A gas mixed signal feature extraction and blind source separation method based on fast independent component analysis

Abstract

The application relates to the technical field of mixed signal processing of a gas sensor, in particular to a gas mixed signal feature extraction and blind source separation method based on fast independent component analysis, which comprises the following steps: collecting mixed gas signals obtained by a multi-channel gas sensor array to form an observation matrix; sequentially performing detrending, normalization and filter pretreatment on the observation matrix to obtain a pretreated observation matrix; and realizing white processing of the pretreated observation matrix through principal component analysis.The application combines signal pretreatment, fast independent component analysis, blind source separation and dynamic interference compensation, realizes mixed gas signal feature extraction and blind source separation without labeled data and with low calculation complexity, and effectively improves the detection precision, stability and real-time performance of the gas sensor array in a complex environment.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of gas sensor mixed signal processing, and in particular to a gas mixed signal feature extraction and blind source separation method based on fast independent component analysis. BACKGROUND

[0002] With the wide application of gas sensors in environmental monitoring, industrial safety and smart home fields, there is an urgent need for high-precision, real-time identification and concentration inversion of multi-component mixed gas. In actual detection scenarios, the signals collected by the gas sensor array are often mixed responses under the joint action of multiple target gases and complex environmental interference. Traditional signal processing methods such as principal component analysis, fast Fourier transform and wavelet transform often have problems such as feature loss, limited separation performance, high computational complexity and difficulty in embedded deployment when facing non-stationary, high-noise and strong interference mixed signals.

[0003] In recent years, some researches have tried to combine blind source separation technology with deep learning to improve the accuracy of gas identification and concentration prediction. For example, Chinese Patent No. CN115860056A proposes a mixed gas concentration prediction method based on a sensor array and a neural network. The method expands the samples by nearest neighbor interpolation, extracts features by combining an automatic encoder and independent component analysis, and finally realizes concentration prediction through a fully connected neural network.

[0004] However, such methods rely heavily on a large amount of labeled data for supervised training, and in actual applications, they face problems such as high sample labeling cost and limited model generalization ability. Their multi-level processing structure and deep network inference process consume a lot of computing resources, making it difficult to realize real-time processing on resource-constrained embedded terminals, especially in high-dynamic, multi-interference industrial field environments. Their high latency and high energy consumption further limit their deployment feasibility. In addition, such methods take concentration prediction as the final goal and do not fundamentally solve the problem of blind source separation and feature extraction of mixed gas signals, resulting in a significant decrease in performance in unknown gas components or concentration fluctuations, which cannot meet the real-time, online and low-power gas monitoring requirements. SUMMARY

[0005] In order to improve the detection accuracy, stability and real-time performance of the gas sensor array in complex environments, the application provides a gas mixed signal feature extraction and blind source separation method based on fast independent component analysis.

[0006] In a first aspect, the application provides a gas mixed signal feature extraction method based on fast independent component analysis, which adopts the following technical solution: a gas mixed signal feature extraction method based on fast independent component analysis, comprising the following steps:

[0007] Collecting mixed gas signals obtained by a multi-channel gas sensor array to form an observation matrix;

[0008] Performing detrending, normalization and filtering pretreatment on the observation matrix in sequence to obtain a pretreated observation matrix;

[0009] Performing whitening processing on the pretreated observation matrix by principal component analysis, including calculating a covariance matrix of the pretreated observation matrix and performing eigenvalue decomposition to obtain eigenvalues and eigenvectors; estimating the number N of source signals according to the eigenvalue distribution by using an eigenvalue inflection point method; selecting the first N principal component eigenvectors to construct a whitening matrix; and performing whitening transformation on the pretreated observation matrix by using the whitening matrix to obtain whitened signals.

[0010] Optionally, the detrending, normalization and filtering pretreatment includes:

[0011] Performing detrending processing on the observation matrix by using a sliding window median method to obtain a detrended signal;

[0012] Performing normalization processing on the detrended signal by using a Z-score normalization method, the normalization coefficient being fixed or updated with the sliding window to obtain a normalized signal;

[0013] Performing filtering processing on the normalized signal by using a FIR filter to obtain the pretreated observation matrix.

[0014] In a second aspect, the application provides a gas mixed signal blind source separation method based on fast independent component analysis, which adopts the following technical scheme: a gas mixed signal blind source separation method based on fast independent component analysis, including the following steps:

[0015] Performing feature extraction processing on the mixed gas signal to obtain whitened signals;

[0016] Performing blind source separation on the whitened signals by using a fast independent component analysis algorithm, extracting independent components of the whitened signals, and obtaining independent feature signals of each target gas;

[0017] Performing feature analysis and quantitative identification on the independent feature signals, realizing real-time classification and concentration determination of the target gas by using a classification algorithm, and outputting classification results and concentration information of the target gas.

[0018] Optionally, the fast independent component analysis algorithm takes negative entropy approximation as a contrast function, and solves a demixing matrix by using a fixed-point iteration algorithm; a nonlinear function used in the iteration is adaptively selected or switched according to sparsity prior knowledge of the whitened signals, the sparsity is judged by calculating kurtosis or skewness of the whitened signals, and finally the separated independent components are output.

[0019] Optionally, the iteration convergence criterion of the fast independent component analysis algorithm is that the Frobenius norm of the difference between the unmixing matrices of two adjacent iterations is less than a set threshold, or the variation of the objective function value of two adjacent iterations is less than a set threshold, and the final unmixing matrix is output when the convergence condition is met.

[0020] Optionally, the initial unmixing matrix of the fast independent component analysis algorithm is initialized by the eigenvectors obtained by the principal component analysis decomposition, or initialized by a randomly generated orthogonal matrix to obtain an initial iteration value.

[0021] Optionally, based on the determination result of the real-time classification and concentration information of the target gas, a state space model containing the independent components and sensor drift and cross-sensitivity parameters is constructed, and a Kalman filter is used for dynamic interference compensation to obtain a compensated signal.

[0022] Optionally, the dynamic interference compensation is realized by constructing a Kalman filter based on a state space; the state vector of the Kalman filter includes the separated independent components and a parameter vector representing the sensor drift and cross-sensitivity; the state space model is used to describe the evolution law of the state vector with time and the relationship between the observation signal and the state vector and the environmental parameters; through the model, the Kalman filter recursively estimates the state vector using the observation signal, and outputs the optimized state estimation value.

[0023] Optionally, the process noise covariance matrix and the observation noise covariance matrix of the Kalman filter are adaptively estimated online using a recursive algorithm with a forgetting factor, and the adaptively adjusted noise covariance matrix is output.

[0024] Optionally, based on a fixed time period or a trigger condition that the sensor drift exceeds a threshold value, the parameters of the state space model and the Kalman filter are updated online; the updating process includes re-executing the whitening process and the fast independent component analysis algorithm using the compensated signal to update the unmixing matrix and re-estimate the parameters in the dynamic interference model, and output the updated model parameters.

[0025] In summary, the present application has the following beneficial technical effects:

[0026] This application achieves supervised training without relying on large amounts of labeled data through signal preprocessing, rapid independent component analysis, blind source separation, and dynamic interference compensation. This significantly reduces data preparation costs and model training thresholds, while avoiding the problem of limited model generalization ability. As a result, this application exhibits high accuracy, high stability, high real-time performance, and strong environmental adaptability in multi-component gas detection, providing effective technical support for the reliable application of gas sensor arrays in complex industrial and environmental monitoring scenarios. Furthermore, the entire processing flow has low computational complexity, relying only on matrix operations and iterative calculations without the need for deep neural networks. This allows the application to run efficiently on resource-constrained embedded platforms, meeting the stringent requirements for real-time performance and low power consumption in industrial and environmental monitoring. This application employs preprocessing techniques such as sliding window midpoint detrending, Z-score normalization, and FIR filtering. The methods effectively eliminate interference from sensor baseline drift, slow environmental changes, and high-frequency noise, improving signal quality and providing stable, clean, and standardized input for subsequent processing steps, significantly enhancing the system's anti-interference capability in complex environments. This application uses principal component analysis for whitening, which not only eliminates the second-order correlation between channels in the observed signal but also adaptively estimates the number of source signals using the eigenvalue inflection point method, achieving data dimensionality reduction and redundant information compression. This lays an ideal input foundation for the fast independent component analysis algorithm, improving separation efficiency and result reliability. Furthermore, this application introduces a Kalman filter based on a state-space model for dynamic interference compensation, real-time estimating and correcting the effects of environmental factors such as sensor drift and temperature and humidity changes, significantly improving the accuracy of gas signal separation and concentration measurement, and enhancing the long-term stability and reliability of the system. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the feature extraction and blind source separation of gas mixing signals according to an embodiment of this application.

[0028] Figure 2 This is a logical flowchart of step S4 in an embodiment of this application;

[0029] Figure 3 This is a logic flowchart of step S6 in an embodiment of this application. Detailed Implementation

[0030] The following is in conjunction with the appendix Figures 1-3 This application will be described in further detail.

[0031] This application discloses a method for feature extraction of gas mixture signals based on rapid independent component analysis. For example... Figure 1 As shown, a method for feature extraction of gas mixture signals based on rapid independent component analysis includes the following steps:

[0032] S1, collect mixed gas signals to form an observation matrix.

[0033] Specifically, a multi-channel gas sensor array is used in this step, which includes M different types of gas sensitive sensor elements, such as metal oxide semiconductor sensors, electrochemical sensors or optical sensors, to cover the characteristic response characteristics of different target gases. The array synchronously collects mixed gas signals in the measured environment at a fixed sampling frequency to obtain multi-channel raw time domain response data and form an observation matrix. In the observation matrix, each row represents a time sequence signal of a sensor channel, and each column represents the response value of all sensors at a sampling time; this mixing process can be described by the following formula using a noisy instantaneous mixing model:

[0034]

[0035] where X is the observation matrix, with dimensions M x T, M representing the number of sensor channels and T representing the number of time sampling points, the matrix containing the observation values of M sensors at T time points; A is the mixing matrix, with dimensions M x N, N representing the number of source signals, the matrix containing the mixing coefficients of N source signals to M sensors; S is the source signal matrix, with dimensions N x T, representing the amplitude of N gas source signals to be separated at T time points; E is the noise matrix, with dimensions M x T, representing the environmental noise and additive noise introduced by the sensor itself.

[0036] This step enhances the signal capture capability through a multi-channel gas sensor array, ensuring the integrity and diversity of the original information and providing sufficient data support for subsequent high-precision blind source separation.

[0037] S2, pre-process the observation matrix to obtain a pre-processed observation matrix.

[0038] Step S2 includes the following sub-steps:

[0039] S21, center and baseline correct the original time sequence signals of each sensor channel. This step specifically uses the sliding window median method to remove the low-frequency baseline interference introduced by slow drift of the sensor or slow change of the environment. This detrending process is performed independently on each channel. For the original signal sequence of the mth channel, the median detrending calculation formula with a sliding window length of L is:

[0040]

[0041] where, represents the signal value of the mth channel at time t after detrending processing; represents the original signal value of the mth channel at time t; median represents the median operation; L is a preset sliding window length.

[0042] S22, the normalized signal is obtained by performing normalization processing on the de-trended signal using a Z-score normalization method, and the calculation formula of the Z-score normalization is:

[0043]

[0044] represents the normalized signal value of the mth sensor channel at time t; represents the mean reference for normalization, which is usually the mean of the mth channel signal in a period of time; represents the standard deviation reference for normalization, which is usually the standard deviation of the mth channel signal in the same period of time.

[0045] The specific normalization process is as follows: first, according to the application requirements, the normalization coefficient is selected, that is, the value of the mean and the standard deviation . If the fixed coefficient is selected, the mean and the standard deviation are fixed values calculated in advance according to prior knowledge or training stage data; if the normalization coefficient is updated with the sliding window, the system will maintain a sliding time window with a certain length, and when processing the data at each time t, the mean and standard deviation of all signal values of the mth channel in the window are calculated in real time, and they are immediately used as the mean and the standard deviation for the normalization calculation of the current time , so that the normalization coefficient can dynamically adapt to the slow change of the signal amplitude.

[0046] This step eliminates the inherent sensitivity difference between different sensors and the problem of non-uniform output amplitude dimension, transforms each channel signal into a distribution with zero mean and unit variance, enhances the stability and comparability of the data, and provides standardized and baseline-removed signal input for subsequent processing.

[0047] ​S23, a FIR filter is used to filter the normalized signal to obtain a preprocessed observation matrix. The FIR filter has a strict linear phase characteristic, which can avoid introducing phase distortion in the filtering process, thereby maintaining the time structure characteristics of the response waveform of each gas component. The FIR filter effectively suppresses high-frequency noise and residual very low-frequency interference by pre-setting the cutoff frequency and filter order, further improving the signal quality. The filtering process is performed independently on each sensor channel. By applying the FIR filter to the normalized signal sequence of each channel, noise filtering and signal purification are achieved, providing more pure and high-quality input signals for the subsequent blind source separation algorithm.

[0048] S3, the preprocessed observation matrix is whitened to obtain a whitened signal.

[0049] Specifically, the step first calculates the covariance matrix of the preprocessed observation matrix X, and performs eigenvalue decomposition on the covariance matrix to obtain a set of eigenvalues and their corresponding eigenvectors. Then, according to the distribution of the eigenvalues, the eigenvalue inflection point method is used to estimate the number of source signals N actually existing in the mixed signal. After determining the number of source signals N, the principal component eigenvectors corresponding to the first N largest eigenvalues are selected to construct a whitening matrix V. Then, the preprocessed observation matrix is whitened using the whitening matrix, and finally the whitened signal is obtained.

[0050] The calculation formula of the whitening transformation is:

[0051]

[0052] wherein, represents the output signal after whitening transformation, i.e. the whitened signal; represents the mean vector of the observation matrix X, i.e. the vector composed of the mean values of the signals of each sensor channel in the time dimension; V is a whitening matrix constructed by the first N principal component eigenvectors; X represents the preprocessed observation matrix, which is the input of the whitening transformation.

[0053] Specifically, the whitening transformation preferably uses the ZCA whitening method, which can maximize the preservation of the geometric structure of the original data while eliminating the correlation between the signals of each sensor channel in the preprocessed observation matrix, so that each component in the whitened signal has unit variance and is mutually independent. This step effectively eliminates redundant information and compresses the data volume by dimension reduction, and at the same time removes the second-order correlation between the signals of each channel in the preprocessed observation matrix through whitening processing, thereby providing more ideal input conditions for the subsequent fast independent component analysis algorithm based on high-order statistics. This not only enables the fast independent component analysis algorithm to converge to the correct demixing matrix more quickly and stably, but also significantly improves the computational efficiency and result reliability of the entire blind source separation process.

[0054] The implementation principle of the embodiment of the gas mixed signal feature extraction method based on fast independent component analysis is as follows: the method first synchronously collects mixed gas signals through a multi-channel gas sensor array to form an observation matrix; then the observation matrix is sequentially subjected to median detrending in a sliding window, Z-score normalization and FIR filter pretreatment to obtain a standardized and high-quality pretreated observation matrix; and then principal component analysis is used to whiten the pretreated observation matrix to eliminate the second-order correlation between channels and obtain whitened signals that are mutually independent and have unit variance. The method combines pretreatment and whitening to significantly improve the signal-to-noise ratio and separability of the signals, and lays an ideal input foundation for subsequent fast independent component analysis. Compared with traditional feature extraction methods, the method does not need to rely on labeled data and has low computational complexity, effectively overcoming the problems of feature loss and limited separation performance in a non-stationary high-noise environment, significantly improving the precision, stability and real-time performance of gas detection, and is especially suitable for resource-constrained embedded real-time processing scenarios.

[0055] The embodiment of the application also discloses a gas mixed signal blind source separation method based on fast independent component analysis. Figure 1 and Figure 2 As shown in the gas mixed signal blind source separation method based on fast independent component analysis, the method comprises the following steps:

[0056] S4, blind source separation is performed on the whitened signals to obtain independent feature signals of each target gas.

[0057] Step S4 comprises the following sub-steps:

[0058] S41, a fast independent component analysis algorithm is used to perform blind source separation on the whitened signals obtained in step S3 to obtain independent feature signals of each target gas. The fast independent component analysis algorithm takes negative entropy approximation as the core target of the contrast function, thereby maximizing the non-Gaussianity of each signal component separated from the whitened signals, and further ensuring the statistical independence thereof. In the actual iterative solving process of the fast independent component analysis algorithm, the selected nonlinear function can be at least one selected from a hyperbolic tangent function, a cubic function and a Gaussian function, wherein the parameter in the hyperbolic tangent function usually ranges from 1.0 to 2.0.

[0059] To improve the adaptability of the fast independent component analysis algorithm to different gas signal characteristics, the step can also be based on the prior sparsity knowledge of each component of the whitened signal. Specifically, the skewness or kurtosis index is calculated to measure the peakedness and symmetry of the distribution, and then the most suitable nonlinear function is adaptively selected or dynamically switched according to a predetermined information criterion in the iteration process, so as to significantly improve the separation accuracy of the algorithm for different statistical characteristic gas signals.

[0060] S42, in order to ensure that the fast independent component analysis algorithm can stably and efficiently converge to the global optimal solution, an explicit iteration convergence criterion and initialization rule are set in this step. Specifically, the iteration convergence criterion can be preferably the Frobenius norm of the difference between the solution mixing matrix obtained by the adjacent two iterations is less than 10⁻ 6 , or the change of the objective function value in the adjacent two iterations is less than 10⁻ 8 . At the same time, the fast independent component analysis algorithm sets an upper limit for the number of iterations, which is in the range of 100 to 500 times, in order to avoid infinite loop. The initial value of the demixing matrix can be selected by directly initializing the eigenvector obtained by principal component analysis decomposition, or using a randomly generated orthogonal matrix for initialization.

[0061] In order to further enhance the robustness of the fast independent component analysis algorithm in complex scenarios, this step also introduces a variety of robustness enhancement mechanisms in the iteration process. Specifically, by setting a step size upper bound constraint mechanism, the update amplitude of the demixing matrix in each iteration is limited, effectively preventing the algorithm from diverging or unstable convergence due to too large step size; by using the extreme value escape restart strategy, when it is detected that the iteration process falls into a local extreme value or stagnation, some parameters are automatically reinitialized and the optimization process is restarted, in order to enhance the ability of the algorithm to escape from the local optimum; by applying the suppression weight method for abnormal points, the weight of each data point is dynamically adjusted according to its statistical characteristics, reducing the influence of outliers or strong noise points on the iteration process. Through the synergistic effect of these rigorous convergence control, parameter initialization and robustness enhancement mechanisms, it is ensured that the fast independent component analysis algorithm can reliably converge under various complex conditions, and obtain a demixing result with clear physical meaning.

[0062] S43, for the underdetermined condition that the number of sensor channels M is less than the number of source signals N to be estimated, or the case where the noise in the observed data is significant, this step enhances the fast independent component analysis algorithm. Specifically, first, the effective dimension of the signal subspace is estimated using the subspace method based on eigenvalue decomposition, and then the fast independent component analysis algorithm is solved after regularization processing. By introducing a regularization term to the demixing matrix or the objective function, the numerical stability and noise resistance are improved.

[0063] In addition, for special working conditions with severe nonlinear mixing, this step also takes nonlinear independent component analysis as an optional dependent implementation scheme. In specific implementation, appropriate nonlinear blind source separation model can be selected according to the actual mixing characteristics, and separation algorithm based on mutual information minimization or nonlinear decorrelation is used to process nonlinear mixing relationship by extending nonlinear function type, and finally realize effective separation of nonlinear mixed gas.

[0064] The step systematically expands the application range of the method by subspace dimension estimation, regularization and nonlinear extension, etc. so that it can effectively handle practical complex scenarios of underdetermination, strong noise and nonlinear mixing.

[0065] S44, to ensure that the independent characteristic signals obtained after blind source separation have good physical interpretability and can be clearly corresponded to actual target gases, a soft constraint based on prior knowledge is imposed on the independent characteristic signals. The constraints mainly depend on the non-negativity of the gas concentration signal and the sparsity that it may exhibit on a particular sensor response. The specific implementation includes threshold processing of the independent characteristic signals to set zero to meaningless small fluctuations with an amplitude below a set threshold, or using a sparse reweighting iterative algorithm to gradually enhance the sparsity of signal components in the iteration process. By introducing such physical prior constraints, the final independent characteristic signals obtained are more consistent with the actual physical reality of the gas signal, significantly improving the interpretability and reliability of the separation results.

[0066] S5, performing feature analysis and quantitative identification on the independent characteristic signals to output the classification results and concentration information of the target gases.

[0067] Specifically, a set of feature indicators capable of representing the characteristics of different gas species are systematically extracted from each independent characteristic signal obtained in step S4. These features include peak amplitude, signal rise time, signal recovery time, signal energy in the time domain, and high-order statistical characteristics such as kurtosis and negative entropy approximation, which together form a multi-dimensional feature vector for distinguishing different gases.

[0068] Based on feature extraction, a feature database containing standard response characteristics of known target gases is constructed. This database serves as a prior knowledge base for storing standard feature vectors of various target gases on a particular sensor array, as well as their corresponding gas categories and concentration information. In actual detection, the real-time extracted gas feature vector to be identified is compared and matched with the standard templates in the feature database.

[0069] By using efficient classification algorithms such as support vector machines, decision trees or distance-based nearest neighbor classifiers, the feature vectors extracted from the independent characteristic signals separated from the mixed gas signals are quickly classified and identified, and the corresponding target gas species are output. At the same time, based on the mapping relationship between feature values and gas concentrations, by establishing a concentration calibration curve or regression model, quantitative determination of the concentrations of each target gas is further realized, and finally clear gas categories and accurate concentration information are output. This step converts the independent characteristic signals obtained by blind source separation into gas categories and concentration readings with clear physical meaning, completes the value transformation from signal processing to final gas detection application, and greatly improves the practicality of the entire system and the intuitiveness of the output results.

[0070] S6. Based on the real-time classification and concentration information of the target gas, a state-space model is constructed, and dynamic interference compensation is performed to obtain the compensated signal.

[0071] like Figure 3 As shown, step S6 includes the following sub-steps:

[0072] S61. Modeling and State Definition. In the state-space model constructed in step S6, the state vector of the model is first defined. The state vector consists of independent components separated by the fast independent component analysis algorithm and sensor drift sensitivity parameters, which together describe the internal dynamic state of the state-space model. The specific form of the state vector is as follows:

[0073]

[0074] in, This represents the state vector at time k. This represents the N independent components separated by the Fast Independent Component Analysis algorithm at time k, i.e., the estimated signals of each target gas. This represents the vector of drift-sensitive parameters of the sensor at time k, such as the cross-sensitivity coefficient and baseline drift. The definition of this state vector unifies the gas signal to be estimated and the sensor drift parameters within a single state framework, providing a mathematical basis for subsequent dynamic estimation and compensation.

[0075] Based on this, the environment input vector is further defined. It includes temperature ,humidity Temperature change rate Humidity change rate Flow rate Equal environmental quantities, specifically in the form of This environment's input vector As an external disturbance input, it is used to describe those measurable physical quantities in the environment that have a significant impact on the sensor output. Their changes directly affect the evolution of the state vector and the generation of the observed signal.

[0076] Furthermore, based on the aforementioned state vector With environment input vector The process model and observation model of the state-space model are defined as follows:

[0077] The process model describes the evolution of the state vector over time steps:

[0078]

[0079] is the state transition matrix, which describes the dynamic evolution of the state space model; G is the input matrix, which represents the environmental input on the state evolution; is the process noise. This equation describes the state vector how it evolves from the previous time step .

[0080] The observation model describes the relationship between the observation signal and the state vector and the environmental input:

[0081]

[0082] where, is the external disturbance input, which is usually related to the environmental input ; is the observation vector, which is the actual output of the sensor or the signal after post-processing; H is the observation matrix, which represents the contribution of the state to the observation; B is the disturbance input matrix, which represents the direct influence of the external disturbance on the observation; is the observation noise, which is used to model the random error in the measurement process. This equation establishes the relationship between the observation signal and the state vector and the external disturbance .

[0083] In particular, for the drift-sensitive parameters in the state vector, their dynamic evolution and influence on the observation can be further expressed as:

[0084] This equation specifically describes the dynamic evolution of the drift parameters ; where, is the state transition matrix of the drift parameters, which describes their own change over time; is the input matrix of the environmental quantity to the drift parameters, which represents the influence of environmental changes on the sensor drift; is the process noise of the drift parameters.

[0085]

[0086] This equation further refines the observation model; where, is the contribution matrix of the independent components to the observation, which represents the contribution weight of each gas signal to the sensor reading; is the direct influence matrix of the environmental quantity to the observation, which represents the direct influence of environmental factors on the sensor output; is the influence matrix of the drift parameters to the observation, which represents the contribution of the sensor drift to the final reading; are the observation noises, respectively.

[0087] By establishing the above model, and using the subsequent Kalman filter to recursively process the observation signal , the influence of drift-sensitive parameters can be estimated and compensated in real time, thereby improving the accuracy and robustness of gas signal separation and identification.

[0088] S62, online estimation and compensation based on Kalman filtering. The Kalman filter is used to recursively estimate the state vector , and the specific recursive process is as follows:

[0089] Time update:

[0090]

[0091] represents the priori estimation of the state at the kth moment, given all observation data up to the (k-1)th moment; represents the posteriori estimation of the state at the (k-1)th moment, given all observation data up to the (k-1)th moment; this formula is the state prediction equation, which is used to predict the state at the current moment k from the state posteriori estimation at the last moment k-1 and the environmental input vector at the current moment k, so as to estimate the state at the current moment k .

[0092]

[0093] is the priori error covariance matrix, representing the uncertainty of state prediction ; is the posteriori error covariance matrix at the last moment, representing the uncertainty of state estimation at the last moment; is the transpose of the state transition matrix F, used to map the error covariance from the last moment to the current moment; is the process noise covariance matrix, representing the uncertainty of the system model itself or unmodeled disturbances; this formula is the error covariance prediction equation, which is used to predict the uncertainty of state estimation at the current moment.

[0094] Measurement update:

[0095]

[0096] is the Kalman gain matrix, used to weigh the trust between the predicted value and the observed value, and to determine how to correct the state prediction with the observation residual; is the transpose of the observation matrix H, used to map the priori error covariance to the observation space; ​is the covariance matrix of the measurement noise, representing the noise level in the sensor observation; this formula calculates the Kalman gain, which is used to weigh the trust between the predicted value and the actual observation value.

[0097]

[0098] is the state posterior estimation at time k, which is the optimal estimation value after observation correction; is the direct influence of external disturbance on observation, which is compensated as known input; is the observation residual, which is the difference between the actual observation value and the model predicted value; this formula is the state correction equation, which uses the actual observation value to correct the prior state estimation and obtain a more accurate posterior state estimation .

[0099]

[0100] is the corresponding error covariance matrix; is the identity matrix; is the correction factor, which represents the reduction of uncertainty after updating by observation; this formula updates the posterior error covariance matrix , reflecting the uncertainty of the state estimation after observation correction.

[0101] Through the above recursive process, the Kalman filter realizes the real-time optimal estimation of the state vector . The time update stage is based on the system model to predict the state, and the measurement update stage corrects the prediction using the actual observation value, thereby significantly improving the accuracy of state estimation; finally, the drift parameter is estimated to generate a compensation term to correct the observation signal in real time, thereby effectively suppressing sensor drift and environmental interference, and improving the precision and robustness of gas signal separation and identification.

[0102] S63, adaptive estimation of noise covariance. To further improve the performance of the filter in time-varying environment, a recursive algorithm with forgetting factor is used to adaptively estimate the noise covariance online, the specific steps are as follows:

[0103] The formula for calculating the filtering residual is:

[0104]

[0105] is the filtering residual, representing the difference between the actual observation value and the model predicted value , The inconsistency between the model prediction and the actual observation reflects the model accuracy and the noise statistical characteristics.

[0106] The formula for updating the observation noise covariance matrix is:

[0107]

[0108] is the observation noise covariance matrix at time k; is the forgetting factor, with a value range of 0.9 to 0.995, used to control the decay rate of historical information; represents the mapping of state prediction uncertainty to the observation space; this formula dynamically adjusts the statistical characteristics of the observation noise by a weighted combination of the residual and the extrapolated uncertainty, so that it can adapt to changes in sensor noise levels.

[0109] The formula for updating the process noise covariance matrix is:

[0110]

[0111] is the process noise covariance matrix at time k; is the forgetting factor, with a value range of 0.9 to 0.995, used to adjust the weight of historical information and current information; represents the contribution of the residual to the state update process, used to estimate the uncertainty of the process noise; this formula propagates the residual information back to the state space through the Kalman gain, achieving online estimation of the process noise covariance, and improving the system's adaptability to unmodeled dynamics.

[0112] This step constitutes a complete noise covariance adaptive estimation closed loop. First, through the residual evaluate the prediction error of the current model, and then use the recursive mechanism with the forgetting factor to update the observation noise covariance and the process noise covariance respectively, so that the Kalman filter can dynamically track the changes in system noise characteristics, significantly improving the filtering accuracy and robustness in time-varying environments.

[0113] S64, closed-loop update and abnormality processing. Take the signal after dynamic disturbance compensation by the Kalman filter as input, trigger the following processing flow at a period of 1 to 5 minutes or according to the drift detection threshold value:

[0114] The signal compensated by the Kalman filter is used as a new observation signal to reconstruct an observation matrix; the covariance matrix of the signal is recalculated, feature decomposition is performed, and a new whitening matrix is constructed; the new whitening signal is used as input to re-run the fast independent component analysis algorithm to solve a new demixing matrix; the new demixing matrix replaces the original demixing matrix and is used for subsequent blind source separation; the newly estimated independent components and observation signals are used to re-estimate the drift parameters in the Kalman filter, and the matrices in the state space model are updated, to realize collaborative online updating of the demixing model and the interference compensation model, and to improve the adaptability of the system to dynamic environments.

[0115] The drift detection threshold is usually set based on the following indicators:

[0116] Variance rate of each independent component: the variance in a sliding window is calculated, and if it exceeds a set threshold, updating is triggered;

[0117] Statistical characteristics of Kalman filter residuals: if the mean or variance of the residuals continuously exceeds the normal range, it is considered that the system has drifted, and updating is triggered at this time;

[0118] Rate of change of environmental parameters: if the rate of change of temperature and humidity exceeds a set threshold, updating is triggered.

[0119] At the same time, the kurtosis or variance of each independent component is monitored in real time, and if its value exceeds the 3σ interval of the historical statistical range, it is determined to be abnormal; under the condition that no target gas is introduced, the baseline signal is re-collected, and the normalization coefficient is updated; if the abnormality persists, the principal component analysis and whitening process are completely re-executed, and the number of sources and the whitening matrix are re-estimated to ensure the stability of the system during long-term operation.

[0120] This step realizes dynamic optimization of the demixing model and interference compensation parameters through a closed-loop updating mechanism, and guarantees the stability of the system during long-term operation through abnormality detection and self-calibration. The combination of the two significantly improves the adaptability and reliability of the system in complex industrial environments.

[0121] The implementation principle of the embodiment is as follows: the application performs pretreatment such as detrending, normalization and filtering on the mixed signals collected by the multi-channel gas sensor array, performs whitening dimension reduction combined with principal component analysis, and then realizes blind source separation by using the fast independent component analysis algorithm to extract independent feature signals of each gas; then, the classification algorithm is used to realize gas type recognition and concentration determination, and the Kalman filter based on the state space model is introduced for dynamic interference compensation to realize online correction of sensor drift and environmental changes. The application does not require labeled data and has low computational complexity, significantly improves the precision, stability and real-time performance of gas detection in complex environments, and is especially suitable for industrial and environmental monitoring scenarios on embedded platforms.

[0122] The above are all preferred embodiments of the present application, and do not limit the protection scope of the present application, so that: all equivalent changes made according to the structure, shape, principle of the present application should be covered in the protection scope of the present application.

Claims

1. A method for blind source separation of gas mixture signals based on rapid independent component analysis, characterized in that, Includes the following steps: The mixed gas signals acquired by the multi-channel gas sensor array are used to form an observation matrix; The observation matrix is ​​sequentially subjected to detrending, normalization, and filtering preprocessing to obtain the preprocessed observation matrix. The whitening process of the preprocessed observation matrix is ​​achieved through principal component analysis, including calculating the covariance matrix of the preprocessed observation matrix and performing eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors. Based on the eigenvalue distribution, the eigenvalue inflection point method is used to estimate the number of source signals N; The whitening matrix is ​​constructed by selecting the first N principal component eigenvectors; the whitening matrix is ​​then used to perform a whitening transformation on the preprocessed observation matrix to obtain the whitened signal; A fast independent component analysis (CFI) algorithm is used to perform blind source separation on the whitened signal, extract the independent components of the whitened signal, and obtain the independent characteristic signals of each target gas. The CFI algorithm uses a negative entropy approximation as the comparison function and solves the unmixing matrix through a fixed-point iterative algorithm. The nonlinear function used in the iteration is adaptively selected or switched based on prior knowledge of the sparsity of the whitened signal. The sparsity is determined by calculating the kurtosis or skewness of the whitened signal, and finally, the separated independent components are output. The independent feature signals are subjected to feature analysis and quantitative identification. A classification algorithm is used to achieve real-time classification and concentration measurement of the target gas, outputting the classification results and concentration information. Based on the real-time classification and concentration measurement results of the target gas, a state-space model containing the independent components and sensor drift and cross-sensitivity parameters is constructed. A Kalman filter is used for dynamic interference compensation to obtain the compensated signal. The dynamic interference compensation is achieved by constructing a state-space based Kalman filter. The state vector of the Kalman filter includes the separated independent components and parameter vectors representing sensor drift and cross-sensitivity. The state-space model is used to describe the evolution of the state vector over time and the relationship between the observed signal, the state vector, and environmental parameters. Through this model, the Kalman filter recursively estimates the state vector using the observed signal, outputting an optimized state estimate. In the constructed state-space model, the state vector is first defined. The state vector consists of independent components separated by the fast independent component analysis algorithm and sensor drift-sensitive parameters, collectively describing the internal dynamic state of the state-space model. The specific form of this state vector is as follows: ,in, This represents the state vector at time k. This represents the N independent components separated by the Fast Independent Component Analysis algorithm at time k. This represents the vector of drift-sensitive parameters of the sensor at time k; Further define the environment input vector as the input of external disturbances. Based on state vector With environment input vector Define the process model and observation model of the state-space model: Process model: ,in, F is the environment input vector; G is the state transition matrix; This is process noise; Observation model: ,in, Input from external disturbances; H is the observation vector; H is the observation matrix; B is the perturbation input matrix; To observe noise; Drift-sensitive parameters in the state vector The expression is as follows: ,in, It is the state transition matrix of the drift parameters; It is the input matrix of environmental quantities to drift parameters; The process noise is for drift parameters; The observation model is further refined as follows: ,in, It is the contribution matrix of independent components to the observation; It is the matrix showing the direct impact of environmental quantities on observations; It is the matrix showing the influence of drift parameters on observations; These represent observation noise.

2. The method according to claim 1, characterized in that, The iterative convergence criterion of the fast independent component analysis algorithm is that the Frobenius norm of the difference between the unmixed matrices of two adjacent iterations is less than a set threshold, or the change in the objective function value of two adjacent iterations is less than a set threshold. When the convergence condition is met, the final unmixed matrix is ​​output.

3. The method according to claim 1, characterized in that, The initial unmixing matrix of the fast independent component analysis algorithm is initialized by the eigenvectors obtained from the principal component analysis decomposition, or by a randomly generated orthogonal matrix, to obtain the initial iteration value.

4. The method according to claim 1, characterized in that, The process noise covariance matrix and observation noise covariance matrix of the Kalman filter are adaptively estimated online using a recursive algorithm with a forgetting factor, and the output is an adaptively adjusted noise covariance matrix.

5. The method according to claim 1, characterized in that, Based on a fixed time period or a trigger condition where the sensor drift exceeds a threshold, the parameters of the state-space model and the Kalman filter are updated online. The update process includes re-executing whitening processing and fast independent component analysis algorithm using the compensated signal to update the unmixing matrix and re-estimate the parameters in the dynamic interference model, and outputting the updated model parameters.

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