Training method and device for aerodynamic force prediction model of aircraft

Abstract

The invention provides a training method and device for an aircraft aerodynamic force prediction model, and the method comprises the steps: generating a shape grid file through generation software; simulation software is used for estimation on the appearance grid file, an aerodynamic force actual value under the set flow field parameters is estimated, appearance point data are extracted from the appearance grid file, and an appearance point cloud file is obtained; generating a training set comprising flow field parameters, aerodynamic force actual values and appearance point cloud files; inputting the training set into a depth model consisting of an encoder group and a prediction module, respectively encoding the flow field parameters and the appearance point cloud file in the encoder group, adding two encoding results to obtain a comprehensive code, and inputting the comprehensive code into the prediction module to obtain an aerodynamic force predicted value; according to the error between the aerodynamic force predicted value and the aerodynamic force actual value, the depth model is updated through repeated iteration, and after iteration is finished, a trained aircraft aerodynamic force prediction model is obtained. The aerodynamic characteristics of the aircraft are described from fluid mechanics and geometrical shapes.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a training method and device for an aircraft aerodynamic prediction model. Background Art

[0002] In the initial stage of aircraft shape design, it is necessary to obtain aerodynamic data of the aircraft aerodynamic shape under specific flow field parameter conditions for performance analysis, which is a key link in the aircraft design and performance evaluation process.

[0003] Among the related technologies, traditional methods include wind tunnel tests and computational fluid dynamics (CFD) simulations. The results of wind tunnel tests are relatively accurate, but they are expensive and have a long period, and cannot predict aerodynamic data in a timely and rapid manner. Although CFD software simulation costs are low, they are highly dependent on the quality of the computational grid, so extra effort is required to produce a computational grid with a higher standard. In recent years, deep learning technology has made breakthrough progress in various fields. It can automatically extract features and make predictions by learning a large amount of sample data, and has broad application prospects. However, deep learning technology is rarely used in the field of aerodynamic design.

[0004] Based on the above analysis of the development status of this technical field, the existing technology lacks an aircraft aerodynamic prediction model based on a deep model. Summary of the invention

[0005] The purpose of the present invention is to provide a training method and device for an aircraft aerodynamic prediction model, aiming to solve the above-mentioned problems in the prior art.

[0006] According to a first aspect of an embodiment of the present invention, there is provided a method for training an aircraft aerodynamic force prediction model, comprising:

[0007] Use generation software to generate shape mesh files;

[0008] Use simulation software to estimate the actual value of aerodynamic force under set flow field parameters on the shape grid file, extract shape point data from the shape grid file, and obtain a shape point cloud file;

[0009] Generate a training set including flow field parameters, actual values ​​of aerodynamic forces and shape point cloud files;

[0010] The training set is input into the deep model composed of an encoder group and a prediction module. The flow field parameters and the shape point cloud file are encoded in the encoder group respectively. The two encoding results are added together to obtain a comprehensive encoding. The comprehensive encoding is input into the prediction module to obtain the aerodynamic prediction value.

[0011] According to the error between the predicted aerodynamic value and the actual aerodynamic value, the deep model is updated iteratively, and a trained aircraft aerodynamic prediction model is obtained after the iteration.

[0012] According to a second aspect of an embodiment of the present invention, there is provided a training device for an aircraft aerodynamic force prediction model, comprising:

[0013] A mesh file generation module is used to generate an outline mesh file using generation software;

[0014] A point cloud file generation module is used to estimate the actual value of the aerodynamic force under the set flow field parameters by using simulation software on the shape grid file, extract shape point data from the shape grid file, and obtain the shape point cloud file;

[0015] A training set forming module is used to generate a training set including flow field parameters, actual values ​​of aerodynamic forces and shape point cloud files;

[0016] The encoding prediction module is used to input the training set into the deep model composed of the encoder group and the prediction module, encode the flow field parameters and the shape point cloud file in the encoder group respectively, add the two encoding results to obtain the comprehensive encoding, and input the comprehensive encoding into the prediction module to obtain the aerodynamic force prediction value;

[0017] The iteration module is used to repeatedly iterate and update the deep model according to the error between the predicted aerodynamic value and the actual aerodynamic value, and obtain the trained aircraft aerodynamic prediction model after the iteration.

[0018] According to a third aspect of an embodiment of the present invention, there is provided an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, the steps of the training method for an aircraft aerodynamic prediction model as provided in the first aspect of the present disclosure are implemented.

[0019] According to a fourth aspect of an embodiment of the present invention, there is provided a computer-readable storage medium on which is stored an implementation program for information transmission, which, when executed by a processor, implements the steps of the training method for an aircraft aerodynamic prediction model provided in the first aspect of the present disclosure.

[0020] The technical solution provided by the embodiment of the present invention includes the following beneficial effects: converting the shape grid into a point cloud data format that is easy to encode, using an encoder group to encode the flow field parameters and the shape point cloud file respectively during the training process of the deep model, and then fusing them to obtain a comprehensive encoding input prediction model, which describes the aerodynamic characteristics of the aircraft from two aspects: fluid mechanics characteristics and the geometric shape of the aircraft itself, thereby improving the accuracy of model prediction.

[0021] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate one or more embodiments of this specification or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0023] Figure 1 is a flow chart of a method for training an aircraft aerodynamic prediction model according to an embodiment of the present invention;

[0024] Figure 2 is a schematic diagram of a point cloud file according to an embodiment of the present invention;

[0025] Figure 3 is a schematic diagram of aerodynamic force prediction result of an embodiment of the present invention;

[0026] Figure 4 is a schematic diagram of the overall framework of the prediction model of an embodiment of the present invention;

[0027] Figure 5 is a schematic diagram of a training device for an aircraft aerodynamic force prediction model according to an embodiment of the present invention;

[0028] Figure 6 is a schematic diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the following will be combined with the drawings in one or more embodiments of this specification to clearly and completely describe the technical solutions in one or more embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this document.

[0030] Method Embodiment

[0031] According to an embodiment of the present invention, a method for training an aircraft aerodynamic prediction model is provided. Figure 1 FIG. 1 is a flow chart of a method for training an aircraft aerodynamic prediction model according to an embodiment of the present invention. Figure 1 As shown, the training method of the aircraft aerodynamic prediction model according to an embodiment of the present invention specifically includes:

[0032] In step S110, the shape grid file is generated using the generation software, which specifically includes:

[0033] A large number of shape grid files are generated using parameterized aerodynamic shape generation software, and 4000 training samples are generated in the embodiment of the present invention;

[0034] In step S120, the simulation software is used to estimate the actual value of the aerodynamic force under the set flow field parameters on the shape grid file, and the shape point data is extracted from the shape grid file to obtain the shape point cloud file, which specifically includes:

[0035] The simulation software used is computational fluid dynamics (CFD) software, which obtains the actual value of aerodynamic force under different flow field parameters. The flow field parameters can be set in the CFD software.

[0036] Extracting a first preset amount of shape point data from the shape grid file using a random sampling method;

[0037] Use the farthest point sampling method to extract the second preset amount of shape point data from the shape grid file. The farthest point sampling is a point cloud data sampling method that is widely used in 3D point cloud processing. It should be noted that the farthest point sampling method does not only extract the farthest sampling point, but iteratively selects a group of farthest points.

[0038] Random sampling and farthest point sampling can effectively reduce the dimension of data to improve computational efficiency;

[0039] In the embodiment of the present invention, the first preset amount and the second preset amount are both 2048, and a point cloud file including 4096 data points is generated. Figure 2 is a schematic diagram of a point cloud file according to an embodiment of the present invention. Figure 2 As shown, the point cloud file is displayed after the duplicate points are removed.

[0040] In step S130, a training set including flow field parameters, actual values ​​of aerodynamic forces and shape point cloud files is generated, specifically including:

[0041] The set flow field parameters, the actual values ​​of aerodynamic forces corresponding to the flow field parameters, and the shape point cloud files are used as one piece of data in a training set, and the training set includes multiple pieces of data; wherein, the indicators of the flow field parameters include the Mach number Ma and the angle of attack α, and preferably the flight altitude or other indicators can be introduced. In the embodiment of the present invention, the Mach numbers of the training set include 0.6, 0.8, and 1.0, the angles of attack include -2, 0, 2, 4, 6, 8, 10, 12, 16, and 20 degrees, and the indicators of the actual values ​​of aerodynamic forces include the normal force CN, the axial force CA, and the pitch moment MZ.

[0042] In step S140, the training set is input into the deep model composed of the encoder group and the prediction module, the flow field parameters and the shape point cloud file are encoded in the encoder group respectively, the two encoding results are added to obtain a comprehensive code, and the comprehensive code is input into the prediction module to obtain the aerodynamic force prediction value, which specifically includes:

[0043] The flow field parameters are encoded using a flow field encoder based on a multi-layer perceptron to obtain a first feature vector, wherein the last layer of the flow field encoder does not use an activation function, because the multi-layer perceptron here hopes to output an implicit representation of a feature so that the subsequent prediction module can flexibly use the implicit representation of the feature; in the embodiment of the present invention, the flow field encoder includes two hidden layers;

[0044] Encode the shape point cloud file using a shape encoder based on the Pointnet point cloud model to obtain the second eigenvector. Pointnet is a groundbreaking deep learning model that can directly operate on point clouds without converting them into a regular grid structure.

[0045] It is determined whether the feature dimensions of the first feature vector and the second feature vector are the same; in the embodiment of the present invention, the feature dimensions of the generated first feature vector and the second feature vector are both 512.

[0046] If the feature dimensions are different, the feature dimensions of the first feature vector or the second feature vector are adjusted by linear transformation, and the adjusted two encoding results are added to obtain a comprehensive code. Otherwise, the comprehensive code is obtained by directly adding them. In the embodiment of the present invention, the two encoding results can be directly added.

[0047] The comprehensive code is input into a prediction module based on a multi-layer perceptron to obtain an aerodynamic force prediction value, wherein the last layer of the prediction module uses an activation function because the multi-layer perceptron needs to output a prediction result, and the indicators of the aerodynamic force prediction value include normal force, axial force and pitching moment; in the embodiment of the present invention, the prediction module includes two hidden layers;

[0048] The activation function is used in the flow encoder and other layers of the multilayer perceptron in the prediction module.

[0049] In step S150, the deep model is repeatedly updated according to the error between the predicted aerodynamic force and the actual aerodynamic force. After the iteration, a trained aircraft aerodynamic force prediction model is obtained, which specifically includes:

[0050] The mean square error between the predicted aerodynamic value and the actual aerodynamic value is calculated. The deep model is iteratively updated based on the mean square error using the Adam optimizer. The deep model is verified using a test set of 1000 samples to ensure that the model reaches the optimal state.

[0051] Figure 3 Schematic diagram of the aerodynamic force prediction result of the embodiment of the present invention. Figure 3As shown in the figure, the prediction results of the normal force CN in the aerodynamic force are shown. The horizontal axis is the angle of attack value and the vertical axis is the normal vector value. CN-Truth represents the actual value of the normal force, and CN-Pred represents the predicted value of the normal force. This proves that the trained aircraft aerodynamic prediction model has better prediction accuracy and is closer to the actual value.

[0052] The above technical solutions of the embodiments of the present invention are illustrated with reference to the following drawings.

[0053] Figure 4 Schematic diagram of the overall framework of the prediction model of the embodiment of the present invention. Figure 4 As shown in the figure, the overall architecture of the aircraft aerodynamic prediction model is demonstrated, including the data set construction architecture and the model training architecture. The actual aerodynamic values ​​in the data set are used as true labels for iterative updates, and other indicators are used to participate in model training. The deep neural network model includes a dual-branch encoding structure, which describes the aerodynamic characteristics of the aircraft from two aspects: fluid mechanics characteristics and the geometric shape of the aircraft itself.

[0054] To sum up, in response to the existing problems, the training method of the aircraft aerodynamic prediction model is invented. The shape grid is converted into a point cloud data format that is easy to encode, and the shape grid is sampled by combining the random sampling method and the farthest point sampling method. The generated point cloud file retains the grid details and reduces the number of data points, which is beneficial to reducing the calculation amount of the deep model. In the training process of the deep model, a dual-branch encoder group structure is used, and the flow field parameters are encoded using a flow field encoder based on a multi-layer perceptron. The shape encoder based on the Pointnet point cloud model is used to encode the shape point cloud file, and then the comprehensive encoding input prediction model is obtained by fusion, which describes the aerodynamic characteristics of the aircraft from two aspects: fluid mechanics characteristics and the geometric shape of the aircraft itself, thereby improving the accuracy of model prediction.

[0055] Device Embodiment

[0056] According to an embodiment of the present invention, a training device for an aircraft aerodynamic prediction model is provided. Figure 5 Schematic diagram of a training device for an aircraft aerodynamic prediction model according to an embodiment of the present invention. Figure 5 As shown, the training device of the aircraft aerodynamic prediction model according to the embodiment of the present invention specifically includes:

[0057] The mesh file generating module 50 is used to generate the shape mesh file using the generating software.

[0058] The point cloud file generation module 52 is used to estimate the actual value of the aerodynamic force under the set flow field parameters using the simulation software on the shape grid file, extract the shape point data from the shape grid file, and obtain the shape point cloud file, which is specifically used for:

[0059] Extracting a first preset amount of shape point data from the shape grid file using a random sampling method;

[0060] A second preset amount of shape point data is extracted from the shape grid file using the farthest point sampling method.

[0061] The training set forming module 54 is used to generate a training set including flow field parameters, actual values ​​of aerodynamic forces and shape point cloud files, specifically for:

[0062] The set flow field parameters, the actual values ​​of aerodynamic forces corresponding to the flow field parameters, and the shape point cloud files are used as a piece of data in the training set, wherein the indicators of the flow field parameters include the Mach number and the angle of attack, and the indicators of the actual values ​​of aerodynamic forces include the normal force, the axial force, and the pitching moment.

[0063] The coding prediction module 56 is used to input the training set into the deep model composed of the encoder group and the prediction module, encode the flow field parameters and the shape point cloud file in the encoder group respectively, add the two encoding results to obtain a comprehensive code, input the comprehensive code into the prediction module, and obtain the aerodynamic force prediction value, which is specifically used for:

[0064] Using a flow field encoder based on a multi-layer perceptron to encode the flow field parameters to obtain a first feature vector, wherein the last layer of the flow field encoder does not use an activation function;

[0065] The shape point cloud file is encoded using a shape encoder based on the Pointnet point cloud model to obtain the second eigenvector.

[0066] Determine whether the feature dimensions of the first feature vector and the second feature vector are the same;

[0067] If the feature dimensions are different, the feature dimensions of the first feature vector or the second feature vector are adjusted by linear transformation, and the two adjusted encoding results are added together to obtain a comprehensive code; otherwise, the two encoding results are directly added together to obtain a comprehensive code.

[0068] The comprehensive code is input into the prediction module based on the multi-layer perceptron to obtain the aerodynamic force prediction value, wherein the last layer of the prediction module uses an activation function, and the indicators of the aerodynamic force prediction value include normal force, axial force and pitching moment.

[0069] The iteration module 58 is used to repeatedly iterate and update the deep model according to the error between the predicted aerodynamic force value and the actual aerodynamic force value, and obtain a trained aircraft aerodynamic force prediction model after the iteration, which is specifically used for:

[0070] The mean square error between the predicted aerodynamic value and the actual aerodynamic value is calculated, and the deep model is iteratively updated using the Adam optimizer based on the mean square error.

[0071] To sum up, in response to the existing problems, the training device of the aircraft aerodynamic prediction model invented this time converts the shape grid into a point cloud data format that is easy to encode, and uses a combination of random sampling and farthest point sampling to sample the shape grid, so that the generated point cloud file retains the grid details and reduces the number of data points, which is beneficial to reducing the calculation amount of the deep model; in the training process of the deep model, a dual-branch encoder group structure is used, a flow field encoder based on a multi-layer perceptron is used to encode the flow field parameters, and a shape encoder based on the Pointnet point cloud model is used to encode the shape point cloud file, and then the comprehensive encoding input prediction model is obtained by fusion, which describes the aerodynamic characteristics of the aircraft from two aspects: fluid mechanics characteristics and the geometric shape of the aircraft itself, thereby improving the accuracy of model prediction.

[0072] Electronic device embodiment

[0073] Figure 6 6 is a schematic diagram of an electronic device according to an embodiment of the present invention. The electronic device 600 may include at least one processor 610 and a memory 620. The processor 610 may execute instructions stored in the memory 620. The processor 610 is connected to the memory 620 through a data bus. In addition to the memory 620, the processor 610 may also be connected to an input device 630, an output device 640, and a communication device 650 through a data bus.

[0074] The processor 610 may be any conventional processor, such as a commercially available CPU. The processor may also include a graphics processor (Graphic Process Unit, GPU), a field programmable gate array (Field Programmable Gate Array, FPGA), a system on chip (System on Chip, SOC), an application specific integrated circuit (Application Specific Integrated Circuit, ASIC) or a combination thereof.

[0075] The memory 620 may be implemented by any type of volatile or nonvolatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk.

[0076] In the disclosed embodiment, executable instructions are stored in the memory 620, and the processor 610 can read the executable instructions from the memory 620 and execute the instructions to implement all or part of the steps of the training method of the aircraft aerodynamic prediction model in any of the above exemplary embodiments.

[0077] Computer Readable Storage Medium Embodiments

[0078] In addition to the above-mentioned methods and devices, an exemplary embodiment of the present disclosure may also be a computer program product or a computer-readable storage medium storing the computer program product, wherein the computer product includes computer program instructions that can be executed by a processor to implement all or part of the steps described in the training method of the aircraft aerodynamic prediction model in any of the above-mentioned exemplary embodiments.

[0079] The computer program product may be written in any combination of one or more programming languages ​​to write program codes for performing the operations of the embodiments of the present application, including object-oriented programming languages ​​such as Java, C++, etc., and also conventional procedural programming languages ​​such as "C" language or similar programming languages ​​and scripting languages ​​(e.g., Python). The program code may be executed entirely on the user computing device, partially on the user computing device, as an independent software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0080] Computer readable storage media can adopt any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium can include, for example, but is not limited to, a system, device or device of electricity, magnetism, light, electromagnetic, infrared, or semiconductor, or any combination of the above. More specific examples of readable storage media include: a static random access memory (SRAM) with one or more wires electrically connected, an electrically erasable programmable read-only memory (EEPROM), an erasable programmable read-only memory (EPROM), a programmable read-only memory (PROM), a read-only memory (ROM), a magnetic memory, a flash memory, a magnetic disk or an optical disk, or any suitable combination of the above.

[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A training method for an aircraft aerodynamic prediction model, characterized in that: include: Use generation software to generate shape mesh files; Using simulation software to estimate on the shape grid file, estimate the actual value of the aerodynamic force under the set flow field parameters, extract shape point data from the shape grid file, and obtain a shape point cloud file; Generate a training set including the flow field parameters, the actual value of the aerodynamic force and the shape point cloud file; Inputting the training set into a deep model composed of an encoder group and a prediction module, respectively encoding the flow field parameters and the shape point cloud file in the encoder group, adding the two encoding results to obtain a comprehensive code, and inputting the comprehensive code into the prediction module to obtain an aerodynamic force prediction value; The deep model is updated repeatedly according to the error between the predicted aerodynamic force value and the actual aerodynamic force value, and a trained aircraft aerodynamic force prediction model is obtained after the iteration.

2. The method according to claim 1, characterized in that The extracting of the shape point data from the shape grid file to obtain the shape point cloud file specifically includes: Extracting a first preset amount of shape point data from the shape grid file using a random sampling method; A second preset amount of shape point data is extracted from the shape grid file using the farthest point sampling method.

3. The method according to claim 1, characterized in that The generating of the training set including the flow field parameters, the actual value of the aerodynamic force and the shape point cloud file specifically includes: The set flow field parameters, the actual values ​​of aerodynamic forces corresponding to the flow field parameters, and the shape point cloud files are used as a piece of data in the training set, wherein the indicators of the flow field parameters include Mach number and angle of attack, and the indicators of the actual values ​​of aerodynamic forces include normal force, axial force, and pitch moment.

4. The method according to claim 1, characterized in that: The encoding of the flow field parameters and the shape point cloud files in the encoder group specifically includes: Using a flow field encoder based on a multi-layer perceptron to encode the flow field parameters to obtain a first feature vector, wherein the last layer of the flow field encoder does not use an activation function; The shape point cloud file is encoded using a shape encoder based on the Pointnet point cloud model to obtain the second eigenvector.

5. The method according to claim 4, characterized in that The step of adding the two encoding results to obtain the comprehensive encoding specifically includes: Determining whether the first feature vector and the second feature vector have the same feature dimension; If the feature dimensions are different, the feature dimensions of the first feature vector or the second feature vector are adjusted by linear transformation, and the two adjusted encoding results are added together to obtain a comprehensive code; otherwise, the two encoding results are directly added together to obtain a comprehensive code.

6. The method according to claim 1, characterized in that The step of inputting the integrated code into the prediction module to obtain the aerodynamic force prediction value specifically includes: The integrated code is input into a prediction module based on a multi-layer perceptron to obtain an aerodynamic force prediction value, wherein the last layer of the prediction module uses an activation function, and the indicators of the aerodynamic force prediction value include normal force, axial force and pitch moment.

7. The method according to claim 1, characterized in that The repeatedly iteratively updating the depth model according to the error between the predicted aerodynamic force value and the actual aerodynamic force value specifically includes: The mean square error between the predicted aerodynamic force value and the actual aerodynamic force value is calculated, and the deep model is iteratively updated using an Adam optimizer according to the mean square error.

8. A training device for an aircraft aerodynamic prediction model, characterized in that: include: A mesh file generation module is used to generate an outline mesh file using generation software; A point cloud file generation module is used to estimate the actual value of the aerodynamic force under the set flow field parameters by using simulation software on the shape grid file, extract shape point data from the shape grid file, and obtain a shape point cloud file; A training set forming module, used for generating a training set including the flow field parameters, the actual value of the aerodynamic force and the shape point cloud file; A coding prediction module, used for inputting the training set into a deep model composed of an encoder group and a prediction module, encoding the flow field parameters and the shape point cloud file in the encoder group respectively, adding the two encoding results to obtain a comprehensive code, and inputting the comprehensive code into the prediction module to obtain an aerodynamic force prediction value; The iteration module is used to repeatedly iterate and update the deep model according to the error between the aerodynamic force prediction value and the aerodynamic force actual value, and obtain a trained aircraft aerodynamic force prediction model after the iteration.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, the steps of the training method for an aircraft aerodynamic prediction model as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores an implementation program for information transmission, and when the program is executed by a processor, the steps of the training method for an aircraft aerodynamic prediction model as described in any one of claims 1 to 7 are implemented.

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