Method for estimating residual life of bearing of sludge dewatering centrifugal machine

Abstract

The invention discloses a method for estimating the residual service life of a bearing of a sludge dewatering centrifugal machine. The method provides a model for estimating the residual service life of the bearing of the sludge dewatering centrifugal machine based on SAE, SOINN and 1D-CNN. According to the model, vibration sequence features are extracted through a stacked auto-encoder, then the extracted features are divided into a health sample set and a fault sample set, and the health sample set and the fault sample set are respectively input into two self-organizing incremental neural networks to construct bearing health assessment factors. And finally, combining and inputting the health factor, the accumulated working time and the accumulated processing amount into a one-dimensional convolutional network for fusion scoring. The method can effectively avoid the problems of single feature dependence, insufficient generalization ability and the like easily occurring in a traditional algorithm, and can accurately estimate the residual service life in the whole life cycle of the bearing. In order to adapt to a strong interference environment of a water plant and solve the problem of sample imbalance, a wavelet denoising method is adopted to process a vibration signal, and a VAE-GAN-WGP algorithm is proposed to enhance a fault sample.

Description

Technical Field

[0001] This invention relates to the field of mechanical equipment health monitoring technology, and in particular to a method for estimating the remaining useful life (RUL) of bearings in sludge dewatering centrifuges. Background Technology

[0002] High-efficiency dewatering equipment such as horizontal screw centrifuges achieve solid-liquid separation through centrifugal force. Calculations show that the volume of sludge after preliminary dewatering is reduced to one-tenth of its original size, and further reduction to one-twentieth after deep dewatering. Driven by policy and market forces, horizontal screw centrifuges have become the mainstream equipment for sludge treatment due to their high dewatering efficiency.

[0003] As the core transmission component of a centrifuge, the health of bearings directly determines the centrifuge's continuous operating capability. Dehydration centrifuges operate under harsh conditions of high speed, high solid load, and strong corrosion, often resulting in a shorter mean time between failures (MTBF) than their design life. Bearing failure is the leading cause of centrifuge downtime, accounting for up to 70% of unplanned downtime. Therefore, establishing a predictive maintenance mechanism for bearings is crucial.

[0004] Currently, most wastewater treatment plants install sensors in their centrifuges to monitor key operating parameters such as vibration and temperature, constructing threshold alarm systems and recording data such as cumulative treatment volume and cumulative working time for planning maintenance cycles. This equipment management model fails to fully utilize the potential of existing monitoring data in estimating the remaining lifespan of bearings and requires highly experienced maintenance personnel. Furthermore, to ensure reliable centrifuge operation and production safety, water plants often tend to shorten equipment maintenance cycles and increase bearing replacement frequency. At this point, the bearings' lifespan has not yet expired, resulting in wasted human and material resources and economic losses.

[0005] Therefore, this study aims to construct a centrifuge bearing remaining useful life (RUL) prediction model that can fully tap the potential of existing monitoring data, improve the intelligence level of water plant equipment monitoring, and provide a scientific reference for water plants to schedule equipment maintenance cycles. This will help reduce unplanned downtime, ensure the stable operation of the entire sludge treatment process, reduce waste of manpower and resources, and effectively lower the operating costs of the water plant.

[0006] A similar study, "Identification of the Degradation Start Point and Remaining Life Prediction of Rolling Bearings Based on Multi-Head Attention (MHA) and Bi-directional Long Short-Term Memory (BiLSTM) Models," proposes a method for identifying the degradation start point and predicting the remaining life (RUL) of rolling bearings based on multi-head attention (MHA) and bi-directional long short-term memory (BiLSTM) models. First, a composite loss function constructed from the reconstruction error (RE) and maximum mean discrepancy (MMD) of the autoencoder (AE) is used as the bearing health indicator (HI). The peaks over threshold (POT) method and local mean increase detection (LMID) are then employed to determine the degradation start point (DSP) in the bearing performance degradation process. Secondly, a multi-dimensional feature space is constructed using features extracted by AE (Advanced Effects Analysis), MMD (Mean Mean Difference), RE (Reference Error), and the root mean square error (RMSE) between the features extracted by AE. These multi-dimensional features are then input into a multi-head attention mechanism (MHA) and a bidirectional long short-term memory (BiLSTM) model to predict the bearing's relative uptime (RUL). The multi-head attention mechanism dynamically selects highly relevant features to further improve the accuracy of RUL prediction. This study has the following limitations: 1. The dehydration centrifuge operates in a harsh environment with high noise levels. The vibration signal includes the inherent vibration of the equipment, as well as external interference such as the vibration of the surrounding plant structure and fluid pulsation in the pipelines. External interference can mask the inherent characteristics of the centrifuge's vibration signal. Furthermore, the vibration signal is not monotonically changing throughout the bearing's lifespan; relying on a single variable for RUL prediction may lead to significant fluctuations and large errors in the prediction results. 2. This study is based on existing datasets from the laboratory, but the actual production environment differs from the laboratory. To ensure production safety, water plants tend to shut down equipment quickly after it exhibits abnormalities. This results in a severe shortage of fault sample data obtained in the real environment. In this case, the algorithm may tend to ignore small samples and classify more data as normal samples to improve the accuracy of the model on the full sample set, leading to a decrease in the prediction accuracy in the later stages of bearing operation. Summary of the Invention

[0007] Firstly, current data-driven methods for estimating the remaining life of bearings primarily rely on vibration signals to quantify the degree of bearing wear and then infer the remaining service life. Vibration signals are indeed an important indicator of bearing health; when bearings are severely worn or experience malfunctions, the bearing amplitude typically increases significantly. This is why many wastewater treatment plants use centrifuge amplitude as a threshold alarm indicator. However, throughout the bearing's lifespan, the bearing amplitude does not increase monotonically. The monitored bearing amplitude often shows a slight decreasing trend during the initial period of operation, followed by a relatively long period of stable operation, and finally a sudden increase at the end of its service life. Figure 1 As shown.

[0008] Under these changing patterns, using a single vibration index for estimating remaining lifespan may result in significant errors, especially in the early to mid-stages of bearing operation. Currently, water plants primarily estimate bearing remaining lifespan and schedule maintenance cycles based on indicators such as cumulative operating time and cumulative treatment volume. However, in actual operation, centrifuges operate under harsh conditions including high temperatures, high loads, and strong vibrations. Furthermore, the equipment's operating status is affected by multiple factors such as seasonal changes, load fluctuations, and environmental disturbances. Consequently, the actual wear rate of bearings varies considerably. Relying solely on cumulative treatment volume and cumulative operating time is insufficient to accurately estimate the actual degradation of bearings, ultimately leading to prolonged periods of under- or over-maintenance, resulting in unplanned downtime and wasted human and material resources.

[0009] Furthermore, most current data-driven evaluation models rely on the assumption of sufficient sample data. However, because the normal operating time of equipment is much longer than the failure time, and manufacturers often shut down equipment quickly after it exhibits abnormalities for safety reasons, the dataset of normally operating equipment far exceeds the dataset of failed equipment, resulting in a severely imbalanced sample distribution. In this situation, traditional models may discard some small samples, tending to classify more samples as normal to improve the model's classification accuracy on the entire dataset, leading to a lower identification rate for failed samples. Traditional oversampling and undersampling techniques still have limitations in addressing the imbalanced sample problem; for example, oversampling can easily lead to overfitting of new samples, while undersampling can easily lose information.

[0010] Finally, the operating environment of water plant centrifuges is complex and harsh, with significant noise interference within the plant where the equipment is located, resulting in poor data quality. In particular, vibration signals closely related to bearing health are affected not only by the inherent vibrations of the equipment itself but also by external interference such as plant structure vibrations and fluid pulsations in pipelines. These external noises severely mask the inherent characteristics of the centrifuge vibration signals, making it difficult for existing models to achieve the expected accuracy and thus hindering their practical application.

[0011] To address the aforementioned issues, this invention proposes a model for predicting the remaining service life of bearings in sludge dewatering centrifuges based on SAE, SOINN, and 1D-CNN. This model combines a method for constructing health factors based on vibration signal monitoring with operational data from wastewater treatment plants, such as cumulative treatment volume, used to estimate the remaining bearing life. This fully leverages the potential of commonly used monitoring data from water treatment plants to construct a more accurate bearing remaining service life prediction model. The model extracts vibration sequence features using a Stacked Autoencoder (SAE), then divides the extracted features into a healthy sample set and a fault sample set, respectively inputting them into two Self-organizing Incremental Neural Networks (SOINN) to construct bearing health assessment factors. Finally, the health factors, cumulative operating time, and cumulative treatment volume are combined and input into a 1D Convolutional Neural Network (1D-CNN) for fusion scoring. This method effectively avoids the problems of single feature dependence and insufficient generalization ability that traditional algorithms often suffer from, achieving accurate prediction of remaining service life over the entire bearing lifecycle. To adapt to the strong interference environment of water plants and solve the problem of sample imbalance, this invention uses wavelet denoising to process vibration signals and proposes the VAE-GAN-WGP algorithm to enhance fault samples.

[0012] The algorithm requires low computing power when deployed in the field and can be directly deployed on industrial control computers or edge platforms such as ARM. It enables low-latency evaluation of target equipment in water plants and uploads data that meets the confidentiality requirements of water plants to the cloud for viewing by an APP through its built-in communication module, thus meeting the resource constraints and security compliance requirements of industrial sites.

[0013] The method proposed in this invention fully leverages the potential of common monitoring data from wastewater treatment plants in predicting the remaining life of centrifuge bearings, and provides corresponding solutions for common data issues in wastewater treatment plants. This method boasts advantages such as low cost, high practicality, and wide applicability. It effectively improves the intelligence level of equipment management, helps plants monitor bearing health status in real time, scientifically formulate equipment maintenance cycles, reduce unplanned downtime and waste of manpower and resources, lower wastewater plant operating costs, and achieve predictive maintenance. Attached Figure Description

[0014] Figure 1 This is a graph showing the trend of vibration signals throughout the bearing's entire life cycle.

[0015] Figure 2 This is a flowchart of the model training process.

[0016] Figure 3 This is a diagram of the VAE-GAN-WGP network structure.

[0017] Figure 4 The flowchart shows the training process for VAE-GAN-WGP.

[0018] Figure 5 This is a diagram of a dual self-organizing incremental neural network structure.

[0019] Figure 6 This describes the training process for a self-organizing incremental neural network. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] A method for estimating the remaining life of bearings in a sludge dewatering centrifuge, the method comprising the following steps:

[0022] Step 1: Obtain the initial dataset collected by the monitoring equipment. The initial dataset includes, but is not limited to, common dewatering centrifuge monitoring indicators such as the centrifuge's vibration signal, the cumulative operating time corresponding to the bearing, and the cumulative sludge treatment volume corresponding to the bearing.

[0023] Step 2: To improve data quality, perform data cleaning on the acquired dataset, such as deleting outliers.

[0024] Step 3: The acquired vibration signal is denoised using discrete wavelet denoising. Wavelet transform can be divided into continuous wavelet transform and discrete wavelet transform, but continuous wavelet transform suffers from information redundancy. In practical signal processing, discrete wavelet transform has better performance and is therefore widely used.

[0025] ;

[0026] Formula (1) is the transform formula for discrete wavelets. The scale of the transform, i.e., the resolution control parameter in wavelet transform. The displacement position is used to control the translation of the wavelet basis. The original signal, Discrete wavelet basis functions are the core of wavelet transform, constructing sub-signals of different frequencies by shifting k and scaling j. The transform decomposes the signal into wavelet coefficients at different scales and locations, representing the signal's characteristics at each scale.

[0027] Due to their orthogonality, tight support, and strong adaptability, Daubechies wavelets are suitable for the decomposition and denoising of complex signals. Soft thresholding denoising can effectively remove high-frequency noise while maintaining signal smoothness. Therefore, choosing Daubechies wavelets as basis functions and applying soft thresholding denoising methods can preserve key signal information while removing noise, achieving ideal signal processing results.

[0028] Step 4: Divide the denoised vibration data into a healthy sample set and a faulty sample set. At this point, the quality of the sample data has been significantly improved, but the healthy sample set is much larger than the faulty sample set. If these samples are used directly as training samples for the model, it may lead to imbalanced model training. Therefore, it is necessary to augment the faulty sample set.

[0029] Variational autoencoders (VAEs) and generative adversarial networks (GANs) have achieved good results in many tasks, but traditional VAEs suffer from problems such as ambiguous sample generation and a lack of diversity in generated samples. The training process of traditional GANs is unstable, and pattern collapse is prone to occur, leading to fluctuations in the quality of generated samples. The generator learns as many data patterns as possible, resulting in duplicate generated samples. Therefore, this invention borrows the ability of VAEs to learn data distribution, providing a stable latent variable sampling mechanism for the generator to alleviate the pattern collapse problem in GANs. Simultaneously, it combines explicit probability models and adversarial training, using a discriminator to guide the generator to generate samples that better conform to the real distribution, compensating for the shortcomings of VAEs in global construction. Using the WAGN-GP training method, and leveraging gradient penalty to address the training difficulties of GAN structures, a VAE-GAN-WGP model is proposed. This model uses VAEs to encode real samples, and resampled latent variables Z replace random vectors input to the generator to improve the network. During training, a gradient penalty term is added to optimize the loss function. The network structure consists of three parts: an encoding network, a generation network, and a discriminator network, as shown in the figure. Figure 3 As shown.

[0030] Fault sample sets are used as input to VAE-GAN-WGP for fault sample augmentation. The input data first passes through the VAE encoder, which maps the input data to the latent space. The encoder consists of a main convolutional path, a skip connection path, and a latent space projection layer. The main convolutional path extracts features through a series of residual blocks. Each residual block contains two convolutional layers, a batch normalization layer, and a LeakyReLU activation function. During convolution, the size of the feature map is progressively reduced while the number of channels is increased. The skip connection path processes the original input using a one-dimensional convolutional layer, a batch normalization layer, and a LeakyReLU activation function. The latent space projection layer contains two fully connected layers, which are used to output the mean and log-variance of the latent space, respectively. Furthermore, the weights of the convolutional and batch normalization layers are initialized. The convolutional layers use Kaiming normalization, and the weights of the batch normalization layer are initialized to 1, while the biases are initialized to 0.

[0031] The core function of the encoding network is to compress the input data into the latent space, learning feature representations of the data to provide suitable latent variables for the subsequent generative network. The use of residual connections helps alleviate the vanishing gradient problem, enabling the network to learn deeper features more effectively. Skip connections can fuse features at different scales, improving the richness of feature representations. The final output mean and log-variance are used in the subsequent reparameterization process for sampling in the latent space.

[0032] The core purpose of the loss function in the encoder VAE is to constrain the distribution of the latent space while reconstructing the input data. To make the model more stable, several improvement strategies are adopted, including enhancing numerical stability, using a smoothing loss function, dynamically adjusting the KL divergence weights, and adding latent space regularization. It consists of three parts: reconstruction loss, KL divergence loss, and latent space regularization term, as shown in Equation (2). These are the dynamic weights of the KL divergence loss. It is the weight of the latent space regularization term.

[0033] ;

[0034] The smooth L1 loss function is used instead of the traditional mean squared error (MSE) loss. Smooth L1 loss is insensitive to outliers, reducing their impact on reconstruction loss and making the model more stable during training. The smooth L1 loss function is shown in equation (3), where... This is the reconstructed sample. It is a real sample.

[0035] ;

[0036] KL divergence loss is used to measure the difference between the latent spatial distribution and the standard normal distribution, as shown in formula (4). Let be the mean of the potential space. It is the variance of the latent space. It is the logarithmic variance.

[0037] ;

[0038] Dynamic weights of KL divergence An exponential decay method is adopted, as shown in formula (5), where step is the current training step number. As the training step number increases, the weight of the KL divergence loss gradually decreases. The initial weight is 0.01. This dynamic adjustment helps the model focus more on the regularization of the latent space in the early stage of training, and more on the reconstruction loss in the later stage.

[0039] ;

[0040] Mean of the potential space Perform L2 norm regularization as shown in formula (6), and the weight of this term... Adding a small penalty term to prevent the mean of the latent space from becoming too large helps the model learn a more reasonable latent space representation.

[0041] ;

[0042] The generator network receives the latent variables from the encoder network's output and attempts to generate samples similar to the input data. It first adjusts the dimensions of the latent variables and then projects them to a higher dimension through fully connected layers. Next, learnable positional encodings and decay coefficients are introduced to enhance the representation of sequence positional information. A Transformer structure with skip connections is constructed using multiple Transformer encoder layers to learn the dependencies between latent variables. Finally, progressive upsampling is performed through a series of fully connected layers and activation functions such as GELU and Sigmoid to generate the final output. Learnable positional encodings and decay coefficients enable the model to better capture the positional information of the sequence, improving the quality of the generated samples. The use of the Transformer structure helps learn complex dependencies between latent variables, resulting in more logical and coherent samples. Progressive upsampling gradually expands the information of the latent variables to the same dimension as the input data.

[0043] The discriminative network distinguishes between samples generated by the generator network and real samples. It first divides the input data into blocks, then embeds each block into a higher dimension through fully connected layers, adding learnable positional encodings. Next, a Transformer encoder processes the embedded blocks and records intermediate layer features. Finally, a fully connected layer outputs the discriminative result. The core role of the discriminative network is to provide feedback to the generator network, prompting it to continuously optimize the quality of generated samples. By dividing the input data into blocks and using Transformer encoding, it learns global features and dependencies between blocks, thus more accurately determining the authenticity of samples. Simultaneously, the recorded intermediate layer features can be used for subsequent feature analysis and model optimization, such as when calculating feature matching loss. In the entire VAE-GAN-WGP model, the discriminative network and the generator network train adversarially, driving the convergence and performance improvement of the entire model.

[0044] Adversarial loss function This is the loss function designed for generative adversarial structures, as shown in Equation (7). Its purpose is to enable the samples generated by the generator to better deceive the discriminator, while simultaneously improving the quality of the generated samples through feature matching loss. This function employs a strategy of Wasserstein loss, hierarchical feature matching loss, and dynamic weight adjustment to improve training stability and the quality of generated samples. These are the dynamic weights of the Wasserstein loss. It is the dynamic weight of the hierarchical feature matching loss.

[0045] ;

[0046] The hierarchical feature matching loss is calculated by comparing the feature representations of generated samples and real samples at each layer of the discriminator, as shown in formula (8), where and These are the feature representations of the generated sample and the real sample in the i-th layer of the discriminator, respectively. The cosine similarity is defined as shown in formula (9), and the L1 loss is shown as shown in formula (10).

[0047] ;

[0048] ;

[0049] ;

[0050] The weights of the Wasserstein loss increase dynamically with the number of training steps, as shown in Equation (11), while the hierarchical feature matching loss decreases dynamically with the number of training steps, as shown in Equation (12).

[0051] ;

[0052] ;

[0053] After the model is finally built, the training process is as follows: Figure 4 As shown, data preprocessing is first performed by applying Fast Fourier Transform (FFT) to the vibration signal, transforming the time-domain vibration signal into frequency-domain data and extracting frequency-domain features. During training, a step-by-step training approach is adopted. First, the VAE structure is pre-trained to optimize its reconstruction and latent space learning capabilities. Then, the VAE is jointly trained with a GAN, using an adversarial mechanism to improve the model's generation ability. After training, the optimal model parameters are saved, and new sample data is generated using the model. Finally, the generated samples are compared with real samples to evaluate the generation effect.

[0054] Step 5: Merge the newly added samples into the original sample set for training the SAE-SOINN bearing degradation factor calculation model. The SAE is responsible for extracting features from the centrifuge vibration sequence, transforming the vibration signals from several past operating cycles into several feature values ​​that are easier for SOINN to process. The autoencoder (AE) is an unsupervised learning neural network consisting of an encoder and a decoder. The encoder consists of a hidden layer and an input layer, transforming the input vector through a nonlinear transformation. Extract latent features (n=1,2,...,N):

[0055] (13);

[0056] (14);

[0057] In formula (13) Here is the weight coefficient matrix of the encoder. This is the bias coefficient matrix of the encoder. This is the encoder activation function. In formula (14) This is the weight coefficient matrix of the decoder. This is the bias coefficient matrix of the decoder. This is the activation function for the decoder.

[0058] A single Advanced Feature Extraction (SAE) is composed of multiple stacked Advanced Feature Extractions (AEs). After the first AE is trained, its features are input into the second AE; after the second AE is trained, its extracted features are used as input into the third AE. This process is repeated to train all AEs, thus achieving feature extraction from shallow to deep layers.

[0059] Step 6: After SAE processing, the vibration sequence is transformed into a low-dimensional feature value sequence. The samples are then divided into healthy sample sets and faulty sample sets. SOINN1 and SOINN2 networks are trained using healthy samples and faulty samples respectively to learn their features. The network structure diagram is shown below. Figure 5 As shown.

[0060] SOINN typically employs a two-layer structure. The first layer learns basic clustering, and the second layer reprocesses the output of the first layer to generate a more abstract representation. It calculates the similarity between samples using distance, achieving efficient processing of high-dimensional, high-volume data. Its training process is as follows: Figure 6 As shown.

[0061] The first layer of SOINN receives the raw data input and generates an initial topology representing nodes and edges within the network. The second layer receives the learning results from the first layer and performs another learning iteration after each time interval (LT) to obtain a more concise and stable learning result.

[0062] When constructing the decay factor, SOINN1 and SOINN2 respectively output... and This method quantifies the similarity between the current vibration sequence samples of the equipment and healthy and faulty samples, thereby constructing a bearing degradation factor based on vibration indicators. The formula for calculating the bearing degradation factor H is as follows:

[0063] ;

[0064] Step 7: Combine the degradation factor H with the cumulative processing volume and cumulative working time corresponding to the bearing, and predict the remaining service life of the bearing using 1D-CNN.

[0065] One-dimensional convolutional neural networks (1D-CNNs) are variants of convolutional neural networks specifically designed to process one-dimensional sequential data (such as time series, text, and audio signals). Their core idea is similar to that of two-dimensional CNNs, but they are optimized for the temporal or sequential characteristics of one-dimensional data.

[0066] In one-dimensional convolution, the convolution kernel is a one-dimensional vector that slides along the time of the input sequence. Each neuron only links to a local window of the input, capturing local features of the sequence. All neurons in the same convolutional layer share the same one-dimensional kernel, reducing the number of parameters and improving translation invariance. The calculation formula is shown in Equation (16), where t is the time step length and k is the convolution kernel length.

[0067] (16);

[0068] By using the merged dataset as input to a 1D-CNN, hierarchical learning can be achieved through stacked convolutional layers. Shallow layers capture basic features, while deeper layers combine these features. The 1D-CNN can effectively fit the mapping relationship between bearing degradation factors, cumulative running time, cumulative processing volume, and remaining bearing life, enabling the prediction of bearing life using common monitoring variables in actual water plant production environments.

[0069] Step 8: After model training is complete, it can be deployed on industrial control computers or edge platforms such as ARM to achieve low-latency evaluation of target equipment in the water plant. The algorithm proposed in this invention has been verified in a complete hardware system. During field deployment, the hardware device connects to the water plant database, and reads the corresponding data to predict bearing life after detecting an update to the target data. The calculation results can be displayed on the hardware system's built-in screen (including numerical values ​​and curves) and can also be uploaded to the cloud for use by the APP via the hardware system's built-in communication module.

Claims

1. A method for estimating the remaining life of bearings in a sludge dewatering centrifuge, characterized in that, The method includes the following steps: Step 1: Obtain the initial dataset collected by the monitoring equipment; the initial dataset includes the vibration signal of the centrifuge, the cumulative working time corresponding to the centrifuge bearing, and the cumulative sludge treatment volume corresponding to the centrifuge bearing, which are monitoring indicators for the dewatering centrifuge. Step 2: To improve the data quality of the vibration signal, the acquired dataset is cleaned by removing outliers. Step 3: The collected vibration signal is denoised using the discrete wavelet denoising method; ； Formula (1) is the transform formula for discrete wavelets. The scale of the transform, i.e., the resolution control parameter in wavelet transform. The displacement position is used to control the translation of the wavelet basis. The original signal, Discrete wavelet basis functions are the core of wavelet transform. They are used to construct sub-signals of different frequencies by shifting k and scaling j. Daubechies wavelets are selected as basis functions, and a soft thresholding denoising method is applied. Step 4: Divide the denoised vibration data into a healthy sample set and a faulty sample set; A VAE-GAN-WGP model is proposed using the WAGN-GP training method. The VAE is used to encode real samples, and the resampled latent variable Z is used to replace the random vector input generator to improve the network. Gradient penalty terms are added during training to optimize the loss function. The network structure includes three parts: encoding network, generation network and discriminator network. The fault sample set is used as the input of VAE-GAN-WGP to perform fault sample augmentation. Step 5: Merge the new samples into the original sample set to train the SAE-SOINN bearing degradation factor calculation model; SAE is responsible for extracting features from the centrifuge vibration sequence and converting the vibration signals from the past few operating cycles into several feature values ​​processed by SOINN. An autoencoder (AE) is an unsupervised learning neural network consisting of an encoder and a decoder. The encoder comprises a hidden layer and an input layer, which transforms the input vector through a nonlinear transformation. Extract latent features n=1,2,...,N: （13）； （14）； In formula (13) Here is the weight coefficient matrix of the encoder. This is the bias coefficient matrix of the encoder. For encoder activation function; in formula (14) This is the weight coefficient matrix of the decoder. This is the bias coefficient matrix of the decoder. is the activation function for the decoder; SAE is composed of multiple stacked AEs. After the first AE is trained, the features are input into the second AE. After the second AE is trained, the extracted features are used as the input of the third AE; and so on, training of all AEs is completed, thereby realizing feature extraction from shallow to deep layers. Step 6: After SAE processing, the vibration sequence is transformed into a low-dimensional feature value sequence. The samples are then divided into a healthy sample set and a faulty sample set. The SOINN1 and SOINN2 networks are trained using healthy samples and faulty samples respectively to learn their features. Step 7: Combine the degradation factor H with the cumulative processing volume and cumulative working time corresponding to the bearing, and predict the remaining service life of the bearing using 1D-CNN; Step 8: After the model training is completed, it can be deployed on an industrial control computer or ARM edge platform to achieve low-latency evaluation of target equipment in the water plant.

2. The method for estimating the remaining life of a sludge dewatering centrifuge bearing according to claim 1, characterized in that, The input data first passes through a VAE encoder, which maps the input data to the latent space. The encoder consists of a main convolutional path, a skip connection path, and a latent space projection layer. The main convolutional path extracts features through a series of residual blocks. Each residual block contains two convolutional layers, a batch normalization layer, and a LeakyReLU activation function. During convolution, the size of the feature map is gradually reduced while the number of channels is increased. The skip connection path processes the original input using a one-dimensional convolutional layer, a batch normalization layer, and a LeakyReLU activation function. The latent space projection layer contains two fully connected layers, which are used to output the mean and log-variance of the latent space, respectively. In addition, the weights of the convolutional layers and the batch normalization layer are initialized. The convolutional layers are initialized using Kaiming normalization, and the weights of the batch normalization layer are initialized to 1, while the biases are initialized to 0.

3. The method for estimating the remaining life of a sludge dewatering centrifuge bearing according to claim 2, characterized in that, The core function of the encoding network is to compress the input data into the latent space and provide suitable latent variables for the subsequent generative network by learning the feature representation of the data. Skip connection paths can fuse features at different scales and improve the richness of feature representation. The mean and log-variance of the final output are used in the subsequent reparameterization process so that sampling can be performed in the latent space.

4. The method for estimating the remaining life of a sludge dewatering centrifuge bearing according to claim 3, characterized in that, The loss function of the encoder VAE constrains the distribution of the latent space while reconstructing the input data; Several improvement strategies are adopted, including enhancing numerical stability, using a smooth loss function, dynamically adjusting the KL divergence weights, and adding latent space regularization; It consists of three parts: reconstruction loss, KL divergence loss, and latent space regularization term, as shown in Equation (2). These are the dynamic weights of the KL divergence loss. These are the weights of the latent space regularization term; ； The smoothed L1 loss function is used instead of the traditional mean squared error (MSE) loss; the smoothed L1 loss function is shown in formula (3), where This is the reconstructed sample. These are real samples; ； KL divergence loss is used to measure the difference between the latent spatial distribution and the standard normal distribution, as shown in formula (4); where Let be the mean of the potential space. It is the variance of the latent space. It is the logarithmic variance; ； Dynamic weights of KL divergence The exponential decay method is adopted, and the formula is (5), where step is the current training step; As the number of training steps increases, the weight of the KL divergence loss gradually decreases; ； Mean of the potential space Perform L2 norm regularization as shown in formula (6), and the weight of this term... Adding a small penalty term prevents the mean of the latent space from becoming too large, which helps the model learn a more reasonable latent space representation. ； The generator network receives the latent variables from the encoder network output and attempts to generate samples similar to the input data. First, the latent variables are dimensionally adjusted, and then projected to a higher dimension through fully connected layers. Learnable positional encoding and attenuation coefficients are introduced to enhance the representation of sequence positional information. A Transformer structure with skip connections is constructed using multiple Transformer encoder layers. Finally, progressive upsampling is performed through a series of fully connected layers and activation functions to generate the final output.

5. The method for estimating the remaining life of a sludge dewatering centrifuge bearing according to claim 4, characterized in that, The discriminant network distinguishes between samples generated by the generator network and real samples. First, the input data is divided into blocks, and then each block is embedded into a higher dimension through a fully connected layer, adding learnable positional encodings. Next, a Transformer encoder processes the embedded blocks and records intermediate layer features. Finally, a fully connected layer outputs the discriminant result. The core function of the discriminant network is to provide feedback to the generator network, prompting it to continuously optimize the quality of generated samples. By processing the input data into blocks and using Transformer encoding, it can learn global features of the data and dependencies between blocks, thus more accurately judging the authenticity of samples. Recording intermediate layer features is used for subsequent feature analysis and model optimization. In the entire VAE-GAN-WGP model, the discriminant network and the generator network train adversarially, driving the convergence and performance improvement of the entire model.

6. The method for estimating the remaining life of a sludge dewatering centrifuge bearing according to claim 5, characterized in that, Adversarial loss function It is a loss function designed for generative adversarial structures, as shown in Equation (7); it enables the samples generated by the generator to better deceive the discriminator, while improving the quality of the generated samples through feature matching loss; These are the dynamic weights of the Wasserstein loss. It is the dynamic weight of the hierarchical feature matching loss; ； The hierarchical feature matching loss is calculated by comparing the feature representations of generated samples and real samples at each layer of the discriminator, as shown in formula (8), where and These are the feature representations of the generated sample and the real sample in the i-th layer of the discriminator, respectively; the cosine similarity is defined as shown in formula (9), and the L1 loss is defined as shown in formula (10); ； ； ； The weights of the Wasserstein loss increase dynamically with the number of training steps, as shown in Equation (11), while the hierarchical feature matching loss decreases dynamically with the number of training steps, as shown in Equation (12). ； ； After the model is finally built, the data is preprocessed by performing a Fast Fourier Transform (FFT) on the vibration signal to transform the time-domain vibration signal into frequency-domain data and extract frequency-domain features. During training, a step-by-step training approach is adopted. First, the VAE structure is pre-trained to optimize its reconstruction and latent space learning capabilities. Then, the VAE is jointly trained with a GAN to improve the model's generation capability through an adversarial mechanism. After training, the optimal model parameters are saved, and the model is used to generate new sample data. Finally, the generated samples are compared and analyzed with real samples to evaluate the generation effect.

7. The method for estimating the remaining life of a sludge dewatering centrifuge bearing according to claim 1, characterized in that, In step 6, SOINN employs a two-layer structure. The first layer learns basic clusters, and the second layer reprocesses the output of the first layer to generate a more abstract representation. The first layer of SOINN receives the raw data input and generates an initial topology in the network represented by nodes and edges. The input to the second layer network is the learning result of the first layer. After each LT cycle, it is trained again to obtain a more concise and stable learning result. When constructing the decay factor, SOINN1 and SOINN2 respectively output... and To quantify the similarity between the current vibration sequence sample of the equipment and healthy and faulty samples, a bearing degradation factor based on vibration indices is constructed; the calculation formula for the bearing degradation factor H is as follows: 。 8. The method for estimating the remaining life of a sludge dewatering centrifuge bearing according to claim 1, characterized in that, In step 7, the one-dimensional convolutional neural network 1D-CNN is a variant of the convolutional neural network, specifically designed to process one-dimensional sequential data; In one-dimensional convolution operations, the convolution kernel is a one-dimensional vector that slides along the time of the input sequence. Each neuron only links to the local window of the input to capture the local features of the sequence. All neurons in the same convolutional layer share the same one-dimensional kernel, reducing the number of parameters and improving translation invariance. The calculation formula is shown in Equation (16), where t is the time step length and k is the convolution kernel length. （16）； The merged dataset is used as input to the 1D-CNN, and hierarchical learning is performed by stacking convolutional layers. The shallow layers capture basic features, and the deep layers combine features.

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