Gas sensor dynamic response modeling method based on liquid continuous time network

Abstract

The invention discloses a gas sensor dynamic response modeling method based on a liquid continuous time network, and belongs to the technical field of gas sensors, and the method specifically comprises the following steps: testing mixed gas through a gas sensor array, generating a response curve group, forming a sample point with a concentration sequence group, and intercepting the response sequence group; constructing an initial sample set comprising a concentration sequence group, a response sequence and a real time interval sequence; a continuous time dynamic response neural network model is constructed and trained, and a continuous time closed-form solution neural network unit is specifically used as a core calculation unit. According to the method, the real time interval sequence is used as input, so that the modeling precision and the physical authenticity can be improved. The invention further discloses a self-training data enhancement strategy, an effective way is provided for solving the model training problem under the small sample condition, and the generalization ability and robustness of the model on the aspect of unseen data are improved.

Description

Technical Field

[0001] This invention belongs to the field of gas sensor technology, specifically relating to a dynamic response modeling method for gas sensors based on a liquid continuous-time network. Background Technology

[0002] In the fields of industrial process monitoring and environmental pollutant detection, the demand for dynamic detection of multi-component mixed gases using resistive gas sensors is increasing. Traditional dynamic modeling methods mainly rely on discrete time series analysis or kinetic modeling based on empirical equations. While these methods can describe the response trend of gas sensors to some extent, their inherent discretization makes it difficult to accurately capture the transient response characteristics of gas sensors under conditions of abrupt concentration changes. The working mechanism of a gas sensor is essentially a continuous dynamic process involving multiple coupled physicochemical processes, such as the diffusion of gas molecules on the surface of the sensitive material, the establishment of adsorption-desorption equilibrium, and the real-time changes in carrier mobility. Forcibly discretizing these continuous processes not only leads to the loss of dynamic information but also introduces additional modeling errors.

[0003] In recent years, liquid neural networks have emerged as a novel method for processing dynamic systems. They directly describe the state evolution of a system through differential equations, and the continuous time-varying nature of their internal states aligns closely with the actual working mechanism of gas sensors. This continuous-time modeling approach naturally describes the multi-timescale dynamic behavior involved in the gas sensor response, offering new possibilities for accurate modeling. However, the original implementation of liquid neural networks typically requires solving differential equations using complex numerical integration methods, which not only incurs high computational costs but also limits its feasibility in real-time applications.

[0004] Closed-loop continuous-time networks, as an important evolution of liquid neural networks, cleverly circumvent the computational bottleneck of numerical integration by introducing a closed-loop approximation solution method. This method significantly improves the training and inference efficiency of the model while retaining the ability of liquid networks to continuously describe dynamic systems. Specifically, in modeling the dynamic response of gas sensors, closed-loop continuous-time networks naturally describe the continuous evolution of the gas sensor's response state over time through parameterized differential equations. This accurately captures the competitive adsorption kinetics of different gas molecules on surface active sites in mixed gas environments, and the resulting nonlinear changes in carrier mobility. This mechanism-based modeling approach not only improves the physical interpretability of the model but also enhances its generalization ability to unknown concentration combinations.

[0005] More importantly, closed-loop continuous-time networks exhibit superior few-sample learning characteristics. Their closed-loop solution mechanism enables them to quickly extract dynamic response features of gas sensors from limited experimental data, significantly reducing the complexity and cost of mixed gas testing. Simultaneously, this method inherits the inherent dynamic stability and robustness to input perturbations of liquid neural networks, making the constructed model more adaptable to gas sensor response noise and environmental changes.

[0006] Based on this, this invention proposes a dynamic response modeling method for gas sensors based on closed-loop continuous-time networks, which is more suitable for small-sample modeling. Compared with traditional modeling methods, this invention achieves a better balance between modeling accuracy, efficiency, and practicality, providing a novel technical approach for real-time dynamic monitoring of mixed gas sensors. Summary of the Invention

[0007] To address the technical problems existing in the prior art, this invention provides a method for modeling the dynamic response of gas sensors based on a liquid continuous-time network. By utilizing a closed-form continuous-time (CfC) neural network model, it explicitly handles non-uniform real time intervals to accurately fit the continuous physical dynamic process of the sensor. Simultaneously, it incorporates a coarse-to-fine training strategy to enhance the data samples. This invention aims to reduce the difficulty of training a high-precision dynamic response model under small sample and non-uniform sampling conditions, enabling the final model to achieve high-precision predictions with limited data, quickly adapting to the nonlinear dynamic characteristics of different gas sensors, and providing reliable and effective data for gas sensor dynamic response simulation and subsequent component identification and concentration prediction tasks.

[0008] The technical solution adopted in this invention is as follows:

[0009] A method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network includes the following steps:

[0010] Step 1: Test the mixed gas using a gas sensor array. The number of sensors in the gas sensor array is N, and the number of gas types in the mixed gas is N. Each sensor corresponds one-to-one with a gas type. Each sensor outputs a response curve with a timestamp. The N-dimensional timestamp-aligned response curve set output by the gas sensor array, together with the N-dimensional concentration sequence set of the tested mixed gas, constitutes a single sample point. The initial timestamp in the N-dimensional concentration sequence set... The corresponding N-dimensional concentrations are all 0, and the N-dimensional concentrations corresponding to subsequent timestamps remain unchanged.

[0011] M sample points were obtained by testing mixed gases with M different component concentrations;

[0012] Step 2: For M sample points, extract a response sequence of length L from the response curve group of each sample point, starting from the initial response.

[0013] Step 3, construct the first The initial sample set of the gases, the specific process is as follows:

[0014] For the The response sequence set of each sample point is used to extract the N-dimensional concentration sequence set of the tested gas mixture. , No. One-dimensional response sequence of a gas And, based on the timestamp sequence corresponding to the response sequence group, calculate the difference between adjacent timestamps. , Indicates the first Each timestamp, initial timestamp difference , generation and 1D True Time Interval Sequence Aligned with Timestamps ;

[0015] and then , and Constituting the first The initial samples corresponding to the nth sample point, and the initial samples of all sample points constitute the nth sample point. An initial sample set of the gases;

[0016] Step 4, for the first The initial sample set of the gas and Perform Z-score standardization to obtain the [number]th [score]. The standardized initial sample set of the gases is used as the training set;

[0017] Step 5: Construct a continuous-time dynamic response neural network model and train it based on the training set, specifically using an N-dimensional concentration sequence set and a 1-dimensional true time interval sequence as input. The one-dimensional response sequence of a gas is used as the output. A continuous-time closed-loop neural network unit is used as the core computational unit for iterative solution to obtain the first... A training-based continuous-time dynamic response neural network model for a gas.

[0018] Furthermore, in step 5, the solution is iteratively performed for each timestamp of each sample point in the training set, totaling... The specific process of solving one iteration is as follows:

[0019] Step 5.1, record the first training session. The sample point at the th th The N-dimensional concentration group of timestamps is The hidden state of the previous timestamp is Then the two are spliced ​​together to obtain the fusion feature. Among them, the hidden state of the initial timestamp It is a random value; Indicates feature splicing;

[0020] Step 5.2: Merge features The input is a sequentially stacked network consisting of one fully connected layer and one dropout layer. High-dimensional shared features are extracted. ;in, Indicates a sequentially stacked network;

[0021] Step 5.3: Shared features Input three independent fully connected layers respectively , get output , and ;

[0022] Step 5.4, utilize and Computational gating And thus update the first Hidden state of timestamps ;in, and All of these are trainable state parameters; Represents the sigmoid function;

[0023] Step 5.5, place the first Hidden state after timestamp update Through a fully connected output layer, we obtain the first... Predicted response value for each timestamp ;in, and These represent the weights and biases of the fully connected output layer, respectively.

[0024] Furthermore, the activation function of the fully connected layer in step 5.2 is... .

[0025] Furthermore, in step 5.3 , and The activation functions are respectively , and .

[0026] Furthermore, in order to achieve model training under small sample conditions, the result obtained in step 5 is... After training the continuous-time dynamic response neural network model for the gas, the following steps are also included:

[0027] Step 6: Apply random perturbation to the response sequence group of M sample points according to the corresponding timestamp sequence to generate Q enhanced concentration feature sequences. and the corresponding enhanced time interval sequence To obtain the augmented dataset ;in, ;

[0028] Step 7, using the result obtained in Step 5... Using the trained continuous-time dynamic response neural network model of the gas as the initial model, the augmented dataset will be... Input into the initial model to generate the first... Predicted response value label set for a type of gas , with augmented dataset Together they form the enhanced training set;

[0029] Step 8: Merge the dimensions of the enhanced training set obtained in Step 7 and the training set obtained in Step 4 to form a new training set; construct a new model identical to the continuous-time dynamic response neural network model described in Step 5, and train it based on the new training set to obtain the first... An enhanced continuous-time dynamic response neural network model for a certain gas.

[0030] Furthermore, in step 6, based on the first The first sample point One-dimensional response sequence of a gas All the generated enhanced concentration feature sequences constitute a sequence set. Its generation formula is:

[0031]

[0032] in, For the first The first sample point The L-dimensional concentration sequence of a gas; It is an N-dimensional amplitude scaling vector based on a uniform distribution; For Gaussian distribution The noise tensor of dimension 1.

[0033] Furthermore, the uniform distribution is as follows: Gaussian distribution .

[0034] Furthermore, in step 7, the first... Predicted response value label set for a type of gas The specific calculation process is as follows:

[0035] Step 7.1: Based on Step 4, obtain the statistics calculated during the Z-score standardization process, including... mean and standard deviation ,as well as mean and standard deviation ;

[0036] Step 7.2, for Z-score normalization was performed to obtain the normalized enhanced concentration feature sequence. ;

[0037] Step 7.3: Using the initial model, generate the first... Predicted response value tag set for a type of gas before treatment ;in, Indicates the initial model;

[0038] Step 7.4, for Perform destandardization to obtain .

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] 1. This invention proposes a dynamic response modeling method for gas sensors based on a liquid continuous-time network. By introducing a continuous-time closed-loop solution neural network, it effectively addresses some limitations of traditional discrete-time models in processing gas sensor data. Specifically, existing time-series models are generally based on the "discrete-time" assumption, assuming that the time step is uniform and fixed. However, this assumption differs from the reality of the physical process of gas sensors (a continuous dynamic evolution) and actual data acquisition (often non-uniform sampling). This invention explicitly uses the "real time interval" sequence as model input, enabling the neural network to solve the evolution of hidden states based on the actual passage of time. This design aims to solve the model distortion problem caused by irregular sampling data. Its model mechanism is more consistent with the continuous physicochemical dynamic process of the sensor, thus helping to improve modeling accuracy and physical realism.

[0041] 2. The model structure of this invention is simple, realizing end-to-end dynamic response modeling and significantly simplifying the complexity of data preprocessing. Specifically, the model reduces reliance on complex artificial feature engineering; it directly uses the original (normalized) concentration sequence and time interval sequence as input and directly outputs the target response sequence. The backbone network and functional heads within the model can automatically extract the required high-dimensional features from the original time-series data, capturing the transient dynamic characteristics of the gas adsorption-desorption process. This end-to-end characteristic greatly reduces the difficulty of model implementation and the complexity of parameter tuning.

[0042] 3. Preferably, the present invention proposes a self-training data augmentation strategy, which provides an effective way to solve the model training problem under small sample conditions. Specifically, it adopts the strategy of "initial model - generating samples - augmenting model", which can expand the amount of training data from dozens to thousands. The augmented data generated can also help alleviate the overfitting problem of deep learning under small sample conditions, and effectively improve the generalization ability and robustness of the model on unseen data.

[0043] 4. The model proposed in this invention has a simple structure and a concise and efficient training process, which helps to shorten the model iteration cycle and training time. Specifically, the hidden state dimension of the model is a fixed hyperparameter that does not require complex offline computation, and the number of parameters in the backbone network is also small. Both the "initial model" and the "enhanced model" are trained using the same end-to-end model structure. When training the "enhanced model", the model is trained completely from the merged dataset without changing the model structure. This simplified training process reduces cumbersome model reorganization or multi-stage analysis steps, making the model iteration faster, deployment and maintenance more convenient, and the computational resources and time costs required for training relatively low. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the response signal of the mixed gas in Example 1;

[0045] Figure 2 This is a schematic diagram of the overall network structure of the continuous-time dynamic response neural network model in Example 1;

[0046] Figure 3 This is a detailed internal structural diagram of the continuous-time closed-loop neural network unit in Example 1;

[0047] Figure 4 This is a schematic diagram of the response curve of the predicted response value label generated by the initial model in Example 2;

[0048] Figure 5 The curve showing the decrease in the mean squared error loss function (MSE) of the enhanced model during the training process in Example 2 is shown.

[0049] Figure 6 This shows the fitting of the predicted response curve and the true response curve of the enhanced model in Example 2;

[0050] Figure 7 This is a relative error distribution diagram of the enhanced model in Example 2. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this invention are only for explaining this invention and are not intended to limit this invention.

[0052] Example 1

[0053] This embodiment proposes a dynamic response modeling method for gas sensors based on liquid continuous-time networks, including the following steps:

[0054] Step 1: The mixed gas is tested using a gas sensor array. The number of sensors in the array is N=3, and the number of gas types in the mixed gas is N=3. Each sensor corresponds one-to-one with a gas type. The components of the mixed gas include hydrogen (H2), ammonia (NH3), and nitrogen dioxide (NO2). During the test, all N sensors operate simultaneously, and each sensor outputs a response curve with a timestamp, such as... Figure 1 As shown, the N-dimensional timestamp-aligned response curves output by the gas sensor array, together with the N-dimensional concentration sequence of the tested gas mixture, form a single sample point; the initial timestamp in the N-dimensional concentration sequence... The corresponding N-dimensional concentrations are all 0, and the N-dimensional concentrations corresponding to subsequent timestamps remain unchanged.

[0055] M sample points were obtained by testing mixed gases with M different component concentrations;

[0056] In this embodiment, the preset gas concentrations of H2 component are 8000ppm, 16000ppm, 24000ppm and 32000ppm, the gas concentrations of NH3 component are 10ppm, 20ppm, 30ppm, 40ppm and 50ppm, and the gas concentrations of NO2 component are 2ppm, 4ppm, 6ppm, 8ppm and 10ppm.

[0057] Step 2: For M sample points, for each sample point, take the initial response as the starting point and extract a response sequence of length L=50, such as... Figure 1 As shown;

[0058] Step 3, construct the first The initial sample set of the gases, the specific process is as follows:

[0059] For the The response sequence set of each sample point is used to extract the N-dimensional concentration sequence set of the tested gas mixture. , No. One-dimensional response sequence of a gas And, based on the timestamp sequence corresponding to the response sequence group, calculate the difference between adjacent timestamps. , Indicates the first Each timestamp, initial timestamp difference , generation and 1D True Time Interval Sequence Aligned with Timestamps This is used to characterize the continuous-time characteristics and sampling non-uniformity of the sensor response;

[0060] in, , and The length in the time dimension is L;

[0061] and then , and Constituting the first The initial samples corresponding to the nth sample point, and the initial samples of all sample points constitute the nth sample point. An initial sample set of the gases;

[0062] Step 4: To eliminate the influence of different physical dimensions, the first... The initial sample set of the gas and Perform Z-score standardization to obtain the [number]th [score]. The standardized initial sample set of the gases is used as the training set;

[0063] The specific formula for Z-score standardization is as follows:

[0064]

[0065] In the formula, Represents the original data points; This indicates that the data points have been standardized. and These represent the mean and standard deviation of all original data points for this feature, respectively.

[0066] Step 5: Construct the structure as follows Figure 2 The continuous-time dynamic response neural network model shown is trained on a training set, specifically using an N-dimensional concentration sequence set and a 1-dimensional real time interval sequence as input. The output is a one-dimensional response sequence of a gas, using a structure such as Figure 3 The continuous-time closed-loop solution neural network unit shown is used as the core computational unit (forward propagation) for iterative solution to obtain the th... A training-based continuous-time dynamic response neural network model for a gas;

[0067] This involves iteratively solving for each timestamp of each sample point in the training set, totaling... The specific process of solving one iteration is as follows:

[0068] Step 5.1, record the first training session. The sample point at the th th The N-dimensional concentration of each timestamp is The hidden state of the previous timestamp is Then the two are spliced ​​together to obtain the fusion feature. Among them, the hidden state of the initial timestamp It is a random value; Indicates feature splicing;

[0069] Step 5.2: Merge features The input is a sequentially stacked network consisting of one fully connected layer and one randomly deactivated layer. High-dimensional shared features are extracted. ;in, This represents a sequentially stacked network; the fully connected layer has 32 units, and the activation function is... The proportion of randomly deactivated layers is 0.1.

[0070] Step 5.3: Shared features Input three independent fully connected layers respectively , get output , and ;in, The time constant of the system determines how much information is retained and how much new information is accepted. It is the proposed update value calculated based on the current input and state, which represents the direction that the external input wants to push the system state in at the current time step (nonlinear transformation). The baseline component, typically responsible for maintaining long-term memory or processing states, and Complementarity ensures the stability of system behavior when the time constant is extremely large or extremely small;

[0071] , and The activation functions are respectively , and The mathematical expression is as follows:

[0072]

[0073]

[0074]

[0075] In the formula, Indicates the input value; Represents the hyperbolic tangent function;

[0076] Step 5.4, utilize and Computational gating And thus update the first Hidden state of timestamps ;in, and All of these are trainable state parameters; Represents the sigmoid function;

[0077] Step 5.5, place the first Hidden state after timestamp update Through a fully connected output layer, we obtain the first... Predicted response value for each timestamp ;in, and These represent the weights and biases of the fully connected output layer, respectively.

[0078] Furthermore, during the training process in step 5, the loss function is the Mean Squared Error (MSE); the optimizer uses an Adaptive Moment Estimator (AdamW) with weight decay, setting the learning rate to 0.001 and the weight decay to 1e. -5 The iteration count is 200 rounds; the batch size is 16; the callback function uses a dynamic learning rate decay strategy, with a waiting period of 15 rounds. After training, the model weights are saved, and the result is obtained. A training-based continuous-time dynamic response neural network model for a gas.

[0079] Example 2

[0080] Assuming the total number of sample points M=69 in Example 1, in order to achieve model training under small sample conditions, this example proposes a self-training data augmentation strategy based on Example 1, which specifically includes the following steps:

[0081] Steps 1-5: Referring to Example 1, obtain the first... A continuous-time dynamic response neural network model of a certain gas was trained and used as the initial model;

[0082] Step 6: Apply random perturbation to the response sequence group of M sample points according to the corresponding timestamp sequence to generate Q=2000 enhanced concentration feature sequences. and the corresponding enhanced time interval sequence To obtain the augmented dataset ;

[0083] Specifically, based on the first The first sample point One-dimensional response sequence of a gas All the generated enhanced concentration feature sequences constitute a sequence set. Its generation formula is:

[0084]

[0085] in, For the first The first sample point The L-dimensional concentration sequence of a gas; Based on uniform distribution An N-dimensional magnitude scaling vector; Based on Gaussian distribution of The noise tensor of a dimension;

[0086] Step 7: Augment the dataset Input into the initial model to generate the first Predicted response value label set for a type of gas , with augmented dataset Together they form the enhanced training set;

[0087] Among them, the generation of the first Predicted response value label set for a type of gas The specific calculation process is as follows:

[0088] Step 7.1: Obtain the statistics calculated during the Z-score standardization process based on Step 4 of Example 1, including... mean and standard deviation ,as well as mean and standard deviation ;

[0089] Step 7.2, for Z-score normalization was performed to obtain the normalized enhanced concentration feature sequence. ;

[0090] Step 7.3: Using the initial model, generate the first... Predicted response value tag set for a type of gas before treatment ;in, Indicates the initial model;

[0091] Step 7.4, for Perform destandardization to obtain ;

[0092] Figure 4 Two randomly selected items A schematic diagram of the response curves of the predicted response value labels for a gas;

[0093] Step 8: Merge the dimensions of the enhanced training set obtained in Step 7 and the training set obtained in Step 4 of Example 1 to form a new training set containing 2069 sample points; construct a new model identical to the continuous-time dynamic response neural network model described in Step 5 of Example 1, and train it based on the new training set to obtain the first... An enhanced continuous-time dynamic response neural network model for a gas, also known as an enhanced model.

[0094] Furthermore, during the training process in step 8, the loss function is the mean squared error (MSE), and the loss function descent curve is shown below. Figure 5 As shown; the optimizer uses AdamW, with a learning rate of 0.0005 and weight decay of 1e. -5 The iteration count is 400 rounds; the batch size is 128; the callback function uses a dynamic learning rate decay strategy, with a waiting period of 15 rounds. After training, the model weights are saved, and the result is obtained. An enhanced continuous-time dynamic response neural network model for a certain gas.

[0095] Taking the H2 sensor (PdNi) as an example, this embodiment uses the above model parameters to model the dynamic response of the H2 sensor. The fitting relationship between the predicted response curve of the enhanced model and the actual response curve is as follows: Figure 6 As shown; the relative error results obtained from the test are as follows. Figure 7 As shown, the mean relative error (MRE) of the model prediction is only 0.03%, and the relative errors of all data are within the range of 3σ; at the 95% confidence interval, the confidence range is [-0.1297%, 0.1382%], achieving the effect of simplified requirements and accurate prediction.

[0096] In summary, this invention provides a method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network. In practical applications, high-precision modeling of the dynamic response of a gas sensor can be achieved by using a combination of test concentrations and real time intervals. Combined with a self-training data augmentation strategy, a response curve covering the working concentration range of the gas sensor can be reconstructed using a small number of actual test samples.

[0097] It should be noted that this is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network, characterized in that, Includes the following steps: Step 1: Test the mixed gas using a gas sensor array. The number of sensors in the gas sensor array is N, and the number of gas types in the mixed gas is N. Each sensor corresponds one-to-one with a gas type. Each sensor outputs a response curve with a timestamp. The N-dimensional timestamp-aligned response curve set output by the gas sensor array, together with the N-dimensional concentration sequence set of the tested mixed gas, constitutes a single sample point. The initial timestamp in the N-dimensional concentration sequence set... The corresponding N-dimensional concentrations are all 0, and the N-dimensional concentrations corresponding to subsequent timestamps remain unchanged. M sample points were obtained by testing mixed gases with M different component concentrations; Step 2: For M sample points, for each response curve group, take the start response as the starting point and extract a response sequence group of length L; Step 3, construct the first The initial sample set of the gases, the specific process is as follows: For the From the response sequence set of each sample point, extract the N-dimensional concentration sequence set. , No. One-dimensional response sequence of a gas And, based on the timestamp sequence corresponding to the response sequence group, calculate the difference between adjacent timestamps. , Indicates the first Each timestamp, initial timestamp difference , generation and 1D True Time Interval Sequence Aligned with Timestamps ; and then , and Constituting the first The initial samples corresponding to the nth sample point, and the initial samples of all sample points constitute the nth sample point. An initial sample set of the gases; Step 4, for and Perform Z-score standardization to obtain the [number]th [score]. The standardized initial sample set of the gases is used as the training set; Step 5: Construct a continuous-time dynamic response neural network model and train it based on the training set, specifically using an N-dimensional concentration sequence set and a 1-dimensional true time interval sequence as input. The one-dimensional response sequence of a gas is used as the output. A continuous-time closed-loop neural network unit is used as the core computational unit for iterative solution to obtain the first... A training-based continuous-time dynamic response neural network model for a gas.

2. The method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network according to claim 1, characterized in that, In step 5, the solution is iteratively performed for each timestamp of each sample point in the training set, totaling... The specific process of solving one iteration is as follows: Step 5.1, record the first training session. The sample point at the th th The N-dimensional concentration group of timestamps is The hidden state of the previous timestamp is Then the two are spliced ​​together to obtain the fusion feature. Among them, the hidden state of the initial timestamp It is a random value; Indicates feature splicing; Step 5.2: Merge features Input a sequentially stacked network consisting of one fully connected layer and one randomly deactivated layer, and extract shared features. ;in, Indicates a sequentially stacked network; Step 5.3: Shared features Input three independent fully connected layers respectively , get output , and ; Step 5.4, utilize and Computational gating And thus update the first Hidden state of timestamps ;in, and All are state parameters; Represents the sigmoid function; Step 5.5, Through a fully connected output layer, we obtain the first... Predicted response value for each timestamp ;in, and These represent the weights and biases of the fully connected output layer, respectively.

3. The method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network according to claim 2, characterized in that, The activation function of the fully connected layer in step 5.2 is: .

4. The method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network according to claim 2, characterized in that, In step 5.3 , and The activation functions are respectively , and .

5. The method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network according to claim 2, characterized in that, The following steps are included after step 5: Step 6: Apply random perturbation to the response sequence group of M sample points according to the corresponding timestamp sequence to generate Q enhanced concentration feature sequences. and the corresponding enhanced time interval sequence To obtain the augmented dataset ;in, ; Step 7, using the result obtained in Step 5... Using the trained continuous-time dynamic response neural network model of the gas as the initial model, Input into the initial model to generate the first Predicted response value label set for a type of gas ,and Together they form the enhanced training set; Step 8: Merge the dimensions of the enhanced training set obtained in Step 7 and the training set obtained in Step 4 to form a new training set; construct a new model identical to the continuous-time dynamic response neural network model described in Step 5, and train it based on the new training set to obtain the first... An enhanced continuous-time dynamic response neural network model for a certain gas.

6. The method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network according to claim 5, characterized in that, In step 6, based on All the generated enhanced concentration feature sequences constitute a sequence group. Its generation formula is:

7. Among them, For the first The first sample point The L-dimensional concentration sequence of a gas; It is an N-dimensional amplitude scaling vector based on a uniform distribution; For Gaussian distribution The noise tensor of dimension 1.

8. The method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network according to claim 6, characterized in that, The uniform distribution is Gaussian distribution .

9. The method for modeling the dynamic response of a gas sensor based on a liquid continuous-time network according to claim 5, characterized in that, In step 7, generate The specific calculation process is as follows: Step 7.1: Based on Step 4, obtain the statistics calculated during the Z-score standardization process, including... mean and standard deviation ,as well as mean and standard deviation ; Step 7.2, for Z-score normalization was performed to obtain the normalized enhanced concentration feature sequence. ; Step 7.3: Using the initial model, generate the first... Predicted response value tag set for a type of gas before treatment ;in, Indicates the initial model; Step 7.4, for Perform destandardization to obtain .

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