An Adaptive Soft Measurement Method for Smooth Interpolation in Industrial Processes with Multiple Sampling Rates

Abstract

This invention discloses an adaptive soft measurement method for smooth interpolation in industrial processes with multiple sampling rates. The method constructs a unified time axis for time alignment of multi-sampling rate data using a reference sampling interval. Variable groups are divided based on the sampling multiple, sampling offset, and time lag relationship of process variables, and a true sampling mask is established. Causal Gaussian time-weighted smooth interpolation is performed on the sparse true observations of each variable group to form continuous auxiliary input. Furthermore, a flexible clock-gated recurrent unit network is employed to perform gated recursive updates on sampled variable groups and to decay the hidden layer states of unsampled variable groups based on the time interval from the nearest true sampling moment. During training, the hidden layer nodes are incrementally expanded according to the sensitivity of the variable groups to the loss function, and the output layer parameters are expanded using a function-preserving method to ensure consistent estimated outputs at the moment of structural expansion. This method is suitable for cross-scale dynamic soft measurement modeling of low-frequency operating indicators in complex industrial processes.

Description

Technical Field

[0001] This invention relates to the field of industrial process soft measurement modeling technology, and in particular to an adaptive soft measurement method for smooth interpolation of multi-sampling-rate industrial processes. Background Technology

[0002] In modern industrial production, key operational indicators such as product quality, output, energy consumption, efficiency, concentration, particle size, conversion rate, yield, and pollutant emissions are crucial for process optimization, advanced control, fault diagnosis, and safe operation. However, due to limitations such as the high cost, complex maintenance, long detection cycle, and significant measurement lag of online analytical instruments, as well as the difficulty in directly installing sensors on some indicators, many key operational indicators cannot be measured at high frequency, continuously, and in real time.

[0003] Compared to operational indicators, conventional process variables in industrial settings, such as temperature, pressure, flow rate, liquid level, current, voltage, speed, valve position, concentration, pH value, acoustic signals, electrical signals, and image features, can usually be easily acquired through sensors or distributed control systems. Therefore, using easily measurable process variables to establish soft sensor models for difficult-to-measurable operational indicators has become an important technical approach for intelligent modeling, optimized control, and operational status evaluation of complex industrial processes.

[0004] However, in actual industrial processes, different process variables often have different sampling frequencies and sampling triggering patterns. For example, variables such as temperature, pressure, and flow rate are usually collected on a second- or minute-level sampling cycle; laboratory analytical indicators are usually collected on an hourly or shift-level sampling cycle; some variables are only recorded when triggered by specific operating conditions, specific operations, or specific events. This forms a typical multi-sampling-rate industrial process data structure. Under the above multi-sampling-rate industrial process data structure, if we simply use methods such as upsampling, downsampling, linear interpolation, or nearest neighbor preservation to roughly align data from different sampling rates, the following problems can easily occur: First, the role of interpolated values ​​and true observations in the model input can easily be confused. Although interpolated values ​​can form a continuous input sequence, they are not essentially the true sampling results obtained by sensors or analytical instruments at that moment. If the model uses interpolated values ​​as true observation events in state updates, it may lead to over-updating of hidden state, thereby weakening the control effect of sampling events on dynamic state updates.

[0005] Second, hidden states corresponding to variables that have not been sampled for a long time are prone to losing their ability to represent the current process state. In multi-sampling rate scenarios, low-frequency variables or sparse trigger variables may not have new real observations for a long time. If the model directly uses its previous state, that state may gradually lose its ability to represent the current process state, leading to problems such as feature obsolescence, state invalidation, and long-term dependency degradation.

[0006] Third, existing fixed-structure neural network models struggle to adaptively adjust their structure based on the varying contributions of different variable groups to the estimation of operational indicators. Different sampling rate variable groups often have different degrees of influence on operational indicators, and the importance of the same variable group may change under different operating conditions. If the network capacity is fixed and evenly distributed, it may result in insufficient representation of key variable groups, while non-key variable groups consume excessive redundant model capacity.

[0007] Therefore, there is an urgent need to propose a soft measurement modeling method for industrial process data with multiple sampling rates. This method should be able to utilize interpolated data to form continuous auxiliary inputs, maintain the control effect of sampling events on model state updates, preserve the validity of the hidden state of unsampled variable groups, and adaptively expand the model structure according to the differences in the contribution of variable groups, thereby improving the accuracy of estimating the operating indicators of complex industrial processes. Summary of the Invention

[0008] Purpose of the invention: To address the aforementioned shortcomings of existing technologies, this invention provides an adaptive soft measurement method for smooth interpolation in industrial processes with multiple sampling rates.

[0009] Technical Solution: To address the problems of easy confusion between interpolated values ​​and sampled events, decreased representation ability of hidden states of unsampled variable groups, and difficulty in adaptively adjusting fixed-structure models based on differences in variable group contributions in multi-sampling-rate industrial process soft measurement, this invention provides a smooth interpolation adaptive soft measurement method for multi-sampling-rate industrial processes. This method includes the following steps: Step S1: Collect multi-sampling-rate process variable data and low-frequency operating index data of the target industrial process, based on a benchmark sampling interval... Construct a unified time axis for time alignment of multi-sampling rate data; based on sampling multiples. Sampling offset index and time delay steps Indicates the first Sampling and alignment relationships of process variables; based on sampling multiples and equivalent sampling offset after time delay correction Process variables with consistent sampling alignment patterns are divided into Group of variables Establish group-level real sampling masks .

[0010] Step S2: Establish a sparse observation matrix on a unified time axis. For each group of variables The smoothed auxiliary input value is generated by using a causal grouping Gaussian time-weighted smoothing method based on the current time and its historical true sample values. The smoothed auxiliary input values ​​of each process variable are combined to form a continuous auxiliary input vector.

[0011] Step S3: Based on continuous auxiliary input vectors Constructing a time-series sliding window sample A grouped hidden layer structure corresponding to the variable group is established using a flexible clock-gated cyclic unit network model.

[0012] Step S4: Based on the group-level true sampling mask and hidden layer subspace index set Generate hidden layer update mask Update the mask according to the hidden layer. The global hidden state at the current moment is obtained by fusing the gated recursive update state and the time-distance decay update state.

[0013] Step S5: During model training, calculate the importance value of each variable group based on the sensitivity of the hidden layer nodes to the loss function. When the preset expansion conditions are met, select the variable group with the highest smoothing importance value to perform incremental expansion of the hidden layer nodes; expand the output layer parameters using a function-preserving approach, and based on real low-frequency operating metrics. With estimation of low-frequency operating indicators The error between them is used to optimize the model parameters.

[0014] As a further improvement of the present invention, in step S1, the target industrial process includes an industrial grinding process, and the low-frequency operating index is the hydrocyclone feed concentration. The set of process variables is set as follows: ;in, Indicates the number of process variables. Indicates the first One process variable, The process variables include ball mill current, ball mill auger current, ball mill pre-mill water flow rate, and ball mill feed rate; the low-frequency operating indicators are expressed as follows: And the low-frequency operating indicators The sampling interval is greater than or equal to the maximum sampling interval of the process variable.

[0015] Let the unified timeline be: ;in, Indicates the initial time. Indicates the reference sampling interval. This indicates the number of sampling time points on a unified time axis. Indicates the first A unified timeline moment; the unified timeline refers to a timeline based on a reference sampling interval. A common discrete-time benchmark is constructed for discrete step lengths to map process variables and low-frequency operating indicators with different sampling periods and sampling offsets to the same discrete-time index system, and to characterize the input-output time delay relationship of process variables relative to low-frequency operating indicators.

[0016] No. The sampling interval, sampling offset time, and input / output delay of each process variable are expressed as follows: ;in, A positive integer, representing the first... Each process variable relative to the baseline sampling interval The sampling multiple; It is a non-negative integer and satisfies , indicating the first The sampling offset index of each process variable; A non-negative integer, representing the first... The number of time delay steps of each process variable relative to a low-frequency operating indicator.

[0017] No. The set of actual sampled indices for each process variable is: ;in, Indicates the first A set of true sampling indices of process variables on a unified time axis Indicates the sampling sequence number. Indicates the first The maximum sampling sequence number of each process variable.

[0018] Low-frequency operating indicators The actual set of sampling indices is: ;in, It is a positive integer, and is greater than or equal to the maximum sampling multiple of the process variable. , The sampling offset index represents the low-frequency operating index. Indicators of low-frequency operation sampling interval, This indicates the maximum sampling sequence number of the low-frequency operating indicator.

[0019] No. Each process variable is indexed on a unified time axis. The effective observation index after time delay correction is: ;in, Indicates the estimated time When corresponding to low-frequency operating indicators, the first The observation index to be used for each process variable.

[0020] The variable-level true sampling mask is defined as: ;in, Indicates the first The process variables at time 1 After alignment, there are actual sampled values. Indicates the first The process variables at time 1 After alignment, there are no true sampled values.

[0021] Based on the sampling multiple and the equivalent sampling offset after time delay correction, process variables with consistent sampling alignment are divided into... The nth variable group, the th The equivalent sampling offset after time delay correction for each process variable is defined as: ; All process variables corresponding to different pairs As different sampling alignment modes, and let the number of different sampling alignment modes be . Different sampling alignment modes are numbered one-to-one with variable groups, and the first... Each sampling alignment pattern is denoted as Then the first The variable group is defined as follows: ;in, Indicates the first The sampling multiple corresponding to each variable group Indicates the first The equivalent sampling offset after time delay correction for each variable group.

[0022] Different sets of variables do not overlap and satisfy the following conditions: Furthermore, all variable groups cover all process variables, that is: .

[0023] No. The number of process variables contained in each variable group is: .

[0024] The group-level true sampling mask is defined as: ;in, Indicates the first The set of variables at time... A sampling event occurred. Indicates the first The set of variables at time... No sampling event occurred.

[0025] As a further improvement of the present invention, in step S2, the sparse observation matrix, smooth auxiliary input value, and continuous auxiliary input vector are constructed as follows: A sparse observation matrix is ​​established: ;in, Indicates the first The first unified timeline index, the first Matrix elements corresponding to each process variable for A matrix of dimension; the elements of the sparse observation matrix are defined as: ;in, Indicates the first The process variables at the observation time after time delay correction The original observations, Indicates a null or missing value.

[0026] For the Group of variables process variables in Define the causal historical observation set as: ;in, Represents a unified historical timeline index. Indicates the first The historical maximum backtracking step count for each variable group, wherein the causal historical observation set only includes the actual sampled values ​​at the current moment and before, and does not include data at future moments.

[0027] No. The Gaussian time weights for the variable groups are: ;in, Indicates the first Gaussian smoothing parameters for each variable group, and The unit is the number of steps on a unified timeline.

[0028] No. Each process variable is indexed on a unified time axis. The smoothing auxiliary input value at the location is: ;in, To prevent constants with a denominator of zero, For the first The mean of each process variable in the training samples; the smoothing auxiliary input value retains the original observation value at the actual sampling time, and performs causal smoothing fill based on the historical actual sampling value at the unsampled time.

[0029] Arrange all smoothed auxiliary input values ​​of process variables in the order of their original variable numbers to obtain a continuous auxiliary input vector: ;in, It is only used to provide continuous numerical input to the network and does not replace the variable-level true sampling mask. Group-level true sampling mask Control over the hidden state update method.

[0030] As a further improvement of the present invention, in step S3, the method for constructing the time-series sliding window samples and the method for determining the grouped hidden layer structure are as follows: Let the low-frequency operating index... The available tag index set is: ;in, This indicates the unified time axis index corresponding to the low-frequency operation indicator label. Indicates the length of the sliding window; when using the sliding step size At that time, from the set The label indexes are selected in chronological order with the sliding step size to obtain a set of label indices for training, validation or testing.

[0031] For any Construct an ordered time series sample using a sliding window: The labels for the sliding window samples are: ;in, Indicates time The corresponding low-frequency operating indicators are real observed values, and the model is based on a unified time axis from... to Continuous recursion, and in The low-frequency label time-time output estimate; sliding window length Used to truncate backpropagation training, the initial state of the window is given by the forward recursion cache state, and the hidden state is not shared between the training, validation and test intervals.

[0032] Sliding window samples Variable-level true sampling mask within the window Window-level group-level true sampling mask and tags Together they constitute the supervised samples, which are then divided into training samples, validation samples, and test samples in chronological order.

[0033] No. The dimension of the hidden subspace of the variable group is: ;in, This represents the allocation coefficient for hidden layer nodes. , This indicates rounding up to the nearest integer.

[0034] The dimension of the global hidden state is: .

[0035] Order No. The starting index of the hidden subspace of each variable group is: .

[0036] No. Hidden subspace index set corresponding to each variable group Defined as: .

[0037] The hidden subspace index sets corresponding to different variable groups do not overlap and satisfy the following: ; ;No. Each variable group is indexed on a unified time axis. The hidden state at that point is .

[0038] The hidden states of all variable groups are concatenated as follows: ;in, Indicates a unified timeline index The corresponding global hidden state.

[0039] As a further improvement of the present invention, in step S4, the hidden layer update mask, gated recursive update, time-distance decay update, and global hidden layer state fusion method are as follows: The hidden update mask for each variable group is: ;in, Indicates length is The whole vector.

[0040] The global hidden layer update mask is: ;in, Used to control whether each hidden layer node performs gated recursive updates.

[0041] For continuous auxiliary input vectors and the global hidden state at the previous time step Initial global hidden state Initialize the vector to 0, and calculate the candidate gating update state according to the gating loop unit formula: ; ; ; ;in, Indicates an update to the door. This indicates that the door is being reset. This represents the candidate hidden state. Indicates the candidate gating update status; This represents the input weight matrix. Represents the recursive weight matrix. Represents the bias vector; express function, Represents the hyperbolic tangent function. This indicates element-wise multiplication. Continuous auxiliary input vectors are used to provide coupling information across variable groups. The hidden layer update mask only controls whether each hidden layer subspace performs a state update, without restricting the use of smooth auxiliary inputs from other variable groups by the candidate gating update state.

[0042] For the A set of variables, in At that moment, let: The above formula represents the index up to the unified timeline. The index of the most recently occurring sampling event; if this index does not exist, the initial hidden state is used; when If it exists, define the interval step number: .

[0043] Define the time-distance attenuation coefficient: ;in, Indicates the first The decay parameters of the variable group And follow The increase and monotonically decrease cause the hidden state of the unsampled variable group to gradually decay.

[0044] No. The time-lapse decay update status for each variable group is as follows: ;in, Indicates the first The hidden state of each variable group after the most recent real sampling update. For the first The initial state of the hidden layer of each variable group is concatenated with the time-distance decay update state of each variable group as follows: .

[0045] The current global hidden state is obtained by fusing the hidden layer update mask: For variable groups that have experienced sampling events, gated recursive updates are used to absorb new observation information at the current time. For variable groups that have not experienced sampling events, time-distance decay updates are performed based on the number of steps between the current time and the most recent actual sampling time of the variable group.

[0046] As a further improvement of the present invention, in step S5, the calculation method of the sensitivity of the hidden layer nodes of each variable group, the function preservation method, the method of expanding the output layer parameters, and the model parameter optimization method are as follows: Let the training sample set used for one parameter update be: ,in, Indicates the sample size; for any sample Let its loss function value be... , record In the group of variables, the first The state value of each hidden node at the end of the sample window is... ,in: .

[0047] Regarding the first The first variable in the group of variables Each hidden node introduces a multiplicative gated perturbation coefficient. and in Calculate the first-order sensitivity of the hidden layer node relative to the loss function: ;in, This indicates the degree of first-order local change in the loss function when a multiplicative perturbation is applied to the hidden layer node.

[0048] For the The root mean square aggregation of the node sensitivities of each hidden node within each variable group yields the nth... Groups of variables in the sample Group sensitivity values: .

[0049] The training sample set used for a single parameter update Calculate the average to obtain the first... Current importance values ​​for each variable group: .

[0050] The exponential moving average is used to obtain the first... Smoothed importance values ​​for each variable group: ;in, Represents the smoothing coefficient. This indicates the number of parameters updated since the last time. The smoothed importance values ​​for each variable group are initially set to 0. This represents the smooth importance value after the current parameter is updated.

[0051] When the decrease in validation sample loss is less than a preset threshold, and the maximum smoothing importance value is not less than a preset importance threshold, the variable group with the largest smoothing importance value is selected as the expansion object: The preset expansion conditions include: the smooth importance value of the expanded object is not lower than a preset importance threshold and the decrease in the loss of the verification sample within a preset training round is lower than a preset threshold.

[0052] In the New variables added to the hidden subspace corresponding to each variable group There are hidden layer nodes, among which... The value is a positive integer; the newly added hidden layer node logically belongs to the first... The nth variable group, the th The extended hidden subspace index set of the variable groups is defined as follows: Meanwhile, the first The dimension of the hidden subspace corresponding to each variable group is determined by... Updated to: .

[0053] For other variable groups not selected as expansion objects, their hidden subspace index set and hidden subspace dimension remain unchanged, and newly added hidden nodes are incorporated into the first subspace. In the expanded contiguous hidden subspace of each variable group; after expansion, the starting index and index set of each variable group are recalculated based on the updated dimension of the hidden subspace of each variable group; after expansion, the dimension of the global hidden state is... Updated to: The output layer before expansion is: ;in, Indicates the last time of the window Estimated values ​​of low-frequency operating indicators corresponding to the time sample; This represents the global hidden layer state at the end of the sample window. Indicates the output layer weights. This indicates the output layer bias.

[0054] The extended global hidden state is represented as follows: ;in, This represents the global hidden state at the end of the sample window after structural expansion. This indicates the state of the newly added hidden layer node at the end of the sample window.

[0055] When adding a new hidden layer node, the input weight matrix, recursive weight matrix, and bias vector in the gated recurrent unit network are simultaneously expanded in dimension. The parameters corresponding to the original hidden layer nodes remain unchanged. The initial recursive connection from the new hidden layer node to the original hidden layer node is set to zero. The input weights, recursive weights, and biases corresponding to the new hidden layer node are initialized with a small amount of randomization. The expanded output layer parameters are initialized as follows: ; ;in, and These represent the output layer weights and output layer biases after the structure expansion, respectively. This represents the zero-weight column corresponding to the newly added hidden layer node. Since the newly added weight in the output layer is zero, the expansion instantaneously yields: ;in, This represents the estimated low-frequency operating parameters after structural expansion. This represents the estimated low-frequency operating index value before the structure expansion; therefore, the output layer weight corresponding to the newly added hidden layer node is zero, so that the estimated low-frequency operating index value at the moment of structure expansion remains the same as the estimated low-frequency operating index value before expansion.

[0056] During model training, the model loss function is: ;in, Indicates time The corresponding low-frequency operating index values ​​are used to jointly optimize the gated recurrent unit network parameters, time interval decay parameters, newly added parameters after incremental expansion, and output layer parameters based on the loss function during model training.

[0057] Compared with the prior art, the present invention has the following technical effects: (1) The present invention uses a dual mechanism of smooth interpolation data input and real sampling triggering update to achieve functional separation of interpolation information and sampling events in the model, which not only improves the continuity of the input sequence, but also avoids mistaking interpolated values ​​as real observations.

[0058] (2) The present invention controls the hidden layer update by using a real sampling mask, and triggers gated recursion only when the corresponding variable group is sampled, thereby preserving the real sampling structure of the industrial process under a unified time axis.

[0059] (3) The present invention introduces a time-distance decay mechanism, which adaptively decays the hidden layer state variables according to the time interval between the unsampled variable group and the most recent real sample, which can alleviate the problems of state staleness, feature failure and long-term dependency degradation in the unsampled interval.

[0060] (4) The present invention adopts an incremental expansion strategy based on group sensitivity, so that the model capacity is preferentially allocated to the variable group that contributes more to the current task, thereby improving the representation ability of the key variable group.

[0061] (5) The present invention uses a function-preserving method to expand the output layer parameters, which can keep the output mapping stable during the structural expansion and improve the stability of the model training process.

[0062] (6) Because this invention decouples the smooth interpolation input from the actual sampling event, the model will not mistakenly trigger the gated recursive update of the corresponding variable group due to the interpolation value when no actual sampling occurs, thus preserving the true sampling structure of industrial multi-sampling rate data. Since the hidden state of the unsampled variable group decays according to the interval from the nearest actual sampling time, the impact of the stale state that has not been updated for a long time on the estimation of the current low-frequency operating index is reduced. Since the incremental expansion of the hidden node is performed according to the sensitivity of the variable group to the loss function, the model capacity can be preferentially allocated to the sampled variable group that contributes more to the estimation of low-frequency operating index, thereby improving the stability and accuracy of online estimation of low-frequency operating index of industrial process. Attached Figure Description

[0063] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention above and in other aspects will become clearer.

[0064] Figure 1 This is the overall modeling flowchart of the present invention, which is used to illustrate the overall process from multi-sampling rate industrial process data acquisition, unified time axis construction, variable grouping, grouped smooth interpolation, sample window construction, flexible clock-gated loop unit modeling, time interval decay update, grouped sensitivity assessment, incremental expansion to operational index estimation output.

[0065] Figure 2 This is a schematic diagram of the soft measurement objects and variable relationships in the industrial grinding process in this embodiment of the invention, used to illustrate the correspondence between process variables such as ball mill current, ball mill ear current, ball mill pre-mill water flow rate, and ball mill feed rate and low-frequency operating indicators of hydrocyclone feed concentration.

[0066] Figure 3This is a schematic diagram of multi-sampling rate process data and real sampling mask of the present invention, used to illustrate the real sampling positions of different process variables on a unified time axis and the real sampling mask matrix formed therefrom.

[0067] Figure 4 This is a schematic diagram of Gaussian smoothing interpolation of different grouped sampled data according to the present invention, used to illustrate the process of performing grouped Gaussian smoothing interpolation on sparse sampled data of different variable groups respectively, and forming a continuous auxiliary input sequence.

[0068] Figure 5 This is a comparison chart of the hydrocyclone feed concentration estimation results using the VPTN method, used to illustrate the deviation between the true value and the soft-sensor estimate on the test sample using the VPTN method.

[0069] Figure 6 This is a comparison chart of hydrocyclone feed concentration estimation results using the MR-PVAE method, used to illustrate the deviation between the true value and the soft-sensor estimate on the test sample using the MR-PVAE method.

[0070] Figure 7 This is a comparison chart of hydrocyclone feed concentration estimation results using the TTPA-LSTM method, used to illustrate the deviation between the true value and the soft sensor estimate of the TTPA-LSTM method on the test sample.

[0071] Figure 8 This is a comparison chart of the hydrocyclone feed concentration estimation results using the method of the present invention, used to illustrate the tracking effect of the method of the present invention on the actual trend of hydrocyclone feed concentration change on the test sample. Detailed Implementation

[0072] like Figure 1 As shown, this invention proposes an adaptive soft measurement method for smooth interpolation of multi-sampling-rate industrial processes. The method includes the following steps: Step S1, collecting multi-sampling-rate process variable data and low-frequency operating index data of the target industrial process, and setting a baseline sampling interval. and based on the reference sampling interval Construct a unified time axis for time alignment of multi-sampling rate data; the unified time axis refers to a time axis based on a reference sampling interval. A common discrete-time benchmark is constructed for discrete step lengths to map process variables and low-frequency operating indicators with different sampling periods and sampling offsets to the same discrete-time index system. This benchmark is used to characterize the input-output time delay relationship of process variables relative to low-frequency operating indicators, using sampling multiples. Sampling offset index and time delay steps Indicates the first The sampling and alignment relationship of the process variable; determine the sampling and alignment relationship of the first process variable. The set of true sampled indexes of process variables And establish a variable-level true sampling mask. According to the sampling multiple and equivalent sampling offset after time delay correction Process variables with consistent sampling alignment patterns are divided into Groups of variables and establish group-level true sampling masks. ,in, Represents the index of discrete moments on a unified time axis. Indicates the variable group index, unless otherwise specified, followed by a subscript or superscript. The variables, parameters, sets, masks, hidden states, attenuation coefficients, sensitivity values, importance values, and incremental expansion amounts all represent the relationship with the first... The quantities corresponding to each group of variables, the The meaning of the variable group index is used throughout the text and does not represent a new independent index.

[0073] Step S2: Establish a sparse observation matrix on a unified time axis. For each group of variables The smoothed auxiliary input value is generated by using a causal grouping Gaussian time-weighted smoothing method based on the current time and its historical true sample values. ,in, Indicates the process variable index. This indicates the variable group index to which the process variable belongs. In grouped Gaussian time-weighted smoothing, all relevant parameters are assigned according to the variable group index. Configure the system; arrange the smoothed auxiliary input values ​​of all process variables in the order of their original variable numbers to form a continuous auxiliary input vector. .

[0074] Step S3: Based on low-frequency operation indicators Real sampling index set Sliding window length and sliding step size Based on continuous auxiliary input vectors Constructing a time-series sliding window sample ;Use a flexible clock-gated cyclic unit network, according to the first Number of process variables in each variable group Hidden layer node allocation coefficients , for the first The hidden subspace dimension is assigned to each set of variables. and index the set using the hidden subspace. Indicates the first The range of hidden nodes corresponding to each variable group; where the first... The hidden subspace and the first Each variable group corresponds one-to-one. , And subsequent In All indicate the first The correspondence between each set of variables in the hidden layer structure of the network is shown; the hidden layer states corresponding to all sets of variables are concatenated to obtain the global hidden layer state. .

[0075] Step S4: Based on the group-level true sampling mask and hidden layer subspace index set Generate hidden layer update mask , Indicates the first The set of variables at time... Did a real sampling event occur? Indicates the first The hidden subspaces corresponding to each set of variables, and the two... They have the same variable group index meaning; and perform grouped selective updates at each time step on a unified time axis; updating masks according to hidden layers. By fusing the gated recursive update state and the time-lapse decay update state, the global hidden state at the current time step is obtained. .

[0076] Step S5: During model training, calculate the importance value of each variable group's hidden layer nodes based on their sensitivity to the loss function. When the preset expansion period is reached and the preset expansion conditions are met, select the variable group with the highest smoothing importance value to perform incremental expansion of the hidden layer nodes. Expand the output layer parameters using a function-preserving approach, ensuring that the newly added hidden layer nodes do not change the estimated low-frequency operating indicators before expansion. Input the global hidden layer state at the end of the time series sample window into the output layer and output the estimated low-frequency operating indicators. Based on real low-frequency operating indicators With estimation of low-frequency operating indicators The error between them is used to optimize the model parameters.

[0077] I. Example of soft measurement modeling for industrial grinding process.

[0078] In this embodiment, a soft measurement model is performed on the hydrocyclone feed concentration, taking the industrial grinding process as the object. Process variables in the industrial grinding process are usually collected by field sensors or distributed control systems, while key operating indicators such as hydrocyclone feed concentration are usually obtained at low frequency by online analysis devices or manual testing methods, thus forming typical multi-sampling rate industrial process data.

[0079] To facilitate understanding of the symbol system in this embodiment, the main index symbols are explained uniformly as follows: Indicates the process variable index. ; Represents the index of discrete moments on a unified time axis; Indicates the variable group index. ; Indicates the first Each variable group corresponds to a hidden layer node index within the hidden layer subspace; This indicates the unified time axis index corresponding to the low-frequency operation indicator label; This indicates the index of the training samples. Unless otherwise specified, this text uses subscripts or superscripts. The quantities are all the first The corresponding quantities of each variable group in the respective calculation steps include sampling parameters, interpolation parameters, hidden layer subspace parameters, time-distance decay parameters, sensitivity evaluation quantities, and incremental expansion quantities. (Superscript) It only indicates a grouping identifier, not an exponentiation operation; when When it appears in a summation or maximum value selection formula, it indicates that all variable group indices are traversed.

[0080] Table 1. Description of Variables and Low-Frequency Operating Indicators in Industrial Grinding Processes

[0081]

[0082] The ball mill current, ball mill auger current, pre-mill water flow rate, and ball mill feed rate are selected as process variables, and the hydrocyclone feed concentration is selected as a low-frequency operating index. Let the set of process variables be: ;in, This represents the ball mill current, in units of... ; This indicates the current of the ball mill's electric ear, in units of... ; This indicates the water supply flow rate before the ball mill, in units of... ; This indicates the feed rate of the ball mill, in units of... Low-frequency operation is indicated as... This indicates the hydrocyclone feed concentration, in units of... .

[0083] In one specific implementation, the sampling plan for process variables and low-frequency operating indicators is shown in Table 1 above. In Table 1, the three values ​​corresponding to each variable represent the sampling offset time, sampling interval, and process delay, respectively. The sampling offset time is used to determine the initial sampling position of the variable on a unified time axis; the sampling interval is used to determine the sampling multiple of the variable relative to the reference sampling interval; and the process delay is used to describe the possible process response lag of the variable to the low-frequency operating indicators. In practical applications, the input and output delays can be determined based on the process mechanism, cross-correlation analysis, or field experience.

[0084] This embodiment uses As the reference sampling interval, that is: .

[0085] Therefore, the ball mill current and ball mill electric ear current The sampling intervals are all This is equivalent to having actual sampling at each reference sampling moment on a unified time axis; ball mill pre-mill water replenishment flow rate. The sampling interval is equivalent to each Sampling is performed once at each baseline sampling interval; ball mill feed rate and low-frequency operating indicators The sampling interval is equivalent to each Each baseline sampling interval is sampled once.

[0086] The industrial grinding process data used comes from the online acquisition data of the field distributed control system of the grinding loop in the concentrator, such as... Figure 2 The diagram shows the equipment and simplified flow chart of the industrial grinding process. The raw data covers various typical operating conditions during the long-term operation of the unit, including stable operation, mill load fluctuations, and minor operating disturbances, reflecting the dynamic coupling relationship between process variables with multiple sampling rates and low-frequency operating indicators in the industrial field. The original data volume is approximately 200,000 records. To ensure the quality of the modeling data and the reliability of the soft measurement model evaluation, after removing downtime, sensor failure, obvious abnormal jumps, and time periods with severe missing labels for low-frequency operating indicators, three high-quality continuous and valid sample sequences were selected as experimental data. The lengths of the three valid sample sequences are 9959, 8895, and 12062 baseline sampling times, respectively.

[0087] For the aforementioned valid sample sequences, a unified time axis is constructed according to the baseline sampling interval. Based on the sampling interval, sampling offset, and process delay of each process variable, variable-level true sampling masks, group-level true sampling masks, and true sampling indices for low-frequency operating indicators are generated. Training, validation, and test samples are divided chronologically, with the first 60% of the time window sequence samples serving as the training set, the middle 20% as the validation set, and the last 20% as the test set. The test set is located at the end of the time series and is not used for model parameter training, normalized parameter calculation, early model termination detection, or hidden layer node incremental expansion condition detection.

[0088] During data preprocessing, the normalized parameters of process variables and low-frequency operating indicators are obtained only from the training set statistics and applied to the validation and test sets respectively to avoid leakage of test information. Test samples are constructed using the same unified time axis as the training samples, with the establishment of a true sampling mask, causal grouping Gaussian time-weighted smoothing interpolation, and sliding window construction rules. At any given test moment, the model generates continuous auxiliary inputs using only the current moment and its historical true sampling data, without utilizing future sampling values ​​or future low-frequency operating indicator labels. The resulting test samples can be used to evaluate the method's online estimation capability of hydrocyclone feed concentration under real industrial grinding multi-sampling rate data conditions.

[0089] II. Construction of a unified timeline and determination of the actual sampling index.

[0090] To perform time-series recursive modeling of multi-sampling-rate data without disrupting the true sampling structure of each process variable, this embodiment uses a baseline sampling interval. A unified time axis is constructed. This unified time axis is used to determine the sampling index of each process variable and low-frequency operating index on a common discrete-time benchmark, and is used to subsequently establish the true sampling mask, sparse observation matrix, smoothing auxiliary input, and sliding window samples. It should be noted that the unified time axis is only used to provide a common discrete index benchmark and does not imply that each process variable has true sampling at every time point of the unified time axis; whether each process variable has true sampling at a corresponding time point is determined by the variable-level true sampling mask and the group-level true sampling mask.

[0091] Let the unified timeline be: ;in, Indicates the initial time. Indicates the reference sampling interval. This indicates the number of sampling time points on a unified time axis. Indicates the first A unified timeline moment.

[0092] No. The sampling interval, sampling offset time, and input / output delay of each process variable are expressed as follows: ; in, A positive integer, representing the first... Each process variable relative to the baseline sampling interval The sampling multiple; It is a non-negative integer and satisfies , indicating the first The sampling offset index of each process variable; A non-negative integer, representing the first... The number of time delay steps of each process variable relative to a low-frequency operating indicator.

[0093] No. The set of actual sampled indices for each process variable is defined as: ; in: , indicating the first The maximum sampling sequence number of each process variable.

[0094] Low-frequency operating indicators The true sample index set is defined as: ; in, This indicates the sampling multiple of the low-frequency operating parameters relative to the reference sampling interval. This represents the sampling offset index of low-frequency operating indicators.

[0095] In this embodiment, when using the process delay shown in Table 1 for time delay correction, due to the reference sampling interval The input and output time delay steps corresponding to each process variable are respectively , , , According to the sampling plan in Table 1, the sampling offset index and sampling multiple on the unified time axis can be set as follows: .

[0096] That is, the ball mill current and the ball mill ear current are sampled at every reference sampling time starting from the beginning of the unified time axis; the ball mill pre-mixed water flow rate is sampled once every 5 reference sampling intervals after being offset by 4 reference sampling intervals relative to the unified time axis; the ball mill feed rate and the hydrocyclone feed concentration are sampled once every 10 reference sampling intervals after being offset by 9 reference sampling intervals relative to the unified time axis.

[0097] III. Construction of variable-level and group-level true sampling masks.

[0098] To preserve the true sampling structure of each process variable under a unified timeline, this embodiment constructs a variable-level true sampling mask. Each process variable is indexed on a unified time axis. The effective observation index after time delay correction is: .

[0099] The variable-level true sampling mask is defined as: ;in, Indicates the first The process variables at time 1 After alignment, the actual sampled values ​​exist; Indicates the first The process variables at time 1 After alignment, there are no true sampled values.

[0100] Based on the sampling multiple and the equivalent sampling offset after time delay correction, process variables with consistent sampling alignment are grouped into variable groups. The equivalent sampling offset after time delay correction for each process variable is defined as: .

[0101] All process variables corresponding to different pairs Process variables with the same sampling alignment pattern are grouped into the same variable group, representing different sampling alignment patterns. Let the number of different sampling alignment patterns be... , No. The variable groups are denoted as .

[0102] In this embodiment, when the input and output time delay steps are processed according to the experimental procedure settings, the ball mill current... and ball mill electric ear current Variables with the same sampling multiple and equivalent sampling offset can be grouped into the same variable group; pre-milling water supply flow rate. and ball mill feed rate Each variable has a different sampling factor and equivalent sampling offset, and can be divided into different variable groups. Therefore: ; ; ;in, For high-frequency sampled variable groups, For intermediate frequency sampling variable groups, This is a low-frequency sampling variable group.

[0103] No. The group-level true sampling mask for each variable group is defined as: ;in, Indicates the first The set of variables at time... A sampling event occurred; Indicates the first The set of variables at time... No sampling event occurred, such as Figure 3 The figure shows the real sampled data matrix and data mask matrix for three different sets of sampled variables.

[0104] By using the above variable-level true sampling mask and group-level true sampling mask, this embodiment can distinguish between sampling events and continuous auxiliary inputs obtained by interpolation. The subsequent model only controls whether the corresponding hidden subspace is gated recursive update based on the sampling events.

[0105] IV. Construction of sparse observation matrix.

[0106] Establish a sparse observation matrix on a unified time axis: ;in, Indicates the first The first unified timeline index, the first The matrix elements corresponding to each process variable.

[0107] The elements of the sparse observation matrix are defined as follows: ;in, Indicates the first The process variables at the observation time after time delay correction The actual observed value, Indicates a null or missing value.

[0108] In this embodiment, for each segment of industrial operation data, a sparse observation matrix, a variable-level true sampling mask matrix, and a group-level true sampling mask matrix are constructed in the manner described above. Thus, on a unified time axis, a data sequence of uniform length can be formed while retaining information about the true sampling positions of different process variables.

[0109] V. Causal grouping Gaussian time-weighted smooth interpolation.

[0110] Since gated recurrent unit networks require continuous numerical input, this embodiment performs causal grouping Gaussian time-weighted smoothing interpolation on the sparse observation matrix. This interpolation process uses only the true sampled values ​​at the current time and before, excluding data from future times, to meet the causality requirements of online soft-sensor modeling. For the first... Group of variables process variables in Define the causal historical observation set as: ;in, Represents a unified historical timeline index. Indicates the first The maximum number of historical backtracking steps for a group of variables.

[0111] No. The Gaussian time weights for the variable groups are: ;in, Indicates the first Gaussian smoothing parameters for a set of variables.

[0112] No. Each process variable is indexed on a unified time axis. The smoothing auxiliary input value at point is defined as: ;in, To prevent constants with a denominator of zero, For the first The mean of each process variable in the training sample.

[0113] In one specific implementation, the maximum number of historical backtracking steps Determined based on the sampling multiple of the variable group: ; in, This represents the minimum number of backtracking steps. Represents the backtracking coefficient. Indicates the first The sampling multiple corresponding to each variable group.

[0114] Gaussian smoothing parameters It can be determined in the following way: ;in, This represents the smoothing parameter coefficient.

[0115] In this embodiment, It can be set to 10. It can be set to 3. It can be set to 1.0. Thus, the lower frequency sampled variable group can be smoothly interpolated using the true observations over a longer historical period, while the high frequency sampled variable group can retain stronger local dynamic information.

[0116] Arrange the smoothed auxiliary input values ​​of all process variables in the order of their original variable numbers to obtain a continuous auxiliary input vector: ,like Figure 4 The figure shows the continuous auxiliary smoothed data input matrix obtained after interpolation of three different sets of sampled variables.

[0117] It should be noted that, It is only used to provide continuous numerical input to the network and does not replace the variable-level true sampling mask. Group-level true sampling mask Control over the hidden state update method. That is, even if continuous input values ​​are obtained through smooth interpolation when no sampling event occurs, the interpolated value will not be used as a sampling event to trigger the gated recursive update of the corresponding variable group.

[0118] VI. Construction of Time-Sequence Sliding Window Samples.

[0119] Set low-frequency operation indicators The available tag index set is: ;in, This indicates the unified time axis index corresponding to the low-frequency operation indicator label. Indicates the length of the sliding window.

[0120] When using sliding step size At that time, from the set The label indices are selected in chronological order with the sliding step size to obtain a set of label indices for training, validation, or testing. For any... Construct an ordered time series sample using a sliding window: .

[0121] The labels of the sliding window samples are: ;in, Indicates time The corresponding actual observed values ​​of low-frequency operating indicators.

[0122] In this embodiment, the sliding window length is set as follows: .

[0123] The sliding step size is set as follows: .

[0124] Since the hydrocyclone feed concentration is sampled once every 10 baseline sampling intervals, the above sliding step size can keep the monitoring sample window consistent with the actual sampling time of the low-frequency operating indicators.

[0125] Each supervised sample includes a continuous auxiliary input vector within a sliding window, a variable-level true sampling mask, a group-level true sampling mask, a unified time axis index, and a corresponding low-frequency performance indicator label. The model is recursively processed according to the unified time axis order, and outputs the estimated value and calculates the loss only at the true sampling time of the low-frequency performance indicator.

[0126] Regarding the partitioning of training, validation, and testing data, this embodiment divides the samples according to chronological order, with the training set, validation set, and test set ratios set to 60%, 20%, and 20%, respectively. The training set is used for model parameter optimization, the validation set for model selection, early stopping judgment, and incremental expansion trigger judgment, and the test set is used for the final evaluation of the model's generalization performance. The normalized parameters of process variables and low-frequency operating indicators are calculated only from the training set and used in the validation and test sets to avoid leakage of test information.

[0127] VII. Hidden Subspace Allocation.

[0128] This embodiment uses a flexible clock-gated cyclic unit network for dynamic modeling. Different variable groups correspond to different hidden subspaces. The dimension of the hidden subspace of a set of variables is defined as: ;in, This represents the allocation coefficient for hidden layer nodes. Indicates the first The number of process variables contained in each variable group.

[0129] The dimension of the global hidden state is: .

[0130] In this embodiment, the hidden layer node allocation coefficient can be set as follows: .

[0131] because The three variable groups contain a total of four process variables, therefore the initial hidden subspace dimension is: .

[0132] The initial global hidden state dimension is: .

[0133] Order No. The starting index of the hidden subspace of each variable group is: .

[0134] No. The hidden subspace index set corresponding to each variable group is defined as follows: .

[0135] The hidden subspace index sets corresponding to different variable groups do not overlap, and the hidden subspace index sets corresponding to all variable groups together cover all dimensions of the global hidden state.

[0136] No. Each variable group is indexed on a unified time axis. The hidden state at that point is denoted as The hidden states of all variable groups are concatenated as follows: ;in, Indicates a unified timeline index The corresponding global hidden state.

[0137] 8. Calculation of gated recursive candidate update state.

[0138] For continuous auxiliary input vectors and the global hidden state at the previous time step The initial global hidden state is set to zero. At that time, the global hidden state vector of the previous time step is zero.

[0139] The gated recursive candidate update state is calculated according to the following formula: ; ; ; ;in, Indicates an update to the door. This indicates that the door is being reset. This represents the candidate hidden state. Indicates the candidate gating update status; , , This represents the input weight matrix. , , Represents the recursive weight matrix. , , Represents the bias vector; express function, Represents the hyperbolic tangent function. This indicates element-wise multiplication.

[0140] Continuous auxiliary input vector Used to provide the network with numerical coupling information across variable groups, while group-level true sampling masks This is used to control whether the corresponding hidden subspace is updated using gated recursion. Thus, the model can utilize the interpolated continuous inputs without misinterpreting the interpolated values ​​as sampling events.

[0141] 9. Time-distance decay update based on unsampled variable groups.

[0142] For the A set of variables, in At that moment, let: ;in, Indicates the index up to the unified timeline. The index of the most recently occurring sampling event. If the index does not exist, the initial hidden state is used.

[0143] when If it exists, the interval step number is defined as: .

[0144] The time-distance attenuation coefficient is defined as: ; in, Indicates the first The decay parameters of the variable group And follow It increases while monotonically decreasing.

[0145] In this embodiment, the attenuation parameter Learning can be performed using a positive constraint method, with an initial value set to 0.08. The time-distance attenuation coefficient allows the hidden state of variable groups that have not experienced sampling events for a long time to gradually decay, thereby reducing the impact of outdated states on the estimation results of current low-frequency operating indicators.

[0146] No. The time-decrease update state of a variable group is defined as follows: ;in, Indicates the first The hidden state of each variable group after the most recent real sampling update. Indicates the first The initial hidden state of the variable group.

[0147] No. The hidden update mask for each variable group is defined as: ;in, Indicates length is A vector of all 1s.

[0148] The global hidden layer update mask is: .

[0149] when At that time, the first Each set of variables experiences a sampling event at the current moment, and the state is updated using candidate gating. The portion corresponding to the hidden subspace of that variable group is taken as the current state; when At that time, the first If no sampling event occurs in the variable group at the current time, the normal gated recursive update is not performed; instead, the time-distance decay update is performed.

[0150] The time-distance decay update states of each variable group are concatenated to obtain: .

[0151] The current global hidden state is obtained by fusing the hidden layer update mask: For variable groups that have experienced sampling events, gated recursive updates are used to absorb new observation information at the current time. For variable groups that have not experienced sampling events, time-distance decay updates are performed based on the number of steps between the current time and the most recent actual sampling time of the variable group.

[0152] Through the above-described selective update method, this embodiment enables the high-frequency sampling variable group to absorb new observation information in a timely manner at each real sampling moment, while allowing the low-frequency sampling variable group to update its state only when a sampling event occurs, thus avoiding excessive updates of the hidden layer state caused by interpolation values.

[0153] 10. Incremental expansion of hidden layer nodes based on group sensitivity.

[0154] To prioritize the allocation of model capacity to variable groups that contribute significantly to the estimation of low-frequency operating indicators, this embodiment introduces an incremental expansion mechanism for hidden layer nodes based on group sensitivity during model training.

[0155] Let the set of training samples used in a single parameter update be . ,in Indicates the sample size. For any given sample Let its loss function value be... , record In the group of variables, the first The state value of each hidden node at the end of the sample window is... .

[0156] Regarding the first The first variable in the group of variables Each hidden node introduces a multiplicative gated perturbation coefficient. and in Calculate the first-order sensitivity of the hidden layer node relative to the loss function: ;in, This indicates the degree of first-order local change in the loss function when a multiplicative perturbation is applied to the hidden layer node.

[0157] For the The root mean square aggregation of the node sensitivities of each hidden node within each variable group yields the nth... Groups of variables in the sample Group sensitivity values: .

[0158] The training sample set used for a single parameter update Calculate the average to obtain the first... Current importance values ​​for each variable group: .

[0159] The exponential moving average is used to obtain the first... Smoothed importance values ​​for each variable group: ;in, Represents the smoothing coefficient. This indicates the number of parameters updated since the last time. The smoothed importance values ​​for each variable group are initially set to 0. This represents the smooth importance value after the current parameter is updated.

[0160] In this embodiment, the smoothing coefficient can be set to 0.90, the expansion period can be set to 20 training epochs, the expansion warm-up epochs can be set to 40 training epochs, the validation set plateau period judgment epochs can be set to 10 training epochs, and the importance threshold can be set to... The number of hidden layer nodes added each time can be set to 2, and the maximum number of expansions can be set to 10.

[0161] When the preset expansion period is reached, and the decrease in the loss of the validation samples within the preset training rounds is less than the preset threshold, and the maximum smoothing importance value is not less than the preset importance threshold, the variable group with the largest smoothing importance value is selected as the expansion target: The preset expansion conditions include: the smooth importance value of the expanded object is not lower than a preset importance threshold and the decrease in the loss of the verification sample within a preset training round is lower than a preset threshold.

[0162] In the New variables added to the hidden subspace corresponding to each variable group There are hidden layer nodes, among which... The value is a positive integer; the newly added hidden layer node logically belongs to the first... The nth variable group, the th The extended hidden subspace index set of the variable groups is defined as follows: .

[0163] At the same time, the The dimension of the hidden subspace corresponding to each variable group is determined by... Updated to: .

[0164] For other variable groups not selected as expansion objects, their hidden subspace index set and hidden subspace dimension remain unchanged, and newly added hidden nodes are incorporated into the first subspace. In the expanded contiguous hidden subspace of each variable group. After expansion, the starting index and index set of each variable group are recalculated based on the updated dimension of the hidden subspace of each variable group. The dimension of the global hidden state after expansion is... Updated to: .

[0165] 11. The function maintains the expansion of the output layer.

[0166] To avoid the instantaneous destruction of the existing model output during incremental expansion of hidden layer nodes, this embodiment employs a function-preserving approach to expand the output layer parameters. The output layer before expansion is as follows: .

[0167] The extended global hidden state is represented as follows: ;in, This represents the global hidden state at the end of the sample window after structural expansion. This represents the global hidden layer state at the end of the sample window before structural expansion. This indicates the state of the newly added hidden layer node at the end of the sample window.

[0168] The expanded output layer parameters are initialized as follows: ; ;in, and These represent the output layer weights and output layer biases after the structure expansion, respectively. This represents the zero-weight column corresponding to the newly added hidden layer node.

[0169] Since the output layer weights corresponding to the newly added hidden layer nodes are zero, at the instant of structural expansion we have: .

[0170] Therefore, the estimated value of the low-frequency operating index at the moment of structural expansion remains the same as the estimated value before expansion, thereby avoiding the sudden change in model output caused by the addition of new hidden layer nodes and improving the stability of the incremental expansion process of the model.

[0171] When adding a new hidden layer node, the input weight matrix, recursive weight matrix, and bias vector in the gated recurrent unit network are simultaneously expanded in dimension. The parameters corresponding to the original hidden layer nodes remain unchanged. The initial recursive connection from the new hidden layer node to the original hidden layer node is set to zero. The input weights, recursive weights, and biases corresponding to the new hidden layer node are initialized using a random initialization method within a preset amplitude range.

[0172] The model training loss function can be defined as: ;in, Indicates time The corresponding actual values ​​of low-frequency operating indicators.

[0173] During training, the parameters of the gated recurrent unit network, the time-distance decay parameter, the output layer parameters, and the newly added parameters after incremental expansion are jointly optimized based on the loss function.

[0174] 12. Model Training Settings.

[0175] In this embodiment, the model training uses mean squared error as the objective function and the AdamW optimization algorithm is used to update the model parameters. The learning rate can be set to 0.0025, the maximum number of training epochs can be set to 220, the batch size can be set to 64, and the weight decay coefficient can be set to... The gradient clipping threshold can be set to 1, and the number of early stop patience rounds can be set to 30. During training, multiple historical operating data segments of the industrial grinding process are first read in chronological order; then, sparse observation matrices, variable-level true sampling masks, group-level true sampling masks, and low-frequency operating index true sampling masks are constructed respectively; subsequently, process variables and low-frequency operating indicators are normalized based on training set statistics; then, continuous auxiliary inputs are generated based on the causal grouping Gaussian time-weighted smoothing method; finally, the continuous auxiliary inputs and group-level true sampling masks are input into the flexible clock-gated recurrent unit network for training.

[0176] If the validation set loss does not decrease significantly for several consecutive training epochs, the model is considered to have entered a plateau. If conditions such as expansion period, expansion warm-up, and importance threshold are simultaneously met, then the hidden layer nodes are incrementally expanded according to the group sensitivity selection variable group, and the expanded model is retrained. If the validation set loss does not continue to decrease within the preset early stopping epochs, then training is terminated, and the model with the optimal validation set loss is selected as the final model.

[0177] To evaluate the estimation performance of the method of this invention on low-frequency operating indicators, this embodiment uses the root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), and coefficient of determination. These are used as evaluation indicators. The definitions of each indicator are as follows: ; ; ; ;in, Indicates the number of test samples. Indicates the first The true low-frequency operating index values ​​of each test sample Indicates the first Estimated low-frequency operating index values ​​for each test sample. This represents the average value of the actual low-frequency operating indicators of the test samples. The smaller the RMSE, MAE, and MSE, the lower the model estimation error. The larger the value, the stronger the model's ability to fit the changing trends of real low-frequency operating indicators.

[0178] XIII. Comparative Experiments and Results Analysis.

[0179] To verify the effectiveness of the method of this invention, this embodiment compares the method of this invention with three other methods: VPTN, MR-PVAE, and TTPA-LSTM. VPTN, MR-PVAE, and TTPA-LSTM are all existing multi-rate soft measurement comparison methods. All models use the same process variables as inputs, the hydrocyclone feed concentration as output, and employ the same data partitioning method and evaluation metrics. The evaluation results of each model on the test set are shown in the table below.

[0180] Table 2 Evaluation Indicators for Feed Concentration Estimation of Each Model Hydrocyclone

[0181]

[0182] From Table 2 and Figure 5 , Figure 6 , Figure 7 and Figure 8 The data fitting curves show that, under the conditions of using the same input variables, the same data partitioning method, and the same evaluation indicators, the method of this invention achieves superior results in all four indicators: RMSE, MAE, MSE, and R². Specifically, the RMSE of the method of this invention is 2.938, lower than that of VPTN, MR-PVAE, and TTPA-LSTM methods; the MAE is 2.209, and the MSE is 8.632, both of which are the minimum values ​​among the comparison methods; the R² is 0.753, higher than the three comparison methods.

[0183] Compared with the best-performing comparative method TTPA-LSTM, the method of this invention reduces RMSE by approximately 8.84%, MAE by approximately 12.69%, MSE by approximately 16.84%, and R² by approximately 7.11%. These results demonstrate that the method of this invention not only reduces the estimation error of hydrocyclone feed concentration but also better tracks the changing trends of low-frequency operating parameters.

[0184] The reason for the above effects lies in the fact that this invention does not simply input the interpolated process variables from the multi-sampling-rate process into the recurrent neural network, but rather functionally separates the smoothed interpolation input from the real sampling events. On the one hand, causal grouped Gaussian time-weighted smoothing can provide continuous auxiliary input to the network, ensuring that the model has complete numerical input on a unified time axis; on the other hand, the real sampling mask only triggers gated recursive updates when the corresponding variable group has a real sampling, avoiding the interpolated values ​​being mistaken for real observations and causing excessive updates to the hidden layer state. At the same time, for variable groups that have not had a real sampling for a long time, this invention performs time-distance decay based on the interval from the most recent real sampling time, reducing the interference of stale states on the current concentration estimation; and through grouped sensitivity incremental expansion, the model capacity is preferentially allocated to variable groups that contribute more to the concentration estimation.

[0185] Therefore, compared with comparative methods that directly model multiple sampling rates based on fixed structure networks, the method of this invention is more suitable for dealing with the problems of inconsistent sampling frequencies of different process variables, delayed acquisition of low-frequency indicators, and easy obsolescence of variable states in industrial grinding processes, thereby improving the accuracy and stability of hydrocyclone feed concentration estimation.

[0186] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes that can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention are all within the protection scope of the claims of the present invention.

Claims

1. A method for adaptive soft measurement with smooth interpolation in multi-sampling-rate industrial processes, characterized in that, The method includes the following steps: Step S1: Collect multi-sampling-rate process variable data and low-frequency operating index data of the target industrial process, based on the benchmark sampling interval. Construct a unified time axis for time alignment of multi-sampling rate data; based on sampling multiples. Sampling offset index and time delay steps Indicates the first Sampling and alignment relationships of process variables; based on sampling multiples and equivalent sampling offset after time delay correction Process variables with consistent sampling alignment patterns are divided into Group of variables Establish group-level real sampling masks ; Step S2: Establish a sparse observation matrix on a unified time axis. For each group of variables The smoothed auxiliary input value is generated by using a causal grouping Gaussian time-weighted smoothing method based on the current time and its historical true sample values. And combine the smoothed auxiliary input values ​​of each process variable to form a continuous auxiliary input vector; Step S3: Based on continuous auxiliary input vectors Constructing a time-series sliding window sample ; A grouped hidden layer structure corresponding to the variable group is established using a flexible clock-gated cyclic unit network model. Step S4: Based on the group-level true sampling mask and hidden layer subspace index set Generate hidden layer update mask Update the mask according to the hidden layer. The global hidden state at the current moment is obtained by fusing the gated recursive update state and the time-difference decay update state; Step S5: During model training, calculate the importance value of each variable group based on the sensitivity of the hidden layer nodes to the loss function. When the preset expansion conditions are met, select the variable group with the highest smooth importance value to perform incremental expansion of the hidden layer nodes. The output layer parameters are expanded using a function-preserving approach, and are based on real low-frequency operating metrics. With estimation of low-frequency operating indicators The error between them is used to optimize the model parameters.

2. The adaptive soft measurement method for smooth interpolation of multi-sampling-rate industrial processes according to claim 1, characterized in that, In step S1, the target industrial process includes an industrial grinding process, and the low-frequency operating index is the hydrocyclone feed concentration. Let the set of process variables be: ； in, Indicates the number of process variables. Indicates the first One process variable, The process variables include ball mill current, ball mill auger current, ball mill pre-mill water flow rate, and ball mill feed rate; the low-frequency operating indicators are expressed as follows: And the low-frequency operating indicators The sampling interval is greater than or equal to the maximum sampling interval of the process variable; Let the unified timeline be: ； in, Indicates the initial time. Indicates the reference sampling interval. This indicates the number of sampling time points on a unified time axis. Indicates the first A unified timeline moment; the unified timeline refers to a timeline based on a reference sampling interval. A common discrete-time benchmark is constructed for discrete step lengths to map process variables and low-frequency operating indicators with different sampling periods and sampling offsets to the same discrete-time index system, and to characterize the input-output time delay relationship of process variables relative to low-frequency operating indicators; The sampling interval, sampling offset time, and input / output delay of each process variable are expressed as follows: ； in, A positive integer, representing the first... Each process variable relative to the baseline sampling interval The sampling multiple; It is a non-negative integer and satisfies , indicating the first The sampling offset index of each process variable; A non-negative integer, representing the first... The number of time delay steps of each process variable relative to a low-frequency operating indicator; No. The set of actual sampled indices for each process variable is: ； in, Indicates the first A set of true sampling indices of process variables on a unified time axis Indicates the sampling sequence number. Indicates the first The maximum sampling sequence number of each process variable; Low-frequency operating indicators The actual set of sampling indices is: ； in, It is a positive integer, and is greater than or equal to the maximum sampling multiple of the process variable. , The sampling offset index represents the low-frequency operating index. Indicators of low-frequency operation sampling interval, This indicates the maximum sampling sequence number of the low-frequency operating indicator; No. Each process variable is indexed on a unified time axis. The effective observation index after time delay correction is: ； in, Indicates estimated time When corresponding to low-frequency operating indicators, the first The observation index to be used for each process variable; The variable-level true sampling mask is defined as: ； in, Indicates the first The process variables at time 1 After alignment, there are actual sampled values. Indicates the first The process variables at time 1 After alignment, there are no true sampled values. Based on the sampling multiple and the equivalent sampling offset after time delay correction, process variables with consistent sampling alignment are divided into... The nth variable group, the th The equivalent sampling offset after time delay correction for each process variable is defined as: ； All process variables corresponding to different pairs As different sampling alignment modes, and let the number of different sampling alignment modes be . Different sampling alignment modes are numbered one-to-one with variable groups, and the first... Each sampling alignment pattern is denoted as Then the first The variable group is defined as follows: ； in, Indicates the first The sampling multiple corresponding to each variable group Indicates the first Equivalent sampling offset after time delay correction for each variable group; Different sets of variables do not overlap and satisfy the following conditions: ； And all variable groups cover all process variables, that is: ； No. The number of process variables contained in each variable group is: ； The group-level true sampling mask is defined as: ； in, Indicates the first The set of variables at time... A sampling event occurred. Indicates the first The set of variables at time... No sampling event occurred.

3. The adaptive soft measurement method for smooth interpolation of multi-sampling-rate industrial processes according to claim 2, characterized in that, In step S2, the sparse observation matrix, smoothed auxiliary input value, and continuous auxiliary input vector are constructed as follows: Establish a sparse observation matrix: ； in, Indicates the first The first unified timeline index, the first Matrix elements corresponding to each process variable for A matrix of dimension; the elements of the sparse observation matrix are defined as: ； in, Indicates the first The process variables at the observation time after time delay correction The original observations, Indicates a null or missing value; For the Group of variables process variables in Define the causal historical observation set as: ； in, Represents a unified historical timeline index. Indicates the first The maximum historical backtracking steps for each variable group, wherein the causal historical observation set only includes the true sampled values ​​at the current moment and before, and does not include data at future moments; No. The Gaussian time weights for the variable groups are: ； in, Indicates the first Gaussian smoothing parameters for each variable group, and Use a unified timeline step count as the unit; No. Each process variable is indexed on a unified time axis. The smoothing auxiliary input value at the location is: ； in, To prevent constants with a denominator of zero, For the first The mean of each process variable in the training samples; the smoothing auxiliary input value retains the original observation value at the actual sampling time, and performs causal smoothing fill based on the historical actual sampling value at the unsampled time; Arrange all smoothed auxiliary input values ​​of process variables in the order of their original variable numbers to obtain a continuous auxiliary input vector: ； in, It is only used to provide continuous numerical input to the network and does not replace the variable-level true sampling mask. Group-level true sampling mask Control over the hidden state update method.

4. The adaptive soft measurement method for smooth interpolation of multi-sampling-rate industrial processes according to claim 3, characterized in that, In step S3, the method for constructing the temporal sliding window samples and determining the grouped hidden layer structure is as follows: Set low-frequency operation indicators The available tag index set is: ； in, This indicates the unified time axis index corresponding to the low-frequency operation indicator label. Indicates the length of the sliding window; when using the sliding step size At that time, from the set The label indexes are selected in chronological order with the sliding step size to obtain a set of label indexes for training, validation or testing; For any Construct an ordered time series sample using a sliding window: ； The labels of the sliding window samples are: ； in, Indicates time The corresponding low-frequency operating indicators are real observed values, and the model is based on a unified time axis from... to Continuous recursion, and in The low-frequency label time-time output estimate; sliding window length Used to truncate backpropagation training, the initial state of the window is given by the forward recursive cache state, and the hidden state is not shared between the training, validation and test intervals. Sliding window samples Variable-level true sampling mask within the window Window-level group-level true sampling mask and tags Together they constitute the supervised samples, and are divided into training samples, validation samples, and test samples in chronological order; No. The dimension of the hidden subspace of the variable group is: ； in, This represents the allocation coefficient for hidden layer nodes. , Indicates rounding up; The dimension of the global hidden state is: ； Order No. The starting index of the hidden subspace of each variable group is: ； No. Hidden subspace index set corresponding to each variable group Defined as: ； The hidden subspace index sets corresponding to different variable groups do not overlap and satisfy the following: ； ； No. Each variable group is indexed on a unified time axis. The hidden state at that point is ; The hidden states of all variable groups are concatenated as follows: ； in, Indicates a unified timeline index The corresponding global hidden state.

5. The adaptive soft measurement method for smooth interpolation of multi-sampling-rate industrial processes according to claim 4, characterized in that, In step S4, the hidden layer update mask, gated recursive update, time-distance decay update, and global hidden layer state fusion methods are as follows: No. The hidden update mask for each variable group is: ； in, Indicates length is The whole vector; The global hidden layer update mask is: ； in, Used to control whether each hidden layer node performs gated recursive updates; For continuous auxiliary input vectors and the global hidden state at the previous time step Initial global hidden state Initialize the vector to 0, and calculate the candidate gating update state according to the gating loop unit formula: ； ； ； ； in, Indicates an update to the door. This indicates that the door is being reset. This represents the candidate hidden state. Indicates the candidate gating update status; This represents the input weight matrix. Represents the recursive weight matrix. Represents the bias vector; express function, Represents the hyperbolic tangent function. This indicates element-wise multiplication. Continuous auxiliary input vectors are used to provide coupling information across variable groups. The hidden layer update mask only controls whether each hidden layer subspace performs a state update, without restricting the use of smooth auxiliary inputs from other variable groups by the candidate gated update state. For the A set of variables, in At that moment, let: ； The above formula represents the index up to the unified timeline. The index of the most recently occurring sampling event; if this index does not exist, the initial hidden state is used; when If it exists, define the interval step number: ； Define the time-distance attenuation coefficient: ； in, Indicates the first The decay parameters of the variable group And follow The increase and monotonically decrease cause the hidden state of the unsampled variable group to gradually decay; No. The time-lapse decay update status for each variable group is as follows: ； in, Indicates the first The hidden state of each variable group after the most recent real sampling update. For the first The initial state of the hidden layer of each variable group is concatenated with the time-distance decay update state of each variable group as follows: ； The current global hidden state is obtained by fusing the hidden layer update mask: ； Specifically, for variable groups that have experienced sampling events, gated recursive updates are used to absorb new observation information at the current time; for variable groups that have not experienced sampling events, time-distance decay updates are performed based on the number of steps between the current time and the most recent actual sampling time of the variable group.

6. The adaptive soft measurement method for smooth interpolation of multi-sampling-rate industrial processes according to claim 5, characterized in that, In step S5, the calculation method for the sensitivity of hidden layer nodes of each variable group, the function preservation method, the method for expanding output layer parameters, and the model parameter optimization method are as follows: Let the training sample set used for one parameter update be: ,in, Indicates the sample size; for any sample Let its loss function value be... , record the In the group of variables, the first The state value of each hidden node at the end of the sample window is... ,in: ； Regarding the first The first variable in the group of variables Each hidden node introduces a multiplicative gated perturbation coefficient. and in Calculate the first-order sensitivity of the hidden layer node relative to the loss function: ； in, This indicates the degree of first-order local change in the loss function when a multiplicative perturbation is applied to the hidden layer node; For the The root mean square aggregation of the node sensitivities of each hidden node within each variable group yields the nth... Groups of variables in the sample Group sensitivity values: ； The training sample set used for a single parameter update Calculate the average to obtain the first... Current importance values ​​for each variable group: ； The exponential moving average is used to obtain the first... Smoothed importance values ​​for each variable group: ； in, Represents the smoothing coefficient. This indicates the number of parameters updated since the last time. The smoothed importance values ​​for each variable group are initially set to 0. This represents the smoothed importance value after the current parameter update; When the decrease in validation sample loss is less than a preset threshold, and the maximum smoothing importance value is not less than a preset importance threshold, the variable group with the largest smoothing importance value is selected as the expansion object: ； The preset expansion conditions include: the smooth importance value of the expanded object is not lower than a preset importance threshold and the decrease in the loss of the verification sample within a preset training round is lower than a preset threshold; In the New variables added to the hidden subspace corresponding to each variable group There are hidden layer nodes, among which... The value is a positive integer; the newly added hidden layer node logically belongs to the first... The nth variable group, the th The extended hidden subspace index set of the variable groups is defined as follows: ； At the same time, the The dimension of the hidden subspace corresponding to each variable group is determined by... Updated to: ； For other variable groups not selected as expansion objects, their hidden subspace index set and hidden subspace dimension remain unchanged, and newly added hidden nodes are incorporated into the first subspace. In the expanded contiguous hidden subspace of each variable group; after expansion, the starting index and index set of each variable group are recalculated based on the updated dimension of the hidden subspace of each variable group; after expansion, the dimension of the global hidden state is... Updated to: ； The output layer before expansion is: ； in, Indicates the last time of the window Estimated values ​​of low-frequency operating indicators corresponding to the time sample; This represents the global hidden layer state at the end of the sample window. Indicates the output layer weights. Indicates the output layer bias; The extended global hidden state is represented as follows: ； in, This represents the global hidden state at the end of the sample window after structural expansion. This indicates the state of the newly added hidden layer node at the end of the sample window; When adding a new hidden layer node, the input weight matrix, recursive weight matrix, and bias vector in the gated recurrent unit network are simultaneously expanded in dimension. The parameters corresponding to the original hidden layer nodes remain unchanged. The initial recursive connection from the new hidden layer node to the original hidden layer node is set to zero. The input weights, recursive weights, and biases corresponding to the new hidden layer node are initialized with a small amount of randomization. The expanded output layer parameters are initialized as follows: ； ； in, and These represent the output layer weights and output layer biases after the structure expansion, respectively. This represents the zero-weight column corresponding to the newly added hidden layer node. Since the newly added weight in the output layer is zero, the expansion instantaneously yields: ； in, This represents the estimated low-frequency operating parameters after structural expansion. This represents the estimated value of the low-frequency operating index before the structure expansion; therefore, the output layer weight corresponding to the newly added hidden layer node is zero, so that the estimated value of the low-frequency operating index at the moment of structure expansion remains the same as the estimated value of the low-frequency operating index before expansion. During model training, the model loss function is: ； in, Indicates time The corresponding low-frequency operating index values ​​are used to jointly optimize the gated recurrent unit network parameters, time interval decay parameters, newly added parameters after incremental expansion, and output layer parameters based on the loss function during model training.

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