value and the actual value is within ±0.04 mm. If the prediction accuracy of the model does not meet the requirements, the parameters such as the number of hidden layers, the number of nodes in a single hidden layer, and the learning rate of the artificial neural network are adjusted until the prediction accuracy meets the requirements.

[0057] Preferably, in step (7), for the blades produced subsequently, after the wax pattern pressing process, the measured value of the wax pattern wall thickness is input into the trained prediction model to obtain the casting wall thickness. If the predicted size is out of tolerance, it is marked as an unqualified wax pattern. If the predicted size is within the qualified range, the subsequent process continues.

[0058] Preferably, the hardware used in steps (1) to (7) includes a dedicated wax pattern wall thickness measuring fixture, a dedicated casting wall thickness measuring fixture, a Novascope 6000 ultrasonic thickness gauge (USA), and a PC host computer with a Python programming environment installed. It should be noted that the equipment involved in the hollow turbine blade investment casting production line is not within the scope of this invention; such equipment is only used to provide raw data for machine learning model training and verification.

[0059] To construct a casting wall thickness prediction model for a typical turbine blade, the distribution locations of the selected blade section wall thickness measurement points are shown in [reference needed]. Figure 4 and Figure 5 .

[0060] For the turbine blade wall thickness prediction model described in the example, 100 blades with complete dimensional information are randomly selected from more than 5 production batches for the construction of the machine learning database.

[0061] Since numerous physical factors influence the wall thickness of turbine blade castings, and the prediction model proposed in this invention aims to determine the dimensional transmission relationship between the wax pattern wall thickness and the casting wall thickness during investment casting, other potential influencing factors need to be controlled. Specific measures are as follows: 1. Use core molds and outer molds with the same mold state during production; 2. After sintering, the ceramic cores are inspected for dimensions using blue light scanning, and matched with the theoretical model based on the least squares fitting method. Cores with an overall surface deviation within ±0.10mm are selected for subsequent production; 3. The wax injection process parameters (wax injection pressure, wax injection temperature, wax injection time, holding time), shell forming process parameters (number of shell layers, drying time, firing temperature, firing time), melting process parameters (melting temperature, heater temperature, pulling speed), core removal process parameters (alkali concentration, core removal temperature, core removal time), and vacuum heat treatment process parameters (heat treatment temperature, heat treatment time) all strictly follow the same process specifications.

[0062] In this embodiment, the wax pattern wall thickness data of the turbine working blades is acquired using an ultrasonic measuring instrument, and the casting wall thickness data is acquired using an industrial CT scanner. The wax pattern wall thickness data within the same cross-section is used as the input parameter, and the casting wall thickness parameters at corresponding measuring points after the investment casting process are used as the output parameter to construct a dataset.

[0063] θ=[H1,H2,H3,...]=[(K0,K1,K2,...) H1 ,(K0,K1,K2,...) H2 ,(K0,K1,K2,...) H3 ,...]

[0064] The Z-Score method was used to standardize the wax pattern wall thickness data and the casting wall thickness data. The standardization formula is shown below:

[0065]

[0066] x — The observed value of a sample at a certain measuring point on a certain measurement cross section.

[0067] μ — the sample mean of the wax pattern or casting wall thickness at this location for different samples in the dataset.

[0068] δ — Population standard deviation of all samples in the dataset at this location

[0069] The topology of the artificial neural network was determined, and the preprocessed wax pattern wall thickness dataset was used as the input data, while the casting wall thickness dataset was used as the output data. The artificial neural network was trained n times using different training / test set partitioning strategies, and the optimal dataset partitioning strategy was selected. The determined artificial neural network had 8 neurons in the input layer, 25 neurons in the hidden layer, and 1 neuron in the output layer; the number of hidden layers was 3. Under the same neural network structure, the model was trained with training / test set ratios of 50% / 50%, 60% / 40%, 70% / 30%, 80% / 20%, and 90% / 10%. Comparison showed that the model trained with an 80% / 20% training / test set ratio had the highest fitting accuracy and effectively avoided overfitting and underfitting.

[0070] The prediction performance of the trained machine learning model is tested using a prediction set outside the dataset. If there are cases where the predicted value of the wall thickness measurement point deviates from the measured value by more than ±0.10 mm, the prediction model is corrected by adjusting the structural parameters of the artificial neural network model until the prediction accuracy meets the requirements.

[0071] The artificial neural network model constructed in this embodiment is used to predict the casting wall thickness and determine the wall thickness compliance of two actual hollow turbine blade wax pattern castings. Casting experiments were conducted to verify the results. The prediction and measurement results are shown in Tables 1 and 2. The results show that the method established in this embodiment can accurately predict the turbine blade casting wall thickness. The absolute error range between the predicted and actual measured values ​​is -0.09 to 0.06 mm. Compared with the traditional linear fitting method (-0.26 to 0.10 mm), the average prediction error of the wall thickness value is reduced by 0.09625 mm, demonstrating the superiority of the proposed method in predicting turbine blade wall thickness. This method helps to identify unqualified wax patterns in advance during the production process, thereby reducing the formation of castings with excessive wall thickness during casting and improving the pass rate of investment casting products.

[0072] Table 1

[0073]

[0074] Table 2

[0075]

[0076] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for predicting the wall thickness dimension of a hollow turbine blade casting based on machine learning, characterized by The specific steps are as follows: Step 1: Based on the internal structure and dimensional design requirements of the hollow turbine blade, construct a set of points with wall thickness to be predicted; Step 2: Based on the distribution location and shrinkage coefficient of the wall thickness points, design the wax pattern and casting wall thickness measuring point marking fixture; the wax pattern / casting wall thickness measuring point marking fixture includes a blade basin template and a blade back template, which are connected by a rotating shaft sleeve structure. The contour shape of the inner surface of the blade basin and blade back templates is adapted to the casting to be measured and the wax pattern. The specific dimensions are obtained by three-dimensional non-uniform scaling based on the theoretical casting model; after determining the template shape, a fixing structure is set to ensure the relative positional relationship between the wall thickness marking fixture and the wax pattern and casting to be measured; several conical holes are machined along the normal direction of the curved surface at all measuring point positions of the fixture for marking the wall thickness measuring points of the wax pattern or casting; Step 3: Obtain the measured values ​​of wax pattern wall thickness and casting wall thickness from multiple production batches to build a raw database for machine learning; Step 4: Perform data preprocessing on the raw wall thickness data; Step 5: Using the preprocessed wax pattern wall thickness data as input and the preprocessed casting wall thickness data as output, a size prediction model is established using a machine learning regression model algorithm and a training / test set partitioning strategy. The machine learning regression algorithm code is written based on the Scikit-learn algorithm library functions in the Python programming language. All model input data are unified as the wax pattern sample's [number missing]. i Preprocessed data of wall thickness for each cross section, i.e. The output data of all models are unified as the casting sample number. i Preprocessed data of wall thickness for each cross section, i.e. After setting the model's parameters to default values, the machine learning model was trained, and the goodness-of-fit R-squared was used to compare the models. 2 The value is used as a performance evaluation index for the model, and the goodness of fit R is selected. 2 The largest machine learning regression algorithm was used as the base regression model for predicting casting wall thickness. Further, cross-validation was employed to adjust the input data sample size of the training model. The complete dataset was divided into training / test sets at ratios of 50% / 50%, 60% / 40%, 70% / 30%, 80% / 20%, and 90% / 10% to conduct comparative experiments on the base regression model, verifying the model's goodness of fit (R²) on the training and test sets. 2 The value is used to further optimize the dataset partitioning strategy; Step 6: Validate the prediction performance of the trained model. If the prediction accuracy does not meet the requirements, adjust the basic parameters of the machine learning model until a suitable prediction accuracy is achieved. Step 7: Use the trained machine learning model to predict the wall thickness of other batches of turbine blades and screen out the hollow turbine blade wax patterns of unqualified blades.

2. The method for predicting the wall thickness of hollow turbine blade castings based on machine learning according to claim 1, characterized in that: In step 1, the distribution of the casting wall thickness points is determined by the cross-sectional height H (H1, H2, H3, ...) of the aero-engine rotation center and the location of the internal cavity structural features K (K0, K1, K2, ...).

3. The method for predicting the wall thickness of hollow turbine blade castings based on machine learning according to claim 1, characterized in that: The three-dimensional scaling ratio of the wax pattern wall thickness measuring point marking fixture is: 1.032 in the X direction, 1.032 in the Y direction, and 1.028 in the Z direction; the three-dimensional scaling ratio of the casting wall thickness measuring point fixture is: 1.016 in the X direction, 1.016 in the Y direction, and 1.014 in the Z direction.

4. The method for predicting the wall thickness of hollow turbine blade castings based on machine learning according to claim 1, characterized in that: A boss is provided on the positioning surface, and the wax pattern / casting wall thickness measuring point marking fixture contacts the edge plate surface of the blade to be measured through the boss to ensure accurate positioning.

5. The method for predicting the wall thickness of hollow turbine blade castings based on machine learning according to any one of claims 1-4, characterized in that: In step 3, the wall thickness measurement value is obtained through ultrasonic thickness measurement. First, the wall thickness measurement point positions are determined on the wax pattern or casting surface using a wall thickness measurement point marking fixture. Then, the wall thickness data at each position is measured using ultrasonic measuring equipment. The wall thickness data for each point needs to be measured three times, and the average value is recorded. The format of the wall thickness dimension dataset for each blade is as follows: in, Includes all wall thickness measurement data of the wax model. It refers to the set of parameters of a wax model at section H1, composed of data from various wall thickness measurement points; Includes all wall thickness measurements of the casting corresponding to the wax pattern. This refers to the set of parameters for the casting at section H1, composed of data from various wall thickness measurement points.

6. The method for predicting the wall thickness of hollow turbine blade castings based on machine learning according to claim 5, characterized in that: In step 4, Z-Score standardization is used to preprocess the wall thickness data at the same measuring point of all blade samples. After standardization, all wax pattern wall thickness data and casting wall thickness data are within the dimensionless numerical range of [-1,1].

7. The method for predicting the wall thickness of hollow turbine blade castings based on machine learning according to claim 6, characterized in that: In step 6, the prediction requirement is that the size deviation between the predicted value and the actual value is within ±0.10mm; a BP artificial neural network model is selected, and if the prediction accuracy of the model does not meet the requirements, the number of hidden layers, the number of nodes in a single hidden layer, and the learning rate of the artificial neural network are adjusted until the prediction accuracy meets the requirements.

8. The method for predicting the wall thickness of hollow turbine blade castings based on machine learning according to claim 7, characterized in that: In step 7, for the blades produced subsequently, after the wax pattern pressing process, the measured value of the wax pattern wall thickness is input into the trained prediction model to obtain the casting wall thickness. If the predicted size is out of tolerance, it is marked as an unqualified wax pattern; if the predicted size is within the acceptable range, the subsequent processes continue.

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