A quality index prediction method for complex industrial processes
By constructing time-domain and frequency-domain models in parallel and combining attention mechanisms and slow-varying feature extraction, the drift and lag problems of quality inspection in complex industrial processes are solved, enabling accurate prediction of quality indicators in noisy environments and improving the operational stability of industrial processes and product quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHEASTERN UNIV AT QINHUANGDAO
- Filing Date
- 2026-03-30
- Publication Date
- 2026-06-30
Smart Images
Figure CN122311540A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of industrial artificial intelligence technology, specifically relating to a method for predicting quality indicators for complex industrial processes. Background Technology
[0002] Complex industrial processes typically feature long production flows, complex material and energy transfer relationships, significant system lags, highly nonlinear dynamic characteristics, and frequent changes in operating conditions. Their key quality indicators and process control variables highly overlap, making stable and accurate online monitoring difficult. In actual industrial production, harsh conditions such as high temperature, high pressure, strong corrosion, and material erosion cause quality monitoring instruments to drift, age, or experience accuracy degradation, making long-term reliable operation challenging. Currently, manual sampling and offline testing are still widely used to obtain key quality indicators. However, offline testing has long cycles and significant result lags, making it difficult for operators to grasp the true state of the process in a timely manner and to quickly and accurately adjust control parameters, thus affecting process efficiency and product quality stability. Furthermore, data from complex industrial processes often exhibit significant non-stationary characteristics, containing both slow trends reflecting the system's internal mechanisms and rapidly changing components such as periodic fluctuations, operating condition changes, and random disturbances. Existing quality prediction and soft measurement methods often struggle to effectively distinguish between slowly changing driving factors and high-frequency disturbance information when processing such data. The prediction results are easily affected by noise and changes in operating conditions, making it difficult to meet the requirements of prediction accuracy and robustness in industrial settings. Summary of the Invention
[0003] In view of at least one of the above technical problems, this application provides a method for predicting quality indicators for complex industrial processes, which can effectively mine the inherent dynamic characteristics of the process under noisy industrial data conditions, reduce the impact of measurement lag and uncertainty, effectively improve the operational stability of complex industrial processes, and increase the output of products from the industrial process.
[0004] To achieve the above objectives, the technical solution of the present invention is as follows:
[0005] A method for predicting quality indicators for complex industrial processes includes:
[0006] Collect time series data of multidimensional industrial process variables and construct a training set;
[0007] Constructing a quality indicator prediction model includes: constructing a feature extraction structure based on a time-domain model and a frequency-domain model in parallel; extracting time-domain features of multi-dimensional industrial process variable time series through the time-domain model and extracting frequency-domain features of multi-dimensional industrial process variable time series through the frequency-domain model; and fusing the time-domain features and frequency-domain features through an attention mechanism to obtain time-frequency fusion features.
[0008] A slow-varying feature extraction mechanism is introduced to constrain the rate of change of time-frequency fusion features over time, thereby extracting slow-varying driving features that reflect the intrinsic mechanism of complex industrial processes; the time-frequency fusion features and slow-varying driving features are then adaptively fused.
[0009] The quality indicator prediction model is trained using the training set;
[0010] We use a trained quality indicator prediction model to make online predictions of key quality indicators for complex industrial processes.
[0011] Optionally, the step of extracting the time-domain features of the multidimensional industrial process variable time series through a time-domain model includes:
[0012] Let the batch input data be ,in For batch size, For time-domain characteristics; L is the time step length, and M1 is the number of industrial process variables;
[0013] A bidirectional gated cyclic unit is used to model the time series of industrial process variables. The forward and backward hidden state update forms of the bidirectional gated cyclic unit are as follows:
[0014] ;
[0015] Then, by concatenating the forward hidden state and the backward hidden state, the temporal features are obtained:
[0016] ;
[0017] in, The forward hidden state of the batch input data in the time-domain model; The backward hidden state of the batch input data in the time-domain model; This represents the number of hidden units in a one-way GRU. For time.
[0018] Optionally, the step of extracting the frequency domain features of the time series of multidimensional industrial process variables through a frequency domain model includes:
[0019] For batch input data Perform a short-time Fourier transform to extract the amplitude spectrum to form a frequency domain feature tensor. ;
[0020] frequency domain feature tensor Input a two-dimensional convolutional layer to extract joint spectral and spatial features;
[0021] The feature maps output by the 2D convolution are processed along the time frame number. With frequency dimension Perform a global average pooling operation to obtain initial frequency domain features of fixed dimensions. ;
[0022] Through the fully connected layer Projection to temporal features Using the same feature dimension space, the final frequency domain features are obtained. .
[0023] Optionally, the process of fusing time-domain features and frequency-domain features through an attention mechanism to obtain time-frequency fusion features includes:
[0024] frequency domain features Extending along the time step dimension to make the frequency domain features In terms of time step dimension and temporal features Alignment yields the expanded frequency domain feature sequence. ;
[0025] Based on time domain characteristics For the query vector, with As a value vector, the similarity between the two is calculated through a dot product attention mechanism, thereby dynamically assigning importance weights to the frequency domain features at different time steps. All importance weights constitute the attention weight matrix. ;
[0026] use right We perform a weighted summation to obtain the fused intermediate features. ;
[0027] right Perform a linear mapping and apply the Swish activation function to obtain time-frequency fusion features. .
[0028] Optionally, the pair Perform a linear mapping and apply the Swish activation function to obtain time-frequency fusion features. ;include:
[0029] ;
[0030] in, The weight matrix is trainable. For the bias term of the fusion layer; For number fields; Batch size; The time step length; This represents the number of hidden units in a one-way GRU.
[0031] Optionally, the extended frequency domain feature sequence The calculation formula is as follows:
[0032] ;
[0033] in, To replicate the frequency domain feature F along the time step dimension Second-rate; This represents the time step length.
[0034] Optionally, the attention weight matrix The calculation is as follows:
[0035] ;
[0036] in, This is the scaling factor; This represents the number of hidden units in a one-way GRU. This is the normalization function; For the extended frequency domain feature sequence The transpose of the matrix; For number fields; Batch size; Features in the time domain; This represents the time step length.
[0037] Optionally, the extraction of slowly varying driving features that reflect the intrinsic mechanisms of complex industrial processes includes:
[0038] Assume time-frequency fusion characteristics High-dimensional time-frequency fusion features are fused using linear projection. Mapping to a low-dimensional slowly varying feature space yields the slowly varying driving features, which are calculated using the following formula:
[0039] ;
[0040] in, The linear projection weight matrix is ; This is the bias term for the slowly varying feature extraction layer. , Dimensions of slowly varying driving features.
[0041] Beneficial effects
[0042] This application proposes a quality indicator prediction method for complex industrial processes. In complex industrial process environments, it can effectively mine the inherent dynamic characteristics of the process under noisy industrial data conditions, reduce the impact of measurement lag and uncertainty, solve the problem of difficulty in timely acquisition of key quality indicators in complex industrial processes, effectively improve the operational stability of complex industrial processes, and increase the output of products from the industrial process. Attached Figure Description
[0043] Figure 1 A flowchart illustrating a quality indicator prediction method for complex industrial processes according to an embodiment of this application;
[0044] Figure 2 This is a schematic diagram of the overall structure of the quality index prediction method for complex industrial processes according to an embodiment of this application.
[0045] Figure 3 This is a schematic diagram of the feature extraction structure based on parallel construction in the time and frequency domains according to an embodiment of this application;
[0046] Figure 4 This is a schematic diagram of the slow-varying feature analysis in an embodiment of this application;
[0047] Figure 5 This is a schematic diagram of the alumina leaching process according to an embodiment of this application;
[0048] Figure 6 This is a schematic diagram illustrating the prediction results of key quality indicators in an embodiment of this application. Detailed Implementation
[0049] The terms "first," "second," "third," "fourth," etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus. The technical solutions of the embodiments of this application will now be clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.
[0050] This application belongs to the field of industrial artificial intelligence technology and relates to a supervised deep slow feature extraction enhanced time-frequency fusion network for quality prediction of complex industrial processes. Complex industrial processes are typically characterized by long production processes, numerous process variables, significant system lags, and frequent changes in operating conditions. Their key quality indicators are affected by the complex coupling of multi-process control systems. Online monitoring instruments are susceptible to drift or accuracy degradation due to harsh conditions such as high temperature, high pressure, and strong corrosion. Production sites generally rely on manual sampling and offline testing to obtain quality indicators, but the test results are severely delayed, making it difficult for operators to adjust control parameters in a timely and accurate manner, thus affecting process efficiency and product quality stability. To address these problems, this application models the prediction of quality indicators for complex industrial processes as a supervised learning problem with multidimensional process variable time series as input and key quality indicators as output, and constructs a time-frequency fusion network based on time-domain and frequency-domain models in parallel. This network models the temporal dependencies of process variables through bidirectional gated recurrent units and uses short-time Fourier transform to extract periodic fluctuations and transient change features from the process data. Based on this, an attention mechanism is introduced to achieve adaptive fusion of time-domain and frequency-domain features. Furthermore, to effectively mitigate the impact of measurement noise and short-term disturbances, a supervised deep slow feature extraction method is proposed. By imposing a rate-of-change constraint on the fused features, slowly varying driving features reflecting the intrinsic mechanisms of complex industrial processes are extracted and combined with time-frequency fusion features for quality index prediction. This application was applied to a large alumina plant in Shanxi Province, and the MAE of its leaching results compared with the corresponding time-time test values was 0.0011, fully meeting the actual requirements.
[0051] Example
[0052] This application discloses a method for predicting quality indicators for complex industrial processes, such as... Figure 1 As shown, it includes the following steps:
[0053] Step S1: Collect time series data of multidimensional industrial process variables and construct a training set;
[0054] To describe the dynamic relationship between key quality indicators and process variables, it can be represented as a superposition of a linear model and an unknown nonlinear dynamic system. Let's assume that at time t... Key quality indicators are The process variable input vector is Then we have:
[0055] ;
[0056] in, This is the parameter vector for the linear model, used to describe the main linear influence relationships; It is an unknown nonlinear dynamic function used to characterize unmodeled nonlinear mechanisms and disturbances in complex industrial processes; For random noise; This is the transpose matrix of the linear model parameters. This step decomposes the complex process into an interpretable linear part and a nonlinear part that requires data-driven modeling, laying the foundation for subsequent feature extraction and prediction based on deep learning.
[0057] in, Figure 2 This is a schematic diagram of the overall structure of the quality index prediction method for complex industrial processes in this embodiment.
[0058] Step S2: Construct a quality indicator prediction model, including: constructing a feature extraction structure based on a time-domain model and a frequency-domain model in parallel; extracting time-domain features of multi-dimensional industrial process variable time series through the time-domain model and frequency-domain features of multi-dimensional industrial process variable time series through the frequency-domain model; fusing the time-domain features and frequency-domain features through an attention mechanism to obtain time-frequency fusion features; introducing a slow-varying feature extraction mechanism to constrain the rate of change of the time-frequency fusion features over time and extracting slow-varying driving features that reflect the intrinsic mechanism of complex industrial processes; and adaptively fusing the time-frequency fusion features and the slow-varying driving features.
[0059] Step S2.1: In order to simultaneously characterize the temporal dependencies and spectral structure features in industrial process data, this embodiment constructs a feature extraction structure based on the time domain model and the frequency domain model in parallel.
[0060] The first step is temporal feature extraction, assuming the batch input data is... ,in For batch size, The time step length, The number of process variables is denoted as . A Bidirectional Gated Recurrent Unit (BiGRU) is used to model the time series, and its forward and backward hidden state update forms are as follows:
[0061] ;
[0062] Then, by concatenating the forward and backward hidden states, the temporal features are obtained. :
[0063] ;
[0064] in, The forward hidden state of the batch input data in the time-domain model; The backward hidden state of the batch input data in the time-domain model; This represents the number of hidden units in a one-way GRU. For time.
[0065] This step can capture both historical and future trend information, improving the ability to represent complex dynamic processes.
[0066] The second is frequency domain feature extraction, which is performed on batch input data. Perform a short-time Fourier transform (STFT) and take the amplitude spectrum to obtain the frequency domain feature tensor S;
[0067] Specifically, a short-time Fourier transform is performed on the batch input data to obtain the frequency domain feature tensor. :
[0068] ;
[0069] in, For batch size, For the number of input variables, Indicates the number of time frames. Indicates the number of frequency points.
[0070] Subsequently, the frequency domain feature tensor Input a 2D convolutional layer to extract joint spectral and spatial features; and along time frames... With frequency dimension Perform a global average pooling operation to obtain the initial frequency domain features. :
[0071] ;
[0072] in, This indicates the number of convolutional filters in a two-dimensional convolutional layer.
[0073] N = [(L' - W) / R] + 1;
[0074] The number of time frames N is determined by the input sequence length L', the window length W, and the sliding step size R of the STFT window. These parameters can be set in the STFT. In this embodiment, sensitivity analysis is performed here, and W is set to 8 and R is set to 4.
[0075] K = [Nfft / 2] + 1;
[0076] Nfft is the number of discrete points used in the Fourier transform;
[0077] The formula for the initial frequency domain features performs global average pooling on both N and K dimensions, so N and K no longer appear explicitly in the formula for the output initial frequency domain features.
[0078] Finally, the frequency domain features are processed through a fully connected layer. Project the features onto a feature dimension space with the same dimension as the time-domain features, so that subsequent time and frequency features can be fused to obtain the final frequency-domain features:
[0079] ;
[0080] in, This is the weight matrix of the fully connected layer. For the bias term of the frequency domain branch, This represents the number of hidden units in a single direction in a BiGRU.
[0081] Step S2.2: Obtaining time-domain features Frequency domain characteristics Subsequently, in order to achieve effective fusion of time information and spectrum information, this embodiment introduces a dual-domain feature fusion method based on attention mechanism.
[0082] First, frequency domain features Extending along the time step dimension aligns the frequency domain features with the time domain features, resulting in the extended frequency domain feature sequence:
[0083] ;
[0084] in, This indicates that the input tensor will be... Replicating in the time step dimension This is done to achieve feature expansion.
[0085] Subsequently, based on time domain characteristics As query features, with expanded frequency domain features Simultaneously serving as both key and value features, the attention weight matrix is calculated using dot product similarity. This characterizes the importance of frequency domain features at different time steps. The attention weight matrix is calculated as follows:
[0086] ;
[0087] in, This is a scaling factor used to prevent the dot product result from becoming too large and affecting training stability. Based on this, the attention weight matrix is used... We perform a weighted summation of the frequency domain features to obtain the fused intermediate feature representation:
[0088] ;
[0089] Finally, regarding the fusion features A linear mapping is performed, and the Swish activation function is applied to obtain the final output of the time-frequency fusion features:
[0090] ;
[0091] in, The weight matrix is trainable. For the bias term of the fusion layer; , It is a sigmoid saturation activation function.
[0092] Figure 3 This is a schematic diagram of the feature extraction structure constructed in parallel in the time and frequency domains in this embodiment.
[0093] Step S2.3: After fusing the time-domain and frequency-domain features, the resulting fused features typically have high dimensionality, rapid changes, and contain a large amount of short-term perturbation information. To further extract features that reflect the intrinsic mechanism changes of complex industrial processes, this embodiment introduces a supervised deep slow-varying feature extraction network to extract low-dimensional slow-varying features that change slowly over time from the high-dimensional fused features.
[0094] Let the features after time-frequency fusion be represented as: By using linear projection, high-dimensional fused features are mapped to a low-dimensional slowly varying feature space to obtain slowly varying feature representations. :
[0095] ;
[0096] in, The linear projection weight matrix is This is the bias term for the slowly varying feature extraction layer. The dimension representing the slowly varying features.
[0097] To ensure that the extracted slowly varying features exhibit the properties of changing as slowly as possible over time and being independent of each feature dimension, this application transforms the objective function and constraints of slow feature analysis into a trainable loss function, and performs joint optimization during model training, such as... Figure 4 The diagram shown is a schematic diagram of the slow-varying feature analysis in this embodiment.
[0098] First is the slow-varying smoothing loss, which is used to constrain the variation of slowly varying features between adjacent time steps to minimize the amplitude, thereby suppressing the influence of short-term fluctuations and high-frequency noise. Its definition is as follows:
[0099] ;
[0100] in, This represents the slowly varying feature of the i-th sample at time t;
[0101] Secondly, to prevent slowly varying features from degenerating into constant solutions, while ensuring that the features have sufficient expressive power, variance constraint loss is introduced:
[0102] ;
[0103] in, Indicates the first The average value of the slowly varying characteristics of each sample within batch B; A preset variance threshold is used to constrain slowly varying features to maintain approximately unit variance.
[0104] Finally, to reduce the correlation between different slowly varying feature dimensions and reduce feature redundancy, a covariance constraint loss is introduced:
[0105] ;
[0106] in, Indicates the first Each sample in the time index The first Dimensional slow variation characteristics; For the first The average value of the slow-varying feature in time and feature dimension.
[0107] Step S2.4: Adaptively fuse the time and frequency fusion features with the slowly varying driving features.
[0108] In the specific implementation process, after completing the time-frequency feature fusion and supervised deep slow-varying feature extraction, this embodiment further constructs a prediction network to predict key quality indicators of complex industrial processes based on the fused features and slow-varying features. As mentioned earlier, both the time-frequency fused features and the slow-varying features are represented in time series form. Considering that the prediction of key quality indicators mainly depends on the process state information at the current moment, this embodiment selects the representation of the above features at the last time step as the prediction input. The fused features... With slow variation characteristics The hidden states at the last time step are concatenated to obtain the input feature vector of the prediction network:
[0109] ;
[0110] in, , representing the hidden state of the time-frequency fusion feature at the last time step; This represents the slow-varying feature at the last time step. This indicates a vector concatenation operation.
[0111] After obtaining the predicted input features, Key quality indicators are predicted via regression using a fully connected prediction network. The prediction network consists of at least one hidden layer and one output layer, and its calculation process is as follows:
[0112] ;
[0113] ;
[0114] in, Here is the weight matrix of the hidden layer; The bias vector of the hidden layer; This represents the number of neurons in the hidden layer. This is the weight matrix of the output layer; This is the bias vector for the output layer; The hyperbolic tangent activation function is used. This represents the predicted value of key quality indicators.
[0115] To measure the error between the predicted results and the actual observed values, mean squared error is introduced as the prediction loss function, which is defined as follows:
[0116] ;
[0117] in, Let the mean squared error loss function be used. Where i is the batch size; i is the number of elements in the first batch. One sample; For the first Observed values of the quality indicators of each sample; For the first Predicted values of individual sample quality indicators.
[0118] In one feasible implementation, step S2 further includes a method for optimizing the quality indicator prediction model as follows:
[0119] To simultaneously ensure prediction accuracy and the quality of slowly varying features, the prediction loss function is combined with the regularization constraint term in the aforementioned slowly varying feature extraction network to construct a joint loss function and optimization objective:
[0120] ;
[0121] ;
[0122] in, As the first hyperparameter, This is the second hyperparameter. The third hyperparameter is used to adjust the relative weight of each loss term in the overall optimization. , represents the set of all trainable parameters in the model; The loss function is defined by covariance constraints. The variance-constrained loss function; For slow-varying smooth loss function; This is the joint loss function.
[0123] Step S3: Train the quality index prediction model established in S2 using the training set from step S1;
[0124] Step S4: Use the trained quality indicator prediction model to predict key quality indicators of complex industrial processes online.
[0125] This application proposes a method for predicting quality indicators for complex industrial processes. This method can effectively mine the inherent dynamic characteristics of the process under noisy industrial data conditions, reduce the impact of measurement lag and uncertainty, effectively improve the operational stability of complex industrial processes, and increase the output of products from the industrial process.
[0126] A specific example of the effectiveness verification after the actual implementation of the method in this application is as follows:
[0127] The leaching process control system of an alumina plant typically consists of subsystems such as alkali addition flow control, leaching feed control, multi-stage slurry preheating control, slurry heating and residence leaching control, and multi-stage slurry self-evaporation control. Figure 5 The diagram shows a schematic of the alumina leaching process. In the process control system, process variables such as heating steam pressure / temperature, slurry flow rate, slurry heating temperature, leaching reaction temperature, slurry aluminum-silicon ratio, caustic alkali concentration, caustic alkali ratio, slurry preheating temperature, and final stage self-evaporator level / temperature / pressure have complex coupled effects on key quality indicators. Due to the non-stationarity and frequent disturbances of the process data, online detection of quality variables exhibits lag or error. Table 1 shows the performance evaluation table for the endpoint prediction of the caustic alkali ratio in the alumina leaching process.
[0128] Table 1
[0129] SDSFE-TF2 mean Standard deviation Root mean square error 0.00140302 0.00020629 Mean Absolute Error 0.00113182 0.00018477 Coefficient of determination 0.96394535 0.00199775 Mean absolute percentage error 0.00081033 0.00013283
[0130] As attached Figure 6 As shown in Table 1, the verification results of this application using data from a large alumina plant are presented. As can be seen from the charts, this application can still accurately and effectively predict the caustic ratio results with long offline testing cycles and significant result lags, even under the influence of actual engineering noise, and has high engineering value.
[0131] It is worth noting that the above embodiments are only used to illustrate the technical solutions of this application, and not to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of protection defined in this application.
Claims
1. A method for predicting quality indicators for complex industrial processes, characterized in that, include: Collect time series data of multidimensional industrial process variables and construct a training set; The quality indicator prediction model is constructed, including: constructing a feature extraction structure based on time-domain and frequency-domain models in parallel; extracting time-domain features of multi-dimensional industrial process variable time series through the time-domain model and frequency-domain features through the frequency-domain model; fusing the time-domain and frequency-domain features through an attention mechanism to obtain time-frequency fusion features; introducing a slow-varying feature extraction mechanism to constrain the rate of change of the time-frequency fusion features over time and extracting slow-varying driving features that reflect the intrinsic mechanism of complex industrial processes; and adaptively fusing the time-frequency fusion features with the slow-varying driving features. The quality indicator prediction model is trained using the training set; We use a trained quality indicator prediction model to make online predictions of key quality indicators for complex industrial processes.
2. The method for predicting quality indicators for complex industrial processes according to claim 1, characterized in that, The extraction of time-domain features of multidimensional industrial process variable time series through a time-domain model includes: Let the batch input data be ,in For batch size, For time-domain characteristics; L is the time step length, and M1 is the number of industrial process variables; A bidirectional gated cyclic unit is used to model the time series of industrial process variables. The forward and backward hidden state update forms of the bidirectional gated cyclic unit are as follows: ； Then, by concatenating the forward hidden state and the backward hidden state, the temporal features are obtained: ； in, The forward hidden state of the batch input data in the time-domain model; The backward hidden state of the batch input data in the time-domain model; This represents the number of hidden units in a one-way GRU. For time.
3. The method for predicting quality indicators for complex industrial processes according to claim 1, characterized in that, The extraction of frequency domain features of multidimensional industrial process variable time series through frequency domain modeling includes: For batch input data Perform a short-time Fourier transform to extract the amplitude spectrum to form a frequency domain feature tensor. ; frequency domain feature tensor Input a two-dimensional convolutional layer to extract joint spectral and spatial features; The feature maps output by the 2D convolution are processed along the time frame number. With frequency dimension Perform a global average pooling operation to obtain initial frequency domain features of fixed dimensions. ; Through the fully connected layer Projection to temporal features Using the same feature dimension space, the final frequency domain features are obtained. .
4. The method for predicting quality indicators for complex industrial processes according to claim 1, characterized in that, The process of fusing time-domain and frequency-domain features through an attention mechanism to obtain time-frequency fusion features includes: frequency domain features Extending along the time step dimension to make the frequency domain features In terms of time step dimension and temporal features Alignment yields the expanded frequency domain feature sequence. ; Based on time domain characteristics For the query vector, with As a value vector, the similarity between the two is calculated through a dot product attention mechanism, thereby dynamically assigning importance weights to the frequency domain features at different time steps. All importance weights constitute the attention weight matrix. ; use right We perform a weighted summation to obtain the fused intermediate features. ; right Perform a linear mapping and apply the Swish activation function to obtain time-frequency fusion features. .
5. The method for predicting quality indicators for complex industrial processes according to claim 4, characterized in that, The pair Perform a linear mapping and apply the Swish activation function to obtain time-frequency fusion features. ; include: ； in, The weight matrix is trainable. For the bias term of the fusion layer; For number fields; Batch size; The time step length; This represents the number of hidden units in a one-way GRU.
6. The method for predicting quality indicators for complex industrial processes according to claim 4, characterized in that, The extended frequency domain feature sequence The calculation formula is as follows: ； in, To replicate the frequency domain feature F along the time step dimension Second-rate; This represents the time step length.
7. The method for predicting quality indicators for complex industrial processes according to claim 4, characterized in that, The attention weight matrix The calculation is as follows: ； in, This is the scaling factor; This represents the number of hidden units in a one-way GRU. This is the normalization function; For the extended frequency domain feature sequence The transpose of the matrix; For number fields; Batch size; Features in the time domain; This represents the time step length.
8. The method for predicting quality indicators for complex industrial processes according to claim 1, characterized in that, The extraction of slowly varying driving characteristics that reflect the intrinsic mechanisms of complex industrial processes includes: Assume time-frequency fusion characteristics High-dimensional time-frequency fusion features are fused using linear projection. Mapping to a low-dimensional slowly varying feature space yields the slowly varying driving features, which are calculated using the following formula: ； in, The linear projection weight matrix is ; This is the bias term for the slowly varying feature extraction layer. , The dimension of the slowly varying driving feature.