Fatigue damage positioning method for metal material

Abstract

The invention discloses a fatigue damage positioning method for a metal material, which comprises the following steps: removing impurities attached to the surface according to pollutants and oxides on the surface of the metal material to obtain the cleaned metal material; measuring the physical characteristics of the cleaned metal material, establishing a material characteristic database, and determining an optimal detection scheme according to the conductivity and magnetic characteristics of the metal material in combination with a preset detection method selection rule; performing three-dimensional imaging on the interior of the metal material, extracting position and form information of a fatigue damage area according to a three-dimensional image, and generating a defect feature map; fusing the identified three-dimensional image data and the defect feature map to obtain fused multi-source heterogeneous data; training the fatigue damage positioning model and optimizing model parameters to obtain a trained fatigue damage positioning model; and inputting data of a metal material to be detected into the trained fatigue damage positioning model to obtain a fatigue damage positioning result of the metal material to be detected.

Description

Technical Field

[0001] The invention belongs to the technical field of fatigue damage location, and in particular relates to a fatigue damage location method for metal materials. Background Art

[0002] When locating fatigue damage in metal materials, there are a series of technical difficulties. First, there are often various contaminants and oxides on the surface of metal materials. These impurities will interfere with the detection signal and cause distortion of the detection results. Therefore, the surface of the material must be thoroughly cleaned and treated before detection, but the cleaning process may cause secondary damage to the surface of the material, affecting the accuracy of the detection. Secondly, different types of metal materials have different physical properties, such as conductivity, magnetism, etc., which requires the selection of appropriate detection methods according to the material properties. However, the shape and size of the material will also affect the applicability of the detection method. Complex shapes and irregular sizes will increase the difficulty of detection, and multiple detection methods may need to be used in combination. Furthermore, fatigue damage presents different distribution characteristics inside the material. Some damage may be concentrated on the surface, while some damage is hidden inside. This requires the detection method to be able to detect the inside of the material. However, the internal structure of the material is complex, with various defects and inhomogeneities. These factors will interfere with the detection signal and affect the accuracy of positioning. Finally, the massive data obtained during the detection process needs to be efficiently processed and analyzed to accurately determine the location and extent of the damage. However, the data formats and features obtained by different detection methods are not the same, and how to achieve data unification and integration is a major challenge. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a fatigue damage location method for metal materials, which realizes the intelligence of the entire process from material cleaning to damage location, and significantly improves the efficiency and accuracy of fatigue damage detection of metal materials.

[0004] To achieve the above-mentioned purpose, the present invention provides a fatigue damage location method for metal materials, comprising: according to the pollutants and oxides on the surface of the metal material, using the cavitation effect generated by high-frequency vibration to remove impurities attached to the surface, and obtain a cleaned metal material;

[0005] Measure the physical properties of cleaned metal materials, obtain the conductivity and magnetic data of metal materials, establish a material property database, and determine the optimal detection scheme based on the conductivity and magnetic characteristics of metal materials and the preset detection method selection rules;

[0006] Perform three-dimensional imaging of the interior of metal materials, extract the location and morphological information of fatigue damage areas based on the three-dimensional images, automatically identify the defects and unevenness of the internal structure of metal materials, and generate defect feature maps;

[0007] The identified three-dimensional image data and the defect feature map are fused to obtain fused multi-source heterogeneous data;

[0008] constructing a fatigue damage localization model according to the fused multi-source heterogeneous data, training the fatigue damage localization model and optimizing model parameters to obtain a trained fatigue damage localization model;

[0009] The data of the metal material to be tested is input into the trained fatigue damage localization model to obtain the fatigue damage localization result of the metal material to be tested, and the result is visualized, and a knowledge base is constructed according to the fatigue damage localization result.

[0010] Technical effect of the invention: The invention discloses a fatigue damage location method for metal materials. Aiming at the cleaning problem of pollutants and oxides on the surface of metal materials, ultrasonic cleaning technology is used to remove surface impurities. A material database is established by measuring physical properties to realize intelligent matching of detection methods. Computer tomography and deep learning algorithms are used to perform three-dimensional imaging and defect identification on the internal structure of the material. A multi-channel data acquisition system is used to synchronously acquire signals from different detection methods, and effective integration of multi-source information is realized through data fusion algorithms. A fatigue damage location model based on neural networks is constructed to improve the accuracy and reliability of damage location. Finally, the model is integrated into the detection system to realize automated and intelligent damage location functions, and the damage situation is presented through three-dimensional visualization technology. The invention also establishes a detection case knowledge base to provide support for subsequent maintenance and decision-making. The method realizes the intelligence of the entire process from material cleaning to damage location, significantly improving the efficiency and accuracy of fatigue damage detection of metal materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0012] Figure 1 The present invention is a schematic flow chart of a fatigue damage location method for metal materials according to an embodiment of the present invention. DETAILED DESCRIPTION

[0013] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0014] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0015] like Figure 1 As shown, in this embodiment, a fatigue damage location method for metal materials is provided, including: according to the pollutants and oxides on the surface of the metal material, using the cavitation effect generated by high-frequency vibration to remove impurities attached to the surface, and obtain a cleaned metal material;

[0016] Measure the physical properties of cleaned metal materials, obtain the conductivity and magnetic data of metal materials, establish a material property database, and determine the optimal detection scheme based on the conductivity and magnetic characteristics of metal materials and the preset detection method selection rules;

[0017] Perform three-dimensional imaging of the interior of metal materials, extract the location and morphological information of fatigue damage areas based on the three-dimensional images, automatically identify the defects and unevenness of the internal structure of metal materials, and generate defect feature maps;

[0018] The identified three-dimensional image data and the defect feature map are fused to obtain fused multi-source heterogeneous data;

[0019] constructing a fatigue damage localization model according to the fused multi-source heterogeneous data, training the fatigue damage localization model and optimizing model parameters to obtain a trained fatigue damage localization model;

[0020] The data of the metal material to be tested is input into the trained fatigue damage localization model to obtain the fatigue damage localization result of the metal material to be tested, and the result is visualized, and a knowledge base is constructed according to the fatigue damage localization result.

[0021] Further, obtaining the cleaned metal material includes:

[0022] Obtain the metal material to be cleaned, identify and locate the pollutants and oxides on the surface of the material, and determine the cleaning area;

[0023] According to the type and degree of contamination of the metal material, appropriate parameters are selected from the preset ultrasonic power and cleaning time parameter library and transmitted to the ultrasonic cleaning system;

[0024] Put the metal material into the ultrasonic cleaning tank, start the ultrasonic cleaning system, and use the cavitation effect generated by high-frequency vibration to clean the pollutants and oxides on the surface of the metal material, remove the residual cleaning liquid and impurities, and obtain the cleaned metal material.

[0025] Furthermore, the optimal detection scheme is determined to include:

[0026] According to the type of metal material and the cleaning process, determine the conductivity and magnetic physical property parameters that need to be tested, and develop a physical testing plan;

[0027] Conducting tests on the conductivity and magnetic characteristics of cleaned metal material samples to obtain physical property data of the metal materials;

[0028] Based on the acquired physical property data of metal materials, the data is stored in a property database in a predetermined data format and organization method to build a material property knowledge base;

[0029] According to the needs of business scenarios, preset multiple material testing methods and formulate corresponding testing method selection rules;

[0030] Match the conductivity and magnetic characteristics of the material to be tested with the data in the characteristic database to find the matching material characteristic records;

[0031] According to the matching material characteristic records and the preset detection method selection rules, the optimal detection scheme is determined from the candidate detection methods.

[0032] Furthermore, generating a defect feature map includes:

[0033] Perform CT scanning inside the metal material to obtain three-dimensional image data inside the metal material;

[0034] Preprocessing the acquired three-dimensional image data to obtain preprocessed three-dimensional image data;

[0035] Segmenting the preprocessed three-dimensional image to extract a fatigue damage area image;

[0036] According to the extracted fatigue damage area image, the three-dimensional position coordinates and three-dimensional morphological characteristics of the fatigue damage area are obtained;

[0037] The extracted fatigue damage area image is input into the pre-trained convolutional neural network model to automatically identify the defects and unevenness of the internal structure of the metal material and generate a defect feature map.

[0038] Specifically, in practical applications, the extracted fatigue damage area image is input into the model to automatically identify the defect type and severity. For example, a model can divide cracks into three levels: early, middle and late, providing a basis for material life assessment. The generation of defect feature images helps to intuitively display the detection results. Visualization techniques such as heat maps are used to indicate the severity of defects in different colors. The crack area is marked in red, the surrounding stress concentration area is marked in yellow, and the normal area is marked in green to form an intuitive defect distribution map. Finally, the position and morphological information of the fatigue damage area are fused with the defect feature image to obtain a comprehensive analysis result of fatigue damage inside the material. This comprehensive analysis can not only determine the specific location and size of the defect, but also evaluate its impact on material properties. For example, the fatigue damage analysis results of a turbine blade show that there is a tiny crack at the root of the blade with a length of 0.5 mm. Although it does not affect the use at present, its development trend needs to be closely monitored to prevent sudden failures.

[0039] Furthermore, the fused multi-source heterogeneous data includes:

[0040] According to the characteristics of the detection object, determine different detection methods and obtain corresponding data signals;

[0041] Through a multi-channel data acquisition system, multi-source heterogeneous data of each detection method is synchronously acquired, wherein the multi-source heterogeneous data includes original signal data and processed three-dimensional image data and defect feature map;

[0042] Preprocessing the acquired multi-source heterogeneous data to obtain preprocessed multi-source heterogeneous data;

[0043] According to the correlation between multi-source heterogeneous data and the fusion algorithm, a mapping relationship between data is established, and correlation analysis is performed to obtain fused multi-source heterogeneous data.

[0044] Specifically, in nondestructive testing, choosing the right testing method is crucial to obtaining accurate defect information. For metal materials, ultrasonic testing is used to detect internal defects, eddy current testing is used for surface crack detection, and magnetic particle testing is suitable for surface and near-surface defects of ferromagnetic materials. Multi-channel data acquisition systems can synchronously acquire signals from these different methods, such as ultrasonic A-scan waveforms, eddy current impedance plane maps, and magnetic particle fluorescence images. Data preprocessing is the basis for fusion analysis. Taking ultrasonic testing as an example, the original A-scan signal may contain noise and interference, and the signal-to-noise ratio needs to be improved through filtering and denoising. Eddy current signals may require phase correction and amplitude normalization. For magnetic particle images, image enhancement and binarization may be required. These preprocessing steps ensure the consistency and comparability of data from different sources. Data fusion algorithms are designed to integrate multi-source information. For example, the Dempster-Shafer evidence theory can be used to fuse ultrasonic and eddy current testing results. Ultrasonic testing can provide depth information of defects, while eddy current testing can more accurately locate surface defects. By establishing a correlation mapping between these two methods, a more comprehensive description of defect characteristics can be obtained. Feature extraction and selection are key steps to reduce data dimensions and improve classification efficiency. For ultrasonic signals, the peak, width, energy and other features of the waveform can be extracted; for eddy current signals, the shape and direction of the impedance plane can be extracted; for magnetic particle images, the length, width, area and other geometric features of the defect can be extracted. Through methods such as principal component analysis or genetic algorithms, the most representative subset can be selected from these features. The selection and training of machine learning models are the core of automatic defect recognition. Support vector machine (SVM) is suitable for classification problems of small samples and high-dimensional data, and can be used to distinguish different types of defects. Random forest has good noise resistance and feature importance evaluation functions, which is suitable for handling complex defect classification tasks. When training the model, the cross-validation method can be used to evaluate the model performance, and the model can be optimized by adjusting the hyperparameters. Finally, the trained model is applied to new inspection data. For example, when inspecting a steel pipe suspected of having cracks, ultrasonic testing shows reflected echoes inside, eddy current testing detects impedance changes on the surface, and magnetic particle testing shows linear indications. After comprehensively analyzing this information, the model may give a judgment result of "surface crack" and estimate the crack depth to be 2mm and the length to be 10mm, which is of medium severity. This integration of multi-source information not only improves the accuracy of detection, but also gives a more comprehensive defect assessment result, providing an important basis for subsequent maintenance decisions.

[0045] Furthermore, obtaining a trained fatigue damage location model includes:

[0046] Preprocess and extract features of the fused multi-source heterogeneous data;

[0047] Determine the number of input layer nodes of the fatigue damage location model according to the dimensions of multi-source heterogeneous data, and set the number of output layer nodes according to the damage location requirements, corresponding to the three-dimensional coordinates of the damage location;

[0048] Construct a multi-layer neural network structure, set the number of nodes and activation function of each layer, and initialize the model parameters;

[0049] The preprocessed multi-source heterogeneous data are divided into training sets and test sets, the fatigue damage location model is trained, and the model parameters are optimized by gradient descent to minimize the loss function;

[0050] The learning rate and regularization parameters are dynamically adjusted according to the error changes to obtain a trained fatigue damage localization model.

[0051] Specifically, during the training process, the mini-batch gradient descent method is used, and 64 samples are selected in each batch for forward propagation and back propagation. The loss function can select the mean square error, and the model parameters are updated through the Adam optimizer. The initial learning rate is set to 0.001, and the learning rate decay strategy is adopted to reduce the learning rate to 0.9 times the original every 50 epochs. At the same time, the L2 regularization term is introduced, and the coefficient is set to 0.0001 to prevent overfitting. Model evaluation is a key step in testing model performance. Using the test set data, the Euclidean distance between the predicted position and the actual position is calculated, and the threshold is set to 5mm. If the distance is less than the threshold, it is considered to be correctly positioned. By counting the number of correctly positioned samples, the precision and recall rate can be calculated. If 1800 samples are correctly positioned out of 2000 test samples, the precision is 90%. In addition, the ROC curve can be drawn, the AUC value can be calculated, and the model performance can be comprehensively evaluated. Model deployment is to apply the trained model to actual scenarios. For example, in aircraft maintenance, the model can be integrated into the detection equipment. When the detection equipment scans the wing surface, the real-time collected data is preprocessed and then input into the model, which then outputs the predicted coordinates of the damage location. Based on these coordinates, maintenance personnel can accurately locate areas where fatigue damage may exist for further inspection and maintenance. This method not only improves detection efficiency, but also reduces the risk of missed detection, which is of great significance to flight safety.

[0052] Furthermore, the fatigue damage location results of the metal material to be tested are obtained including:

[0053] Obtain basic information about the metal material to be tested, and determine the applicable testing method and corresponding testing parameter settings based on the material properties;

[0054] Perform a comprehensive scan on the metal material to be tested to obtain the original test data reflecting the internal structure of the material;

[0055] Preprocessing the acquired original detection data to obtain preprocessed detection data;

[0056] The preprocessed test data is input into the trained fatigue damage location model to obtain the fatigue damage location results of the metal material to be tested.

[0057] Furthermore, the method also includes judging and repairing the fatigue damage location result, including:

[0058] Calculating the damage degree of the fatigue damage area based on the damage location result and the three-dimensional model;

[0059] Determining a repair plan for the fatigue damaged area according to the obtained damage degree, wherein the repair plan includes repair materials and repair processes;

[0060] Apply the determined repair scheme to the fatigue damaged area, repair the fatigue damaged area, and restore the performance of the fatigue damaged area.

[0061] The specific material testing process first needs to obtain the basic information of the material to be tested. Taking the turbine blade of an aircraft engine as an example, the material type may be a nickel-based high-temperature alloy, and the geometric dimensions include blade length, chord length and thickness. According to these characteristics, ultrasonic testing is selected as the main method, and the appropriate ultrasonic frequency and probe type are set. In actual testing, phased array ultrasonic technology can be used to fully scan the turbine blade. This technology can flexibly adjust the direction of the sound beam and the focusing depth, which is conducive to the detection of complex shape parts. The raw data obtained during the scanning process contains information such as the amplitude and time of the reflected wave, which reflects the internal structural characteristics of the blade. The preprocessing of the raw data is a key step to improve the quality of detection. Wavelet transform can be used to remove noise and improve the signal-to-noise ratio; adaptive enhancement algorithm is used to highlight the defect echo characteristics. These processing helps to improve the accuracy and reliability of subsequent analysis. The preprocessed data is input into the fatigue damage localization model, which may adopt a convolutional neural network structure, which can automatically extract data features and perform classification and regression. The model output may show that there is a tiny crack at the root of the blade, with a length of about 0.5 mm and located 30 mm from the tip of the blade. In order to intuitively display the test results, three-dimensional visualization technology can be used. For example, the volume rendering algorithm is used to present the blade structure and damage location at the same time, and the degree of damage is indicated by color mapping. This method can help engineers quickly locate the problem area and assess the severity of the damage. Storing this inspection case in the knowledge base is an important means of accumulating experience. A knowledge storage system based on a graph database can be established to store information such as material properties, inspection parameters, and damage characteristics in the form of nodes and relationships, which is convenient for subsequent similar case retrieval and pattern mining. Based on the damage location results and historical experience, the system can automatically generate maintenance suggestions. For the detected cracks at the root of the blade, it is recommended to use plasma spray repair technology and give specific process parameters. This intelligent suggestion can improve maintenance efficiency and reduce human judgment errors. Through the above process, the whole process from material information acquisition to damage location to maintenance suggestions is automated. This not only improves the efficiency and accuracy of detection, but also provides data support for the full life cycle management of equipment. With the continuous development of artificial intelligence technology, the intelligence level of this process is expected to be further improved, bringing more possibilities for predictive maintenance in the industrial field.

[0062] The present invention discloses a fatigue damage location method for metal materials. Aiming at the cleaning problem of pollutants and oxides on the surface of metal materials, ultrasonic cleaning technology is used to remove surface impurities. A material database is established by measuring physical properties to achieve intelligent matching of detection methods. Computer tomography and deep learning algorithms are used to perform three-dimensional imaging and defect identification on the internal structure of the material. A multi-channel data acquisition system is used to synchronously acquire signals from different detection methods, and effective integration of multi-source information is achieved through data fusion algorithms. A fatigue damage location model based on a neural network is constructed to improve the accuracy and reliability of damage location. Finally, the model is integrated into the detection system to realize automated and intelligent damage location functions, and the damage situation is presented through three-dimensional visualization technology. The present invention also establishes a detection case knowledge base to provide support for subsequent maintenance and decision-making. The method realizes the intelligence of the entire process from material cleaning to damage location, significantly improving the efficiency and accuracy of fatigue damage detection of metal materials.

[0063] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A fatigue damage location method for metal materials, characterized in that: include: According to the pollutants and oxides on the surface of the metal material, the cavitation effect generated by high-frequency vibration is used to remove the impurities attached to the surface to obtain the cleaned metal material; Measure the physical properties of cleaned metal materials, obtain the conductivity and magnetic data of metal materials, establish a material property database, and determine the optimal detection scheme based on the conductivity and magnetic characteristics of metal materials and the preset detection method selection rules; Perform three-dimensional imaging of the interior of metal materials, extract the location and morphological information of fatigue damage areas based on the three-dimensional images, automatically identify the defects and unevenness of the internal structure of metal materials, and generate defect feature maps; The identified three-dimensional image data and the defect feature map are fused to obtain fused multi-source heterogeneous data; constructing a fatigue damage localization model according to the fused multi-source heterogeneous data, training the fatigue damage localization model and optimizing model parameters to obtain a trained fatigue damage localization model; The data of the metal material to be tested is input into the trained fatigue damage localization model to obtain the fatigue damage localization result of the metal material to be tested, and the result is visualized, and a knowledge base is constructed according to the fatigue damage localization result.

2. The fatigue damage location method for metal materials according to claim 1, characterized in that: The cleaned metal materials include: Obtain the metal material to be cleaned, identify and locate the pollutants and oxides on the surface of the material, and determine the cleaning area; According to the type and degree of contamination of the metal material, appropriate parameters are selected from the preset ultrasonic power and cleaning time parameter library and transmitted to the ultrasonic cleaning system; Put the metal material into the ultrasonic cleaning tank, start the ultrasonic cleaning system, and use the cavitation effect generated by high-frequency vibration to clean the pollutants and oxides on the surface of the metal material, remove the residual cleaning liquid and impurities, and obtain the cleaned metal material.

3. The fatigue damage location method for metal materials according to claim 1, characterized in that: Determining the optimal testing solution includes: According to the type of metal material and the cleaning process, determine the conductivity and magnetic physical property parameters that need to be tested, and develop a physical testing plan; Conducting tests on the conductivity and magnetic characteristics of cleaned metal material samples to obtain physical property data of the metal materials; Based on the acquired physical property data of metal materials, the data is stored in a property database in a predetermined data format and organization method to build a material property knowledge base; According to the needs of business scenarios, preset multiple material testing methods and formulate corresponding testing method selection rules; Match the conductivity and magnetic characteristics of the material to be tested with the data in the characteristic database to find the matching material characteristic records; According to the matching material characteristic records and the preset detection method selection rules, the optimal detection scheme is determined from the candidate detection methods.

4. The fatigue damage location method for metal materials according to claim 1, characterized in that: Generating defect feature maps includes: Perform CT scanning inside the metal material to obtain three-dimensional image data inside the metal material; Preprocessing the acquired three-dimensional image data to obtain preprocessed three-dimensional image data; Segmenting the preprocessed three-dimensional image to extract a fatigue damage area image; According to the extracted fatigue damage area image, the three-dimensional position coordinates and three-dimensional morphological characteristics of the fatigue damage area are obtained; The extracted fatigue damage area image is input into the pre-trained convolutional neural network model to automatically identify the defects and unevenness of the internal structure of the metal material and generate a defect feature map.

5. The fatigue damage location method for metal materials according to claim 1, characterized in that: The fused multi-source heterogeneous data include: According to the characteristics of the detection object, determine different detection methods and obtain corresponding data signals; Through a multi-channel data acquisition system, multi-source heterogeneous data of each detection method is synchronously acquired, wherein the multi-source heterogeneous data includes original signal data and processed three-dimensional image data and defect feature map; Preprocessing the acquired multi-source heterogeneous data to obtain preprocessed multi-source heterogeneous data; According to the correlation between multi-source heterogeneous data and the fusion algorithm, a mapping relationship between data is established, and correlation analysis is performed to obtain fused multi-source heterogeneous data.

6. The fatigue damage location method for metal materials according to claim 1, characterized in that: Obtaining a trained fatigue damage localization model includes: Preprocess and extract features of the fused multi-source heterogeneous data; Determine the number of input layer nodes of the fatigue damage location model according to the dimensions of multi-source heterogeneous data, and set the number of output layer nodes according to the damage location requirements, corresponding to the three-dimensional coordinates of the damage location; Construct a multi-layer neural network structure, set the number of nodes and activation function of each layer, and initialize the model parameters; The preprocessed multi-source heterogeneous data are divided into training sets and test sets, the fatigue damage location model is trained, and the model parameters are optimized by gradient descent to minimize the loss function; The learning rate and regularization parameters are dynamically adjusted according to the error changes to obtain a trained fatigue damage localization model.

7. The fatigue damage location method for metal materials according to claim 1, characterized in that: Obtaining fatigue damage location results for the metal material under test includes: Obtain basic information about the metal material to be tested, and determine the applicable testing method and corresponding testing parameter settings based on the material properties; Perform a comprehensive scan on the metal material to be tested to obtain the original test data reflecting the internal structure of the material; Preprocessing the acquired original detection data to obtain preprocessed detection data; The preprocessed test data is input into the trained fatigue damage location model to obtain the fatigue damage location results of the metal material to be tested.

8. The fatigue damage location method for metal materials according to claim 1, characterized in that: The method also includes judging and repairing the fatigue damage location result, including: Calculating the damage degree of the fatigue damage area based on the damage location result and the three-dimensional model; Determining a repair plan for the fatigue damaged area according to the obtained damage degree, wherein the repair plan includes repair materials and repair processes; Apply the determined repair scheme to the fatigue damaged area, repair the fatigue damaged area, and restore the performance of the fatigue damaged area.

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