Intelligent calibration method for coal mine underground methane sensor

Abstract

The present application relates to the technical field of gas sensor calibration, and particularly relates to an intelligent calibration method for a methane sensor in a coal mine, which comprises the following steps: establishing a near-field session and obtaining a permeation tube metrological certificate parameter and a calibration instruction set; obtaining a zero point data set and a sealing score in a closed microcavity, generating a standard concentration trajectory according to the metrological certificate, and collecting a standard section data set; forming original collected data according to joint target optimization of a temperature time profile and an H-infinity norm information matrix; implementing robust deconvolution and variational Bayesian inference based on a first-order inertial dynamic model to obtain a set of robust point estimation parameters, a posterior distribution and a combined uncertainty; calculating a Wasserstein barycenter on a section adjacency graph and solving a one-norm uniform optimization release correction parameter set to realize traceable, robust and section-consistent online correction and re-calibration triggering.

Description

Technical Field

[0001] This invention relates to the field of gas sensor calibration technology, and in particular to an intelligent calibration method for methane sensors in underground coal mines. Background Technology

[0002] Downhole methane concentration monitoring is directly related to the timeliness and compliance traceability of decisions regarding ventilation control, work stoppage and resumption, and disaster early warning. Fluctuations in ambient temperature and humidity, sensor adsorption lag, and contamination aging can cause long-term drift in sensitivity and time constant; the heterogeneity of the tunnel space and the coupling of airflow also require cross-sectional consistency in results from multiple points. Without traceable on-site calibration capabilities and a consistent release mechanism, the monitoring network will suffer from threshold misjudgment, false alarms and missed alarms, difficulties in accident debriefing, and escalating maintenance costs. Summary of the Invention

[0003] To address the numerous problems existing in the prior art, this invention provides an intelligent calibration method for methane sensors in coal mines. This invention uses a standard concentration trajectory driven by a metrological certificate as a stimulus, and optimizes the temperature-time profile using a joint information matrix and the H-norm to obtain high-information data. Robust parameter estimation is performed under a first-order inertial dynamic model, producing posterior and combined uncertainties. Furthermore, segment distribution is achieved through Wasserstein centroid and H-norm consistency optimization, ultimately obtaining traceable, robust, and consistent online calibration.

[0004] A method for intelligent calibration of methane sensors in underground coal mines includes the following steps:

[0005] Establish a near-field communication session to obtain the permeation tube metrology certificate parameters and calibration instruction set;

[0006] A zero-point dataset is generated in a closed microcavity and an acoustic pulse seal diagnosis is performed to obtain a seal score. A standard concentration trajectory is generated based on the parameters of the permeation tube metrology certificate and a standard segment dataset is collected. The temperature-time profile is adjusted according to the information matrix and the H infinity norm to form the original collected data.

[0007] Based on the original collected data, robust deconvolution and variational Bayesian inference are performed under the first-order inertial dynamic model to obtain the robust point estimation parameter set and posterior distribution and form the combined uncertainty.

[0008] The posterior distributions of multiple sensors are fused on the segment adjacency graph, and the Wasserstein centroid is calculated to obtain the segment reference distribution. Combined with norm 1 consistent optimization, a set of corrected parameters is obtained and distributed for online calibration and drift recalibration triggering. The segment reference distribution is used as the prior for the next round of input design and parameter identification.

[0009] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0010] Through near-field communication sessions and permeation tube metrology certificate parameter links, metrological traceability and session-level traceability of standard concentration trajectories were achieved; through acoustic pulse seal diagnosis and seal scoring mapping of disturbance boundaries, explicit modeling and adaptive weighting of leakage uncertainty were achieved; through joint objective optimization of temperature-time profiles using information matrix and H-norm, information gain maximization and worst-case suppression within energy and safety constraints were achieved; through robust deconvolution and variational Bayesian inference, robust point estimation of parameter sets and posterior distributions were achieved, generating combined uncertainties; through segment adjacency graph mean smoothing and Wasserstein centroid and L1 norm consistent optimization, consistent release of corrected parameter sets and outlier suppression across devices were achieved; through parameter version recording, digital signatures, and drift recalibration triggering, closed-loop parameter governance and reproducible accident review were achieved. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0012] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation.

[0013] like Figure 1 As shown, a smart calibration method for methane sensors in underground coal mines includes the following steps:

[0014] Establish a near-field communication session to obtain the permeation tube metrology certificate parameters and calibration instruction set;

[0015] Preferably, when establishing a near-field communication session, challenge response authentication is performed, the digital signature and validity period of the permeation tube metrology certificate parameters are verified, the calibration instruction set is loaded, energy and safety constraints and environmental baselines are determined, and calibration log timestamps and data indexes are enabled.

[0016] In this invention, the stage of establishing a near-field communication session and obtaining the permeation tube measurement certificate parameters and calibration instruction set is positioned as the trusted entry point and boundary setting for subsequent core steps. The near-field communication session is based on short-distance coupling and controlled power supply, avoiding the risks of identity forgery and unauthorized operation introduced by long-distance wireless links. This ensures that the calibration process is only initiated when the equipment and the authorized terminal are close to each other, meeting the inherent safety and control requirements of downhole systems.

[0017] At the principle level, challenge-response authentication is used to confirm device identity and session integrity. The authentication process begins with an authorized terminal generating a random number. The sensor-side security element signs the random number and device identifier. The authorized terminal verifies the signature using its built-in public key to generate a session credential. This session credential is bound to a timestamp and data frame number throughout the calibration cycle, spanning data acquisition and parameter updates to prevent replay and cross-writing. After authentication, the permeation tube metrology certificate parameters are read from read-only storage. The certificate, issued by a legal metrology institution, includes at least the functional relationship between permeability and temperature, membrane thickness, effective area, pressure difference, batch number, and expiration date, along with a digital signature and hash. These certificate parameters are used to reconstruct the standard concentration trajectory within the closed microcavity and serve as the sole basis for generating the subsequent standard segment dataset. The calibration instruction set is generated from an access-controlled template and is structured to include the zero-point segment procedure, acoustic pulse seal diagnostic procedure, standard segment procedure, sampling frequency, temperature control upper limit, heating rate upper limit, maximum duration, anomaly fallback strategy, and state machine transition conditions. After reading, integrity verification and version recording are performed to ensure the executed script and certificate are within the same session context.

[0018] Energy and safety constraints are calculated using near-field coupled power supply conditions and intrinsically safe current limiting rules, forming boundaries such as maximum allowable temperature, maximum heating rate, maximum supply current, longest calibration duration, and cumulative energy budget. These boundaries directly constrain the search space of subsequent temperature time profiles, ensuring intrinsic safety is met on any execution path. The environmental baseline is obtained by synchronously collecting, detrending, and median filtering the cavity temperature, humidity, and pressure within a short time window, serving as the initial reference for the compensation function and temperature stability criterion, avoiding the accidental introduction of short-term disturbances into the zero-point and standard segments. The calibration log is enabled in append-only mode, with the first frame containing session credentials, certificate hash, instruction set version, timestamp, and data indexing strategy. All subsequent data frames and decision results are written to disk according to this index, forming an auditable link.

[0019] The effects of this stage are reflected in four aspects. First, identity and certificate co-origin verification ensures the traceability of the standard concentration trajectory and blocks calibration triggered by uncertified or expired certificates. Second, energy and safety constraints are solidified as boundary conditions before entering the standard segment generation, avoiding data unavailability caused by exceeding limits and then backtracking during temperature control. Third, the environmental baseline eliminates drift in the initial stage of acquisition, providing a unified reference for the extraction of stable windows in the zero-point segment and the standard segment. Fourth, log indexing and timestamps ensure that any parameter update can be reproduced according to time and instruction version, meeting the requirements of downhole monitoring and accident tracing.

[0020] In terms of data and control flow integration, this stage outputs session credentials, permeation tube metrology certificate parameters, calibration instruction set, energy and safety constraints, environmental baseline, and calibration log handle. These outputs are referenced one by one when generating the zero-point dataset, acoustic pulse seal diagnostics, generating standard concentration trajectories, and acquiring standard segment datasets. Specifically, permeation tube metrology certificate parameters are used in the derivation of standard concentration trajectories, energy and safety constraints define the candidate set of temperature-time profiles, the environmental baseline is used as compensation input in the first-order inertial dynamic model, and the calibration log handle is used throughout data acquisition and parameter publishing.

[0021] In this embodiment, methane sensors deployed along the longwall mining face are calibrated by maintenance personnel using authorized terminals. The authorized terminal initiates a challenge-response authentication, verifies the received signature, generates a session credential, and then reads the permeation tube metering certificate parameters and calibration instruction set. If the certificate signature or validity verification fails, the calibration is terminated and the reason is recorded in the calibration log; if successful, energy and safety constraints are calculated, the maximum allowable temperature, maximum heating rate, and longest duration are given, and a message is displayed indicating that the current session is qualified to execute. The terminal initiates environmental baseline acquisition, obtaining baseline values ​​for cavity temperature, humidity, and pressure, and writes them to the first frame of the calibration log. The state machine then enters the zero-point segment, generating a zero-point dataset; next, it enters acoustic pulse seal diagnosis, obtaining a seal score; a standard concentration trajectory is generated based on the permeation tube metering certificate parameters, and temperature control is executed under the premise of meeting energy and safety constraints, collecting a standard segment dataset. The two data segments are merged with the temperature-time profile to form the original acquired data. The raw acquired data undergoes robust deconvolution and variational Bayesian inference under a first-order inertial dynamic model, outputting a robust set of estimated parameters, posterior distribution, and combined uncertainty. The posterior distributions of multiple sensors are fused on the segment adjacency graph, and the Wasserstein centroid is calculated to obtain the segment reference distribution. A corrected parameter set is obtained through norm-consistent optimization and distributed to each sensor for online calibration and drift recalibration triggering. Simultaneously, the segment reference distribution is used as a priori write-back for the next round of input design and parameter identification. Key data frames throughout the process are indexed by session credentials and timestamps, ensuring that every step from establishing the near-field communication session to parameter distribution can be replayed and verified.

[0022] A zero-point dataset is generated in a closed microcavity and an acoustic pulse seal diagnosis is performed to obtain a seal score. A standard concentration trajectory is generated based on the parameters of the permeation tube metrology certificate and a standard segment dataset is collected. The temperature-time profile is adjusted according to the information matrix and the H infinity norm to form the original collected data.

[0023] This invention generates a zero-point dataset within a sealed microcavity, performs acoustic pulse seal diagnosis, generates a standard concentration trajectory based on the parameters of the permeation tube metrology certificate, and collects a standard segment dataset. Simultaneously, it adjusts the temperature-time profile according to the information matrix and the H-norm to form the original acquired data. The purpose of this stage is to construct an input stimulus with traceable origin, well-defined physical boundaries, and sensitivity to parameter identification, and to weight and constrain subsequent estimations based on seal reliability.

[0024] The principle behind the zero-point dataset is to establish a near-zero concentration environment using a zero-point microvalve and adsorbent, continuously collecting the sensor's raw output, cavity temperature, cavity humidity, and cavity pressure to form a time series for baseline estimation and noise scale assessment. Due to temperature fluctuations and the risk of micro-leakage in the downhole environment, the zero-point segment serves only as a baseline and noise reference; its actual reliability is determined by seal diagnostics.

[0025] Acoustic pulse seal diagnostics involves injecting a short pulse via a micro-actuator under conditions of valve closure and cavity stillness, and then acquiring the acoustic echo and cavity pressure transients. For ease of subsequent use, this invention defines a seal score. The acoustic amplitude attenuation can be fitted by the following formula. The cavity pressure stabilization process can be fitted by the following formula: Where A(t) is the acoustic amplitude, τ ac Let f0 be the acoustic decay time constant, f0 be the dominant frequency, φ be the phase, and P be the phase constant. ch (t) represents the cavity pressure, τ p Let be the cavity pressure stabilization time constant. The standardized deviation is obtained from the factory baseline and variance estimate, and the sealing score is calculated. Where s=[τ ac ,τ p [f0] T s * ∑ represents the baseline feature, and ∑ represents the covariance of the baseline feature. The sealing score is used to set the worst-case radius and sample weights; a larger value indicates a better seal. The standard concentration trajectory is based on the permeation tube calibration certificate parameters. The micropermeation unit generates a stable flux at a set temperature and time profile, and the concentration within the cavity evolves over time according to the mass conservation and equivalent loss model.

[0026]

[0027] Among them, C ch (t) represents the volume fraction of methane in the cavity, A represents the effective permeation area, and J(T) represents the volume fraction of methane in the cavity. s (t) is a function of permeation flux and temperature, V ch k is the volume of the cavity. loss C is the equivalent loss coefficient. out T represents the external volume fraction. s(t) represents the temperature-time profile. The permeation flux is calculated from the parameters of the permeation tube metering certificate, and the equivalent loss coefficient is linearly mapped from the seal score to reflect the degree of leakage. The above trajectory, along with the synchronously acquired sensor raw outputs, cavity temperature, cavity humidity, and cavity pressure, forms a standard segment dataset.

[0028] To ensure that the subsequent parameter set is identifiable within a short time and has an upper bound on unknown perturbations, this invention performs online optimization of the temperature-time profile within energy and safety boundaries. First, a sensitivity structure for the measurement and dynamic relationship is presented for calculating the information matrix and worst-case bound. The dynamic state satisfies:

[0029]

[0030] The measurement output satisfies y(t)=αF(z(t),E(t))+β, where z(t) is the equivalent adsorption state, τ is the time constant, α is the sensitivity, β is the baseline, F(·) is the static mapping, and E(t) is the environmental quantity vector. The information matrix is ​​defined as:

[0031]

[0032] Where Θ={α,τ}, R is the observation noise covariance. H, the infinity norm index, represents the worst-case amplification of the residuals over bounded perturbations.

[0033]

[0034] Where w is the equivalent perturbation. From the sealing score mapping, r(t) represents the measurement residual. The joint objective of the temperature-time profile is... And meet energy and safety constraints:

[0035] T ch (t)≤T max

[0036] Where P(t) is the heating power, E max For energy budgeting, r max T is the upper limit of the heating rate. ch (t) represents the temperature inside the cavity, T max Let λ be the upper limit of temperature and λ be the tradeoff coefficient. Optimization uses projected gradients to update the temperature-time profile at piecewise control points. After each update, data is collected and appended to the original data, while the information matrix and the H-norm value are recorded to form design evidence.

[0037] The effects of the above mechanism are reflected in three aspects. First, the zero-point dataset and seal score decouple baseline estimation from leakage uncertainty, avoiding the misinterpretation of leakage as sensor drift. Second, the standard concentration trajectory uses the permeation tube metrology certificate parameters as the sole source of traceability, allowing the standard segment dataset to be verified by third parties. Third, the joint objective improves parameter sensitivity and compresses the worst-case bound without exceeding energy and safety boundaries, significantly shortening the available calibration time window and enhancing robustness to disturbances.

[0038] In this embodiment, the sensor on the return air side of the fully mechanized mining face executes this stage of the process. After establishing a near-field communication session and passing authentication, the valve switches to the zero-point channel, continuously collecting data to form a zero-point dataset. Subsequently, the valve is fully closed, triggering an acoustic pulse seal diagnosis to obtain a seal score. The authorized terminal generates an initial temperature-time profile based on the parameters of the permeation pipe metrology certificate and the energy and safety boundaries, starts heating, and collects a standard section dataset. During the data collection process, the temperature-time profile is slightly updated every fixed time interval based on the joint objective of the information matrix and the H-norm, with the update magnitude constrained by the heating rate and the upper temperature limit. Data collection ends after reaching the predetermined collection duration or information threshold. The final output raw data includes the zero-point dataset, the standard section dataset, the temperature-time profile, and the environmental quantity time series, while also recording the information matrix, the H-norm, and the seal score. This raw data is directly used in the parameter identification stage, with the joint objective and the seal score serving as weights and constraints in parameter identification, ensuring that subsequent parameter sets and online calibrations have traceable and verifiable physical evidence.

[0039] Preferably, when generating a zero-point dataset in a closed microcavity, an approximately zero-concentration environment is established by opening a zero-point microvalve and adsorbent, and the original sensor output, cavity temperature, cavity humidity and cavity pressure are synchronously collected according to a unified sampling clock to form a zero-point dataset with time-series annotation.

[0040] This invention aims to provide baselines, noise scales, and stable window annotations for parameter identification and subsequent online calibration without exposing external gases during the generation of zero-point datasets within a closed microcavity. Methodologically, a near-zero concentration environment is established by opening a zero-point microvalve and adsorbent. Simultaneously, the sensor's raw output, cavity temperature, cavity humidity, and cavity pressure are collected under a unified sampling clock, and then annotated with time series data to form a zero-point dataset.

[0041] The formation of the zero-point environment depends on the control of a closed microcavity and a zero-point microvalve. After the zero-point microvalve opens, the adsorbent rapidly physical adsorbs methane within the cavity, causing the volume fraction within the cavity to approach zero. To characterize this process, an equivalent kinetic model is used to describe the change in the volume fraction within the cavity over time:

[0042]

[0043] Among them, C ch (t) represents the volume fraction of methane in the cavity, k ads C is the adsorption rate constant. eq For the adsorption equilibrium volume fraction, k leak C is the equivalent leakage coefficient. out Let t represent the external volume fraction and t represent time. By introducing a brief period of pressure stabilization at the beginning of the zero-point segment and recording the cavity pressure changes, a priori estimate of the equivalent leakage coefficient can be given in this step, providing a starting point for subsequent seal diagnosis and worst-case constraints.

[0044] A unified sampling clock is provided by a hardware time base, and the unified sampling frequency is set to a fixed value. All channels share the same timestamp and frame number. The acquired signals include the sensor's raw output, cavity temperature, cavity humidity, and cavity pressure. To ensure consistency with subsequent steps, quantization gain and zero bias are recorded in the acquisition frame header to ensure that physical quantities can be reconstructed. Time series labeling is automatically completed by a state machine, distinguishing the start and end of the zero-point segment, the microvalve state, and the adsorption stabilization sub-segment.

[0045] The zero-point dataset is used for baseline and noise estimation, and simultaneously generates a stable window mask for sample selection in subsequent identification. To avoid misjudgments caused by external disturbances, a dual criterion of sliding variance and slope is used to determine the stable window.

[0046]

[0047] Where y(t) is the original output of the sensor, and Δt is the half-width of the sliding window. κ0 is the variance threshold, and κ0 is the slope threshold. For samples within the stable window, median statistics are used to obtain the baseline. Estimating the noise scale using the median absolute deviation in, As the baseline, σ ∈ This is the noise scale. This estimate is used as the initial value for bias and noise in subsequent robust deconvolution and variational Bayesian inference to avoid bias drift caused by short-term disturbances in the zero segment.

[0048] To ensure that the zero-point segment truly represents near-zero concentration rather than dilution caused by brief ventilation, this invention incorporates short-term statistics of cavity pressure and acoustic echo into the zero-point segment consistency check. If the cavity pressure stabilization time constant or acoustic decay time constant deviates significantly from the factory baseline within the zero-point segment, the segment is marked as unreliable and removed from the stabilization window mask. This process ensures that the zero-point dataset originates solely from adsorption removal and not from external flow field disturbances.

[0049] In terms of data quality control, based on a unified sampling clock, the first frame of the zero-point segment is written with a status identifier and session credential summary to ensure subsequent traceability. If the variance and slope thresholds are not reached within a preset time, the state machine automatically extends the duration of the zero-point segment without exceeding the energy and safety boundaries. If the energy and safety boundaries are insufficient to support the extension, the reason for not meeting the standards is recorded and the system enters a rollback state to avoid generating misleading zero-point datasets.

[0050] The effects of the above mechanism are manifested in three aspects. First, the adsorption-dominated kinetic model establishes the physical basis for the zero-point segment and explicitly expresses the sealing uncertainty through prior estimation of the equivalent leakage coefficient. Second, the stable window mask separates short-term disturbances from quantization noise, making the estimation of baseline and noise scales reproducible. Third, the unified sampling clock and frame-level index ensure seamless splicing with the standard segment dataset, providing a consistent time-domain basis for subsequent information matrix and worst-case calculations.

[0051] In this embodiment, a methane sensor deployed in the underground monitoring roadway performs zero-point segment data acquisition. After the near-field communication session is established and authenticated, the state machine switches to the zero-point segment, the zero-point microvalve opens, and the adsorbent begins operation. The uniform sampling frequency is set to a fixed value, acquiring the sensor's raw output, cavity temperature, cavity humidity, and cavity pressure. A short-term voltage stabilization is performed in the first second after acquisition begins to suppress mechanical fluctuations, and the equivalent leakage coefficient prior is estimated based on the cavity pressure sequence. Subsequently, the sliding variance and slope are calculated in real time to form a stable window mask. The samples covered by the mask are used to calculate the baseline and noise scale. If the threshold is not met within 2 seconds, the state machine automatically extends to 3 seconds and re-evaluates; if it is still not met, it is recorded as unqualified and a rollback is initiated. After acquisition, the zero-point dataset is written to the calibration log in time-series format, including the start and end dates of the zero-point segment, microvalve status, stable window mask, baseline and noise scale, equivalent leakage coefficient prior, and session credential summary. This zero-point dataset is directly used in the subsequent generation of standard segment datasets and parameter identification. The baseline is fixed as the bias term, the noise scale is used as the initial value of the observation noise, and the stable window mask is used as the basis for sample selection, thereby ensuring that the calibration results match the requirements of downhole safety boundaries, physical constraints and data consistency.

[0052] Preferably, the acoustic pulse seal diagnosis injects an acoustic pulse through a microactuator and collects the echo and cavity pressure transients. The seal score is calculated based on the echo attenuation constant and the cavity pressure settling time. The seal score is used to set the disturbance boundary and sample weights for the first-order inertial dynamic model.

[0053] The acoustic pulse seal diagnostic of this invention is used to rapidly quantify the sealing state of a closed microcavity under valve-closed and stationary conditions, and to convert the sealing state into numerical variables that can be directly used for subsequent modeling and optimization. The core idea of ​​the diagnostic is to inject a short-duration acoustic pulse into the cavity, and to utilize the characteristics of echo attenuation and cavity pressure stabilization process that are sensitive to micro-leakage and micro-gap to construct a seal score, and to constrain the perturbation boundary and sample weights of the first-order inertial dynamic model accordingly.

[0054] The microactuator is fixed to the rigid wall of the microcavity and generates single pulses or narrow-band pulse trains through a driving voltage. The pulse duration is shorter than the acoustic standing wave decay time. The acoustic sensing unit and the cavity pressure sensing unit synchronously acquire the echo amplitude and cavity pressure transient under a unified sampling clock, and the acquisition window covers the complete decay segment after excitation. The acoustic echo is fitted using an exponential decay sine model, and the cavity pressure is fitted using an exponential stabilization model. For ease of subsequent reference, the following expressions are used to describe the echo and stabilization processes. Where A(t) is the acoustic echo amplitude, A0 is the initial amplitude, and τ ac P is the acoustic decay time constant, f0 is the dominant frequency, and τ is the initial phase; ch (t) represents the cavity pressure, P0 represents the baseline pressure, ΔP represents the disturbance amplitude, and τ represents the t-pressure. p Let τ be the cavity pressure stabilization time constant, and t be time. τ is obtained through least squares or robust fitting. ac f0, τ p The Mahalanobis distance is constructed by comparing it with the mean and covariance of the factory baseline.

[0055]

[0056] in, Let S be the baseline feature vector, and ∑ be the baseline feature covariance matrix. The sealing score is defined as S. seal =exp(-ε seal The closer the value is to 1, the closer the seal is to the baseline.

[0057] The sealing score has two applications in this invention. The first is perturbation boundary mapping, where the perturbation radius is set as a function that monotonically changes with the sealing score in the worst-case design of the first-order inertial dynamic model. in, This is the upper bound of the equivalent perturbation. This is the calibration coefficient. As the sealing score decreases, the perturbation boundary automatically widens, allowing the subsequent H-norm indices to cover greater uncertainty. The second type is sample weight mapping, where sample weights are set as w in the data likelihood and loss function of parameter identification. k =min(1,S) seal ), where w kThese are the sample weights for segments collected after this diagnosis. These sample weights are used as pre-multiplication factors when calculating the information matrix, constructing the variational objective, and the residual metric. Segments with low sealing scores are automatically weighted less to avoid misjudging changes in response caused by leakage as model structure mismatch.

[0058] To ensure the traceability of diagnostic results and alignment with subsequent data, the entire process is conducted under a unified sampling clock, with the acoustic and cavity pressure channels sharing timestamps and frame numbers. Excitation parameters, fitting residuals, time constants, and seal scores are written to the calibration log, using the same indexing system as the zero-point dataset and standard segment dataset, thus supporting subsequent replay and auditing.

[0059] The effects are reflected in three aspects. First, the sealing score, derived from acoustic and pressure attenuation strongly correlated with geometric defects, can quantify the sealing state without introducing external gas, providing data support for the equivalent loss coefficient in the standard concentration trajectory. Second, the perturbation boundary mapping reduces the subjectivity of worst-case design, ensuring consistency between the H-norm index and the physical sealing state, avoiding overly conservative approaches for good sealing samples or overly optimistic approaches for poor sealing samples. Third, the sample weight mapping suppresses the influence of suspicious samples in the information matrix and variational inference, improving the consistency of parameter set estimation.

[0060] In this embodiment, during the stable airflow period at the fully mechanized mining face, the valve remains closed, and the microactuator emits a single pulse lasting less than 1 millisecond. The acoustic channel samples at a fixed frequency, and the cavity pressure channel samples synchronously with it. The acoustic decay time constant and the cavity pressure stabilization time constant are obtained by fitting the above expressions, and the dominant frequency is extracted. The feature vector is compared with the factory baseline, the Mahalanobis distance is calculated, and a sealing score is obtained. The sealing score is written into the calibration log of this session and is read by the standard segment acquisition and online temperature control to be executed. The disturbance boundary is obtained by mapping the sealing score and serves as the input for the H-infinity norm design; the sample weight is obtained by truncating the sealing score and serves as the pre-multiplication factor for the information matrix and variational objective. The subsequent standard concentration trajectory generation and temperature time profile optimization are carried out under the constraints of this boundary and weight. The resulting raw acquisition data and sealing score enter the parameter identification stage together. Through this process, a quantitative characterization of the sealing state is obtained without changing the external gas conditions downhole, and this characterization is transformed into a disturbance boundary and weight that can be used for modeling, which greatly improves the reproducibility and robustness under complex working conditions.

[0061] Preferably, the standard concentration trajectory is calculated based on the permeability coefficient, membrane thickness, effective area and pressure difference to obtain the permeation flux. The standard concentration trajectory is obtained within the closed volume according to the law of mass conservation, and the standard concentration trajectory and temperature-time profile are written into the standard segment dataset.

[0062] This invention generates a standard concentration trajectory and a standard segment dataset within a closed microcavity. It implements a traceable input excitation based on the parameters of the permeation tube calibration certificate and links it with a temperature-time profile, forming an experimental process highly sensitive to parameter identification and constrained by safety boundaries. The core idea is to slowly introduce methane into the closed volume via permeation flux, causing the methane volume fraction within the cavity to increase over time according to a calculable mass conservation law. The entire trajectory is jointly determined by the calibration certificate parameters and the temperature control trajectory. All raw quantities are recorded at a unified clock and written into the standard segment dataset.

[0063] Permeation flux is calculated based on the permeability versus temperature, membrane thickness versus pressure difference given in the metrology certificate. If the certificate provides a temperature function, the flux is defined as follows:

[0064]

[0065] Among them, J(T) s (t) represents the permeation flux, P m (T) is the permeability function, Δp is the pressure difference across the membrane, d is the membrane thickness, and T s (t) represents the temperature-time profile. The temporal evolution of the cavity volume fraction is jointly described by mass conservation and equivalent losses:

[0066]

[0067] Among them, C ch (t) represents the volume fraction of methane in the cavity, A represents the effective permeation area, and V... ch k is the volume of the cavity. loss C is the equivalent loss coefficient. out This represents the external volume fraction. The prior interval for the equivalent loss coefficient is obtained from the aforementioned sealing score mapping, avoiding misjudging attenuation caused by micro-leakage as changes in sensor dynamic parameters.

[0068] The purpose of temperature-time profiles is to shape the trajectory by changing the independent variable of the permeability function, satisfying energy limits, upper temperature limits, and upper heating rate limits, while improving the sensitivity and time constant recognition within a limited time. To this end, during data acquisition, the temperature-time profile is updated online in small increments according to the joint objective of the information matrix and the H-norm. The update magnitude is constrained by safety boundaries, and data acquisition continues after the update to ensure the trajectory is both "identifiable" and "controllable."

[0069] In terms of data organization, the standard segment dataset records the sensor's raw output, cavity temperature, cavity humidity, and cavity pressure according to a unified sampling clock. It also records the standard concentration trajectory calculated by the above formula and the temperature-time profile at that time. All data frames are timestamped and labeled with frame sequence numbers on the acquisition side and written to the calibration log to ensure traceability and replayability.

[0070] To mitigate the impact of thermal inertia and incomplete mixing on trajectory fitting, this invention incorporates two constraints during the data preprocessing stage. First, segments are labeled during the temperature rise and hold phases, with segment boundaries serving as weight switching points during information matrix integration, preventing the transition segment from being mistakenly used as a steady-state response. Second, quality thresholds are set for abnormal fluctuations in cavity pressure and intracavity temperature; frames exceeding these thresholds are labeled as unreliable and reduced in weight from the standard segment dataset, making subsequent identification less sensitive to individual fluctuations.

[0071] The above mechanism directly corresponds to three types of effects. First, the standard concentration trajectory is derived from the parameters of the metrology certificate, forming an input benchmark that can be verified by a third party, avoiding "calibrating the unknown with the unknown." Second, the temperature-time profile is fine-tuned online under the joint objective, so that the trajectory simultaneously contains both rising edge and quasi-steady-state information within a limited time, improving parameter identifiability and automatically relaxing the worst-case scenario without being overly optimistic in the case of poor sealing. Third, a unified clock and log-based storage ensure that each data point can be associated with temperature control commands, flux calculations, and sealing status, meeting the traceability requirements of downhole supervision.

[0072] In this embodiment, the sensor within the return air duct performs this phase using a closed microcavity. After establishing a near-field communication session and loading certificates and instructions, the device first completes the zero-point segment and seal diagnosis, obtaining a seal score and mapping it to a priori interval of the equivalent loss coefficient. Then, it enters the standard segment: the authorized terminal issues a temperature-time profile including heating, holding, and cooling according to energy and safety boundaries; the micro-heating film performs temperature control, and the acquisition side synchronously records the sensor's raw output, cavity temperature, cavity humidity, and cavity pressure at a uniform sampling frequency. The permeation flux is calculated based on the certificate parameters, and a standard concentration trajectory is generated in real-time according to the mass conservation equation. When the preset sampling window is reached, the control points of the temperature-time profile are slightly updated based on the joint objective of the information matrix and the H-norm. After the update, acquisition continues, and the newly added samples and corresponding trajectories are appended to the standard segment dataset. The standard segment ends when the accumulated information reaches a threshold or approaches the energy boundary, and the final temperature-time profile, standard concentration trajectory, mass threshold annotation, and safety boundary occupancy status are written. The standard segment dataset and temperature-time profile serve as inputs for subsequent parameter identification. The equivalent loss coefficient corresponding to the sealing score is used as a priori to limit the propagation of uncertainty, ensuring that verifiable, identifiable and controlled calibration data can still be obtained in complex downhole environments.

[0073] Preferably, the temperature-time profile is iteratively updated by a joint objective consisting of an information matrix as the information content index and the H-norm as the worst-case bound index, to satisfy the energy limit, the upper limit of temperature, and the heating rate limit, and the updated temperature-time profile and the joint objective value are recorded as design evidence.

[0074] The temperature-time profile optimization of this invention aims to generate a heating trajectory that simultaneously facilitates parameter identification and suppresses the amplification of unknown disturbances within the intrinsically safe boundary of the well. The temperature-time profile is represented by a piecewise function composed of control points, with slope-limited interpolation used between the control points to ensure continuous and controllable heating and cooling processes. The optimization does not alter the closed microcavity, permeability calculation, or data sampling framework; it only adjusts the control points within permissible limits, ensuring that the standard segment dataset contains the segments most contributing to sensitivity and time constant identification within a finite time period, while limiting the equivalent disturbances introduced by the sealed state to an acceptable range.

[0075] In principle, an information content metric and a worst-case bound metric are introduced to form a joint objective. The information content metric uses the logarithmic determinant of the Fisher information matrix to measure the identifiability of the parameter set at the current temperature time profile. The worst-case bound metric uses the H-norm concept to estimate the upper bound of the amplification ratio of the energy of the unknown disturbance to the residual energy. A weighted subtraction method is used to obtain a trade-off between identifiability and robustness. The core expression is as follows:

[0076]

[0077]

[0078] Where y(t) is the sensor measurement output, α is the sensitivity, τ is the time constant, J(t) is the sensitivity matrix of the measurement to the parameter, R is the observation noise covariance, and w is the equivalent perturbation. The disturbance radius is obtained from the aforementioned sealing score mapping, λ is the weighting coefficient, and T s (t) represents the temperature-time profile. The above expression is only used to define the objective function and sensitivity; the actual solution is implemented numerically on the device.

[0079] The optimization process is jointly constrained by intrinsic safety and power supply capability. Energy and safety boundaries are derived from near-field power supply, thermal design, and certification limits, and are implemented according to three types of constraints: cumulative energy, cavity temperature, and rate of temperature change. The constraint expressions are as follows: T ch (t)≤T max , Where P(t) is the heating power, E max For energy budgeting, T ch (t) represents the temperature inside the cavity, T max r is the upper limit of temperature. max This is the upper limit of the heating rate. Constraints are forcibly satisfied by the projection operation on each update. If any constraint is critical, the controller automatically reduces the control point step size or extends the interval between segments to ensure that the trajectory is executable.

[0080] In implementation, the temperature time profile is represented by several control points, with the interval and number of control points defined in the calibration script. During iteration, firstly, based on the current standard segment dataset and environmental time series, the observation noise covariance and sensitivity matrix are estimated, and then the information content index and worst-case index are calculated according to the above formula. Subsequently, the numerical gradient of the target with respect to the control point temperature is calculated at each control point, and the control point temperature is updated using the projection gradient method with adaptive step size. The update follows three rules: conforming to energy and safety boundaries; prioritizing the increase of signal rising edge information sensitive to time constants during the temperature rise phase; and prioritizing the suppression of worst-case amplification during the hold and cooling phases. After the update is completed, data acquisition continues immediately, and new samples and synchronous temperature control records are appended to the standard segment dataset. The information content index and worst-case index are recalculated synchronously, forming a closed-loop iteration.

[0081] To avoid overfitting to single perturbations or local noise, iterative termination conditions are set, including an information gain threshold, a worst-case threshold indicating no further improvement, and an energy budget threshold. Updates cease upon reaching any of these thresholds, and the process either enters a natural cooling phase or ends the standard phase. Throughout the process, joint target values, control point values ​​for each round, sensitivity summaries, and constraint occupancy ratios are written to the calibration log in chronological order, collectively referred to as design evidence. This evidence is used for regularization terms and consistency checks in subsequent parameter identification, and also serves as a quality audit record.

[0082] The optimization contributes to the results in three ways. First, driven by the information content index, the standard segment dataset contains more segments with high discrimination of sensitivity and time constant within the same sampling duration, enabling subsequent parameter sets to converge faster. Second, through the synergy of the worst-case index and the sealing score mapping, the temperature time profile automatically reduces the excitation of high-amplification frequency bands when the sealing is poor, reducing the contribution of unknown disturbances to the residuals and improving estimation stability. Third, through strict energy and safety boundary projection, the optimization will not produce unexecutable trajectories, ensuring the feasibility and reproducibility of downhole operations.

[0083] In this embodiment, the initial temperature time profile of a sensor in the return airway consists of three segments: heating, holding, and natural cooling. After data acquisition begins, the authorized terminal calculates the first round of information content and worst-case indicators, finding the worst-case indicator to be too high. Due to the moderate sealing score and large disturbance radius mapping, the optimization strategy first reduces the temperature of the holding segment to decrease amplification during high throughput, while slightly increasing the slope of the heating segment to improve the sensitivity of the rising edge to the time constant. After control point changes, data acquisition continues, new data is added, the information content increases, and the worst-case indicator decreases. In the second iteration, the energy budget approaches the threshold, the algorithm automatically reduces the step size and limits further increases in the heating segment, then terminates the update and enters natural cooling. The design evidence for this calibration includes the joint target value for each round, the control point sequence, and the constraint occupancy ratio, which are written to the calibration log along with the standard segment dataset. Subsequent parameter identification uses the design evidence to constrain the variational objective. After consistency verification, a set of corrected parameters is generated and distributed, realizing a closed loop between online calibration and recalibration triggering strategies.

[0084] Based on the original collected data, robust deconvolution and variational Bayesian inference are performed under the first-order inertial dynamic model to obtain the robust point estimation parameter set and posterior distribution and form the combined uncertainty.

[0085] This invention uses raw data acquired through a closed microcavity as input in the parameter identification stage. Under a first-order inertial dynamic model, robust deconvolution is first performed to obtain a robust set of estimated parameters. Then, variational Bayesian inference is used to obtain the posterior distribution of the parameters, and the two types of uncertainty are combined into a combined uncertainty, thus providing a confidence interval and confidence weights for online correction and recalibration triggering. The raw acquired data includes a zero-point dataset, a standard segment dataset, a temperature time profile, environmental quantity time series, and a sealing score. The zero-point dataset provides baseline and initial noise scale values, and the sealing score is used for weight and perturbation boundary mapping to avoid leakage effects being misinterpreted as model mismatch.

[0086] The first-order inertial dynamic model simplifies the hysteresis of sensor adsorption and desorption into a single-pole state equation, where the state is the equivalent adsorption state, the input is the volume fraction of methane in the cavity, and the output is the sensor's electrical signal. The continuous and discrete forms are respectively...

[0087]

[0088] y(t)=αF(z(t),E(t))+β+∈(t),r k =y k -αF(z k E k )-β

[0089] Where z(t) is the equivalent adsorption state, C ch(t) represents the intracavity volume fraction, τ is the time constant, α is the sensitivity, β is the baseline, F(·) is the static mapping, E(t) is the environmental vector, ∈(t) is the observation noise, y(t) is the sensor output, Δt is the sampling interval, and r k For discrete residuals, the parameter set is denoted as Θ = {α, β, τ}.

[0090] Robust deconvolution uses consistent segments as the sample set, employs weighted loss to suppress outliers, and regularizes the sensitivity in the worst-case sense. The weights are obtained from a sealed score mapping, and the perturbation boundary is used to control the amplification of unknown perturbations by the residuals. The objective function is:

[0091]

[0092] Where ρ(·) is the robust cost function, λ ∞ S is determined by the worst-case radius. seal For sealing rating, The calibration coefficients are used. Optimization is achieved by adjusting the outer search time constant and the inner analytical update sensitivity, with the baseline β fixed by the median of the zero-point dataset. This process outputs a robust set of estimated parameters. Compared with the worst-case scenario indicator.

[0093] Based on the feasible solution provided by point estimation, variational Bayesian inference is introduced to characterize statistical uncertainty. Student's t-distribution is used for observation noise to accommodate peak interference, and the prior is constrained by the physical feasible region and zero-point baseline. A family of Gaussian approximations is chosen for the variational approximation, and the lower bound of the evidence is optimized.

[0094]

[0095] Where q(Θ) is the posterior approximation, μ is the mean, ∑ is the covariance, KL is the relative entropy, p(Θ) is the prior density, and p(y) is the relative density. k |Θ) represents the likelihood of student t, w k The sample weights are used. The mean is initialized with a robust point estimate parameter set, and the initial covariance is given by physical upper and lower bounds. Iteration with reparameterized gradients and adaptive step sizes is employed until the lower bound of evidence converges. This process outputs the posterior distribution of the parameters. Combined uncertainty integrates statistical variance and worst-case amplification, reflecting both the effects of random noise and structural disturbances caused by incomplete sealing and mixing. Definition:

[0096]

[0097] Where, ∑ αα ,∑ ττ ,∑ ββ κ is the main diagonal element of the covariance. ∞ J is the scaling factor. ∞This serves as the worst-case bound indicator. The combined uncertainty is then used for the confidence band and the node weights of the segment-level fusion in online correction.

[0098] The effects of this stage are reflected in three aspects. First, robust deconvolution is insensitive to occasional disturbances when estimating time constants and sensitivity within consistent segments, and point estimation remains stable within short time windows. Second, variational Bayes provides posterior and correlation information for parameters, providing statistical input for optimizing segment reference distributions and graph consistency. Third, combined uncertainty explicitly includes structural uncertainties caused by sealing in the confidence band, avoiding overconfidence in online correction.

[0099] In this embodiment, after a sensor completes standard section data acquisition in the return air roadway, consistent sub-segments are selected based on sealing scores, sample weights are calculated, and perturbation boundaries are set. The robust deconvolution outer loop searches for initial time constant values ​​on a logarithmic scale, while the inner loop analytically solves for sensitivity, yielding a robust point estimate parameter set and a worst-case index. Subsequently, the variational approximation is initialized with the robust point estimate parameter set, and the lower bound of evidence is optimized using Student's t-likelihood and the prior of the physically feasible region, outputting the posterior mean and covariance of the parameters. Finally, the three uncertainties are calculated according to the combined uncertainty formula and written into the calibration log along with the robust point estimate parameter set and posterior parameters. This result directly generates confidence intervals for online calibration during the deployment phase and participates as node weights in the Wasserstein centroid and L1 norm consistency optimization during segment-level fusion, achieving a traceable governance closed loop triggered by parameter release and recalibration.

[0100] Preferably, the baseline is obtained by statistical analysis of the median of the zero-point dataset within the stable window, and the stable window is determined by the sliding variance threshold and the derivative threshold. The baseline is used to fix the bias term in the first-order inertial dynamic model.

[0101] This invention uses the zero-point dataset to determine the sensor baseline and noise scale, and thereby fixes the bias term in the first-order inertial dynamic model, decoupling the identification of sensitivity and time constant from baseline drift. The zero-point segment is activated after the valve switches to the zero-point channel and the adsorbent operates, collecting the sensor's raw output, cavity temperature, cavity humidity, and cavity pressure. A unified sampling clock and a unified frame number are used to ensure that the data can be spliced ​​with the standard segment data in the time domain.

[0102] The zero-point segment first identifies the stable window. To avoid bias introduced by short-term mechanical disturbances, thermal disturbances, or occasional noise, this invention uses a dual threshold criterion of sliding variance and derivative to give the set of stable times:

[0103]

[0104] Where y(t) represents the sensor electrical signal, and Δt represents the half-width of the sliding window. Let κ0 represent the variance threshold, κ0 represent the derivative threshold, and t represent time. The set of times that satisfy both conditions is denoted as the stability window. If the stability window length is insufficient to support statistical robustness, the state machine extends the duration of the zero-point segment or relaxes the threshold, but does not exceed the energy and safety boundaries. This processing is defined as a fixed priority in the calibration script.

[0105] The baseline was obtained using median statistics within the stability window. in, This represents the baseline estimate. To provide a noise scale for subsequent weight initialization, this invention uses the median absolute deviation form:

[0106]

[0107] Where, σ ∈ This represents the scale estimate of the observed noise. The above two equations are calculated only within the zero-point segment, and the results, along with the stable window mask, are written into the calibration log to form a traceable record. After obtaining the baseline and noise scale, the measurement and dynamic relationship is organized according to a first-order inertial model, and the baseline is fixed as a bias term during parameter identification. The measurement and dynamic relationship is as follows: y(t)=αF(z(t),E(t))+β+∈(t), where z(t) represents the equivalent adsorption state, C ch (t) represents the volume fraction of methane in the cavity, τ represents the time constant, α represents the sensitivity, β represents the bias term, F(·) represents the static mapping, E(t) represents the environmental vector, and ∈(t) represents the observation noise. These are fixed in subsequent solutions. Or equivalently construct a centralized signal Among them, y c (t) represents the centered signal. Through this processing, the contributions of sensitivity and time constant to the residual are separated from the baseline drift, avoiding strong coupling between sensitivity and bias terms, and improving the identifiability of the Fisher information matrix for the parameter set.

[0108] To ensure the stabilization window is not mistakenly triggered by temporary dilution from the external flow field, this invention performs a short-term consistency check on the cavity pressure and acoustic echo statistics within the zero-point segment. If the cavity pressure stabilization time constant or the acoustic decay time constant deviates significantly from the factory baseline, the corresponding time period is removed from the stabilization window. This removal strategy is seamlessly integrated with the seal scoring, avoiding mapping leakage effects to the baseline estimate. If the stabilization window after removal is still insufficient, the state machine extends the acquisition or terminates calibration in a preset order and records the reason, preventing the generation of unreliable baselines when evidence is insufficient.

[0109] The baseline determination method of this invention brings three benefits. First, with the bias term fixed, the cost function in the parameter identification stage no longer uses free parameters to absorb the slow temperature drift and quantization bias, significantly reducing the estimation variance of sensitivity and time constant. Second, the centralized signal unifies the reference system among multiple devices, making mean alignment a natural result when performing distribution fusion and consistency optimization on the segment adjacency graph, thus improving the comparability of parameters across devices. Third, the stability window and noise scale are given by actual measurements of the zero-point segment, allowing subsequent temperature time profile optimization to use consistent noise covariance and weight initialization, reducing the need for repeated trial and error.

[0110] In this embodiment, a sensor on the return air side of the fully mechanized mining face enters the zero-point segment according to the calibration script. A uniform sampling frequency is set to a fixed value, and sensor electrical signals, cavity temperature, cavity humidity, and cavity pressure are continuously collected. The sliding variance and derivative are calculated online to obtain a stable window; the median value is calculated within the stable window to obtain a baseline estimate, and the noise scale is obtained using the median absolute deviation. Subsequently, the baseline is fixed as a bias term, a centered signal is constructed, and the stable window mask, baseline estimate, and noise scale are written to the calibration log. After entering the standard segment, parameter identification directly uses the centered signal and the fixed bias term for robust deconvolution and variational Bayesian inference. The results show that the uncertainty range of sensitivity and time constant is significantly reduced compared to the approach without a fixed bias term. This embodiment demonstrates that using the median of the stable window of the zero-point dataset to statistically fix the bias term can stably and reproducibly provide the baseline reference required for parameter identification under complex downhole thermal conditions, and improve cross-device consistency in subsequent segment-level fusion.

[0111] Preferably, robust deconvolution is performed on a consistent segment that satisfies the temperature stability and sealing score thresholds, and a first-order inertial kernel is used to obtain robust point estimates of sensitivity and time constant; variational Bayesian inference uses Student's t-distribution observation noise and physical feasible region prior, and uses robust point estimates as anchors to perform distribution near-end fusion to generate posterior distribution and combined uncertainty.

[0112] In the parameter identification stage, this invention first performs robust deconvolution on the raw acquisition data obtained from the closed microcavity within a consistent segment that meets the temperature stability threshold and the sealing score threshold, and obtains robust point estimates of sensitivity and time constant. Then, variational Bayes inference is used to give the posterior distribution of parameters, and the combined uncertainty is constructed by the synergistic construction of point estimates and statistical variance, providing a traceable and confident basis for online correction and subsequent segment-level fusion.

[0113] The consistency segment is obtained by intersecting the temperature stability mask and the sealing score mask. The temperature stability mask is generated based on the sliding variance threshold and the derivative threshold, while the sealing score mask is generated by acoustic pulse sealing diagnosis. Only samples that simultaneously meet both thresholds are included in this stage of calculation, thus reducing the interference of temperature drift and micro-leakage at the source.

[0114] A first-order inertial dynamic model is used to characterize the hysteresis-static mapping relationship of the sensor. The state evolution and measurement relationship are written as follows: y(t)=αF(z(t),E(t))+β+∈(t), where z(t) is the equivalent adsorption state, C ch (t) represents the volume fraction of methane in the cavity, τ is the time constant, α is the sensitivity, β is the baseline, F() is the static mapping, E(t) is the environmental vector, ∈(t) is the observation noise, and y(t) is the sensor output. The baseline estimate is given in the zero-point dataset, so β ​​is fixed in the identification.

[0115] Robust deconvolution uses first-order inertial kernel discrete convolution as the forward operator, employs a weighted robust cost function to suppress outliers, and uses worst-case bound regularization to constrain sensitivity to combat unmodeled perturbations. The objective function is:

[0116]

[0117] r k =y k -αF(z k E k )-β,w k =min(1,S) seal )

[0118] in, For consistent segment indexes, ρ(·) is the robust cost function, and S seal For sealing score, λ ∞ The worst-case radius and safety strategy are determined. The solution involves a logarithmic search of the time constant on the outer loop, refined with Gauss-Newtonian precision. The inner loop updates the sensitivity analytically or in a closed loop under a given time constant, outputting a robust set of estimated parameters. After the point estimation yields a feasible solution, variational Bayesian inference is used to obtain the posterior distribution of the parameters to characterize the statistical uncertainty. The Student's t-distribution is chosen for the observation noise to accommodate occasional spikes. The prior is constrained by the physical feasible region and the zero-point baseline. A Gaussian variational family is used for the approximate posterior. Maximizing the lower bound of evidence:

[0119]

[0120] Among them, Θ={α,β,τ}, p(y k |Θ) represents the student's t-likelihood, p(Θ) represents the prior, and μ and ∑ represent the variational mean and covariance, respectively. The variational mean is initialized with robust point estimation, and the initial covariance is given by physical upper and lower bounds. Iterations are performed until convergence using reparameterized gradients and adaptive step sizes. To unify worst-case robustness with statistical posterior, this invention introduces distributed near-end fusion, using robust point estimation as an anchor to perform a near-end update on the variational posterior:

[0121]

[0122] Obtain the posterior distribution after fusion Where ξ is the fusion weight, For robust point estimation, the combined uncertainty combines statistical variance with worst-case indexes, used for upper confidence bands and cross-device weighted estimation. in, To determine the diagonal elements of the fused covariance, k ∞ J is the scaling factor. ∞ This is the worst-case indicator.

[0123] The above process yields three benefits. First, robust deconvolution operates only on consistent segments and introduces worst-case regularization, making the point estimates of time constant and sensitivity insensitive to occasional perturbations and micro-leakage. Second, variational Bayes provides information on parameter uncertainty and correlation, offering statistical input for segment reference distribution and graph-wide consistency optimization. Third, distribution proximal fusion and combined uncertainty unify the "worst-case" and "variance" under the same index system, facilitating the use of a unified decision-making logic in online calibration and recalibration triggering.

[0124] In this embodiment, after a sensor completes standard section data acquisition in the return air roadway, consistent sub-segments are selected based on temperature stability threshold and sealing score threshold. Sample weights are calculated, and a worst-case radius is set. Robust deconvolution outer loop performs a 10-point logarithmic grid search on the time constant and refines it with Gauss-Newtonian optimization. The inner loop analytically updates the sensitivity, resulting in a robust set of estimated parameters. Subsequently, Gaussian variational estimation is initialized using this point estimate, and the lower bound of evidence is optimized using Student's t-likelihood and the prior of the physically feasible region, outputting the posterior mean and covariance. Then, near-end fusion of distributions is used to obtain the fused posterior distribution, and three uncertainties are calculated using the combined uncertainty formula. The final result is written to the calibration log and sent to the online module. The online module generates a correction output based on the fused mean and uses the combined uncertainty as the node weight for alarm threshold and section fusion, achieving an integrated closed loop from data, model, to governance strategy.

[0125] The posterior distributions of multiple sensors are fused on the segment adjacency graph, and the Wasserstein centroid is calculated to obtain the segment reference distribution. Combined with norm 1 consistent optimization, a set of corrected parameters is obtained and distributed for online calibration and drift recalibration triggering. The segment reference distribution is used as the prior for the next round of input design and parameter identification.

[0126] This invention fuses and uniformly publishes parameter information from multiple sensors within a segment. Specifically, it maps the posterior distribution of parameters obtained from the previous stage for each sensor to the segment's adjacency graph, performs distribution-level fusion and point-level consistency optimization on the graph, and then issues a set of corrected parameters for online calibration and drift recalibration triggering. Simultaneously, it writes back the segment reference distribution as the prior for the next round. This process transforms the uncertain information of a single device into shared knowledge at the segment level, preventing single-point anomalies from dominating the calibration results.

[0127] The segment adjacency graph is constructed based on the tunnel topology and ventilation connections. Nodes act as sensors, and edge weights reflect spatial adjacency and airflow consistency. Each node carries a posterior parameter distribution, represented by a Gaussian distribution, with the mean being the posterior mean of the parameters and the covariance being the posterior covariance. The parameter vector consists of sensitivity, bias term, and time constant. To measure node reliability, combined uncertainty is introduced to obtain confidence weights for each parameter, thereby obtaining the overall node weight and the joint weight of the edges.

[0128] Distribution-level fusion uses Wasserstein centroids to obtain the reference distribution for each segment. The objective is to minimize the weighted sum of the squared Wasserstein distances from the posterior distribution of each node to the reference distribution.

[0129]

[0130] in, Let μ represent the posterior distribution of the parameters of the i-th sensor. i Let ∑ represent the posterior mean. i Let ω represent the posterior covariance. i W represents the node weight, and W2 represents the Wasserstein distance. In the Gaussian case, the reference distribution remains Gaussian, with the mean being a weighted sum. The covariance is solved using Bures-Wasserstein fixed-point iteration ∑ (k+1) =∑ (k)1 / 2 (∑ i ω i (∑ (k) - 1 / 2 ∑ i ∑ (k)-1 / 2 ) 1 / 2 ) 2 ∑ (k)1 / 2 , where ∑ (k) For the reference covariance estimate of the k-th iteration, ∑ (k+1) To update the results, the iteration is initialized with a positive definite matrix until the norm of the difference between two consecutive values ​​is less than a set threshold. Weight ω i The weight is determined by both the combined uncertainty and the graph connectivity. The smaller the combined uncertainty and the stronger the graph connectivity, the greater the weight.

[0131] After obtaining the segment reference distribution, point-level consistent optimization is performed to output the set of corrected parameters that can be executed online for each sensor. A graph-consistent optimization model is constructed:

[0132]

[0133] Where, Θ i Let w represent the parameter vector of the i-th sensor. ij W represents the edge weight. i Let be a diagonal weight matrix composed of combined uncertainties, where λ and η are tradeoff coefficients, and ε represents the set of edges. The first term compresses the parameter differences between adjacent devices on the graph to achieve consistency; the second term brings the corrected parameters closer to their respective posterior means and adaptively weights them according to uncertainty; and the third term pulls each device toward the segment reference mean. The solution employs a proximal iteration using the alternating direction multiplier method, performing soft thresholding and quadratic shrinkage updates node-by-node, and differential soft thresholding updates edge-by-edge, until both the original residual and the dual residual simultaneously satisfy the convergence condition. The output is the set of corrected parameters.

[0134] The corrected parameter set is distributed to each sensor for online calibration. During the online phase, the device calculates the state evolution based on the corrected sensitivity, bias term, and time constant, and outputs the corrected volume fraction. Simultaneously, alarm thresholds and anomaly limits are set based on the combined uncertainty. To achieve closed-loop management, segment deviation also needs to be defined. Where, d i This represents the distribution distance of the i-th sensor. When the distance exceeds the threshold or the online residual continuously exceeds the limit, the drift recalibration process is triggered and the sensor is added to the priority queue.

[0135] The segment reference distribution is directly written back as the prior for the next round of input design and parameter identification. The prior form is Gaussian, with the mean taken from the segment reference mean and the covariance taken from the segment reference covariance, and it enters the joint objective and variational inference of the information matrix and worst bound in the next round. In this way, the consensus of the segment range is forwarded as "default knowledge" in the next round, making the optimization direction of the temperature time profile more focused on the parameter dimensions with large differences, and shortening the time and energy cost of recalibration.

[0136] This mechanism delivers three benefits. First, distributed fusion complements the posterior uncertainties of individual devices across segments, resulting in a verifiable segmental reference distribution and preventing parameter drift caused by isolated anomalies. Second, graph-consistent optimization achieves cross-device consistency without sacrificing local evidence, outputting an executable set of corrected parameters and naturally suppressing the influence of outliers. Third, prior write-back and drift triggering form a closed loop, enabling subsequent input design and parameter identification to possess historical memory and adaptive capabilities.

[0137] In this embodiment, after parameter identification is completed at multiple measuring points in the return air roadway and transport roadway, the system aggregates the posterior distribution of parameters for each node on the segment adjacency graph, calculates weights according to combined uncertainty, and performs Wasserstein centroid iteration to obtain the segment reference distribution. Then, using the mean of this reference distribution as an anchor, and combining edge weights and node weights, it solves the graph-consistent optimization to obtain the corrected parameter set for each measuring point and distributes it. After going online, the system continuously calculates the distribution distance and online residual from each device to the segment reference distribution. If any indicator exceeds a threshold, the device is added to the recalibration queue. In the next round of calibration, the segment reference distribution is loaded as a priori, the search range of control points for the temperature-time profile is reduced accordingly, and the calibration time and energy consumption decrease, while maintaining the consistency and traceability of parameters across devices.

[0138] Preferably, the posterior distribution of multiple sensors is weighted by node uncertainty and mean smoothed on the segment adjacency graph. Then, the Wasserstein centroid is calculated to obtain the segment reference distribution, which serves as the prior for the next round of input design and parameter identification.

[0139] This invention performs distribution-level fusion of parameter information from multiple sensors within a segment. The aim is to form a verifiable segment reference distribution based on collective evidence, and then write this reference distribution back as the prior for the next round of input design and parameter identification, thereby improving cross-device consistency and shortening recalibration time. The inputs are the posterior parameter distribution of each sensor, the segment adjacency graph, and the node weights derived from combined uncertainty. The parameter vector consists of sensitivity, bias terms, and time constants.

[0140] First, a weighted smoothing is applied to the posterior mean on the segment adjacency graph. Let the posterior distribution of the i-th sensor be... Where μ i For the mean, ∑ i Let w be the covariance. ij The node confidence level γ is obtained from the combined uncertainty. i Define weighted edge weights Mean smoothing is achieved by solving:

[0141]

[0142] get Where λ is the anchoring coefficient. Stacked into vectors and denoted as L by the graph Laplace, the linear system (L+λI)m # =λm can be solved in one step, where m is the original mean vector after concatenation. #This is the smoothed mean vector. This step pulls spatially adjacent nodes with similar airflow towards a common direction while preserving the individual evidence of each node. Subsequently, the Wasserstein centroid is calculated on the Gaussian family to obtain the segment reference distribution. Let the weight ω i ∝γ i Then normalize and solve:

[0143]

[0144] in In the Gaussian case, the centroid remains Gaussian. The mean is... covariance Obtained by iteration using Bures fixed points:

[0145]

[0146] Iterate to ||∑ (k+1) -∑ (k) || F Below the threshold. This approach measures the difference by distribution distance, which preserves the uncertainty structure of each node better than the arithmetic mean.

[0147] get Then, construct the priors for the next round. During the input design phase, the prior joint objective is used to constrain the search direction of the temperature-time profile, prioritizing the concentration of information on the relevant parameters. A key sensitivity dimension is the principal axis. During the parameter identification phase, the prior, as the prior density of variational Bayes, enters the lower bound of evidence, reducing the impact of isolated noise on the posterior. To ensure robustness, a worst-case scaling term can be superimposed on the prior covariance to explicitly preserve historical structural uncertainties.

[0148] To suppress the influence of outliers on the reference distribution, this invention introduces node confidence into the weights, automatically reducing the weights of nodes with high combinatorial uncertainty. A strategy of finding the centroid within connected components is employed in the graph topology to prevent weakly connected regions from being pulled by strongly connected regions. A symmetric positive definite solver is used for the linear system, with Bures iterations initializing from a positive definite diagonal matrix to ensure numerical stability.

[0149] The mechanism's effectiveness is reflected in three aspects. First, distribution-level fusion integrates the posterior a priori information of each node using the Wasserstein metric, resulting in a verifiable segment reference distribution and reducing the impact of single-point anomalies on group decision-making. Second, prior write-back allows the next round of input design and inference to have historical memory, typically reducing the number of control point searches and sampling time. Third, the two-level processing of smoothing and centroid simultaneously utilizes spatial topology and statistical uncertainty, ensuring that the reference distribution both conforms to the physical correlation of segments and preserves node differences.

[0150] In this embodiment, after the eight sensors deployed from the transport roadway to the return airway complete parameter identification, the system constructs an adjacency graph based on the airflow connectivity, calculates the combined uncertainty, and obtains γ. i Solving for the mean smoothing and Wasserstein centroid using the method described above yields the following results. and The next round of calibration scripts will Loading is a priori, and optimization of the temperature-time profile prioritizes excitation and In the direction corresponding to the main axis, the acquisition time was reduced by approximately one fixed sampling window compared to the previous round. The differences in the sets of correction parameters published by each device within the segment converged to a nearby level on the graph, the online residual exceedance rate decreased, and the number of devices triggering recalibration decreased. The above results were written to the calibration log for subsequent auditing and reproduction.

[0151] Preferably, the corrected parameter set is obtained by solving the L1 norm consistent optimization on the segment adjacency graph. The L1 norm consistent optimization is implemented iteratively using the alternating direction multiplier method. The corrected parameter set is written into the parameter version record and digitally signed and issued. The online calibration output is used to calculate the Wasserstein distance between the sliding window drift index and the segment reference distribution. When the set threshold is reached, the calibration instruction set is executed again.

[0152] This invention publishes a set of corrected parameters within a segment, targeting online calibration and recalibration triggering. The process consists of three parts: graph-consistent optimization, parameter version recording, and operational monitoring. The inputs are the posterior distribution of parameters for each sensor, combined uncertainty, segment adjacency graph, and edge weights. The parameter vector consists of sensitivity, bias term, and time constant.

[0153] A norm-consistent optimization model is established on the segment adjacency graph. The goal is to constrain the parameter differences between adjacent nodes while preserving the evidence of each node, and to align with the segment reference mean. The optimization problem is:

[0154]

[0155] Where, Θ i ={α i ,β i ,τ i} represents the parameters of the i-th device, w ij For edge weights, μ i W is the posterior mean of the device. i Let be the diagonal weight matrix composed of combined uncertainties. Let λ be the reference mean for the segment, and η be the weighting coefficients. This problem is solved iteratively using the alternating direction multiplier method, introducing the edge variable z. ij With dual variable u ij In each iteration, node proximal updates, edge variable soft threshold updates, and dual updates are performed. Taking edge variable updates as an example:

[0156]

[0157] Where ρ is the augmented parameter, This is a soft threshold operator. Iteration continues until the original residual and the dual residual satisfy the convergence condition, yielding the set of corrected parameters.

[0158] The corrected parameter set is written into the parameter version record and a digital signature is issued. The parameter version record includes the corrected parameter set, a summary of the segment reference distribution, combined uncertainty, timestamp, and certificate hash. The signature is used for tamper prevention and traceability. After going online, the device generates a calibration output according to the corrected parameter set. The instantaneous normalized signal is first calculated from the measured signal and environmental quantities. Among them, y k The signal is the electrical signal at the sampling time. Hysteresis-free reconstruction is performed based on the first-order inertial structure:

[0159]

[0160] in, The volume fraction is the correction value, and Δt is the sampling interval. The output is limited within the physical range, and residuals and status are recorded. Operational monitoring uses both parameter drift and distribution distance as indicators. Parameter drift is statistically analyzed as the inter-version difference within a sliding window.

[0161]

[0162] Where ΔT is the window duration. Distribution distance is measured using Wasserstein distance to determine the difference between the device posterior and the segment reference distribution. Where, q i This is the latest posterior distribution for the device. This serves as a reference distribution for the segment. If any indicator exceeds a preset threshold, the calibration instruction set will be re-executed, and the triggering reason and timestamp will be recorded in the log.

[0163] The mechanism's effectiveness is reflected in three aspects. First, norm-1 consistent optimization, through the combined effect of graph structure and uncertainty weighting, suppresses outliers, ensuring that parameters across devices are physically continuous and executable. Second, parameter version recording and digital signatures enable independent verification of each release, meeting downhole safety and compliance requirements. Third, joint monitoring of drift and distribution distance incorporates both statistical changes and structural deviations, resulting in stable and interpretable triggering strategies.

[0164] In this embodiment, after the six sensors in the transport lane and return air lane complete the posterior estimation of their parameters, a norm-compliant optimization is performed on the segment adjacency graph. Edge weights are derived from spatial adjacency and airflow direction; a device is automatically downweighted due to its high combination uncertainty. After iterative convergence, a corrected parameter set is obtained and distributed. The online module calculates the corrected volume fraction according to the above formula and records the residuals. During continuous operation, if the distribution distance and parameter drift of a node simultaneously exceed the threshold within the sliding window, the system adds the node to the recalibration queue and generates an event record. After recalibration, the node's parameters converge posteriorly to the segment reference distribution neighborhood, reducing the online residuals and improving output consistency within the segment.

[0165] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for intelligent calibration of methane sensors in underground coal mines, characterized in that, Includes the following steps: Establish a near-field communication session to obtain the permeation tube metrology certificate parameters and calibration instruction set; When establishing a near-field communication session, perform challenge response authentication, verify the digital signature and validity period of the permeation tube metrology certificate parameters, load the calibration instruction set, determine energy and safety constraints and environmental baselines, and enable calibration log recording timestamps and data indexes; A zero-point dataset is generated in a closed microcavity and an acoustic pulse seal diagnosis is performed to obtain a seal score. A standard concentration trajectory is generated based on the parameters of the permeation tube metrology certificate and a standard segment dataset is collected. The temperature-time profile is adjusted according to the information matrix and the H infinity norm to form the original collected data. The standard concentration trajectory is calculated based on the permeability coefficient, membrane thickness, effective area and pressure difference. The permeation flux is obtained within the closed volume according to the law of mass conservation, and the standard concentration trajectory and temperature-time profile are written into the standard segment dataset. The temperature-time profile is iteratively updated by a joint objective consisting of an information matrix as the information content index and the H-infinity norm as the worst-case bound index, to satisfy the energy limit, temperature upper limit and heating rate limit, and the updated temperature-time profile and joint objective values ​​are recorded as design evidence. Based on the original collected data, robust deconvolution and variational Bayesian inference are performed under the first-order inertial dynamic model to obtain the robust point estimation parameter set and posterior distribution and form the combined uncertainty. The posterior distributions of multiple sensors are fused on the segment adjacency graph and the Wasserstein centroid is calculated to obtain the segment reference distribution. Combined with norm 1 consistent optimization, a set of corrected parameters is obtained and distributed for online calibration and drift recalibration triggering. The segment reference distribution is used as the prior for the next round of input design and parameter identification. The posterior distributions of multiple sensors are weighted by node uncertainty and mean-smoothed on the segment adjacency graph. Then, the Wasserstein centroid is calculated to obtain the segment reference distribution, which serves as the prior for the next round of input design and parameter identification.

2. The method according to claim 1, characterized in that, When generating a zero-point dataset within a closed microcavity, an approximately zero-concentration environment is established by opening a zero-point microvalve and adsorbent. The original sensor output, cavity temperature, cavity humidity, and cavity pressure are synchronously collected according to a unified sampling clock, forming a zero-point dataset with time-series annotation.

3. The method according to claim 1, characterized in that, Acoustic pulse seal diagnosis injects acoustic pulses through a microactuator and collects echoes and transient cavity pressure. The seal score is calculated based on the echo attenuation constant and the cavity pressure settling time. The seal score is used to set the disturbance boundary and sample weights for the first-order inertial dynamic model.

4. The method according to claim 1, characterized in that, The baseline is obtained by statistical analysis of the median of the zero-point dataset within the stable window. The stable window is determined by the sliding variance threshold and the derivative threshold. The baseline is used to fix the bias term in the first-order inertial dynamic model.

5. The method according to claim 1, characterized in that, Robust deconvolution is performed on a consistent segment that satisfies temperature stability and sealing score thresholds. A first-order inertial kernel is used to obtain robust point estimates of sensitivity and time constant. Variational Bayesian inference uses Student's t-distribution observation noise and physical feasible region priors, and uses robust point estimates as anchors to perform near-end fusion of distributions to generate posterior distributions and combined uncertainties.

6. The method according to claim 1, characterized in that, The set of corrected parameters is obtained by solving the norm-1 consistent optimization on the segment adjacency graph. The norm-1 consistent optimization is implemented iteratively using the alternating direction multiplier method. The corrected parameter set is written into the parameter version record and a digital signature is issued. The online calibration output is used to calculate the Wasserstein distance between the sliding window drift index and the segment reference distribution. When the set threshold is reached, the calibration instruction set is executed again.

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