Deep learning method for realizing fault diagnosis of rotating machinery
By combining the channel expansion module and multi-stage convolutional neural network, using 1DConvNeXt and joint attention module, the problem of low fault diagnosis accuracy of existing deep learning methods in high noise environments is solved, and higher diagnostic accuracy and generalization capabilities are achieved.
Patent Information
- Application Number
- CN202510010598.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-03
- Publication Date
- 2025-05-06
AI Technical Summary
In the diagnosis of rotating machinery faults in high noise environments, the existing deep learning methods have low diagnostic accuracy and poor generalization. Especially when the data volume is small, the automatic encoder effect becomes worse, long-term and short-term memory networks are difficult to process a large amount of frequency data, and convolutional neural networks have low accuracy when the noise is high.
A deep learning method is adopted, combining channel expansion module and multi-stage convolutional neural network, and using 1DConvNeXt feature extractor and joint attention module, the model's processing ability of noise data is enhanced, and the model's noise resistance and generalization ability is improved through technologies such as dense connection and global average pooling.
The accuracy of rotating machinery fault diagnosis in high noise environments is improved, the model's noise resistance and generalization ability is enhanced, and it can show high diagnostic accuracy on multiple rotating machinery fault data sets.
Smart Images
Figure CN119939340A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of intelligent manufacturing fault prediction and diagnosis, and specifically relates to a deep learning method for realizing rotating machinery fault diagnosis. Background Art
[0002] With the development of the machinery industry, the composition of machinery has become more complex. It is very dangerous for machinery to fail during operation. At the same time, it is very time-consuming to find specific faulty components in complex machinery. Therefore, fault detection and diagnosis are very important in modern industrial operation, because this can ensure safety and reliable operation of equipment.
[0003] Early fault diagnosis mainly relied on signal processing methods, which processed the data by wavelet transform, fast Fourier transform, etc., and then classified the fault samples with appropriate classification methods. These signal processing-based methods achieved good diagnostic results, but they were highly dependent on expert knowledge in signal processing to analyze the signal in the time domain and frequency domain, which was very labor-intensive and not suitable for online fault diagnosis.
[0004] In recent years, machine learning methods have been applied to the field of fault diagnosis. Compared with signal processing methods, machine learning methods can automatically extract features from input signals without expert knowledge. However, ordinary machine learning methods still require selected features, and these methods cannot learn deeper features of signals. Therefore, when using machine learning methods to deal with fault diagnosis problems, high accuracy cannot be achieved and generalization is poor.
[0005] Recently, deep learning has been widely used in pattern recognition, fault diagnosis and life prediction. Compared with traditional machine learning algorithms, deep learning can learn deeper abstract features from input signals, which can provide more effective and accurate information for subsequent classification. Autoencoders, long short-term memory networks, and convolutional neural networks have achieved good results in dealing with fault diagnosis and life prediction problems, but these existing methods still have the following defects: 1) The methods based on autoencoders are data hungry. When the amount of data is small, the effect of autoencoders will deteriorate; 2) Long short-term memory networks have better effects when the input signal is a time series signal, but this type of method is more difficult to process a large amount of frequency data, and cannot effectively extract features when the signal contains noise; 3) The current methods based on convolutional neural networks mostly process high-quality sample data, and when faced with high-noise data, they will expose the problems of low accuracy and poor generalization. Summary of the invention
[0006] In order to improve the diagnostic accuracy of the fault diagnosis method based on deep learning in a high noise environment and improve the defects of the above-mentioned model, the present invention provides a deep learning method for rotating machinery fault diagnosis, which can realize automatic classification of various faults.
[0007] In order to achieve the above object, the present invention adopts the following technical solutions:
[0008] A deep learning method for realizing rotating machinery fault diagnosis is performed according to the following steps:
[0009] Step 1: Build a fault diagnosis classification model;
[0010] Furthermore, the fault diagnosis classification model of step 1 is composed of a channel expansion module and a plurality of stages of convolutional neural networks. The channel expansion module is used to obtain richer spatial features. Each stage contains one or more 1DConvNeXt feature extractors and a joint attention module following it for enhancing the model's anti-noise ability. The 1DConvNeXt feature extractor is the main feature extraction unit of the model. The joint attention module, as a supplementary attention mechanism, enhances the model's attention to effective features, thereby improving the model's diagnostic accuracy for noisy data. Dense connections are used between stages, and channels are expanded in a cascading manner so that the model obtains spatial information during training. Finally, fault classification is achieved through the use of global average pooling (GAP) and a fully connected layer (FC).
[0011] Furthermore, the 1DConvNeXt in the fault diagnosis classification model of step 1 first uses a deep separable convolution with a kernel size of 1×13 for feature extraction. The deep separable convolution uses the grouped convolution technology, where the number of groups is the same as the number of channels, so that the feature extraction can be completed with the least parameters. The large convolution kernel can provide a larger effective receptive field with fewer layers, and then the extracted features are standardized by layer normalization (LN). Two 1×1 convolutions are used after standardization to expand the channel and restore the channel. After the first channel expansion, the GELU activation function is used to activate the feature. GELU is a smoother activation function that can also retain some negative eigenvalues to prevent the gradient from disappearing.
[0012] 1DConvNeXt, which is responsible for feature extraction, uses a larger convolution kernel. This method can increase the receptive field while using fewer layers and avoid subsequent optimization problems caused by an overly deep model.
[0013] Furthermore, the feature image obtained by the joint attention module in the fault diagnosis classification model in step 1 from 1DConvNeXt is:
[0014]
[0015] Among them, C represents the number of channels, L represents the length of each channel data, i∈[1,C] represents the feature image of the i-th channel, and global average pooling (GAP) is used to compress y on each channel i Get the channel information, and the generated vector is 1×1 convolution is used to obtain spatial information The calculation formulas for single channel information and spatial information are as follows:
[0016]
[0017] Among them, w i is the weight parameter in the convolution calculation. The channel information and spatial information are obtained through matrix multiplication to obtain the feature importance image, which has the same size as Y. The calculation process of the feature importance image F is as follows:
[0018] F=σ(BN(F C ×F L )),
[0019] The result of matrix multiplication is batch normalized (BN) and subjected to the Sigmoid function. After two residual operations, the final output feature image is obtained. The formula for the two residual operations is as follows:
[0020]
[0021] in, represents the addition of elements at the same position. w1 and w2 are two learnable parameters that adjust the weights of the first residual connection F and Y during training. Y represents the output of the first residual operation, and Z represents the output of the second residual operation. Compared with the original image, the feature image reduces the influence of noise.
[0022] The joint attention module is used after 1DConvNeXt. The module uses global average pooling and convolution with a kernel size of 1 to extract channel features and spatial features. By using these two features to construct the original features, the purpose of strengthening useful information and reducing noise is achieved.
[0023] Furthermore, the calculation formula of the dense connection in the fault diagnosis classification model in step 1 is as follows:
[0024] X k =Concat(Z k-1 ,X k-1 ,…,X1),
[0025] Among them, Xk Represents the input of each stage, Z k Represents the output of each stage. Between stages, a convolution with a kernel of 1×1 and a step size of 2 is used as downsampling. This ensures that the data length is the same while extracting features once more, retaining more information for subsequent calculations.
[0026] Dense connections are applied between each stage. First, the output size of each stage is kept uniform through one-dimensional convolutions with different times and a step size of 2. Then, the outputs of each stage are combined in a cascade manner. Dense connections can directly obtain feature images from the previous stage, so that the final classifier can obtain low-level features. At the same time, dense connections improve the back propagation ability of gradients, making model training easier. Dense connections are used to connect the features after all feature extraction stages. Dense connections improve the back propagation of gradients, making the model easier to train.
[0027] The specific operations of the 1DConvNeXt module for feature extraction and the joint attention module for enhancing the model's anti-noise ability are as follows: first, a convolution with a kernel size of 1×2 and a step size of 2 is used for downsampling, and the feature length is reduced to half of the input feature while extracting the feature once. Then, feature extraction is achieved through different numbers of 1DConvNeXt modules, and finally, the joint attention module (JAM) is used to complete the noise reduction process.
[0028] Step 2: Select a bearing data set from the existing public fault data sets, preprocess the bearing data, and input it into the fault diagnosis classification model for classification;
[0029] The bearing data is preprocessed and input into the fault diagnosis classification model. The classification model is carried out in stages. Each stage first extracts features through 1DConvNeXt, and then uses the joint attention module to process the extracted features. The joint attention module processes channel features and spatial features at the same time. Dense connections are used between each stage to achieve the expansion of the overall channel.
[0030] According to step 2, an existing public bearing dataset is selected, and a sliding window method is used to extract sufficient datasets from the original data for processing. The dataset is normalized using the (-1, 1) normalization method, and the prepared dataset is divided into a training set, a validation set, and a test set according to a ratio of 7:1:2. The dataset is then sent to the model for training and testing.
[0031] Step 3: Combine OLS loss to constrain the classification results;
[0032] Furthermore, the specific operation of step 3 in conjunction with OLS loss to constrain the classification results is as follows: the soft labels of the first round are provided by uniform distribution, and each subsequent round of calculation supervises the soft labels of the previous round. When the input data is correctly classified after the model calculation, the value of the label matrix is updated according to the prior probability. Online label smoothing solves the problem of model overfitting to a certain extent through real-time update of soft labels.
[0033] Online label smoothing (OLS) loss is used in the model to implement constraints on classification results. OLS combines soft labels with hard labels. At the same time, soft labels can be updated as training progresses. The use of OLS can reduce the overfitting of the model and improve the convergence ability of the model.
[0034] Most previous classification models use hard labels for loss constraints, but the hard label method contains less information, which will lead to overfitting of training. The label smoothing method that directly converts hard labels to soft labels cannot take into account the relationship between different classes. The online label smoothing used in this method solves these problems. Online label smoothing combines hard labels with soft labels, where soft labels are updated with the results after each training. Through the use of online label smoothing, the overfitting problem of the model is eliminated to a certain extent.
[0035] Step 4: Output the final classification results.
[0036] Compared with the prior art, the present invention has the following advantages:
[0037] (1) The present invention provides a deep learning method for realizing rotating machinery fault diagnosis, using 1DConvNeXt as a feature extractor in each stage to extract feature images. 1DConvNeXt uses one-dimensional convolution with a larger convolution kernel, which can provide a larger effective receptive field with fewer layers. Residual connections are also used in 1DConvNeXt, which provides more effective feature extraction.
[0038] (2) A pure convolutional neural network method with dense connections is used for fault diagnosis of rotating machinery in a noisy environment. A joint attention module is set up, which obtains channel information and spatial information at the same time. By using channel information and spatial information to reconstruct features, more effective information can be obtained from the input signal. By setting residual connections, the feature extraction ability of the joint attention module is enhanced, and the loss of information in reconstruction is reduced, so that the overall module obtains more valuable features and reduces the impact of noise.
[0039] (3) The present invention provides a pure convolutional neural network method with dense connections for fault diagnosis of rotating machinery in a noisy environment. Dense connections are set between each stage. The dense connections expand the channels in a cascade manner. The setting of dense connections enables the model to obtain more spatial information during training. The simpler gradient back propagation also facilitates the training of the model. Online label smoothing is used as a loss constraint to combine hard labels with soft labels. At the same time, the soft labels are updated in real time in each round of training, thereby reducing the overfitting of the model during the training stage.
[0040] (4) The method of the present invention is highly versatile and can be used on fault data sets of multiple rotating machinery. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 Schematic diagram of a pure convolutional neural network with dense connections according to the present invention;
[0042] Figure 2 Schematic diagram of modules in each stage;
[0043] Figure 3 Schematic diagram of the 1DConvNeXt module structure;
[0044] Figure 4 Schematic diagram of the joint attention module;
[0045] Figure 5 This is a dense connection diagram;
[0046] Figure 6 Schematic diagram of online label smoothing (OLS);
[0047] Figure 7 This is the test confusion matrix of the present invention when the signal-to-noise ratio is -6 dB. DETAILED DESCRIPTION
[0048] In order to gain a deeper understanding of the present invention, we will provide a comprehensive and detailed description of the present invention. However, the present invention has multiple implementations and is not limited to the specific examples listed herein. The presentation of these examples is intended to deepen the comprehensive understanding of the disclosure of the present invention.
[0049] Step 1: Build a fault diagnosis classification model;
[0050] Furthermore, the fault diagnosis classification model of step 1 is composed of a channel expansion module and a plurality of stages of convolutional neural networks. The channel expansion module is used to obtain richer spatial features. Each stage contains one or more 1DConvNeXt feature extractors and a joint attention module following it to enhance the model's anti-noise capability. The 1DConvNeXt feature extractor is the main feature extraction unit of the model. The joint attention module, as a supplementary attention mechanism, enhances the model's attention to effective features, thereby improving the model's diagnostic accuracy for noisy data. Dense connections are used between stages, and channels are expanded in a cascaded manner so that the model can obtain spatial information during training. Finally, the fault classification is achieved through the use of global average pooling (GAP) and a fully connected layer (FC). As shown in the attached figure Figure 1 shown.
[0051] Furthermore, the 1DConvNeXt in the fault diagnosis classification module of step 1 first uses a deep separable convolution with a kernel size of 1×13 for feature extraction. The deep separable convolution uses the grouped convolution technology, where the number of groups is the same as the number of channels, so that the feature extraction can be completed with the least parameters. The large convolution kernel can provide a larger effective receptive field with fewer layers, and then the extracted features are standardized by layer normalization (LN). Two 1×1 convolutions are used after normalization to expand the channel and restore the channel. After the first channel expansion, the GELU activation function is used to activate the feature. GELU is a smoother activation function that can also retain some negative eigenvalues to prevent gradient disappearance. The structure of the 1DConvNeXt feature extraction module in step 1 is shown in the attached figure. Figure 3 shown.
[0052] 1DConvNeXt, which is responsible for feature extraction, uses a larger convolution kernel. This method can increase the receptive field while using fewer layers and avoid subsequent optimization problems caused by an overly deep model.
[0053] Furthermore, the structure of the joint attention module in the fault diagnosis classification module in step 1 is as follows: Figure 4 As shown, suppose the feature image obtained from 1DConvNeXt is:
[0054]
[0055] Among them, C represents the number of channels, L represents the length of each channel data, i∈[1,C] represents the feature image of the i-th channel, and global average pooling (GAP) is used to compress y on each channel i Get the channel information, and the generated vector is 1×1 convolution is used to obtain spatial information The calculation formulas for single channel information and spatial information are as follows:
[0056]
[0057] Among them, w i is the weight parameter in the convolution calculation. The channel information and spatial information are obtained through matrix multiplication to obtain the feature importance image, which has the same size as Y. The calculation process of the feature importance image F is as follows:
[0058] F=σ(BN(F C ×F L )),
[0059] The result of matrix multiplication is batch normalized (BN) and subjected to the Sigmoid function. After two residual operations, the final output feature image is obtained. The formula for the two residual operations is as follows:
[0060]
[0061] in, represents the addition of elements at the same position. w1 and w2 are two learnable parameters that adjust the weights of the first residual connection F and Y during training. Y represents the output of the first residual operation, and Z represents the output of the second residual operation. Compared with the original image, the feature image reduces the influence of noise.
[0062] The joint attention module is used after 1DConvNeXt. The module uses global average pooling and convolution with a kernel size of 1 to extract channel features and spatial features. By using these two features to construct the original features, the purpose of strengthening useful information and reducing noise is achieved.
[0063] Furthermore, the densely connected structure in the fault diagnosis classification model in step 1 is as follows: Figure 5 As shown, the calculation formula for dense connections is as follows:
[0064] X k =Concat(Z k-1 ,X k-1 ,…,X1),
[0065] Among them, X k Represents the input of each stage, Z k Represents the output of each stage. Between stages, a convolution with a kernel of 1×1 and a step size of 2 is used as downsampling. This ensures that the data length is the same while extracting features once more, retaining more information for subsequent calculations.
[0066] Dense connections are applied between each stage. First, the output size of each stage is kept uniform through one-dimensional convolutions with different times and a step size of 2. Then, the outputs of each stage are combined in a cascade manner. Dense connections can directly obtain feature images from the previous stage, so that the final classifier can obtain low-level features. At the same time, dense connections improve the back propagation ability of gradients, making model training easier. Dense connections are used to connect the features after all feature extraction stages. Dense connections improve the back propagation of gradients, making the model easier to train.
[0067] The specific operations of the 1DConvNeXt module for feature extraction and the joint attention module for enhancing the anti-noise ability of the model are as follows: first, a convolution with a kernel size of 1×2 and a step size of 2 is used for downsampling, and the feature length is reduced to half of the input feature while extracting the feature once, and then the feature is extracted through different numbers of 1DConvNeXt modules, and finally the joint attention module (JAM) is used to complete the noise reduction process, as shown in the attached figure. Figure 2 shown.
[0068] Step 2: Select a bearing data set from the existing public fault data sets, preprocess the bearing data, and input it into the fault diagnosis classification model for classification;
[0069] The bearing data is preprocessed and input into the fault diagnosis classification model. The classification model is carried out in stages. Each stage first extracts features through 1DConvNeXt, and then uses the joint attention module to process the extracted features. The joint attention module processes channel features and spatial features at the same time. Dense connections are used between each stage to achieve the expansion of the overall channel.
[0070] According to step 2, an existing public bearing dataset is selected, and a sliding window method is used to extract sufficient datasets from the original data for processing. The dataset is normalized using the (-1, 1) normalization method, and the prepared dataset is divided into a training set, a validation set, and a test set according to a ratio of 7:1:2. The dataset is then sent to the model for training and testing.
[0071] Step 3: Combine OLS loss to constrain the classification results;
[0072] Furthermore, the specific operation of step 3 in conjunction with OLS loss to constrain the classification results is as follows: the soft labels of the first round are provided by uniform distribution, and each subsequent round of calculation supervises the soft labels of the previous round. When the input data is correctly classified after the model calculation, the value of the label matrix will be updated according to the prior probability. Online label smoothing solves the problem of model overfitting to a certain extent through real-time update of soft labels, as shown in the attached figure. Figure 6 shown.
[0073] Online label smoothing (OLS) loss is used in the model to implement constraints on classification results. OLS combines soft labels with hard labels. At the same time, soft labels can be updated as training progresses. The use of OLS can reduce the overfitting of the model and improve the convergence ability of the model.
[0074] Most previous classification models use hard labels for loss constraints, but the hard label method contains less information, which will lead to overfitting of training. The label smoothing method that directly converts hard labels into soft labels cannot take into account the relationship between different classes. The online label smoothing used in this method solves these problems. Online label smoothing combines hard labels with soft labels, where the soft labels are updated with the results after each training. Through the use of online label smoothing, the overfitting problem of the model is eliminated to a certain extent. The detailed composition of the present invention is shown in Table 1:
[0075] Table 1 Detailed composition of each component of the present invention
[0076]
[0077] Step 4: Output the final classification results.
[0078] In order to verify the effectiveness of the method proposed in the present invention, the methods MRA_CNN, ResNet, and WDCNN are used as references to verify the effectiveness of the present invention. When the signal-to-noise ratio is 4 dB, 0 dB, -4 dB, and -8 dB, the average accuracy of 10 experiments is used as the evaluation index, and the above classification results are analyzed. The comparison results are shown in Table 2:
[0079] Table 2 Analysis of results of different models under different signal-to-noise ratios
[0080]
[0081] The confusion matrix of the fault diagnosis results under the test sample with a signal-to-noise ratio of -6 dB is shown in the attached figure. Figure 7 shown.
[0082] In summary, the present invention proposes an intelligent fault diagnosis method for rotating machinery in a noisy environment, which is composed of modules such as 1DConvNeXt, JAM, OLS, and dense connections between stages. The 1DconvNeXt feature extraction module is the most important feature extraction unit of this method. The use of the joint attention mechanism (JAM) enhances the anti-interference ability of this method in the face of noise. The dense connection between the stages improves the back propagation of the gradient, making the model easier to train. Online label smoothing (OLS) combines updateable soft labels with hard labels to reduce the overfitting of the model and enhance the convergence ability of the model. The example study of the Case Western Reserve University bearing data set with different signal-to-noise ratio noise shows that this method can not only provide effective diagnostic capabilities in low noise, but also can still show a high diagnostic accuracy in the face of high noise data.
[0083] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in the field. Although the illustrative specific embodiments of the present invention are described above to facilitate the understanding of the present invention by the technical personnel in the field, it should be clear that the present invention is not limited to the scope of the specific embodiments. For the ordinary technical personnel in the field, as long as various changes are within the spirit and scope of the present invention defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.
Claims
1. A deep learning method for realizing fault diagnosis of rotating machinery, characterized in that: The method comprises the following steps: Step 1: Build a fault diagnosis classification model; Step 2: Select a bearing data set from the existing public fault data sets, preprocess the bearing data, and input it into the fault diagnosis classification model for classification; Step 3: Combine OLS loss to constrain the classification results; Step 4: Output the final classification results.
2. A deep learning method for realizing fault diagnosis of rotating machinery according to claim 1, characterized in that: The fault diagnosis classification model of step 1 is composed of a channel expansion module and a plurality of stages of convolutional neural networks. Each stage contains one or more 1DConvNeXt feature extractors and a joint attention module for enhancing the anti-noise capability of the model. Dense connections are used between the stages. The channels are expanded by cascading so that the model can obtain spatial information during training.
3. A deep learning method for realizing fault diagnosis of rotating machinery according to claim 2, characterized in that: The 1DConvNeXt in the fault diagnosis classification model in step 1 first uses a depthwise separable convolution with a kernel size of 1×13 to extract features, and then standardizes the extracted features through layer normalization. Two 1×1 convolutions are used to expand the channel and restore the channel after standardization, and the GELU activation function is used to activate the features after the first channel expansion.
4. A deep learning method for realizing fault diagnosis of rotating machinery according to claim 3, characterized in that: The feature image Y obtained by the joint attention module in the fault diagnosis classification model in step 1 from 1DConvNeXt is: Among them, C represents the number of channels, L represents the length of each channel data, Represents the feature image of the i-th channel, and global average pooling compresses y on each channel i Get the channel information, and the generated vector is 1×1 convolution is used to obtain spatial information Single channel information and spatial information The calculation formula is as follows: Among them, w i is the weight parameter in the convolution calculation; the channel information and spatial information are obtained through matrix multiplication to obtain the feature importance image, which has the same size as the feature image Y. The calculation process of the feature importance image F is as follows: F=σ(BN(F C ×F L )) The result of matrix multiplication is subjected to batch normalization (BN) and Sigmoid function; after two residual operations, the final output feature image is obtained. The formula for the two residual operations is as follows: in, represents the addition of elements at the same position. w1 and w2 are two learnable parameters that adjust the weight of the first residual connection F and Y during training. Y represents the output of the first residual operation, and Z represents the output of the second residual operation.
5. A deep learning method for realizing fault diagnosis of rotating machinery according to claim 4, characterized in that: The calculation formula of the dense connection in the fault diagnosis classification model in step 1 is as follows: X k =Concat(Z k-1 ,X k-1 ,…,X1) Among them, X k Represents the input of each stage, Z k Represents the output of each stage, and the convolution with a convolution kernel of 1×1 and a step size of 2 is used as downsampling between stages.
6. A deep learning method for realizing fault diagnosis of rotating machinery according to claim 5, characterized in that: The specific operations of the 1DConvNeXt module for feature extraction and the joint attention module for enhancing the model's anti-noise ability are as follows: first, a convolution with a kernel size of 1×2 and a step size of 2 is used for downsampling, and the feature length is reduced to half of the input feature while extracting the feature once. Then, feature extraction is achieved through different numbers of 1DConvNeXt modules, and finally the joint attention module is used to complete the noise reduction process.
7. A deep learning method for realizing fault diagnosis of rotating machinery according to claim 6, characterized in that: According to step 2, an existing public bearing dataset is selected, and a sliding window method is used to extract sufficient datasets from the original data for processing. The dataset is normalized using the (-1, 1) normalization method, and the prepared dataset is divided into a training set, a validation set, and a test set according to a ratio of 7:1:
2. The dataset is then sent to the model for training and testing.
8. A deep learning method for realizing fault diagnosis of rotating machinery according to claim 7, characterized in that: The specific operation of step 3 in combination with OLS loss to realize the constraint on the classification result is: the soft labels of the first round are provided by uniform distribution, and each subsequent round of calculation supervises the soft labels of the previous round. When the input data is correctly classified after the model calculation, the value of the label matrix will be updated according to the prior probability.