A soft measurement modeling method based on pattern correlation spatiotemporal diffusion

Abstract

This invention belongs to the field of soft measurement modeling technology and discloses a soft measurement modeling method based on mode-related spatiotemporal diffusion generation, which includes the following steps: (1) acquiring data of multi-mode dynamic processes; (2) data partitioning and preprocessing operations; (3) establishing a mode-related spatiotemporal diffusion model and generating virtual samples; (4) predicting pressure variables of three-phase flow processes and evaluating model performance. This invention proposes a soft measurement modeling method based on mode-related spatiotemporal diffusion generation. By using the DSTN-Net noise prediction network to capture the dependence of dynamic data in the time and space dimensions, the mode learner learns the multi-mode distribution characteristics and distinguishes the data distribution of different modes, which can generate virtual samples with high similarity to the original samples, thereby improving the prediction performance of the soft measurement model in the case of small samples.

Description

Technical Field

[0001] This invention relates to the field of soft measurement modeling technology for small-sample multi-mode dynamic processes, specifically to a soft measurement modeling method based on mode-related spatiotemporal diffusion generation. Background Technology

[0002] In complex industrial processes, soft measurement technology, by estimating key quality variables that are difficult to obtain online in real time using easily measurable auxiliary variables, has become an important means to ensure production safety, optimize control, and reduce energy consumption. However, due to harsh testing environments, expensive sensors, or long-term testing, samples of key variables are scarce, severely limiting the training accuracy and generalization ability of soft measurement models. To overcome this bottleneck, virtual sample generation technology has emerged. It effectively expands the scale of datasets by mining the implicit variable correlation characteristics in limited samples and generating virtual samples that conform to the real distribution using reasonable mathematical models or intelligent algorithms.

[0003] Virtual sample generation technology has rapidly evolved from simple perturbation and resampling to deep generative models. Currently, the denoising diffusion probabilistic model (DDPM), as an emerging generative model, is attracting more attention from researchers. Typically, DDPM consists of a forward diffusion process and a backward generation process. In the forward process, Gaussian noise is gradually added to the original data to contaminate it. Then, in the backward process, the original data is gradually restored to augment the data. This process is achieved through a trained noise prediction network that can fit the noise added at each step of the forward process. However, existing generation methods are based on data with a single-pattern distribution, making it difficult to cope with the complex distribution characteristics of real-world industrial processes.

[0004] In industrial production, the same production stage may exhibit multiple patterns due to fluctuations in raw materials, equipment status switching, or adjustments in operating parameters. Therefore, the data no longer follows a single Gaussian distribution, but rather displays complex characteristics such as multimodality and heteroscedasticity. Furthermore, due to inherent production cycles and feedback control mechanisms, industrial data typically possesses significant dynamic characteristics. Traditional deep generative models assume a fixed data distribution, making it difficult to adapt to the time-varying characteristics of dynamic industrial scenarios, resulting in significant differences between generated samples and collected data.

[0005] Currently, dynamic characteristics are prevalent in multimodal processes. When addressing the difficulty of modeling with small samples, focusing solely on dynamic characteristics while ignoring multimodal characteristics can easily lead to the model confusing samples from different operating conditions, failing to accurately capture the unique features of each mode. Conversely, considering only multimodal characteristics while ignoring dynamic evolution makes it difficult to adapt to the drift patterns of each mode over time, ultimately resulting in a significant decrease in the model's fitting and generalization capabilities for complex industrial scenarios. How to simultaneously address the dual challenges of multimodal distribution and dynamic characteristics remains a difficult problem for virtual sample generation technology. Summary of the Invention

[0006] To address the challenge of small-sample modeling caused by the scarcity of key quality variables in multi-modal dynamic processes, this invention proposes a Mode-related Spatiotemporal Diffusion Model (MRSDM). This model integrates a Diffusion Spatiotemporal Noise Network (DSTN-Net) and a distribution-aware pattern learner based on a Gaussian mixture model (GMM). Specifically, DSTN-Net captures the temporal and spatial dependencies simultaneously from the original dynamic samples, while the pattern learner learns the multi-modal distribution characteristics and distinguishes the data distributions of different modes. Next, an end-to-end training model is designed to collaboratively optimize DSTN-Net and the pattern learner. Finally, in the reverse process, new virtual samples are gradually generated based on the trained DSTN-Net network. These generated samples supplement the original limited samples, forming a new training set.

[0007] The technical solution adopted by this invention to solve its technical problem is:

[0008] A mode-dependent spatiotemporal diffusion-based soft measurement modeling method is proposed, comprising the following steps:

[0009] (1) Acquire data from multi-mode dynamic processes;

[0010] Multimodal dynamic process data refers to data that exhibits multimodal characteristics due to factors such as raw material fluctuations, equipment status switching, or adjustments in operating parameters. The data no longer follows a single Gaussian distribution but exhibits a multi-peaked distribution. At the same time, due to the natural cyclical characteristics of the production process and the role of the feedback control system, the data distribution drifts over time, exhibiting dynamic characteristics.

[0011] (2) Data partitioning and preprocessing operations:

[0012] First, the collected samples are divided into training and test sets according to the proportions; then, all features are standardized to unify the units and speed up model convergence; finally, the data is serialized using a sliding window.

[0013] (3) Establish a pattern-related spatiotemporal diffusion model and generate virtual samples:

[0014] (4) Predict the pressure variables of the three-phase flow process and evaluate the model performance:

[0015] The generated virtual samples are combined with the original samples to form a new training set. A regression prediction model is then constructed based on the new training set to predict the pressure variables of the three-phase flow process. To objectively verify the present invention, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) are selected. 2 Three indicators are used to quantitatively evaluate the effect after sample expansion.

[0016] Furthermore, the process of step (3) is as follows:

[0017] Step 3.1: Construct the DSTN-Net noise prediction network:

[0018] DSTN-Net is based on an encoder-decoder architecture. The encoder extracts deep features stepwise through downsampling. The decoder fuses low-level detailed features with high-level data features level by level through upsampling and skip connections. Furthermore, considering the dynamic characteristics of data in both time and space dimensions, it captures the dependencies between data points in both dimensions.

[0019] For dynamic data ,in, , L represents the temporal length determined by the sliding window size, K represents the number of features, and M represents the number of original samples. Long short-term memory (LSTM) units and one-dimensional convolutional neural networks (1-D CNNs) are integrated into the noise prediction network to capture the temporal and spatial characteristics of dynamic samples, respectively.

[0020] First, LSTM cells are used to capture data. arrive Dependency in the time dimension. LSTM consists of three gated units: the input gate, the output gate, and the forget gate. Their relationship can be represented in matrix form as follows: ;

[0021] Where W represents the weights of the input matrix, denoted by , b represents the recursive weight, b represents the bias, and the subscripts a, i, f, and o represent the candidate memory unit, input gate, forget gate, and output gate, respectively. , , and Indicate that W, R, and b are respectively related to , The weight of the product of 1 and 2. Let c represent the input matrix at time c. This represents the hidden state at time c-1. A matrix representing all weights and bias terms. Indicates a containing , A column vector of 1.

[0022] Next, consider the dependencies between spatial features in the data. As the process industry progresses, the features fluctuate at different times, and the dependencies between features change accordingly. Therefore, a 1-D convolutional structure is used to gradually move through the dynamic 3D data to capture both global and local features. (Convolution kernel) With step size Moving across the input feature map, the output of the i-th sliding window is calculated using the following formula. : ;

[0023] in, This represents the input in the sliding window.

[0024] The multi-modal data follows a Gaussian mixture distribution. A pattern learner is then used to capture the distribution characteristics of each pattern. The Gaussian Mixture Model (GMM) combines multiple Gaussian distributions into a global distribution. ;

[0025] Where H represents the number of Gaussian distributions, Represents the set of all unknown parameters. Let represent the mean vector of the h-th Gaussian distribution. Let h represent the covariance matrix of the h-th Gaussian distribution. Let the weights of the h-th Gaussian distribution satisfy: , This indicates that the data follows a Gaussian distribution. This represents the h-th Gaussian distribution data.

[0026] Due to training samples Since the samples are independent and have different distributions, we employ a pattern learner to maximize the product of the probability density functions of all samples, thereby optimizing the linear layer estimation of GMM model parameters. Leveraging the advantage of logarithms, the product of the probability density functions of all samples is transformed into the sum of the logarithmic probability density functions, expressed as: ;

[0027] Step 3.2: Data generation process:

[0028] The reverse process of MRSDM is the noise reduction process, the goal of which is to improve the noise reduction efficiency of the trained neural network. Predict the true distribution ,in, The parameters of the neural network, Let t represent the t-th step of the diffusion process, and T represent the total number of diffusion steps. The reverse process is based on data from the t-th step, which follows a Gaussian mixture distribution. Derive the data at time t After T steps of continuous noise removal, samples similar to the real samples are generated, which can be represented in the form of a Markov chain as follows: ;

[0029] in, and Let represent the predicted mean and variance, respectively. In the above formula, since the mean and variance are unknown... The true distribution is insufficient, therefore it cannot be directly derived from... Derivation Therefore, consider adding conditions, i.e., initial data. get This makes it easy to predict. Furthermore, this can be expressed using Bayes' theorem: ;

[0030] Next, we introduce the negative log-likelihood. The aim is to train the parameters of the neural network. To maximize the probability of equation (5). However, The calculation result depends on the T-step reverse process, which is not easy to compute. To solve this problem, it can be achieved by calculating the variational lower bound: ;

[0031] in, This represents the KL divergence.

[0032] remember The latent variables are , express The true distribution of always satisfies: ;

[0033] The evidence lower bound loss is defined as the training objective. Based on formulas (8) and (9), the loss function is obtained: ;

[0034] in, This represents the loss function.

[0035] Furthermore, we obtain: ;

[0036] Where C is a constant independent of θ. It is data noise, This represents the expectation. Through parameterization, formula (11) simplifies to: ;

[0037] in, This represents a noise prediction network.

[0038] When equation (12) converges, the trained noise prediction network and data are obtained. The distribution of the data. Subsequently, in the virtual sample generation process of MRSDM, the data at step t-1 is calculated based on the data at step t according to the following formula: ;

[0039] in, , Represents the identity matrix. This indicates the variance used in each step. , .

[0040] After T sampling steps, the generated data is obtained. As raw data The addition of these elements forms a new training sample. .

[0041] Furthermore, the specific process of step (4) is as follows:

[0042] Given the advantages of LSTM in processing time series data, based on the amplified training samples Build a soft measurement model to predict key quality indicators of the test set.

[0043] The beneficial effects of this invention are mainly reflected in the following: This invention proposes a soft sensor modeling method based on mode-related spatiotemporal diffusion generation. This method targets multi-mode dynamic small-sample processes, capturing the spatiotemporal dependencies of dynamic samples through the DSTN-Net noise prediction network, mining the distribution characteristics of complex multi-mode data using a mode learner, and generating qualified virtual samples similar to the original samples through collaborative optimization of the DSTN-Net and the mode learner. This overcomes the problem of insufficient original data volume and modeling difficulties, thereby improving the prediction accuracy of the soft sensor model. Attached Figure Description

[0044] Figure 1 This is a diagram of the soft measurement framework based on MRSDM of the present invention;

[0045] Figure 2 This is a scatter plot of the generated sample and the original sample from this invention;

[0046] Figure 3 This invention generates a comparison image of the sample and the original sample in the feature dimension;

[0047] Figure 4 This is a comparison chart of the prediction performance of the present invention on the test set. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0049] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0050] Reference Figures 1-4 A mode-dependent spatiotemporal diffusion-based soft measurement modeling method, taking the construction of a pressure prediction model in a three-phase flow process as an example, includes the following steps:

[0051] (1) Acquire multi-mode dynamic three-phase flow process data;

[0052] The three-phase flow experiment aims to controllably deliver oil, water, and gas to a pressurized system at set flow rates. The experimental setup utilizes pipes of varying diameters and geometries, and is equipped with a gas-liquid separator. This separator can independently supply air, water, or oil phase media, and can also deliver any combination of multiphase fluids at set flow rates. By finely adjusting the preset inlet flow rates of the water and gas phases, various flow field distributions can be obtained throughout the three-phase flow process; this invention sets three operating conditions based on different water and gas phase flow rates.

[0053] The aqueous phase flow rates for the three operating conditions were set to 2 kg / s, 1 kg / s, and 2 kg / s, respectively, with corresponding gas phase flow rates of 0.02 m³ / s, 0.03 m³ / s, and 0.04 m³ / s. During the model building phase, this invention selected pressure as the primary output variable and simultaneously selected 16 closely related process variables as auxiliary input variables. These variables are: valve VC302 opening, input air flow rate, gas delivery pressure, water delivery flow rate, water delivery density, bottom pressure of the riser, top density of the riser, top pressure of the riser, differential pressure between PT401 and PT408, liquid level in the top separator, top separation force, differential pressure of VC404, valve VC501 opening, proportion of the gas-liquid three-phase separator, pump current, and valve VC101 opening.

[0054] (2) Data partitioning and preprocessing of three-phase flow process:

[0055] First, the collected samples are divided into training and test sets according to the proportions; then, all features are standardized to unify the units and speed up model convergence; finally, the data is serialized using a sliding window.

[0056] Step 2.1: Split the dataset

[0057] The collected raw samples were divided into two parts: a training set with 303 samples and a test set with 603 samples.

[0058] Step 2.2: Data Normalization Process

[0059] To eliminate the dimensional differences between different features and improve the convergence speed and prediction accuracy of the model, a normalization preprocessing is performed on the data, as shown in the following formula: ;

[0060] in, , and These represent the original data, the maximum value in the original data, and the minimum value in the original data, respectively. This represents the data obtained after normalization.

[0061] Step 2.3: Serialize data

[0062] The data was preprocessed using a sliding window with a window size of 4, resulting in a training set of 300 groups and a test set of 600 groups.

[0063] (3) Establish a pattern-related spatiotemporal diffusion model and generate virtual samples:

[0064] Step 3.1: Construct the DSTN-Net noise prediction network:

[0065] DSTN-Net is based on an encoder-decoder architecture. The encoder extracts deep features stepwise through downsampling. The decoder fuses low-level detailed features with high-level data features level by level through upsampling and skip connections. Furthermore, considering the dynamic characteristics of data in both time and space dimensions, it captures the dependencies between data points in both dimensions.

[0066] For dynamic data ,in, , L represents the temporal length determined by the sliding window size, K represents the number of features, and M represents the number of original samples. Long short-term memory (LSTM) units and one-dimensional convolutional neural networks (1-D CNNs) are integrated into the noise prediction network to capture the temporal and spatial characteristics of dynamic samples, respectively.

[0067] First, LSTM cells are used to capture data. arrive Dependency in the time dimension. LSTM consists of three gated units: the input gate, the output gate, and the forget gate. Their relationship can be represented in matrix form as follows: ;

[0068] Where W represents the weights of the input matrix, denoted by , b represents the recursive weight, b represents the bias, and the subscripts a, i, f, and o represent the candidate memory unit, input gate, forget gate, and output gate, respectively. , , and Indicate that W, R, and b are respectively related to , The weight of the product of 1 and 2. Let c represent the input matrix at time c. This represents the hidden state at time c-1. A matrix representing all weights and bias terms. Indicates a containing , A column vector of 1.

[0069] Next, consider the dependencies between spatial features in the data. As the process industry progresses, the features fluctuate at different times, and the dependencies between features change accordingly. Therefore, a 1-D convolutional structure is used to gradually move through the dynamic 3D data to capture both global and local features. (Convolution kernel) With step size Moving across the input feature map, the output of the i-th sliding window is calculated using the following formula. : ;

[0070] in, This represents the input in the sliding window.

[0071] The multi-modal data follows a Gaussian mixture distribution. A pattern learner is then used to capture the distribution characteristics of each pattern. The Gaussian Mixture Model (GMM) combines multiple Gaussian distributions into a global distribution. ;

[0072] Where H represents the number of Gaussian distributions, Represents the set of all unknown parameters. Let represent the mean vector of the h-th Gaussian distribution. Let h represent the covariance matrix of the h-th Gaussian distribution. Let the weights of the h-th Gaussian distribution satisfy: , This indicates that the data follows a Gaussian distribution. This represents the h-th Gaussian distribution data.

[0073] Due to training samples Since the samples are independent and have different distributions, we employ a pattern learner to maximize the product of the probability density functions of all samples, thereby optimizing the linear layer estimation of GMM model parameters. Leveraging the advantage of logarithms, the product of the probability density functions of all samples is transformed into the sum of the logarithmic probability density functions, expressed as: ;

[0074] Step 3.2: Data generation process:

[0075] The reverse process of MRSDM is the noise reduction process, the goal of which is to improve the noise reduction efficiency of the trained neural network. Predict the true distribution ,in, The parameters of the neural network, Let t represent the t-th step of the diffusion process, and T represent the total number of diffusion steps. The reverse process is based on data from the t-th step, which follows a Gaussian mixture distribution. Derive the data at time t After T steps of continuous noise removal, samples similar to the real samples are generated, which can be represented in the form of a Markov chain as follows: ; ;

[0076] in, and Let represent the predicted mean and variance, respectively. In the above formula, since the mean and variance are unknown... The true distribution is insufficient, therefore it cannot be directly derived from... Derivation Therefore, consider adding conditions, i.e., initial data. get This makes it easy to predict. Furthermore, this can be expressed using Bayes' theorem: ;

[0077] Next, we introduce the negative log-likelihood. The aim is to train the parameters of the neural network. To maximize the probability of equation (5). However, The calculation result depends on the T-step reverse process, which is not easy to compute. To solve this problem, it can be achieved by calculating the variational lower bound: ;

[0078] in, This represents the KL divergence.

[0079] remember The latent variables are , express The true distribution of always satisfies: ;

[0080] The evidence lower bound loss is defined as the training objective. Based on formulas (8) and (9), the loss function is obtained: ;

[0081] in, This represents the loss function.

[0082] Furthermore, we obtain: ;

[0083] Where C is a constant independent of θ. It is data noise, This represents the expectation. Through parameterization, formula (11) simplifies to: ;

[0084] in, This represents a noise prediction network.

[0085] When equation (12) converges, the trained noise prediction network and data are obtained. The distribution of the data. Subsequently, in the virtual sample generation process of MRSDM, the data at step t-1 is calculated based on the data at step t according to the following formula: ;

[0086] in, I represents the identity matrix. This indicates the variance used in each step. , .

[0087] After T sampling steps, the generated data is obtained. As raw data The addition of these elements forms a new training sample. .

[0088] (4) Predict the pressure variables of the three-phase flow process and evaluate the model performance:

[0089] The generated virtual samples are combined with the original samples to form a new training set. A regression prediction model is then constructed based on the new training set to predict the pressure variables of the three-phase flow process. To objectively verify the present invention, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) are selected. 2 Three indicators are used to quantitatively evaluate the effect after sample expansion.

[0090] ;

[0091] in: For the true value The prediction results The mean of the true values ​​in the test set. The total number of samples in the test set. The smaller the RMSE and MAE, the better the R... 2 The larger the value, the better the model's predictive performance.

[0092] To analyze the effectiveness of the MRSDM method, its performance was compared with the following methods: Time Generative Adversarial Network (TimeGAN), Time Denoising Diffusion Probabilistic Model (TimeDDPM), Semi-identical Twins Variational Autoencoder (STVAE), Mode-related Generative Adversarial Network (MR-GAN), and an LSTM model built based on limited original training samples. Table 1 shows the detailed prediction results of the six methods on the three-phase flow process test set. Although TimeGAN and TimeDDPM can capture the dynamic features of the data, their prediction performance is still inferior to the model trained with only limited original samples. This indicates that if the generated samples fail to fully exploit the distribution characteristics of each mode in the multi-modal process, data augmentation may have a negative impact. STVAE and MR-GAN, which perform better in multi-modal feature modeling, achieved some performance improvement after data augmentation, but because these two methods do not consider dynamic characteristics, their prediction performance is inferior to that of the MRSDM method. The MRSDM method achieves optimal performance mainly because it can simultaneously learn the multimodal distribution patterns of data and capture the spatiotemporal characteristics of dynamic data, resulting in higher similarity between the generated samples and the original samples.

[0093] Table 1 ;

[0094] Figure 2 Scatter plots of samples generated by different methods and projected using Principal Component Analysis (PCA) were presented. The MRSDM method, which captures the spatiotemporal correlation of dynamic data using DSTN-Net and mines multi-modal characteristics using a pattern learner, generated samples with the highest similarity to the original data. Figure 3 The images show a comparison between the samples generated by each method and the original samples along the feature dimension. The samples generated by DDPM, TimeGAN, and TimeDDPM methods have the lowest similarity to the original samples and exhibit significant distribution shifts, while the samples generated by MRSDM method have the best fit. Figure 4The chart compares the prediction performance of six methods on the test set. DDPM, TimeGAN, and TimeDDPM show poor fitting results, confirming the negative impact of their generated samples. Thanks to learning the multimodal structure, STVAE and MR-GAN methods achieved some performance improvement compared to the baseline model with limited samples. MRSDM showed the highest fitting accuracy to real data and achieved the best prediction accuracy.

[0095] The method of this invention employs a mode-related spatiotemporal diffusion generation soft measurement modeling method to capture the temporal dynamics, spatial correlations, and modal boundary features of data. It can generate high-quality virtual samples to expand the original finite dataset, thereby improving the prediction accuracy of key quality variables.

[0096] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A soft-sensing modeling method based on pattern correlation spatiotemporal diffusion, characterized in that, Includes the following steps: 1) Acquiring multi-mode dynamic process data in the process industry: Multi-mode dynamic process data refers to data that exhibits multi-mode characteristics due to factors such as raw material fluctuations, equipment status switching, or adjustments in operating parameters. The data no longer follows a single Gaussian distribution but exhibits a multi-peak distribution. At the same time, due to the natural cyclical characteristics of the production process and the role of the feedback control system, the data distribution drifts over time, exhibiting dynamic characteristics. 2) Data partitioning and preprocessing: First, the collected samples are divided into training and test sets according to the proportions; then, all features are standardized to unify the units and speed up model convergence; finally, the time series is serialized using a sliding window. 3) Establish a pattern-related spatiotemporal diffusion model and generate virtual samples: First, a DSTN-Net noise prediction network is constructed: with an encoder-decoder architecture, LSTM is used to capture the temporal dependence of dynamic data and 1-D CNN is used to capture spatial features. Then, a Gaussian mixture model (GMM) is used to fit the multi-mode data distribution and optimize its parameters. Subsequently, through the reverse noise reduction process of MRSDM, new samples are generated in the form of Markov chains through T-step sampling to supplement the original dataset and form new training samples. 4) Predict pressure variables in three-phase flow process and evaluate model performance: Combine the generated virtual samples with the original samples to form a new training set. Construct a regression prediction model based on the new training set to predict the pressure variables in three-phase flow process. To objectively verify the scheme of this invention, select three indicators: root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) to quantitatively evaluate the effect after sample expansion.

2. The method for generating soft measurement models based on mode-related spatiotemporal diffusion as described in claim 1, characterized in that, The specific process of step 3) is as follows: Step 3.1: Construct the DSTN-Net noise prediction network: A DSTN-Net noise prediction network based on an encoder-decoder structure is constructed. The encoder extracts deep features of the data through downsampling, and the decoder fuses low-level detail features and high-level features of the data through upsampling and skip connections. A Long Short-Term Memory (LSTM) unit and a one-dimensional convolutional neural network (1-D CNN) are integrated into the network to capture the dependencies of dynamic data in the temporal and spatial dimensions, respectively. A Gaussian Mixture Model (GMM) is used to fit the distribution characteristics of the multi-modal data, and the model parameters of the GMM are optimized by maximizing the logarithm of the probability density function of all samples. Step 3.2: Data Generation and Sample Supplementation: The reverse denoising process based on MRSDM uses a Markov chain to reverse-derive T-step data that follows a Gaussian mixture distribution through a trained DSTN-Net network. After T-step continuous denoising and sampling, new data similar to the real samples are generated. The new data is then added to the original dataset to form a new training sample set.

3. The method for generating soft measurement models based on mode-related spatiotemporal diffusion as described in claim 1, characterized in that, In step 3.1): For dynamic data ,in, , L represents the time series length determined by the sliding window size, K represents the number of features, and M represents the number of original samples; LSTM units capture the dependencies of dynamic data in the time dimension through matrix operations of input gate, forget gate, and output gate; ； Where W represents the weights of the input matrix, denoted by , b represents the recursive weight, b represents the bias, and the subscripts a, i, f, and o represent the candidate memory unit, input gate, forget gate, and output gate, respectively. , , and Indicate that W, R, and b are respectively related to , The weights of the product of 1 and 2; This represents the input matrix at time c; This represents the hidden state at time c-1; A matrix representing all weights and bias terms; Indicates a containing , A column vector of 1; 1-D CNNs capture global and local features of dynamic data in a spatial dimension by moving convolutional kernels across the input feature map. convolution kernel With step size Moving across the input feature map, the output of the i-th sliding window is calculated using the following formula. : ； in, This represents the input in the sliding window.

4. The method for generating soft measurement models based on mode-related spatiotemporal diffusion as described in claim 1, characterized in that, In step 3.1: Gaussian Mixture Models (GMMs) fit the global distribution of multi-mode data through a weighted combination of multiple Gaussian distributions. ； Where H represents the number of Gaussian distributions, Represents the set of all unknown parameters. Let represent the mean vector of the h-th Gaussian distribution. Let h represent the covariance matrix of the h-th Gaussian distribution. Let the weights of the h-th Gaussian distribution satisfy: , This indicates that the data follows a Gaussian distribution. This represents the h-th Gaussian distribution data. Indicates training samples; The pattern learner maximizes the product of the probability density functions of all samples, and transforms the product of the probability density functions of all samples into the sum of the log probability density functions, expressed as: 。 5. The method for generating soft measurement models based on mode-related spatiotemporal diffusion as described in claim 1, characterized in that, In step 3.2: The reverse noise reduction process introduces initial data optimization derivation conditions using Bayes' theorem, constructs a loss function using variational lower bounds and KL divergence, and obtains the trained DSTN-Net network after the loss function converges. The new data is generated using a T-step sampling formula and is finally merged with the original dataset to form a new training sample set; the details are as follows: The reverse process of MRSDM is the noise reduction process, and its goal is to: reduce noise through a trained neural network. Predict the true distribution ,in, The parameters of the neural network, This represents the t-th step in the diffusion process, where T represents the total number of diffusion steps. The reverse process is based on data from step T that follows a Gaussian mixture distribution. Derive the data at time t After T steps of continuous noise removal, samples similar to the real samples are generated, which can be represented in the form of a Markov chain as follows: ； in, and These represent the predicted mean and variance, respectively. By adding conditions, i.e., initial data get To predict This can be expressed using Bayes' theorem: ； Next, we introduce the negative log-likelihood. By training the parameters of the neural network Maximize the probability of equation (5); transform maximizing the true distribution probability into minimizing the difference between the variational distribution and the true distribution by calculating the variational lower bound: ； in, Indicates KL divergence; remember The latent variables are , express The true distribution satisfies: ； Define the evidence lower bound loss as the training objective, and based on formulas (8) and (9), obtain the loss function: ； in, Represents the loss function; Combining the Gaussian assumption of the forward diffusion model, the KL divergence term in equation (10) is analytically expanded, and the reparameterization technique is applied to transform the random sampling process into a differentiable form. The variational lower bound loss function is further equivalently transformed into an optimization objective based on noise prediction error, thus obtaining: ； Where C is a constant independent of θ. It is data noise, Expressing the expectation; through parameterization, formula (11) is simplified to: ； in, Represents a noise prediction network; When equation (12) converges, the trained noise prediction network and data are obtained. The distribution; subsequently, in the virtual sample generation process of MRSDM, the data at step t-1 is calculated based on the data at step t according to the following formula: ； in, I represents the identity matrix. This indicates the variance used in each step. , ; After T sampling steps, the generated data is obtained. ; as raw data The addition of these elements forms a new training sample. .

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