Motor casing die casting surface quality detection method and system
By collecting and preprocessing the surface image data of the motor casing die casting in real time, and using the improved Yolo v8 algorithm to train the detection model for quality detection, the problems of low detection accuracy and poor robustness in the prior art are solved, and efficient and accurate surface quality detection is achieved.
Patent Information
- Application Number
- CN202411813929.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-11
- Publication Date
- 2025-03-28
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
The prior art has low detection accuracy and poor robustness in the surface quality detection of motor casing die castings, resulting in inaccurate detection results.
Real-time acquisition of surface image data of the motor casing die casting is carried out, and after data preprocessing is performed, the surface quality detection model trained by the improved Yolo v8 algorithm is used to detect, the surface quality detection results are output, and the preset sorting strategy is performed based on the results.
It improves detection efficiency and accuracy, reduces interference from human factors, enhances detection reliability, and has good adaptability and scalability.
Smart Images

Figure CN119715525A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of motor casing die casting quality detection, and in particular to a motor casing die casting surface quality detection method and system. Background Art
[0002] As an important component of the motor, the surface quality of the motor casing die-casting directly affects the overall performance and life of the motor. Traditionally, the surface quality inspection of motor casing die-castings mainly relies on manual visual inspection, which is not only inefficient but also easily affected by human factors, resulting in inaccurate detection results. With the rapid development of computer vision technology, more and more automated detection methods are being applied in the field of industrial quality inspection. However, the existing automated detection methods often have problems such as low detection accuracy and poor robustness when it comes to surface quality inspection of motor casing die-castings. Therefore, there is an urgent need for an efficient and accurate method for surface quality inspection of motor casing die-castings to improve detection efficiency and accuracy and reduce production costs. Summary of the invention
[0003] In view of the above-mentioned technical deficiencies, an object of the present invention is to provide a method and system for detecting the surface quality of die-casting parts of a motor casing, so as to solve the problems of low detection accuracy and poor robustness in the prior art.
[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions: In a first aspect, the present invention provides a method for detecting the surface quality of a motor housing die casting, the method comprising: Step S100: collecting surface image data of the motor housing die casting in real time; Step S200: performing data preprocessing on the collected surface image data; Step S300: training a surface quality inspection model using historical surface image data and historical surface defect data based on an improved Yolo v8 algorithm; Step S400: inputting the real-time surface image data after data preprocessing into the trained surface quality detection model, and outputting the surface quality detection result; Step S500: Execute a preset sorting strategy according to the surface quality detection result.
[0005] Preferably, in a possible implementation manner of the first aspect, the surface image data is obtained by photographing the surface of the motor housing die-casting in real time using an image acquisition device.
[0006] Preferably, in a possible implementation manner of the first aspect, the data preprocessing includes denoising and contrast enhancement.
[0007] Preferably, in a possible implementation of the first aspect, the improved Yolo v8 algorithm adopts efficientViT as the backbone network.
[0008] Preferably, in a possible implementation manner of the first aspect, the surface quality detection model structure includes: Input layer, used to input surface image data; The feature extraction layer uses efficientViT to extract image features from the input surface image data to obtain deep feature information in the image; Feature fusion layer, which fuses the extracted image features; The detection head layer performs target detection based on the fused image feature information; The output layer outputs the defect type, probability and location information based on the detection results of the detection head layer.
[0009] Preferably, in a possible implementation manner of the first aspect, step S400 specifically includes: Input the real-time surface image data after data preprocessing into the trained surface quality detection model; The surface quality inspection model processes the input image data and outputs the surface quality inspection results, including the types of surface defects of the motor housing die casting and their probability of occurrence, and determines the location information of the defects in the image.
[0010] Preferably, in a possible implementation manner of the first aspect, step S500 specifically includes: According to the surface quality inspection results, if the probability of a certain defect in the motor housing die casting is greater than the preset threshold, it will be sorted into the defective area; If the probability of various defects appearing on the surface of the motor housing die-casting is not greater than the preset threshold, it will be sorted into the qualified product area.
[0011] Preferably, in a possible implementation manner of the first aspect, the method further includes recording the surface quality detection result into a database.
[0012] In a second aspect, the present invention provides a surface quality detection system for a motor housing die casting, the system comprising: Image acquisition module, used for real-time acquisition of surface image data of motor housing die castings; A data preprocessing module is used to perform preprocessing operations such as denoising and contrast enhancement on the collected surface image data; Model training module, based on the improved Yolo v8 algorithm, uses historical surface image data and historical surface defect data to train the surface quality inspection model; A quality inspection module, used to input the pre-processed real-time surface image data into the trained surface quality inspection model and output the surface quality inspection result; The sorting control module executes the preset sorting strategy according to the surface quality inspection results and sorts the motor casing die-castings into the qualified product area or the defective product area.
[0013] The beneficial effects of the present invention are: by collecting the surface image data of the motor casing die-casting in real time and performing data preprocessing, the preprocessed image data is then quality tested using a surface quality detection model trained based on the improved Yolo v8 algorithm, and finally a preset sorting strategy is executed according to the test results. Not only is the detection efficiency improved, but also the interference of human factors is reduced, and the accuracy and reliability of the detection are improved. At the same time, the method also has good adaptability and scalability, and can perform surface quality detection on different types of motor casing die-castings. In addition, the test results are recorded in a database to facilitate subsequent data analysis and quality management. Therefore, the implementation of the present invention is of great significance for improving the production efficiency and product quality of motor casing die-castings. BRIEF DESCRIPTION OF THE DRAWINGS
[0014] In order to more clearly illustrate the embodiments of the present invention 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 of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0015] Figure 1 A flow chart of a method for detecting surface quality of die-casting parts of a motor casing is provided for the present application.
[0016] Figure 2 A structural diagram of a motor casing die-casting surface quality detection system is provided for this application.
[0017] Explanation of the accompanying drawings: 1-data acquisition module, 2-data preprocessing module, 3-model building module, 4-fault detection module, 5-early warning module. DETAILED DESCRIPTION
[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0019] Embodiment 1: Figure 1As shown, the present invention provides a method for detecting the surface quality of a motor casing die casting, comprising: Step S100: collecting surface image data of the motor housing die casting in real time.
[0020] Specifically, the surface image data is obtained by real-time photographing the surface of the motor housing die-casting using an image acquisition device, and the surface image data is transmitted to a data center.
[0021] In this embodiment, an industrial camera of model "Basler acA1920-40gc" is used as an image acquisition device. The camera is deployed at the inspection station on the production line, and the shooting process adopts a continuous shooting mode, that is, the camera continuously shoots the motor housing die-casting to capture real-time image data of its surface. When the motor housing die-casting arrives at the inspection station, the camera's shooting signal is triggered to ensure that each shot can accurately correspond to the motor housing die-casting. It not only ensures the real-time nature of the image data, but also ensures the one-to-one correspondence between the image data and the motor housing die-casting.
[0022] Step S200: performing data preprocessing on the collected surface image data.
[0023] Specifically, data preprocessing is a key step to ensure that the subsequent quality inspection model can accurately and efficiently process and analyze image data, which mainly includes two steps: denoising and contrast enhancement. The purpose of denoising is to remove noise points or interference information that may exist in the image. These noises may come from sensor noise of the image acquisition device, changes in ambient light, errors in the transmission process, etc. In order to effectively remove these noises, the Gaussian filter algorithm is used. Gaussian filtering is a linear smoothing filter. Its principle is to replace the gray value of each pixel in the image with the weighted average gray value of the pixels in its neighborhood, and the weight of the weighted average is determined by the Gaussian function.
[0024] In terms of contrast enhancement, an adaptive histogram equalization algorithm is used. Since the surface image of the motor housing die-casting may have problems such as uneven lighting and reflection, the image contrast is inconsistent, which affects the accuracy of subsequent defect detection. The adaptive histogram equalization algorithm calculates the histogram of the local area of the image and performs equalization processing on it, thereby enhancing the local contrast of the image and making the details in the image clearer.
[0025] In the process of denoising and contrast enhancement, the image also needs to be resized to ensure that it meets the input requirements of the subsequent quality detection model. The resizing uses a bilinear interpolation algorithm, which can achieve fast image scaling while maintaining image quality.
[0026] In this embodiment, the image data is preprocessed in the data center, and the noise in the image is first removed by the Gaussian filtering method. Specifically, a Gaussian filtering function gaussian_filter is defined, which receives three parameters: the image to be processed image, the size of the Gaussian kernel kernel_size, and the standard deviation sigma of the Gaussian kernel. Inside the function, the cv2.GaussianBlur method in the OpenCV library is used to perform Gaussian filtering on the image to obtain the denoised image denoised_image.
[0027] Next, the denoised image is subjected to adaptive histogram equalization to enhance the image contrast. Define an adaptive histogram equalization function adaptive_histogram_equalization, which receives three parameters: the image to be processed, the contrast limit value clip_limit, and the grid size tile_grid_size for adaptive histogram equalization. Inside the function, use the cv2.createCLAHE method in the OpenCV library to create an adaptive histogram equalization object clahe, and set its contrast limit value and grid size. Then, use the clahe.apply method to perform adaptive histogram equalization on the image to obtain the contrast-enhanced image enhanced_image.
[0028] Finally, resize the contrast-enhanced image. Define an image resize function resize_image, which receives two parameters: the image to be processed and the target size target_size. Inside the function, use the cv2.resize method in the OpenCV library to resize the image, and use the bilinear interpolation algorithm to obtain the resized image resized_image.
[0029] Step S300: training a surface quality inspection model using historical surface image data and historical surface defect data based on an improved Yolo v8 algorithm.
[0030] Specifically, in the process of building and training the surface quality inspection model, the improved Yolo v8 algorithm was selected and efficientViT was introduced as the backbone network. efficientViT is a model that combines the advantages of the Transformer architecture and convolutional neural network. It can effectively capture the global and local features in the image while maintaining high computational efficiency.
[0031] Under the improved Yolo v8 algorithm framework, the model first includes an input layer for receiving preprocessed surface image data. Next is the feature extraction layer, which uses the efficientViT network to perform deep feature extraction on the input image. EfficientViT can capture key feature information in the image, including texture, shape, color, etc. through self-attention mechanism and position embedding. Then the model enters the feature fusion layer, in which multiple feature maps from the efficientViT network are fused together to form a more comprehensive and robust feature representation. Next is the detection head layer, which performs target detection tasks based on the fused feature information. It adopts a multi-scale prediction strategy and can simultaneously detect defective targets of different sizes and shapes. By setting multiple anchor boxes and regression heads, the model can accurately predict the type, probability and location information of the defect. Finally, the detection head layer is responsible for organizing and outputting the detection results of the detection head layer. The output content includes the type of surface defects of the motor housing die-casting, the probability value of each defect, and the precise location information of the defect in the image (expressed in the form of a bounding box).
[0032] In this embodiment, historical surface image data is first collected and sorted from the data center to ensure that the data contains samples of various surface defects, and the image data is annotated to mark the type, location and size of each defect, including scratches, cracks, pits and bubbles. The data set is divided into a training set, a validation set and a test set according to an 8:1:1 ratio.
[0033] For the data annotation process, first start the LabelImg tool. Load the historical surface image data through the LabelImg graphical interface. In the LabelImg interface, select the rectangular box for defect annotation. Draw a bounding box around each defect, making sure that the bounding box fits tightly to the edge of the defect, and enter the corresponding defect type label for each bounding box, including "scratches", "cracks", "pits", and "bubbles". After completing the annotation of each image, use the save function of LabelImg to save the annotation information (including defect type, bounding box location, and size) in a JSON format annotation file.
[0034] Then, we build the model, select the improved Yolo v8 algorithm as the model framework, and introduce efficientViT as the backbone network to build the input layer, feature extraction layer, feature fusion layer, detection head layer, and output layer. Finally, we train the model using the training set data, and verify the model using the validation set and test set data.
[0035] For the surface quality inspection model, the input layer uses the PIL.Image.open() function to open the image file in the specified path and converts it to RGB format through the .convert('RGB') method to ensure the compatibility of the image data. Then, the converted image data is passed to the preprocessing function preprocess to obtain the processed image tensor image_tensor.
[0036] The feature extraction layer first defines the PatchEmbedding class with 3 input channels and 768 embedding dimensions. The PatchEmbedding class divides the input image into image patches through the convolution layer and maps each image patch into the embedding space. Adding a category tag and position embedding provides additional information. Next, the Mlp class is defined, which is a multi-layer perceptron module used for feature transformation in the Transformer block. The Mlp class contains two fully connected layers self.fc1 and self.fc2, and a self.dropout to prevent overfitting. Then the Attention class is used as the attention mechanism module to calculate the correlation between input features. The embedding dimension embed_dim, the number of attention heads num_heads, whether to add bias qkv_bias, the scaling factor qk_scale, and the dropout rate dropout are set during initialization. On this basis, the TransformerBlock class is used, which is a Transformer block that combines the attention mechanism and the multi-layer perceptron module. The TransformerBlock class contains two normalization layers self.norm1 and self.norm2, an attention module self.attn and a multi-layer perceptron module self.mlp. During the forward propagation process, the input features first pass through the first normalization layer, then pass through the attention module for update, then pass through the second normalization layer, and finally pass through the multi-layer perceptron module for feature transformation. Finally, the EfficientViT class is used, which contains a drop layer self.pos_drop, a Transformer block list self.layers, and a fully connected layer self.head for classification tasks. During the forward propagation process, the input image is first processed by the feature extractor or PatchEmbedding class, then passes through the Transformer block list for feature extraction and transformation, and finally passes through the fully connected layer for classification.
[0037] The feature fusion layer class is named FeatureFusionLayer, which inherits from the nn.Module base class. In the class initialization method, the number of channels of the input feature map in_channels and the number of channels of the output feature map out_channels are defined. These two parameters correspond to the number of feature maps output by the efficientViT network and the number of feature maps required after fusion, respectively. First, a 1x1 convolution kernel self.conv1 is used to perform a convolution operation on the input feature map to achieve the purpose of feature fusion. The advantage of 1x1 convolution is that it has a small amount of calculation and can flexibly change the number of channels of the feature map. Then, batch normalization self.bn1 is used to normalize the feature map after convolution to improve the stability and convergence speed of the model. Finally, the ReLU activation function self.relu is used to perform nonlinear transformation on the feature map to enhance the expression ability of the model. In the forward propagation method of the feature fusion layer, a tensor list x containing multiple feature maps is received as input. These feature maps come from different levels of the efficientViT network, have the same batch size and spatial dimension, but may have different numbers of channels. First, these feature maps are concatenated in the channel dimension to form a new feature map. Then, the concatenated feature map is processed using 1x1 convolution, batch normalization, and ReLU activation function to obtain the fused feature map.
[0038] The detection head layer first uses the DetectionHead class, which inherits from the nn.Module base class in the PyTorch framework. In the class initialization method, three parameters are received: in_channels, num_classes, and num_anchors. Among them, in_channels represents the number of channels of the input feature map, that is, the number of channels of the fused feature map; num_classes represents the number of defect types, which is used for classification tasks; num_anchors represents the number of anchor boxes on each grid unit, which is used for target positioning tasks. In the DetectionHead class, first initialize the current class by calling the initialization method of the base class nn.Module. Then define two convolutional layers self.conv1 and self.conv2. self.conv1 is a two-dimensional convolutional layer with an input channel number of in_channels, an output channel number of in_channels * 2, a convolution kernel size of 3x3, and padding=1 is used to keep the spatial dimension of the feature map unchanged. The function of this layer is to further extract features and expand the number of channels of the input feature map. self.conv2 is another 2D convolutional layer with in_channels * 2 input channels, num_classes * num_anchors * 5 output channels, and a kernel size of 1x1. The purpose of this layer is to convert feature maps into prediction results, where each anchor box outputs a vector containing class probability, confidence, and bounding box information. In addition, a batch normalization layer self.bn1 and a ReLU activation function self.relu are used to normalize and nonlinearly transform the output of the convolutional layer, respectively, to improve the stability and expression of the model. In the forward propagation method of the DetectionHead class, a feature map x with a shape of [batch_size, in_channels, height, width] is received as input. First, the input feature map is processed by self.conv1, self.bn1, and self.relu to obtain the enhanced feature map. Then, the enhanced feature map is converted into a prediction result by self.conv2. Finally, the prediction results are rearranged into the shape of [batch_size, height / / stride, width / / stride, num_anchors, num_classes + 5]. This shape means that there are num_anchors anchor boxes for each grid cell, and each anchor box outputs a vector containing num_classes + 5 elements (category probability, confidence, and bounding box information).
[0039] The output layer outputs the defect type, confidence level, and bounding box information based on the detection results of the detection head layer.
[0040] Step S400: input the real-time surface image data after data preprocessing into the trained surface quality detection model, and output the surface quality detection result.
[0041] Specifically, the real-time surface image data after data preprocessing is input into the trained surface quality detection model; the surface quality detection model processes the input image data and outputs the surface quality detection results, including the types of surface defects of the motor casing die-casting and their probability of occurrence, and determines the location information of the defects in the image.
[0042] In this embodiment, when the motor housing die-casting completes image acquisition and data preprocessing at the inspection station on the production line, the obtained real-time surface image data is immediately input into the surface quality inspection model that has been fully trained and verified. The model is built based on the improved Yolo v8 algorithm, which efficiently integrates efficientViT as the backbone network, so that it has the ability to capture and analyze complex image features with high precision. When the model receives the preprocessed image data, it first passes through the feature extraction layer, which uses the self-attention mechanism and position embedding function of the efficientViT network to deeply mine the global and local features in the image, including but not limited to key information such as texture details, shape contours, and color distribution. Subsequently, these features are passed to the feature fusion layer, in which feature maps at different levels are effectively fused through processing methods such as 1x1 convolution, batch normalization, and ReLU activation function to form a richer and more robust feature representation. Next, the detection head layer uses a multi-scale prediction strategy based on these fused feature maps to accurately identify various defect targets in the image, including scratches, cracks, etc., and simultaneously calculates the defect type, confidence level, and precise location information (intuitively displayed in the form of a bounding box). Finally, the surface quality inspection model outputs the inspection results, including the specific type of surface defects on the motor housing die casting, the confidence score for each defect, and the precise location coordinates of the defect in the image.
[0043] Step S500: Execute a preset sorting strategy according to the surface quality detection result.
[0044] Specifically, according to the surface quality inspection results, if the probability of a certain defect in the motor casing die-casting is greater than a preset threshold, it will be sorted to the defective product area; if the probability of various defects on the surface of the motor casing die-casting is not greater than the preset threshold, it will be sorted to the qualified product area. This embodiment sets the threshold value to 0.5. When the probability of a certain defect in the motor casing die-casting exceeds the preset threshold, it is considered that the die-casting has quality problems and needs to be sorted to the defective product area. The sorting process is implemented by automated sorting equipment, which includes components such as robotic arms, conveyor belts, and sorting gates. They can sort the motor casing die-castings from the production line according to system instructions and place them in designated areas.
[0045] In this embodiment, when the system detects that the defect probability of a motor casing die-casting exceeds 0.5, the action command of the sorting device is immediately triggered, and the robot arm or conveyor belt grabs or pushes the die-casting from the production line to the defective product area. At the same time, the system records the relevant information of the die-casting, including the defect type, defect location, and sorting time. On the contrary, if the probability of various defects appearing on the surface of the motor casing die-casting is not greater than the preset threshold, the system considers that the die-casting is of qualified quality and needs to be sorted to the qualified product area for subsequent assembly or packaging processes. In addition, in order to ensure the accuracy and reliability of the sorting strategy, the system will also regularly maintain and calibrate the sorting equipment to ensure that it is in good working condition.
[0046] In one embodiment, the method further comprises recording the surface quality inspection result into a database.
[0047] Specifically, every time the surface quality inspection model completes an inspection and outputs the inspection results, these results will be captured by the system and stored in the database. The stored inspection data includes key fields such as the unique identifier of the motor housing die-casting, inspection time, defect type, defect confidence, and defect location information in the image. By recording these inspection data in the database, it is easy to trace and analyze the quality status of the motor housing die-casting, timely discover potential problems in the production process, and take effective improvement measures. In addition, these inspection data can also serve as an important reference for subsequent quality control and product improvement, providing strong data support for the company's quality management and continuous improvement.
[0048] Embodiment 2: Figure 2 As shown, the present invention provides a motor casing die casting surface quality detection system, comprising: Image acquisition module 1, used for real-time acquisition of surface image data of motor housing die castings; Data preprocessing module 2, used for performing preprocessing operations such as denoising and contrast enhancement on the collected surface image data; Model training module 3, based on the improved Yolo v8 algorithm, uses historical surface image data and historical surface defect data to train the surface quality inspection model; The quality detection module 4 is used to input the pre-processed real-time surface image data into the trained surface quality detection model and output the surface quality detection result; The sorting control module 5 executes a preset sorting strategy according to the surface quality detection result, and sorts the motor housing die-casting parts into a qualified product area or a defective product area.
[0049] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.
Claims
1. A method for detecting the surface quality of a motor housing die casting, characterized in that: The method comprises: Step S100: collecting surface image data of the motor housing die casting in real time; Step S200: performing data preprocessing on the collected surface image data; Step S300: training a surface quality inspection model using historical surface image data and historical surface defect data based on an improved Yolo v8 algorithm; Step S400: inputting the real-time surface image data after data preprocessing into the trained surface quality detection model, and outputting the surface quality detection result; Step S500: Execute a preset sorting strategy according to the surface quality detection result.
2. The motor housing die casting surface quality detection method according to claim 1, characterized in that: The surface image data is obtained by real-time photographing the surface of the motor housing die-casting using an image acquisition device.
3. The motor housing die casting surface quality detection method according to claim 1, characterized in that: The data preprocessing includes denoising and contrast enhancement.
4. The motor housing die casting surface quality detection method according to claim 1, characterized in that: The improved Yolov8 algorithm adopts efficientViT as the backbone network.
5. The motor housing die casting surface quality detection method as claimed in claim 4, characterized in that: The surface quality detection model structure includes: Input layer, used to input surface image data; The feature extraction layer uses efficientViT to extract image features from the input surface image data to obtain deep feature information in the image; Feature fusion layer, which fuses the extracted image features; The detection head layer performs target detection based on the fused image feature information; The output layer outputs the defect type, probability and location information based on the detection results of the detection head layer.
6. The motor housing die casting surface quality detection method as claimed in claim 1, characterized in that: The step S400 specifically includes: Input the real-time surface image data after data preprocessing into the trained surface quality detection model; The surface quality inspection model processes the input image data and outputs the surface quality inspection results, including the types of surface defects of the motor housing die casting and their probability of occurrence, and determines the location information of the defects in the image.
7. The motor housing die casting surface quality detection method according to claim 1, characterized in that: The step S500 specifically includes: According to the surface quality inspection results, if the probability of a certain defect in the motor housing die casting is greater than the preset threshold, it will be sorted into the defective area; If the probability of various defects appearing on the surface of the motor housing die-casting is not greater than the preset threshold, it will be sorted into the qualified product area.
8. The motor housing die casting surface quality detection method as claimed in claim 1, characterized in that: The method further comprises recording the surface quality detection result into a database.
9. A motor housing die casting surface quality detection system, characterized in that: The system comprises: Image acquisition module, used for real-time acquisition of surface image data of motor housing die castings; A data preprocessing module is used to perform preprocessing operations such as denoising and contrast enhancement on the collected surface image data; Model training module, based on the improved Yolo v8 algorithm, uses historical surface image data and historical surface defect data to train the surface quality inspection model; A quality inspection module, used to input the pre-processed real-time surface image data into the trained surface quality inspection model and output the surface quality inspection result; The sorting control module executes the preset sorting strategy according to the surface quality inspection results and sorts the motor casing die-castings into the qualified product area or the defective product area.
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