Model deformation prediction method and device, terminal equipment and storage medium

Abstract

The invention relates to the technical field of machine learning, in particular to a model deformation prediction method and device, terminal equipment and a storage medium. The method comprises the following steps of: acquiring deformation characteristics of a mold through acquiring and scanning modes of a manufacturing execution system and a technical support system; preprocessing the deformation features to obtain preprocessed features, and standardizing the preprocessed features to obtain standardized features; and inputting the standardized features into a trained deformation prediction model to obtain the compressible allowance of the mold. In this way, automatic prediction and output of the pressure allowance of the model are achieved.

Description

Technical Field

[0001] This application relates to the field of machine learning technology, and in particular to a model deformation prediction method, apparatus, terminal device and storage medium. Background Technology

[0002] Based on historical and current data from the aluminum profile production process (such as the ratio of theoretical to actual weight, aluminum rod material, extrusion breakthrough pressure, surface quality of the extruded profile, wall thickness, and other related factors), it is necessary to accurately predict the degree of mold deformation to reach the allowable compression before mold repair is required. Currently, mold deformation prediction is limited to experience-based maintenance methods involving manual inspections, which are costly, time-consuming, and have low accuracy, making them difficult to adapt to the current production environment. Summary of the Invention

[0003] In view of this, the embodiments of this application provide a model deformation prediction method, which can effectively solve the problems of high cost and long time.

[0004] In a first aspect, embodiments of this application provide a model deformation prediction method, including: Deformation characteristics of the mold are obtained through manufacturing execution systems and technical support systems, as well as scanning. The deformation features are preprocessed to obtain preprocessed features, and the preprocessed features are standardized to obtain standardized features. The standardized features are input into the trained deformation prediction model to obtain the compressibility allowance of the mold.

[0005] In some embodiments, the training method for the deformation prediction model includes: Deformation characteristics of the mold are obtained through manufacturing execution systems and technical support systems, as well as scanning. The deformation features are preprocessed to obtain preprocessed features, and the preprocessed features are standardized to obtain standardized features. The standardized features are then encoded to obtain the encoded features; Feature selection is performed on the encoded features to obtain training features; The training features are input into the pre-trained model for training, and the parameters are adjusted according to the loss function until the loss value converges or the number of iterations reaches the preset number to end the training, thus obtaining the deformation prediction model.

[0006] In some embodiments, the preprocessing of the deformation features to obtain preprocessed features includes: Check for duplicate data in the deformation features and remove duplicate data; Identify missing values ​​in the deformation features and eliminate them by interpolation, deletion, or adding default values; Noise values ​​are removed from the deformation features to obtain smooth data.

[0007] In some embodiments, the preprocessed features are standardized to obtain standardized features, including: By means shifting and standard deviation scaling, the preprocessed features are converted into distributed data with a mean of 0 and a standard deviation of 1, thereby obtaining standardized features.

[0008] In some embodiments, the step of feature encoding the standardized features to obtain encoded features includes: The non-numerical data in the standardized features are one-hot encoded and converted into binary vectors.

[0009] In some embodiments, the step of performing feature selection on the encoded features to obtain training features includes: The correlation strength between the features and the target variable is quantified by hypothesis testing or correlation indicators, and the encoded features with a statistical correlation strength greater than the pre-defined strength are selected.

[0010] In some embodiments, the step of quantifying the association strength between the feature and the target variable through hypothesis testing or correlation indicators includes: determining the association strength between the quantified feature and the target variable through one of information gain, mutual information, information gain ratio, chi-square test, Pearson correlation coefficient, and analysis of variance.

[0011] Secondly, this application also provides a model deformation prediction device, comprising: The feature acquisition module is used to acquire the deformation features of the mold through the manufacturing execution system and technical support system by means of acquisition and scanning. The feature processing module is used to preprocess the deformation features to obtain preprocessed features, and to standardize the preprocessed features to obtain standardized features. The deformation prediction module is used to input the standardized features into the trained deformation prediction model to obtain the compressibility margin of the mold.

[0012] Thirdly, this application also provides a terminal device, the terminal device including a processor and a memory, the memory storing a computer program, and the processor executing the computer program to implement the model deformation prediction method.

[0013] Fourthly, this application also provides a computer-readable storage medium storing a computer program that, when executed on a processor, implements the model deformation prediction method described above.

[0014] The embodiments of this application have the following beneficial effects: This application embodiment acquires the deformation characteristics of the mold through a manufacturing execution system and a technical support system by scanning; preprocesses the deformation characteristics to obtain preprocessed characteristics, and standardizes the preprocessed characteristics to obtain standardized characteristics; inputs the standardized characteristics into a trained deformation prediction model to obtain the compressibility allowance of the mold, thereby realizing the automatic prediction of the compressibility allowance of the mold and automating the entire process, which greatly reduces time costs. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 A schematic flowchart of a model deformation prediction method according to an embodiment of this application is shown; Figure 2 This paper illustrates a model training process according to an embodiment of the present application. Figure 3 This illustration shows a thermodynamic diagram of correlation analysis according to an embodiment of this application; Figure 4 A schematic diagram of a model deformation prediction device according to an embodiment of this application is shown. Detailed Implementation

[0017] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0018] The components of the embodiments of this application described and illustrated in the accompanying drawings can be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of this application provided in the drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0019] In the following text, the terms "comprising," "having," and their cognates, which may be used in various embodiments of this application, are intended only to indicate a particular feature, number, step, operation, element, component, or combination thereof, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations thereof, or adding the possibility of one or more combinations thereof. Furthermore, the terms "first," "second," "third," etc., are used only for distinguishing descriptions and should not be construed as indicating or implying relative importance.

[0020] Unless otherwise specified, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of this application pertain. Terms (such as those defined in commonly used dictionaries) shall be interpreted as having the same meaning as in their contextual meaning in the relevant technical field and shall not be construed as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of this application.

[0021] The following detailed description of some embodiments of this application is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0022] Currently, there is a need to accurately predict the degree of deformation in the aluminum profile production process. For scenarios where only manual prediction is available, this application provides a model-based deformation prediction method. By processing the deformation characteristics through a deformation prediction model, the compressible allowance of the mold can be obtained, thereby realizing automated prediction of the degree of mold deformation in the process flow.

[0023] The deformation prediction method of this model will be explained below with some specific examples.

[0024] Figure 1 A flowchart of a model deformation prediction method according to an embodiment of this application is shown. Exemplarily, the model deformation prediction method includes the following steps: Step S100: Obtain the deformation characteristics of the mold by means of acquisition and scanning through the manufacturing execution system and technical support system.

[0025] This embodiment is applied in the production process and is mainly used to detect the degree of deformation of the mold. In the production process, various deformation characteristics of the target mold are obtained through Daas (Manufacturing Execution System), cross-section scanner equipment and MES (Technical Support System).

[0026] These characteristics may include: whether heat treatment is performed, the surface quality of the profile output, the original geometric dimensions of the mold, the current geometric dimensions of the mold, the temperature of the aluminum rod, the auxiliary temperature of the extrusion cylinder, the mold heating temperature, the length of the rod used, the mold steel, and other related characteristics.

[0027] It is understandable that the above features are raw features and need to be processed before they can be applied to the model for recognition operations.

[0028] Step S200: Preprocess the deformation features to obtain preprocessed features, and standardize the preprocessed features to obtain standardized features.

[0029] The acquired deformation features are preprocessed and cleaned to make them usable.

[0030] Among the acquired features, there may be duplicate data, missing data, and noisy data. Duplicate data needs to be removed. For example, if the data for the auxiliary temperature of the extrusion cylinder appears twice at the same time point and the values ​​are the same, it can be determined as duplicate data, and one of them can be deleted.

[0031] For missing data, such as some continuous data, interpolation can be used to supplement the missing data. For example, for aluminum rod temperature data, the data for the first and third seconds are available, but the data for the second second is missing. In this case, an interpolation algorithm can be used to take the average of the aluminum rod temperature for the first and third seconds as the aluminum rod temperature for the second second.

[0032] In addition, for some non-continuous features, such as the original geometric dimensions of the mold, which represent the initial state of the target and are fixed values ​​that do not change with time and process flow, if such values ​​are missing, the corresponding default values ​​can be queried from the database to fill in the missing values.

[0033] Noisy data refers to outliers that deviate from the norm. Noise can be removed using various algorithms, such as mean filtering, to smooth the data.

[0034] After preprocessing, data standardization will also be performed.

[0035] There are many ways to standardize data, such as using range standardization to linearly map data to the interval [0, 1].

[0036] For example, by shifting the mean and scaling the standard deviation, the data can be transformed into a distribution with a mean of 0 and a standard deviation of 1.

[0037] Standardization can also be achieved by performing a logarithmic transformation on the data to eliminate the skewness of the data distribution.

[0038] In conclusion, standardized operations can improve the accuracy and efficiency of algorithms.

[0039] Step S300: Input the standardized features into the trained deformation prediction model to obtain the compressibility allowance of the mold.

[0040] The processed data is input into the trained deformation prediction model for prediction. In this embodiment, the prediction model used is the Random Forest time-series prediction algorithm, which effectively handles nonlinear relationships and feature importance ranking by integrating multiple decision trees. The bagging strategy and decision tree structure of Random Forest make it naturally suitable for capturing the temporal characteristics of mold deformation under complex working conditions, avoiding the gradient vanishing problem and complex parameter tuning process of traditional GRU models. In the mold deformation prediction scenario, Random Forest, through its ensemble learning mechanism, can accurately capture the nonlinear evolution trend of mold deformation over time caused by factors such as thermal stress accumulation and mechanical fatigue during the manufacturing process. Each decision tree is trained on a randomly selected subset of features, effectively improving the model's generalization ability and noise resistance.

[0041] The model will eventually output the degree of mold deformation to the compressible allowance before mold repair is required, thus enabling real-time monitoring of the degree of mold deformation during the manufacturing process.

[0042] Furthermore, this embodiment also provides the above-mentioned deformation prediction model training method, such as... Figure 2 As shown, the training method includes the following steps: In step S400, the deformation characteristics of the mold are acquired through the manufacturing execution system and technical support system by means of acquisition and scanning.

[0043] This step is mainly used to obtain deformation features to create training data. Its main operations are similar to step S100, and will not be described again here.

[0044] Step S500: Preprocess the deformation features to obtain preprocessed features, and standardize the preprocessed features to obtain standardized features.

[0045] This step is similar to step S200, and will not be described again here.

[0046] Step S600: Perform feature encoding on the standardized features to obtain encoded features.

[0047] During training, the acquired features also need to be encoded to address the lack of numerical continuity between classification labels, which poses a challenge to deep learning in capturing hidden features. Therefore, it is necessary to process non-numerical data for one-hot encoding, converting classification variables into binary vectors to avoid order misunderstandings.

[0048] One-hot encoding is a coding method for handling discrete categorical features. Its core principle is to convert each category into a binary vector. The encoding rule is that for a feature with N categories, a vector of length N is generated, where only the position corresponding to the category is 1, and the rest are 0. For example, in the "color" feature, "red" is encoded as [1,0,0], and "green" is [0,1,0]. The one-hot encoding results for profile surface treatment methods in this project are shown in Table 1 below: Table 1

[0049] Because errors in the admission data may occur during data collection, resulting in outliers in the data table, it is necessary to handle these outliers.

[0050] Step S700: Perform feature selection on the encoded features to obtain training features.

[0051] To avoid introducing irrelevant input features that could negatively impact overall model performance and waste resources, it is necessary to determine the correlation between input and output features. This typically involves information theory and statistical methods. Information theory assesses the information contribution of features through measures of information uncertainty (entropy, mutual information), focusing on the degree of information sharing between features and the target. Common methods include information gain, mutual information, and information gain ratio.

[0052] Statistical methods: Hypothesis testing or correlation indicators are used to quantify the strength of the association between the feature and the target variable, and to screen for statistically significant features. Common methods include chi-square test, Pearson correlation coefficient, and analysis of variance.

[0053] As an example, Pearson correlation analysis measures the degree of linear correlation between two continuous variables. It requires the data to be approximately normally distributed and the relationship to be linear. The closer the correlation coefficient is to 0, the weaker the correlation; the closer it is to 1, the stronger the positive correlation; and the closer it is to -1, the stronger the positive correlation. The resulting correlation analysis heatmap is shown below. Figure 3 As shown.

[0054] Observe the last three lines of output data: the correlation coefficients between the extrusion speed, the set temperature of the bar feeding zone, the set temperature of the bar discharging zone and the input data (the closer the value is to 0, the smaller the correlation between the two; the closer the value is to 1, the more positive the correlation between the two; the closer the value is to -1, the more positive the correlation between the two).

[0055] (1) Extrusion speed: It is highly correlated with weight per meter, work order output, die temperature and short bar length, but has a weak correlation with product difficulty coefficient.

[0056] (2) Temperature setting in the bar feeding zone: It is highly correlated with the alloy grade and the temperature of the upper part of the mold.

[0057] (3) Temperature setting in the output area: It is highly correlated with the product difficulty coefficient, alloy grade, and mold temperature.

[0058] For example, Spearman correlation analysis assesses monotonic relationships based on variable ranks, making it suitable for ordinal data or non-linear but monotonic associations. The closer the correlation coefficient between the same features is to 0, the weaker the correlation; the closer it is to 1, the stronger the positive correlation; and the closer it is to -1, the stronger the positive correlation. (Continuing with...) Figure 3 For example.

[0059] (1) Extrusion speed: This output characteristic has a large positive correlation with weight per meter, work order output, die temperature and short bar length.

[0060] (2) Temperature setting of bar feeding area: This output characteristic has a large negative correlation with work order output and mold loading temperature, and a large positive correlation with alloy grade.

[0061] (3) Setting temperature of the bar output area: This output characteristic has a large positive correlation with the weight per meter, alloy grade, and surface treatment method of the profile, and a large negative correlation with the product difficulty coefficient, work order output, and mold temperature.

[0062] Furthermore, data interconnection can be achieved by maximizing mutual information. The core idea of ​​maximizing mutual information is to optimize model parameters to maximize the amount of shared information between two random variables, thereby enhancing the ability to represent the correlation between variables. A mutual information score of 0 indicates that the two variables are completely independent, while a score greater than 0 indicates that the two variables are correlated; the larger the value, the greater the dependence.

[0063] After the above processing, the obtained data is ready for training.

[0064] Step S800: Input the training features into the pre-trained model for training, and adjust the parameters according to the loss function until the loss value converges or the number of iterations reaches the preset number to end the training, thereby obtaining the deformation prediction model.

[0065] Finally, the training data that has undergone data preprocessing, standardization, feature encoding, and feature selection is input into the pre-trained model for training.

[0066] The model in this embodiment uses a random forest. In the mold deformation prediction scenario, the random forest, through an ensemble learning mechanism, can accurately capture the nonlinear evolution trend of the mold deformation over time caused by factors such as thermal stress accumulation and mechanical fatigue during the manufacturing process. Each decision tree is trained on a randomly selected subset of features, which effectively improves the model's generalization ability and noise resistance. As an example, a random forest regression model is used based on the multi-dimensional input features and single-dimensional output of the mold deformation data. The key hyperparameters of the model are set as follows: • Number of trees (n_estimators): Set to 100-300, adjust according to the amount and complexity of data, and control the number of decision trees in the ensemble.

[0067] • Maximum depth (max_depth): Unlimited by default, can be set to 5-20 to control the maximum growth depth of the tree and prevent overfitting.

[0068] • Minimum number of sample splits (min_samples_split): Set to 2-10 to control the minimum number of samples required for a node to split.

[0069] • Minimum number of leaf node samples (min_samples_leaf): Set to 1-5 to control the minimum number of samples for each leaf node.

[0070] • Maximum number of features (max_features): Set to "auto" or a specific value to control the maximum number of features considered during each split of the decision tree.

[0071] During training, hyperparameter optimization is performed using grid search or random search, and model performance is evaluated through cross-validation. The entire training set is directly fitted during training, eliminating the need for batch training.

[0072] During model validation, a 7-fold time series cross-validation method can be used, strictly adhering to the chronological order in dividing the training and test sets to avoid future data leakage. Specifically, the dataset is arranged chronologically, with the first six folds serving as the training set and the seventh fold as the test set. During each validation, the training set includes data from all previous folds, ensuring the model learns the evolutionary patterns of the time series. Furthermore, evaluation metrics such as MAE (Mean Absolute Error) are introduced to quantify the prediction bias of the mold wear model, improving its accuracy.

[0073] Once the model passes the validation, training ends, and it can then be deployed online.

[0074] This embodiment provides a deformation prediction method and a training method for the deformation prediction model. By leveraging the advantages of random forests—multiple decision trees—in effectively handling nonlinear relationships and feature importance ranking, and by accurately capturing the nonlinear evolution trend of mold deformation over time due to factors such as thermal stress accumulation and mechanical fatigue during the manufacturing process, the accuracy of the model's prediction results is greatly improved. Simultaneously, the deformation prediction model in this embodiment uses grid search or random search for hyperparameter optimization during training and evaluates model performance through cross-validation. Training directly fits the entire training set, eliminating the need for batch training. This significantly saves training resources, improves training efficiency, and provides a solid foundation for future model iterations and expansions.

[0075] Figure 4 A schematic diagram of a model deformation prediction device according to an embodiment of this application is shown. Exemplarily, the device includes: The feature acquisition module 10 is used to acquire the deformation features of the mold through the manufacturing execution system and the technical support system by means of acquisition and scanning. The feature processing module 20 is used to preprocess the deformation features to obtain preprocessed features, and to standardize the preprocessed features to obtain standardized features. The deformation prediction module 30 is used to input the standardized features into the trained deformation prediction model to obtain the compressibility allowance of the mold.

[0076] It is understood that the apparatus of this embodiment corresponds to the method of the above embodiments, and the options in the above embodiments are also applicable to this embodiment, so they will not be described again here.

[0077] The processor can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, including at least one of a Central Processing Unit (CPU), Graphics Processing Unit (GPU), Network Processor (NP), Digital Signal Processor (DSP), Application-Specific Integrated Circuit (ASIC), Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. The general-purpose processor can be a microprocessor or any conventional processor, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments of this application.

[0078] The memory can be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc. The memory is used to store computer programs, and the processor can execute the computer programs accordingly after receiving execution instructions.

[0079] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can also be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that, in alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0080] In addition, the functional modules or units in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0081] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a smartphone, personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0082] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A model morphing prediction method characterized by, The method comprises the following steps: Obtaining the deformation characteristics of the mold through the manufacturing execution system and the technical support system; Preprocessing the deformation characteristics to obtain preprocessed characteristics, and standardizing the preprocessed characteristics to obtain standardized characteristics; Inputting the standardized characteristics into the trained deformation prediction model to obtain the compressible residual amount of the mold.

2. The model morphing prediction method according to claim 1, characterized in that, The training method of the deformation prediction model comprises the following steps: Obtaining the deformation characteristics of the mold through the manufacturing execution system and the technical support system; Preprocessing the deformation characteristics to obtain preprocessed characteristics, and standardizing the preprocessed characteristics to obtain standardized characteristics; Encoding the standardized characteristics to obtain encoded characteristics; Selecting the encoded characteristics to obtain training characteristics; Training the training characteristics in the pre-training model, and adjusting the parameters according to the loss function until the loss value converges or the number of iterations reaches the preset number to end the training, thereby obtaining the deformation prediction model.

3. The model morphing prediction method according to claim 1 or 2, characterized by, The preprocessing of the deformation characteristics to obtain preprocessed characteristics comprises the following steps: Checking the repeated data in the deformation characteristics and removing the repeated data; Determining the missing values in the deformation characteristics, and eliminating the missing values by interpolation, deletion or adding default values; Removing the noise values in the deformation characteristics to obtain smooth data.

4. The model deformation prediction method according to claim 1 or 2, characterized by, The standardization of the preprocessed characteristics to obtain standardized characteristics comprises the following steps: Converting the preprocessed characteristics into distribution data with a mean of 0 and a standard deviation of 1 through mean translation and standard deviation scaling, thereby obtaining standardized characteristics.

5. The model morphing prediction method according to claim 2, wherein, The encoding of the standardized characteristics to obtain encoded characteristics comprises the following steps: One-hot encoding the non-numeric data in the standardized characteristics to convert the non-numeric data into a binary vector.

6. The model morphing prediction method according to claim 2, wherein, The feature selection of the encoded characteristics to obtain training characteristics comprises the following steps: Quantifying the correlation strength of the features and the target variables through hypothesis testing or correlation indicators, and screening the encoded characteristics with a statistical correlation strength greater than a preset strength.

7. The model morphing prediction method according to claim 6, characterized in that, The quantification of the correlation strength of the features and the target variables through hypothesis testing or correlation indicators comprises the following steps: Determining the correlation strength of the quantified features and the target variables through one of information gain, mutual information, information gain ratio, chi-square test, Pearson correlation coefficient and analysis of variance.

8. A model morphing prediction apparatus characterized by comprising: The method comprises the following steps: A feature acquisition module is configured to obtain the deformation characteristics of the mold through the manufacturing execution system and the technical support system; A feature processing module is configured to preprocess the deformation characteristics to obtain preprocessed characteristics, and standardize the preprocessed characteristics to obtain standardized characteristics; A deformation prediction module is configured to input the standardized characteristics into the trained deformation prediction model to obtain the compressible residual amount of the mold.

9. A terminal device, comprising: The terminal device comprises a processor and a memory, and the memory stores a computer program, and the processor is configured to execute the computer program to implement the model deformation prediction method of any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer program is stored in the computer storage and is executed on the processor to implement the model deformation prediction method according to any one of claims 1-7.

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