A method for real-time monitoring of operating parameters of a gas production well
By constructing a production correlation index and a dynamic monitoring matrix, and combining deep learning and graph attention features, the problems of monitoring accuracy and adaptability of multi-layered syndicated gas wells were solved, achieving real-time and accurate anomaly early warning, and improving gas well extraction efficiency and safety.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN ACAD OF SAFETY SCI & TECH
- Filing Date
- 2026-05-20
- Publication Date
- 2026-06-16
AI Technical Summary
Existing monitoring technologies for multi-layer syngas wells suffer from problems such as misjudgment of inter-layer interference, low monitoring accuracy, inaccurate feature extraction, and poor model adaptability, making it difficult to achieve real-time monitoring and accurate diagnosis.
By collecting real-time parameters of multi-layer syngas wells, a production correlation index and dynamic monitoring matrix are constructed. Deep learning algorithms are used for feature extraction and processing. Combined with inter-layer dynamic graph attention and temporal multi-scale dilated convolution, the anomaly probability of each layer is output.
It enables real-time and precise monitoring of multi-layered syngas wells, timely detection of subtle anomalies in production parameters, provision of early warnings, and reduction of economic losses.
Smart Images
Figure CN122221116A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of gas well monitoring technology, and specifically to a method for real-time monitoring of the operating parameters of gas wells. Background Technology
[0002] As natural gas extraction enters its middle and late stages, multi-layer syngas extraction, as an efficient extraction method, is widely used in the development of multi-producing gas reservoirs. Syngas technology allows for the simultaneous extraction of multiple independent producing layers through a single wellbore, effectively increasing gas well production and reducing extraction costs. However, abnormal problems encountered during production, such as inter-layer interference and casing leakage, severely impact well extraction efficiency and safe production, becoming a core bottleneck restricting the efficient development of multi-layer syngas reservoirs.
[0003] Currently, existing anomaly monitoring technologies for multi-layered syngas wells suffer from the following shortcomings: First, traditional monitoring methods often rely on static parameters of a single production layer for judgment, neglecting the dynamic interference relationships between different production layers. This can easily lead to misjudging normal inter-layer interference as casing leakage, resulting in low monitoring accuracy. Second, existing monitoring models often employ conventional time-series analysis or single feature extraction methods, failing to effectively capture short-term mutations, medium-term fluctuations, and long-term evolution patterns of production layer parameters. Their sensitivity to early anomalies is insufficient, making early warning difficult. Furthermore, existing deep learning-based monitoring models often use general neural network structures without being customized for the layered characteristics of multi-layered syngas wells. This results in inaccurate feature extraction, poor model adaptability, and low computational efficiency, failing to meet the practical needs of real-time monitoring and accurate diagnosis of multi-layered syngas wells. Summary of the Invention
[0004] To address the above problems, this invention proposes a method for real-time monitoring of operating parameters of gas production wells.
[0005] The technical solution of this invention is: a method for real-time monitoring of operating parameters of a gas production well, comprising the following steps: S1. Use a pressure gauge to collect real-time parameters of multi-layer syngas wells and calculate the production correlation index of each production layer. S2. Construct a dynamic monitoring matrix for each production layer based on the production correlation index of each production layer; S3. Use deep learning algorithms to extract and process features from the dynamic monitoring matrix of each production layer to obtain monitoring results.
[0006] Furthermore, S1 includes the following sub-steps: S11. Use downhole pressure gauges to collect bottom hole flowing pressure of each producing layer in a multi-layered syngas well. S12. Perform squared difference calculation on the formation pressure and bottom hole flowing pressure of each production layer to obtain the expansion pressure coefficient of each production layer. S13. Calculate the ratio between the gas density at the surface and the gas density at the corresponding wellbore location of each production layer, and use it as the extended density coefficient of each layer. S14. Based on the expansion pressure coefficient and expansion density of each production layer, construct a correlation model between pressure drop and production, and obtain the production correlation index of each production layer.
[0007] Furthermore, in S14, the expression for the correlation model between pressure drop and output is: ; in, Indicates the first Output correlation index of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the inner diameter of the wellbore, Indicates the first The output of each production layer.
[0008] In multi-layer commingled wells, fluid composition (especially water cut) significantly affects production capacity. When water production intensifies in a particular layer, the gas density within the wellbore increases, the relative permeability of the gas phase decreases, and production drops at the same pressure differential. To incorporate this change in fluid properties, this invention defines an extended density coefficient. During normal gas production, When the water production is ≈1 or slightly greater than 1, Decrease. Therefore It is the inverse indicator of moisture content.
[0009] This is the density-corrected productivity coefficient. When this layer becomes clogged or accumulates liquid... Increase (a larger pressure differential is needed to maintain production). It may decline, therefore Significantly increased. When water production in this layer intensifies, Decrease, but at the same time It may increase (because the production of water increases flow resistance). A significant decline was the dominant factor, and the overall effect was... An increase (indicating a decrease in efficiency). Therefore, The larger the value, the lower the production efficiency of that layer, and the more likely there are abnormal operating conditions such as blockage, liquid accumulation, or water production.
[0010] Furthermore, in S2, the dynamic monitoring matrix The expression is: ; ; ; ; in, Indicates the first The degree of change in output of each production layer Indicates the first Output correlation index of each production layer Indicates the first Output correlation index of each production layer Indicates the first Output correlation index of each production layer Indicates the first The degree of density variation in the expansion of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The degree of expansion pressure variation in each production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the first The expansion pressure coefficient of each production layer.
[0011] Furthermore, S3 includes the following sub-steps: S31. Normalize the elements of the dynamic monitoring matrix of all production layers at each time step to obtain standardized features. S32. Stack the normalized features of all layers at all time steps to obtain the temporal input tensor; S33. Process each feature slice of the temporal input tensor to obtain multi-scale temporal features and generate a multi-scale temporal feature tensor. S34. After converting the multi-scale temporal features of the feature slices into inter-layer attention features, we obtain the graph attention feature tensor. S34. Concatenate the multi-scale temporal feature tensor and the graph attention feature tensor to generate a fused feature tensor; S35. Perform adaptive average pooling on the fused feature tensor to obtain the global branch; S36. Perform a one-dimensional convolution on the fused feature tensor to obtain local branches; S37. Concatenate the global and local branches along the channel dimension to obtain the fused features, and input the feature vector of each layer of the fused features into the fully connected layer to obtain the anomaly probability of each layer.
[0012] The beneficial effect of the above further scheme is that, in this invention, at each time step, the dynamic monitoring matrix of all layers is obtained. , Indicates the layer number, Indicates the time step number. For each layer The features of all time steps are standardized to obtain the standardized dynamic monitoring matrix. All standardized Stacking them in dimensional order yields a temporal input tensor. Among them, Indicates the first Layer in time step The degree of change in output, Indicates the first Layer in time step The degree of expansion density variation Indicates the first Layer in time step The degree of expansion pressure change, , and These correspond to the standardized degree of change results.
[0013] Multi-scale temporal features can capture characteristics from different time periods, while graph attention features can determine the interference relationships between layers. The multi-scale temporal feature tensor and the graph attention feature tensor are concatenated along the channel dimension to create a more comprehensive feature set. Adaptive average pooling is then applied to the concatenated features to obtain the long-term average state of each layer, ignoring short-term fluctuations and focusing only on the overall trend of the well.
[0014] One-dimensional convolution is performed on the concatenated features using a kernel the same size as the time window, scanning the entire time series at once to capture abrupt changes in a specific layer during this period (e.g., a sudden drop in output or a sudden increase in pressure). The results of the global and local branches are concatenated along the channel dimension, allowing each layer to simultaneously possess both long-term average state and short-term mutation details, and anomaly probabilities are calculated for each layer.
[0015] Furthermore, S33 includes the following sub-steps: S331. The feature slices corresponding to each time step of each layer in the temporal input tensor are processed by the gating bias matrix, gating bias and activation function to obtain the adaptive feature gating weights of each layer at each time step. S332. Use adaptive feature gating weights to perform weighted fusion of feature slices to obtain gated features; S333. Three parallel dilated convolution branches are used to process the gated features of each production layer at each time step, and the outputs of the three branches are concatenated in the channel dimension to obtain multi-scale temporal features. S334. Generate a multi-scale temporal feature tensor based on all multi-scale temporal features.
[0016] The beneficial effects of the above-mentioned further solutions are: In this invention, for the first... Layer in time step The feature slices are compressed using 1×1 one-dimensional convolution, and then subjected to gating weights, biases, and sigmoid activation to dynamically generate feature retention weights for each layer and time step. Inflation coefficients d=1, 2, 4 are used to capture short-term, medium-term, and long-term trends, with each branch corresponding to a convolution kernel and bias.
[0017] Furthermore, in S34, the multi-scale temporal features of each production layer are used as attribute features of nodes in the graph structure to construct a graph topology including several nodes; the multi-scale temporal features of each production layer are concatenated and nonlinearly transformed with the multi-scale temporal features of the other production layers to obtain dynamic edge attention scores, which are then normalized; based on the normalized dynamic attention scores, inter-layer attention features are obtained. Its expression is: ; in, Indicates the first Time step The production layer and the rest of the first Normalized edge weights between production layers This represents the graph convolution weight matrix. This indicates the graph convolution bias. Indicates the total number of floors. Indicates the first Time step Multi-scale temporal characteristics of individual production layers This represents the activation function.
[0018] The beneficial effect of the above-mentioned further solutions is that, in this invention, each production layer... Corresponding to a node in the graph ,node The feature vectors represent the multi-scale temporal features of this layer. Each node in the graph carries the time-varying trends of the layer's productivity, density, and pressure. Time step, number The rest of the layer Inter-layer edge attention scores (unnormalized) Quantitative First The rest of the layer The correlation strength between layers at the current moment. The larger the value, the more synchronized the changes in characteristics such as production capacity and pressure between the two layers, and the stronger the inter-layer interference.
[0019] No. Time step, number The rest of the layer Normalized weights between layers Indicates the first When updating features, the layer starts from the remaining layers. The proportion of information absorbed by each layer; The larger the value, the more likely it is to be the first. Layer of the first The stronger the interference from the layer.
[0020] For each production layer All time steps within the time window of By concatenating along the time dimension, the temporal graph feature matrix of the product layer is obtained. By stacking the temporal graph feature matrices of all product layers along the product layer dimension, the complete graph attention feature tensor is obtained. It is a global 3D tensor for all production layers and all time steps.
[0021] The beneficial effects of this invention are: (1) This invention collects real-time parameters, constructs multiple expansion coefficients, establishes a correlation model between pressure drop and output, obtains the output correlation index, realizes continuous monitoring of stratified output, compares the parameters of each production layer with the upper and lower adjacent layers, and constructs a dynamic monitoring matrix. (2) The present invention designs a deep learning-based inter-layer dynamic graph attention, temporal multi-scale dilated convolution and global-local dual-branch fusion structure to output the abnormal probability of each layer, which can determine whether there is an abnormality in the production layer, detect subtle abnormalities in the production layer parameters in a timely manner, realize early warning of abnormalities, buy time for maintenance and adjustment, and reduce economic losses. Attached Figure Description
[0022] Figure 1 This is a flowchart of a method for real-time monitoring of operating parameters of gas production wells. Detailed Implementation
[0023] The embodiments of the present invention will be further described below with reference to the accompanying drawings.
[0024] like Figure 1 As shown, this invention provides a method for real-time monitoring of operating parameters of a gas production well, comprising the following steps: S1. Use a pressure gauge to collect real-time parameters of multi-layer syngas wells and calculate the production correlation index of each production layer. S2. Construct a dynamic monitoring matrix for each production layer based on the production correlation index of each production layer; S3. Use deep learning algorithms to extract and process features from the dynamic monitoring matrix of each production layer to obtain monitoring results.
[0025] In this embodiment of the invention, S1 includes the following sub-steps: S11. Use downhole pressure gauges to collect bottom hole flowing pressure of each producing layer in a multi-layered syngas well. S12. Perform squared difference calculation on the formation pressure and bottom hole flowing pressure of each production layer to obtain the expansion pressure coefficient of each production layer. S13. Calculate the ratio between the gas density at the surface and the gas density at the corresponding wellbore location of each production layer, and use it as the extended density coefficient of each layer. S14. Based on the expansion pressure coefficient and expansion density of each production layer, construct a correlation model between pressure drop and production, and obtain the production correlation index of each production layer.
[0026] In this embodiment of the invention, in S14, the expression for the correlation model between pressure drop and output is: ; in, Indicates the first Output correlation index of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the inner diameter of the wellbore, Indicates the first The flow rate of the produced gas in the wellbore. This indicates the unit conversion factor.
[0027] In this embodiment of the invention, in multi-layer commingled wells, fluid composition (especially water cut) significantly affects production capacity. When water production intensifies in a certain layer, the gas density within the wellbore increases, the relative permeability of the gas phase decreases, and production decreases under the same pressure differential. To take this change in fluid properties into account, this invention defines an extended density coefficient. During normal gas production, When the water production is ≈1 or slightly greater than 1, Decrease. Therefore It is the inverse indicator of moisture content.
[0028] This is the density-corrected productivity coefficient. When this layer becomes clogged or accumulates liquid... Increase (a larger pressure differential is needed to maintain production). It may decline, therefore Significantly increased. When water production in this layer intensifies, Decrease, but at the same time It may increase (because the production of water increases flow resistance). A significant decline was the dominant factor, and the overall effect was... An increase (indicating a decrease in efficiency). Therefore, The larger the value, the lower the production efficiency of that layer, and the more likely there are abnormal operating conditions such as blockage, liquid accumulation, or water production.
[0029] In this embodiment of the invention, in S2, the dynamic monitoring matrix The expression is: ; ; ; ; in, Indicates the first The degree of change in output of each production layer Indicates the first Output correlation index of each production layer Indicates the first Output correlation index of each production layer Indicates the first Output correlation index of each production layer Indicates the first The degree of density variation in the expansion of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The degree of expansion pressure variation in each production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the first The expansion pressure coefficient of each production layer.
[0030] In this embodiment of the invention, S3 includes the following sub-steps: S31. Normalize the elements of the dynamic monitoring matrix of all production layers at each time step to obtain standardized features. S32. Stack the normalized features of all layers at all time steps to obtain the temporal input tensor; S33. Process each feature slice of the temporal input tensor to obtain multi-scale temporal features and generate a multi-scale temporal feature tensor. S34. After converting the multi-scale temporal features of the feature slices into inter-layer attention features, we obtain the graph attention feature tensor. S34. Concatenate the multi-scale temporal feature tensor and the graph attention feature tensor to generate a fused feature tensor; S35. Perform adaptive average pooling on the fused feature tensor to obtain the global branch; S36. Perform a one-dimensional convolution on the fused feature tensor to obtain local branches; S37. Concatenate the global and local branches along the channel dimension to obtain the fused features, and input the feature vector of each layer of the fused features into the fully connected layer to obtain the anomaly probability of each layer.
[0031] The beneficial effect of the above further scheme is that, in this invention, at each time step, the dynamic monitoring matrix of all layers is obtained. , Indicates the layer number, Indicates the time step number. For each layer The features of all time steps are standardized to obtain the standardized dynamic monitoring matrix. All standardized Stacking them in dimensional order yields a temporal input tensor. Among them, Indicates the first Layer in time step The degree of change in output, Indicates the first Layer in time step The degree of expansion density variation Indicates the first Layer in time step The degree of expansion pressure change, , and These correspond to the standardized degree of change results.
[0032] Multi-scale temporal features can capture characteristics from different time periods, while graph attention features can determine the interference relationships between layers. The multi-scale temporal feature tensor and the graph attention feature tensor are concatenated along the channel dimension to create a more comprehensive feature set. Adaptive average pooling is then applied to the concatenated features to obtain the long-term average state of each layer, ignoring short-term fluctuations and focusing only on the overall trend of the well.
[0033] One-dimensional convolution is performed on the concatenated features using a kernel the same size as the time window, scanning the entire time series at once to capture abrupt changes in a specific layer during this period (e.g., a sudden drop in output or a sudden increase in pressure). The results of the global and local branches are concatenated along the channel dimension, allowing each layer to simultaneously possess both long-term average state and short-term mutation details, and anomaly probabilities are calculated for each layer.
[0034] In this embodiment of the invention, S33 includes the following sub-steps: S331. The feature slices corresponding to each time step of each layer in the temporal input tensor are processed by the gating bias matrix, gating bias and activation function to obtain the adaptive feature gating weights of each layer at each time step. S332. Use adaptive feature gating weights to perform weighted fusion of feature slices to obtain gated features; S333. Three parallel dilated convolution branches are used to process the gated features of each production layer at each time step, and the outputs of the three branches are concatenated in the channel dimension to obtain multi-scale temporal features. S334. Generate a multi-scale temporal feature tensor based on all multi-scale temporal features.
[0035] The beneficial effects of the above-mentioned further solutions are: In this invention, for the first... Layer in time step The feature slices are compressed using 1×1 one-dimensional convolution, and then subjected to gating weights, biases, and sigmoid activation to dynamically generate feature retention weights for each layer and time step. Inflation coefficients d=1, 2, 4 are used to capture short-term, medium-term, and long-term trends, with each branch corresponding to a convolution kernel and bias.
[0036] In this embodiment of the invention, in step S34, the multi-scale temporal features of each production layer are used as attribute features of nodes in the graph structure to construct a graph topology including several nodes; the multi-scale temporal features of each production layer are concatenated and nonlinearly transformed with the multi-scale temporal features of the remaining production layers to obtain dynamic edge attention scores, which are then normalized; based on the normalized dynamic attention scores, inter-layer attention features are obtained. Its expression is: ; in, Indicates the first Time step The production layer and the rest of the first Normalized edge weights between production layers This represents the graph convolution weight matrix. This indicates the graph convolution bias. Indicates the total number of floors. Indicates the first Time step Multi-scale temporal characteristics of individual production layers This represents the activation function.
[0037] The beneficial effect of the above-mentioned further solutions is that, in this invention, each production layer... Corresponding to a node in the graph ,node The feature vectors represent the multi-scale temporal features of this layer. Each node in the graph carries the time-varying trends of the layer's productivity, density, and pressure. Time step, number The rest of the layer Inter-layer edge attention scores (unnormalized) Quantitative First The rest of the layer The correlation strength between layers at the current moment. The larger the value, the more synchronized the changes in characteristics such as production capacity and pressure between the two layers, and the stronger the inter-layer interference.
[0038] No. Time step, number The rest of the layer Normalized weights between layers Indicates the first When updating features, the layer starts from the remaining layers. The proportion of information absorbed by each layer; The larger the value, the more likely it is to be the first. Layer of the first The stronger the interference from the layer.
[0039] For each production layer All time steps within the time window of By concatenating along the time dimension, the temporal graph feature matrix of the product layer is obtained. By stacking the temporal graph feature matrices of all product layers along the product layer dimension, the complete graph attention feature tensor is obtained. It is a global 3D tensor for all production layers and all time steps.
[0040] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.
Claims
1. A method for real-time monitoring of operating parameters of a gas production well, characterized in that, Includes the following steps: S1. Use a pressure gauge to collect real-time parameters of multi-layer syngas wells and calculate the production correlation index of each production layer. S2. Construct a dynamic monitoring matrix for each production layer based on the production correlation index of each production layer; S3. Use deep learning algorithms to extract and process features from the dynamic monitoring matrix of each production layer to obtain monitoring results.
2. The method for real-time monitoring of operating parameters of a gas production well according to claim 1, characterized in that, S1 includes the following sub-steps: S11. Use downhole pressure gauges to collect bottom hole flowing pressure of each producing layer in a multi-layered syngas well. S12. Perform squared difference calculation on the formation pressure and bottom hole flowing pressure of each production layer to obtain the expansion pressure coefficient of each production layer. S13. Calculate the ratio between the gas density at the surface and the gas density at the corresponding wellbore location of each production layer, and use it as the extended density coefficient of each layer. S14. Based on the expansion pressure coefficient and expansion density of each production layer, construct a correlation model between pressure drop and production, and obtain the production correlation index of each production layer.
3. The method for real-time monitoring of operating parameters of a gas production well according to claim 2, characterized in that, In S14, the expression for the correlation model between pressure drop and output is: ； in, Indicates the first Output correlation index of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the inner diameter of the wellbore, Indicates the first The flow rate of the produced gas in the wellbore. This indicates the unit conversion factor.
4. The method for real-time monitoring of operating parameters of a gas production well according to claim 1, characterized in that, In S2, the dynamic monitoring matrix The expression is: ； ； ； ； in, Indicates the first The degree of change in output of each production layer Indicates the first Output correlation index of each production layer Indicates the first Output correlation index of each production layer Indicates the first Output correlation index of each production layer Indicates the first The degree of density variation in the expansion of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The expansion density coefficient of each production layer Indicates the first The degree of expansion pressure variation in each production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the first The expansion pressure coefficient of the individual production layer Indicates the first The expansion pressure coefficient of each production layer.
5. The method for real-time monitoring of operating parameters of a gas production well according to claim 1, characterized in that, S3 includes the following sub-steps: S31. Normalize the elements of the dynamic monitoring matrix of all production layers at each time step to obtain standardized features. S32. Stack the normalized features of all layers at all time steps to obtain the temporal input tensor; S33. Process each feature slice of the temporal input tensor to obtain multi-scale temporal features and generate a multi-scale temporal feature tensor. S34. After converting the multi-scale temporal features of the feature slices into inter-layer attention features, we obtain the graph attention feature tensor. S34. Concatenate the multi-scale temporal feature tensor and the graph attention feature tensor to generate a fused feature tensor; S35. Perform adaptive average pooling on the fused feature tensor to obtain the global branch; S36. Perform a one-dimensional convolution on the fused feature tensor to obtain local branches; S37. Concatenate the global and local branches along the channel dimension to obtain the fused features, and input the feature vector of each layer of the fused features into the fully connected layer to obtain the anomaly probability of each layer.
6. The method for real-time monitoring of operating parameters of a gas production well according to claim 5, characterized in that, S33 includes the following sub-steps: S331. The feature slices corresponding to each time step of each layer in the temporal input tensor are processed by the gating bias matrix, gating bias and activation function to obtain the adaptive feature gating weights of each layer at each time step. S332. Use adaptive feature gating weights to perform weighted fusion of feature slices to obtain gated features; S333. Three parallel dilated convolution branches are used to process the gated features of each production layer at each time step, and the outputs of the three branches are concatenated in the channel dimension to obtain multi-scale temporal features. S334. Generate a multi-scale temporal feature tensor based on all multi-scale temporal features.
7. The method for real-time monitoring of operating parameters of a gas production well according to claim 5, characterized in that, In step S34, the multi-scale temporal features of each production layer are used as attribute features of nodes in the graph structure to construct a graph topology including several nodes; the multi-scale temporal features of each production layer are concatenated and nonlinearly transformed with the multi-scale temporal features of the other production layers to obtain dynamic edge attention scores, which are then normalized; based on the normalized dynamic attention scores, inter-layer attention features are obtained. Its expression is: ； in, Indicates the first Time step The production layer and the rest of the first Normalized edge weights between production layers This represents the graph convolution weight matrix. This indicates the graph convolution bias. Indicates the total number of floors. Indicates the first Time step Multi-scale temporal characteristics of individual production layers This represents the activation function.