Digital calibration method for tiltmeter based on intelligent sensor

Abstract

The application discloses a digital calibration method for an inclinometer based on an intelligent sensor and belongs to the technical field of intelligent sensors, which comprises the following steps: collecting data synchronously by integrating a multi-source environment sensor and an inclinometer, and fusing reference data; the application precisely quantifies the nonlinear coupling contribution of environmental factors such as temperature gradient and vibration spectrum to the inclination error by fusing error perception weighting and principal component dynamic correlation analysis; the application maps the mathematical principal components into interpretable physical interference mechanisms such as temperature change rate and low-frequency vibration, and inversely calculates the original parameter weight, thereby not only identifying key dynamic characteristics but also marking nonlinear sensitive areas, significantly improving the physical interpretability and engineering guidance value of error separation, enabling the subsequent model to targetly inhibit the dominant interference, avoiding the overfitting risk caused by black box modeling, providing a weight basis for confidence evaluation, and greatly enhancing the robustness and adaptability of the calibration system under complex working conditions.

Description

Technical Field

[0002] This invention belongs to the field of intelligent sensor technology, specifically referring to a digital calibration method for inclinometers based on intelligent sensors. Background Technology

[0004] Inclinometers, as core sensors for measuring the tilt angle of an object relative to the direction of gravity, are widely used in structural health monitoring and attitude control of critical infrastructure and high-end equipment such as bridges and dams, slopes and landslides, wind turbine towers, engineering machinery, and aerospace. Their measurement accuracy and long-term stability directly affect the reliability of safety warnings and the efficiency of system operation. However, under complex actual working conditions, inclinometer outputs are susceptible to interference from various environmental factors, leading to significant drift and error accumulation, severely impacting measurement reliability.

[0005] However, existing digital calibration methods for inclinometers using smart sensors still have certain shortcomings. Existing technologies use static calibration parameters or linear compensation models, which cannot dynamically decouple the nonlinear coupling effects of multiple environmental factors such as temperature gradients and vibration spectra. Error feature extraction lacks physical interpretability and weight quantification capabilities, resulting in weak targeting of compensation strategies. The design of compensation models is either difficult to deploy on edge devices due to parameter redundancy or ignores physical laws such as sensor thermodynamics due to oversimplification. During system operation, only the compensated inclinometer value is output, lacking a real-time quantitative evaluation mechanism for the reliability of the compensation result. It cannot identify risks such as distribution shifts and sudden environmental changes, and there is a risk of blindly trusting the output, affecting the reliability of monitoring decisions. The calibration process relies heavily on manual periodic returns to the factory or the intervention of external high-precision reference stations, and cannot achieve environmentally adaptive online calibration in unattended scenarios. It also has a lag response when facing sensor drift or sudden changes in operating conditions, resulting in long-term inaccurate measurement data and high maintenance costs. Therefore, a digital calibration method for inclinometers based on smart sensors is proposed. Summary of the Invention

[0007] The purpose of this invention is to provide a digital calibration method for inclinometers based on intelligent sensors, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a digital calibration method for an inclinometer based on a smart sensor, comprising the following steps:

[0009] S1. Baseline data fusion is performed by synchronously collecting data from integrated multi-source environmental sensors and an inclinometer;

[0010] S2. Based on synchronous data, principal component analysis is used to quantify the weight of environmental parameters on the tilt angle output and to extract dynamic error features.

[0011] S3. Construct a lightweight neural network model using the extracted dynamic error feature parameters and perform initial AI compensation model training.

[0012] S4. Real-time tilt compensation and confidence assessment are performed using an AI compensation model;

[0013] S5. Based on low-confidence results, dynamic calibration data is generated by controlling micro-motors to perform triggered self-calibration and data augmentation.

[0014] S6. By aggregating calibration data and multi-node low-confidence data, cloud-based collaborative model retraining and parameter updates are performed.

[0015] S7. By analyzing long-term calibration history and performance trends, system stability verification and aging warning are conducted.

[0016] Preferably, in step S1, miniature temperature, humidity, and triaxial vibration sensors are embedded in the inclinometer body in a structured manner on the inclinometer's hardware platform. In a temperature- and humidity-controlled laboratory, the integrated system is fixed to a high-precision inclinometer reference stage at preset angle intervals. Set the coverage range of the inclinometer sequentially (e.g., to The standard tilt angle position within the range is maintained at each point until the environmental parameters and tilt angle output reach a steady state; the original tilt angle signal, environmental parameter sequence, and equipment operating status are captured synchronously; the environmental conditions, equipment parameters, and data quality indicators are recorded in real time; sliding window filtering is performed to eliminate high-frequency noise; and instantaneous outliers are removed using statistical criteria; frequency domain analysis is performed on the vibration data to identify and mark the periods of external interference; the data is classified into confidence levels based on dimensions such as synchronization accuracy, environmental stability, and signal-to-noise ratio; high-reliability samples are selected; and data packets are stored according to the reference point angle.

[0017] Preferably, in step S2, synchronized data is acquired, and the difference between the original output of the inclinometer and the standard value is calculated point by point based on the inclinometer reference value to form a time-continuous inclinometer measurement error sequence. The synchronously acquired original environmental parameters are integrated, and key dynamic features are derived. A multi-dimensional environmental feature matrix containing static parameters and dynamically derived features is constructed, and the covariance matrix of the standardized environmental feature matrix is ​​calculated. Eigenvalue decomposition is then performed, resulting in:

[0018] ,

[0019] In the formula, This represents the error-aware weighted covariance matrix. Let I represent the standardized environmental feature matrix, and let I represent the identity matrix. identity matrix Represents the error sensitivity coefficient. This represents the construction function for a diagonal matrix, which converts the input vector into a diagonal matrix, and e represents the tilt angle error sequence.

[0020] Based on the error-aware weighted covariance matrix, the linear correlation coefficient between the principal component score sequence and the tilt angle error sequence is calculated as follows:

[0021] ,

[0022] In the formula, This represents the dynamic correlation strength between the k-th component and the error. express The k-th unit features in the data, where, , This represents the cross-correlation vector between environmental characteristics and errors. Indicates error Norm, Let w represent the variance of the weight vector w. , Indicates the corresponding eigenvalue. Indicates the stability adjustment parameter. Indicates the attenuation intensity. This indicates that division by zero is prevented; as β increases, the value of the entire exponent term decreases, leading to... The value of β also decreases, meaning the dynamic correlation strength weakens; when β decreases, the value of the exponential term increases. The value of β also increases accordingly, and the dynamic correlation strength is enhanced. β is used to adjust the influence of the variance of the weight vector on the dynamic correlation strength between the principal components and the error.

[0023] Preferably, in step S2, the combined influence weight of each principal component on the tilt angle error is calculated by integrating the variance contribution rate of the principal components and the absolute value of the correlation coefficient, as follows:

[0024] ,

[0025] In the formula, This represents the normalized comprehensive influence weight of the k-th principal component on the tilt error, where m represents the number of selected principal components. This represents the dynamic correlation strength between the k-th component and the error. This represents the variance contribution of the k-th principal component after adjustment, which is dynamically adjusted according to the operating conditions. Indicates the balance index. This indicates reduced variance and emphasized correlation. This approach enhances the variance contribution by mapping the contributions of significant principal components back to the original environmental features. For each original parameter, the product of the absolute values ​​of the loadings in all significant principal components and the weights of the principal components is aggregated. Through normalization, the relative weight values ​​of the parameters with respect to the tilt error are generated. Based on the weight ranking, the dominant environmental factors are extracted to form a structured dynamic error feature parameter set.

[0026] Preferably, in step S3, dynamic error feature parameters are obtained, a subset of core environmental features with cumulative weight contributions greater than or equal to a threshold is selected, original environmental parameters with corresponding timestamps are extracted from the benchmark database, and dynamic features are generated according to predefined derivation rules; the selected features are grouped according to physical logic to form a structured input vector, and the tilt angle error label is calculated to achieve... It employs a fully connected architecture consisting of an input layer, two hidden layers, and an output layer.

[0027] A small Gaussian noise is applied to the high-confidence baseline data to simulate short-term sensor fluctuations. Stratified sampling is performed according to environmental conditions. The input features are normalized using the same standardized parameters as in step S2, and the dataset is divided into time series segments.

[0028] Preferably, in step S3, the environmental feature normalization weight vector output by S2 is used. This represents the proportion of environmental features contributing to the global error. A standardized environmental feature vector is extracted from the i-th sample in the benchmark database. Calculate the dynamic weights of the samples The implementation is as follows:

[0029] ,

[0030] In the formula, Represents the dynamic weights of the samples. Indicates the interference sensitivity coefficient. Let represent the j-th standardized environmental feature value of the i-th sample, and let p represent the effective environmental feature dimension. Represents a nonlinear enhancement function. for , Let exp be the scale parameter, and let exp represent the natural exponential function.

[0031] Based on the thermodynamic characteristics of the sensor, an increase in elevation typically leads to a positive drift in the tilt angle, therefore the compensation value... Should be with Same sign and matching direction; preset direction constraint items The total loss function is implemented as follows:

[0032] ,

[0033] In the formula, L represents the total loss function value. This represents the tilt angle compensation value predicted by the neural network for the i-th sample. Indicates the true tilt error label. Represents the physical constraint strength coefficient. This represents the temperature change of the i-th sample. , This represents the thermal drift sensitivity coefficient. This indicates the preset tolerance threshold.

[0034] Preferably, in step S4, the trained AI compensation model is loaded; and the original tilt angle value at the current moment is synchronously read based on the tilt meter sampling clock. Dynamic features are calculated in real time according to the defined derivation rules; environmental feature vectors are processed using fixed standardized parameters. Normalization: Input standardized feature vectors into the AI ​​compensation model, and output compensation values. The compensated tilt angle is .

[0035] Preferably, in step S4, the Mahalanobis distance of the current feature in the principal component analysis space is calculated based on the environmental feature vector. , for , The Mahalanobis distance represents the degree of deviation between the current environmental characteristics and the standardized values ​​of the training distribution center. This represents the mean vector of features in the training set, and T represents the transpose operator. The training set covariance matrix is ​​represented by the Mahalanobis distance mapped to the distribution confidence. , for , The sensitivity coefficient is used to calculate the standard deviation of short-term fluctuations in environmental parameters based on a circular buffer. Compare with similar operating conditions in the benchmark library Generate stability confidence , for , This represents the numerical stability constant. It checks whether the compensation direction conforms to the physical laws identified by S2. If it violates the physical constraints, the confidence decay factor is applied. The overall confidence level is , for The overall confidence level is normalized to obtain , , The function is defined as the truncation function. The preset base threshold Th is dynamically fine-tuned in combination with the historical performance trend of S7. The normalized comprehensive confidence is compared with the base threshold for judgment.

[0036] Generate a structured trigger package containing timestamps, current environment features, confidence scores, low-confidence root cause identifiers, and prioritize the data before output.

[0037] Preferably, in step S5, the confidence level result is obtained and the status of the micro-motor is verified; the safety of the current working condition is assessed: the vibration intensity is lower than the safety threshold, the tilt angle change rate is stable, and there are no external impact events; if the environmental risk exceeds the standard, the system switches to standby monitoring mode, analyzes the root cause identifier in the trigger packet, and densely covers the neighborhood of the current environmental parameters through central radial micro-motion; taking the initial position before micro-motion as the reference zero point, the motor encoder feedback angle is used as the standard tilt angle change at the micro-motion position, and the change of the original output of the inclinometer at the micro-motion position relative to the initial position is compared with the standard tilt angle change and the original output change of the inclinometer to determine the measurement error of the inclinometer under the environmental working condition; based on the current environmental parameters and combined with the distribution of similar working conditions in the benchmark database, a virtual environment combination is generated to enhance the sample quality labeling; the model in S3 is fine-tuned by adding a high-confidence calibration point; the updated parameters are applied to calculate the current tilt angle, and the confidence assessment is re-executed.

[0038] Preferably, in step S6, the cloud securely aggregates high-confidence dynamically calibrated data and labeled low-confidence problematic samples uploaded by all network nodes. It performs intelligent weighted fusion based on data quality level and root cause identification, and injects controllable noise using differential privacy technology to strictly protect the original data privacy of each node. Based on the enhanced training set, the global AI compensation model is collaboratively retrained through incremental learning and multi-node knowledge transfer strategies, focusing on optimizing the model's compensation accuracy, physical law compliance, and cross-environment generalization ability under low-confidence conditions. Simultaneously, cross-node cross-validation and physical constraint verification ensure model reliability. After training, a lightweight encrypted incremental update package is generated and securely distributed to edge nodes using a batch-based gray-scale release mechanism. The node automatically completes model hot replacement and effect verification, with second-level rollback in case of anomalies. The cloud monitors the confidence improvement rate and compensation residual changes after the network-wide update in real time, and feeds the verification results back to the training loop.

[0039] The preferred intelligent weighted fusion implementation steps are as follows: Data packets uploaded by all network nodes, including high-confidence dynamically labeled data and low-confidence problematic samples, are classified into quality levels according to preset rules. The quality levels are categorized as high, medium, and low, determined through methods such as historical error statistics and sensor health scores, and mapped to numerical values. Samples marked with low confidence or abnormal root causes, such as environmental interference, sensor aging, or data jumps, are assigned root cause correction coefficients. Rule design: The more severe the impact of root causes on measurement reliability... The greater the weight discount, the higher the discount.

[0040] Fusion weight of a single node i The implementation is as follows:

[0041] ;

[0042] Intelligent weighted fusion based on fusion weights is implemented as follows:

[0043] ,

[0044] In the formula, This represents globally merged data, where N represents the total number of nodes participating in the fusion. This represents the tilt angle measurement of node i at time t.

[0045] Preferably, in step S7, a multi-dimensional performance degradation index system is constructed by continuously aggregating the full lifecycle calibration archives of all network devices; a sliding window trend analysis and exponentially weighted moving average algorithm are used to identify the gradual drift and abrupt change points of key indicators, and the system health is verified in real time by combining preset stability thresholds; when a significant aging trend is detected, the remaining effective lifespan is predicted based on historical degradation curve fitting, and graded early warning and precise maintenance suggestions are automatically generated, and the dynamically calculated aging index is fed back to step S4 in real time for adaptive adjustment of the confidence judgment threshold and optimization of the micro-motion strategy triggering logic in step S5; at the same time, a heat map of device group aging and a calibration strategy optimization report are generated and pushed to the operation and maintenance platform to guide preventive maintenance.

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] 1. To address the core pain points of existing inclinometers, such as poor long-term stability due to combined interference from temperature drift and installation stress, the need for frequent manual calibration, weak real-time performance, and insufficient environmental adaptability, and to improve the accuracy maintenance capability, maintenance-free cycle, and intelligence level of inclinometer measurement under complex working conditions, this invention constructs a new paradigm for digital calibration of inclinometers through a seven-step closed-loop system: multi-source sensor fusion, dynamic error decoupling, lightweight AI compensation, confidence self-assessment, triggered micro-motion calibration, cloud-based collaborative evolution, and full life-cycle early warning. This system enables inclinometers to achieve self-sensing of the environment, self-compensation of errors, and self-evolution of the model, thus realizing a shift from static calibration relying on manual intervention to dynamic calibration without human intervention, significantly improving measurement reliability.

[0048] 2. This invention accurately quantifies the nonlinear coupling contribution of environmental factors such as temperature gradient and vibration spectrum to tilt angle error by integrating error-aware weighting and principal component dynamic correlation analysis. By mapping mathematical principal components to interpretable physical interference mechanisms such as temperature change rate and low-frequency vibration, and inverting the original parameter weights, it not only identifies key dynamic features but also marks nonlinear sensitive areas, providing high-value, low-redundancy feature inputs for the compensation model. This significantly improves the physical interpretability and engineering guidance value of error separation, enabling subsequent models to specifically suppress dominant interferences and avoid overfitting risks caused by black-box modeling. At the same time, it provides weighting basis for confidence assessment, greatly enhancing the robustness and adaptability of the calibration system under complex working conditions.

[0049] 3. This invention introduces a self-verification mechanism for compensation behavior, which correlates the amount of compensation with environmental credibility to avoid large compensation amounts masking model anomalies; it combines the aging index to dynamically adjust the threshold, ensuring that both new and old equipment are reasonably evaluated; the time consumed per evaluation is reduced; when the confidence level is lower than the threshold, the system accurately generates a trigger package containing root cause identification, intercepting risks at the data application front end, significantly improving the reliability of monitoring data and the security of decision-making, while reducing invalid calibration triggers and optimizing system resource allocation;

[0050] 4. This invention transforms low-confidence events into high-quality dynamic calibration opportunities. Based on root cause identification, it intelligently plans micro-motion strategies and generates high-confidence calibration points within a safe amplitude range, using the motor encoder feedback angle as the true value benchmark. Simultaneously, it implements safety pre-inspection, data quality grading, and real-time local effect verification to ensure zero-risk and high-efficiency calibration processes. This enables the inclinometer to have environmental adaptive calibration capabilities, significantly reducing field maintenance costs and reliance on manual labor. Attached Figure Description

[0052] Figure 1 The following is the operation flow of the inclinometer digital calibration method based on intelligent sensors according to the present invention. Figure 1 ;

[0053] Figure 2 The following is the operation flow of the inclinometer digital calibration method based on intelligent sensors according to the present invention. Figure 2 ;

[0054] Figure 3 The following is the operation flow of the inclinometer digital calibration method based on intelligent sensors according to the present invention. Figure 3 ;

[0055] Figure 4 The following is the operation flow of the inclinometer digital calibration method based on intelligent sensors according to the present invention. Figure 4 . Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] Example

[0059] Please see Figure 1-4 As shown, the present invention provides a technical solution comprising the following steps:

[0060] S1. Baseline data fusion is performed by synchronously collecting data from integrated multi-source environmental sensors and an inclinometer;

[0061] S2. Based on synchronous data, principal component analysis is used to quantify the weight of environmental parameters on the tilt angle output and to extract dynamic error features.

[0062] S3. Construct a lightweight neural network model using the extracted dynamic error feature parameters and perform initial AI compensation model training.

[0063] S4. Real-time tilt compensation and confidence assessment are performed using an AI compensation model;

[0064] S5. Based on low-confidence results, dynamic calibration data is generated by controlling micro-motors to perform triggered self-calibration and data augmentation.

[0065] S6. By aggregating calibration data and multi-node low-confidence data, cloud-based collaborative model retraining and parameter updates are performed.

[0066] S7. By analyzing long-term calibration history and performance trends, system stability verification and aging warning are conducted.

[0067] In this embodiment, in step S1, miniature temperature, humidity, and triaxial vibration sensors are embedded into the inclinometer body in a structured manner on the inclinometer hardware platform. Factory-grade static calibration is performed on the inclinometer and each environmental sensor to obtain basic calibration models such as zero-point offset, sensitivity coefficient, and nonlinear correction parameters.

[0068] In a temperature- and humidity-controlled laboratory, the integrated system is fixed on a high-precision tilt reference stage, and standard tilt positions covering the measurement range are set sequentially. Each point is held until the environmental parameters and tilt output reach a steady state. The original tilt signal, environmental parameter sequence, and equipment operating status are captured simultaneously. The environmental conditions, equipment parameters, and data quality indicators are recorded in real time. Sliding window filtering is performed to eliminate high-frequency noise, and instantaneous outliers are removed through statistical criteria.

[0069] Specifically, frequency domain analysis was performed on the vibration data to identify and mark periods of external interference. Subsampling-level alignment was performed based on timestamps, and interpolation compensation was used for minor time offsets. A spatiotemporal correlation mapping table of standard tilt angle value, tilt angle output, and environmental parameters was constructed. The data was graded for confidence level according to dimensions such as synchronization accuracy, environmental stability, and signal-to-noise ratio. High-reliability samples were selected, and data packets were stored according to the reference point angle to form a reference database. Each record includes the standard tilt angle reference value, the calibrated tilt angle output, the synchronization environmental parameter vector, the acquired metadata, and the quality identifier. The repeatability and consistency of data acquired multiple times from the same reference point were analyzed. The physical rationality of the environmental parameters and tilt angle output was verified.

[0070] In this embodiment, in step S2, synchronized data is acquired, and the difference between the original output of the inclinometer and the standard value is calculated point by point based on the inclinometer reference value to form a time-continuous inclinometer measurement error sequence. The synchronously acquired original environmental parameters are integrated, and key dynamic features are derived: the temperature / humidity change rate, vibration signal time-domain statistics, and frequency-domain energy distribution characteristics are calculated. A multi-dimensional environmental feature matrix containing static parameters and dynamically derived features is constructed. The environmental feature matrix is ​​standardized, and based on the labeled data quality identifiers, data segments with abnormal fluctuations, excessive synchronization deviations, or significant external interference are removed, retaining high-reliability samples for analysis. The covariance matrix of the standardized environmental feature matrix is ​​calculated, and eigenvalue decomposition is performed, resulting in:

[0071] ,

[0072] In the formula, This represents the error-aware weighted covariance matrix. Let I represent the standardized environmental feature matrix, and let I represent the identity matrix. identity matrix This represents the error sensitivity coefficient, with a preferred value range of [0, 1], or extended to 0.1, 10, etc., depending on the actual scenario. This represents the constructor for a diagonal matrix, which converts the input vector into a diagonal matrix, where e represents the tilt error sequence. Represents the absolute value of the error Norm.

[0073] Specifically, by combining the preset cumulative variance contribution rate threshold and scree plot inflection point analysis, the principal components that retain the dominant environmental disturbance information are selected, the principal component load vectors are analyzed, and the combination of high load environmental characteristics, such as temperature change rate + low frequency vibration, are identified, and the mathematical principal components are mapped to interpretable physical disturbance mechanisms.

[0074] Based on the error-aware weighted covariance matrix, the linear correlation coefficient between the principal component score sequence and the tilt angle error sequence is calculated as follows:

[0075] ,

[0076] In the formula, This represents the dynamic correlation strength between the k-th component and the error. express The k-th unit features in the data, where, , This represents the cross-correlation vector between environmental characteristics and errors. Indicates error Norm, Let w represent the variance of the weight vector w. , Indicates the corresponding eigenvalue. Indicates the stability adjustment parameter. Indicates the attenuation intensity. Indicates protection against zero.

[0077] Specifically, as β increases, the value of the entire exponential term decreases, leading to... The value of β also decreases, meaning the dynamic correlation strength weakens; when β decreases, the value of the exponential term increases. The value of β also increases accordingly, and the dynamic correlation strength is enhanced. β is used to adjust the influence of the variance of the weight vector on the dynamic correlation strength between the principal components and the error.

[0078] In this embodiment, in step S2, the combined influence weight of each principal component on the tilt angle error is calculated by integrating the variance contribution rate of the principal components and the absolute value of the correlation coefficient, as follows:

[0079] ,

[0080] In the formula, This represents the normalized comprehensive influence weight of the k-th principal component on the tilt error, where m represents the number of selected principal components. This represents the variance contribution of the k-th principal component after adjustment.

[0081] Specifically, adjustments will be made dynamically based on the operating conditions. Indicates the balance index. This indicates reduced variance and emphasized correlation. This approach enhances the variance contribution by mapping the contributions of significant principal components back to the original environmental features. For each original parameter, the product of the absolute values ​​of the loadings in all significant principal components and the weights of the principal components is aggregated. Through normalization, the relative weight values ​​of the parameters with respect to the tilt error are generated. Based on the weight ranking, the dominant environmental factors are extracted to form a structured dynamic error feature parameter set.

[0082] In this embodiment, step S3 involves acquiring dynamic error feature parameters, selecting a subset of core environmental features with a cumulative weight contribution greater than or equal to a threshold, removing low-contribution redundant features, extracting the original environmental parameters corresponding to the timestamp from the benchmark database, and generating dynamic features according to predefined derivation rules. The selected features are then grouped according to physical logic to form a structured input vector, and the tilt angle error label is calculated, thus achieving... .

[0083] Specifically, this is achieved by employing a fully connected architecture consisting of an input layer, two hidden layers, and an output layer:

[0084] Number of input layer nodes = key feature dimension (usually ≤15);

[0085] Hidden layer 1: 32 neurons + ReLU activation + Dropout (0.2);

[0086] Hidden layer 2: 16 neurons + ReLU activation + Dropout (0.1);

[0087] Output layer: 1 neuron + linear activation directly outputs compensation value.

[0088] Specifically, the total number of parameters is controlled within 1.5K, and the computational cost of a single inference is <50KFLOPs, meeting the real-time requirements of XS-10 type edge devices; physical priors are introduced into the loss function: a sign constraint term is added to the temperature monotonic drift interval to ensure that the direction of change of the compensation value conforms to the physical characteristics of the sensor;

[0089] Apply small Gaussian noise to the high-confidence benchmark data to simulate short-term sensor fluctuations, and perform stratified sampling according to environmental conditions. Normalize the input features using the same standardized parameters as in step S2, and divide the dataset according to time series: such as 70% training set, 15% validation set, and 15% test set.

[0090] In this embodiment, S3 is based on the environmental feature normalization weight vector output by S2. This represents the proportion of environmental features contributing to the global error. A standardized environmental feature vector is extracted from the i-th sample in the benchmark database. Calculate the dynamic weights of the samples The implementation is as follows:

[0091] ,

[0092] In the formula, Represents the dynamic weights of the samples. Indicates the interference sensitivity coefficient. Let represent the j-th standardized environmental feature value of the i-th sample, and let p represent the effective environmental feature dimension. Represents a nonlinear enhancement function. for , Let exp be the scale parameter, and let exp represent the natural exponential function.

[0093] Specifically, based on the thermodynamic characteristics of the sensor, an increase in elevation typically leads to a positive drift in the tilt angle, therefore the compensation value... Should be with Same sign and matching direction; preset direction constraint items ,like If the compensation direction is opposite to the physical laws, the constraint term becomes positive, and the loss increases. Temperature weighting The dynamic settings are as follows: the more significant the temperature disturbance, the stricter the directional constraint; the total loss function is then implemented as follows:

[0094] ,

[0095] In the formula, L represents the total loss function value. This represents the tilt angle compensation value predicted by the neural network for the i-th sample. Indicates the true tilt error label. Represents the physical constraint strength coefficient. This represents the temperature change of the i-th sample. , Represents a symbolic function. This represents the thermal drift sensitivity coefficient. This indicates the preset tolerance threshold. This indicates a ReLU-type constrained activation, which imposes a penalty only when physical laws are violated. It is optimized by the Adam optimizer and validated by a validation set. The loss curves during training and validation, as well as the distribution of the compensated residuals, are recorded in real time.

[0096] In this embodiment, in step S4, the trained AI compensation model is loaded, and a circular buffer is pre-allocated to store the original tilt angle, environmental parameters, and compensation values ​​of the most recent L sampling points. L is dynamically set according to the sampling frequency to ensure coverage of typical environmental fluctuation cycles. The confidence history queue is initialized for dynamic threshold calibration.

[0097] Specifically, using the inclinometer's sampling clock as a reference, the original inclinometer value at the current moment is read synchronously. Perform millisecond-level timestamp alignment checks, discard data frames with excessive synchronization deviations, and calculate dynamic features in real time according to defined derivation rules, such as calculating the temperature change rate based on a sliding window with a circular buffer; use fixed standardized parameters for environmental feature vectors. Normalization: Input standardized feature vectors into the AI ​​compensation model, and output compensation values. The compensated tilt angle is .

[0098] In this embodiment, in step S4, the Mahalanobis distance of the current feature in the principal component analysis space is calculated based on the environmental feature vector. , for , The Mahalanobis distance represents the degree of deviation between the current environmental characteristics and the standardized values ​​of the training distribution center. This represents the mean vector of features in the training set, and T represents the transpose operator. Let represent the covariance matrix of the training set.

[0099] Specifically, the Mahalanobis distance is mapped to the distribution confidence. , for , The sensitivity coefficient is used to calculate the standard deviation of short-term fluctuations in environmental parameters based on a circular buffer. Compare with similar operating conditions in the benchmark library Generate stability confidence , for , This represents the numerical stability constant.

[0100] Specifically, check whether the compensation direction conforms to the physical laws identified by S2. If it violates the physical constraints, the confidence decay factor is adjusted. The overall confidence level is , for The overall confidence level is normalized to obtain , , This represents the truncation function, with a preset base threshold Th. It is dynamically fine-tuned based on the historical performance trend of S7. The normalized overall confidence level is compared with the base threshold for determination. For example, if Th = 90%, the determination is as follows:

[0101] High confidence level, normal output. ;

[0102] In the confidence level, record the early warning log;

[0103] Low confidence level triggers S5 self-calibration request;

[0104] Generate a structured trigger package containing timestamps, current environment features, confidence scores, low-confidence root cause identifiers, and prioritize the data before output.

[0105] In this embodiment, step S5 involves obtaining the confidence score and verifying the status of the micro-motor; assessing the safety of the current operating condition: vibration intensity is below the safety threshold, tilt angle change rate is stable, and there are no external impact events; if the environmental risk exceeds the standard, delay calibration and generate an environmental discomfort log, switch to standby monitoring mode, and if the confidence score is below the threshold for multiple consecutive sampling cycles and the root cause identifier is consistent, analyze the root cause identifier in the trigger packet through the center radial micro-motion.

[0106] Specifically, the current environmental parameter neighborhood is densely covered. Gradient-verified micro-motion is used to verify the rationality of the compensation direction. The micro-motion arrival signal is used as the trigger point to synchronously latch the original output sequence of the tilt angle, the full amount of environmental parameters, the motor encoder feedback angle and the timestamp. The initial position before micro-motion is used as the reference zero point. The motor encoder feedback angle is used as the standard tilt angle change at the micro-motion position. The change of the original output of the inclinometer at the micro-motion position relative to the initial position is compared with the standard tilt angle change and the original output change of the inclinometer to determine the measurement error of the inclinometer under environmental conditions.

[0107] Based on the current environmental parameters and the distribution of similar working conditions in the benchmark database, a virtual environment combination is generated to enhance the quality labeling of samples. The S3 model is fine-tuned by adding new high-confidence calibration points, the updated parameters are applied to calculate the current tilt angle, and the confidence assessment is re-executed.

[0108] In this embodiment, in step S6, the cloud securely aggregates high-confidence dynamically labeled data and labeled low-confidence problematic samples uploaded by all network nodes, performs intelligent weighted fusion based on data quality level and root cause identification, and applies differential privacy technology to inject controllable noise to strictly protect the original data privacy of each node.

[0109] Based on the enhanced training set, the global AI compensation model is retrained collaboratively through incremental learning and multi-node knowledge transfer strategies. The focus is on optimizing the model's compensation accuracy, physical law compliance, and cross-environment generalization ability under low confidence conditions. At the same time, cross-node cross-validation and physical constraint verification are used to ensure the model's reliability.

[0110] Specifically, after training is completed, a lightweight encrypted incremental update package is generated and securely distributed to edge nodes using a batch gray-scale release mechanism. The node end automatically completes model hot replacement and effect verification, and rolls back in seconds in case of anomalies. The cloud monitors the confidence improvement rate and compensation residual changes after the entire network is updated in real time, and feeds back the verification results to the training loop.

[0111] In this embodiment, the intelligent weighted fusion implementation steps are as follows: Data packets uploaded by all network nodes, including high-confidence dynamically labeled data and low-confidence problematic samples, are classified into quality levels according to preset rules. The quality levels are categorized as high, medium, and low, determined through methods such as historical error statistics and sensor health scores, and mapped to numerical values. Samples marked with low confidence or abnormal root causes, such as environmental interference, sensor aging, or data jumps, are assigned root cause correction coefficients. Rule design: The more severe the impact of root causes on measurement reliability... The greater the weight discount, the higher the discount.

[0112] Fusion weight of a single node i The implementation is as follows:

[0113] ;

[0114] Intelligent weighted fusion based on fusion weights is implemented as follows:

[0115] ,

[0116] In the formula, This represents globally merged data, where N represents the total number of nodes participating in the fusion. This represents the tilt angle measurement of node i at time t.

[0117] In this embodiment, in step S7, a multi-dimensional performance degradation index system is constructed by continuously aggregating the full lifecycle calibration archives of all network devices; a sliding window trend analysis and exponential weighted moving average algorithm are used to identify the gradual drift and abrupt change points of key indicators, and the system health is verified in real time by combining preset stability thresholds.

[0118] When a significant aging trend is detected, the remaining effective lifespan is predicted based on the fitting of historical decay curves. Graded early warnings and precise maintenance suggestions are automatically generated, and the dynamically calculated aging index is fed back to step S4 in real time for adaptive adjustment of the confidence judgment threshold and optimization of the S5 micro-motion strategy triggering logic. At the same time, a heat map of equipment group aging and a calibration strategy optimization report are generated and pushed to the operation and maintenance platform to guide preventive maintenance.

[0119] In this embodiment, the application background is as follows:

[0120] A smart tilt monitoring system has been deployed on a key pier of a cross-sea bridge to capture micro-deformations of the structure over a long period. The pier is located in a complex environment with significant diurnal temperature variations, continuous sea breeze disturbances, and periodic vibrations caused by tides. Traditional tiltmeters suffer from data drift due to environmental interference, requiring manual calibration every quarter, resulting in high maintenance costs and monitoring blind spots. This embodiment fully applies the seven-step calibration method of this invention, achieving an intelligent upgrade of the tiltmeter with accurate deployment, self-optimizing operation, and predictable early warnings.

[0121] S1: Implementation of benchmark data fusion:

[0122] Before the inclinometer leaves the factory, miniature temperature and humidity sensors and triaxial vibration sensors are integrated into the inclinometer body in an embedded structure, and each sensor is independently statically calibrated. In a constant temperature and humidity laboratory, the integrated system is fixed on a high-precision inclinometer reference platform, and standard inclinometer positions covering the full range of the device are set sequentially at preset angle intervals. After each position is set, once the environmental parameters and inclinometer output reach a steady state, multi-source signals are captured synchronously and metadata is recorded. Sliding window filtering is performed on the raw data to eliminate high-frequency noise, and instantaneous outliers are removed using statistical criteria. Frequency domain analysis is performed on the vibration data to accurately mark the periods of external interference such as the passing of ships. The data are classified into confidence levels based on dimensions such as synchronization accuracy, environmental stability, and signal-to-noise ratio, and high-reliability samples are selected to form a structured reference database. Each record includes the standard inclinometer reference value, the calibrated inclinometer output, the synchronization environmental parameter vector, and the quality label.

[0123] S2: Implementation of Dynamic Error Feature Extraction

[0124] Based on the S1 benchmark database, the tilt angle measurement error sequence is calculated point by point, and synchronous environmental parameters are integrated to derive dynamic features such as temperature change rate and vibration RMS value. After constructing a multidimensional environmental feature matrix, error-aware weighted covariance analysis is used to highlight the influence of high-error samples, and principal component decomposition is performed. The mathematical principal components are mapped to interpretable physical interference mechanisms such as temperature gradient and low-frequency vibration coupling, humidity mutation and structural creep correlation, and the dynamic correlation strength between each principal component and the error is calculated. The comprehensive influence weight of the principal components is generated by combining the variance contribution rate and the correlation strength, and then mapped back to the original environmental features to generate a normalized weight vector of each environmental parameter on the tilt angle error. Based on the weight ranking, the dominant environmental factors are extracted to form a structured dynamic error feature parameter set.

[0125] S3: Initial AI Compensation Model Training Implementation:

[0126] Based on the dynamic error feature parameter set output by S2, a subset of core environmental features whose cumulative weight contribution reaches a threshold is selected, and the original parameters for the corresponding time period are extracted from the benchmark database to generate dynamic feature vectors. A lightweight dual-hidden-layer fully connected neural network architecture is adopted. The input layer matches the feature dimension, the hidden layer is configured with an appropriate number of neurons and activation functions, and the output layer directly predicts the compensation value. The total number of parameters is strictly controlled to meet the deployment requirements of edge devices. During training, small Gaussian noise is applied to high-confidence data to enhance robustness. The dataset is divided into layers according to environmental conditions. Thermodynamic physical prior constraints are embedded in the loss function. When the temperature rises, the sign of the compensation value is forced to be consistent with the historical thermal drift trend. A preset tolerance threshold and physical constraint strength coefficient are introduced, and penalties are applied only when the direction deviates significantly. After training, the model, standardized parameters, and environmental feature weight vector output by S2 are solidified to ensure that there is no risk of circular dependency in subsequent steps.

[0127] S4: Implementation of Real-Time Compensation and Confidence Assessment:

[0128] The training model is deployed to the edge computing unit at the bridge pier site. During system operation, the original tilt angle and environmental parameters are captured synchronously based on the inclinometer sampling clock. Dynamic features such as temperature change rate are calculated and normalized in real time. The input model outputs compensation value to generate the compensated tilt angle. Simultaneously, a three-dimensional confidence assessment is performed: the deviation of the current environmental features from the distribution quantized by Mahalanobis distance in the PCA space is calculated; the short-term fluctuation stability of environmental parameters is analyzed based on the annular buffer; and the compensation direction is verified to conform to the physical laws identified by S2. After the three-dimensional confidence scores are weighted and fused, the judgment threshold is dynamically adjusted in combination with the aging index fed back by S7 to generate a percentage confidence score. When the score is lower than the threshold, a structured trigger package containing root cause indicators such as distribution deviation is accurately generated, marked as high priority for uploading, and risk interception is achieved in advance.

[0129] S5: Triggered self-calibration implementation:

[0130] One day, the system detected a continuous low-confidence event. First, it verified that the micro-motor was in normal condition and that the current bridge deck vibration intensity was below the safety threshold. After parsing the trigger packet, a center-radial micro-motion strategy was adopted: within the safe amplitude, using the motor encoder feedback angle as the true value benchmark, the micro-motion was sequentially performed to multiple positions, and the original tilt angle output, environmental parameters, and encoder angle were latched. Using the initial position as the reference zero point, the measurement error of each micro-motion position was calculated, and a high-confidence calibration point was generated. Combined with the current sea breeze humidity parameters, a virtual environment combination was generated based on the reference database for data augmentation, and samples were labeled according to quality level. After fine-tuning the local model using the newly added calibration points, the confidence level was significantly improved, and the calibration was successful. The entire process required no manual intervention, and the data was automatically packaged and uploaded to the cloud.

[0131] S6: Cloud-based collaborative model retraining implementation:

[0132] The cloud platform aggregates calibration data and low-confidence samples uploaded from dozens of monitoring points across the bridge. Based on data quality levels and root cause identifiers, it performs intelligent weighted fusion: high-quality calibration data is assigned high weights, and abnormal root cause samples have their weights dynamically discounted according to their impact. Differential privacy noise is injected to protect the data security of each node. Based on the enhanced training set, incremental learning is used to fuse knowledge from multiple nodes, focusing on optimizing the model's compensation capability under low-confidence conditions such as strong sea winds and high humidity. At the same time, physical constraint checks are embedded to ensure the rationality of the direction. After training, an encrypted incremental update package is generated and distributed according to a gray-scale strategy of first piloting the bridge piers and then promoting it to the entire bridge. Edge nodes automatically hot-swap the model and verify the effect, and roll back within seconds in case of anomalies. The cloud continuously monitors the confidence improvement rate of the entire network, forming a closed loop of data aggregation, model optimization, security updates, and effect feedback.

[0133] S7: System stability verification and aging warning implementation:

[0134] The cloud-based system continuously analyzes the three-year calibration records of the bridge inclinometer, constructing multi-dimensional attenuation indicators such as the calibration interval shortening rate and the slope of the compensation residual growth. Sliding window trend analysis is used to identify gradual drift in a specific bridge pier device, and an exponentially weighted moving average algorithm is used to confirm the aging inflection point. The system automatically generates intermediate-level early warnings and maintenance recommendations: it suggests arranging on-site re-inspection before the typhoon season, focusing on temperature-sensitive conditions. Simultaneously, the dynamic aging index is fed back to the device's S4 module in real time, adaptively relaxing the confidence threshold to avoid false triggers. A heat map of the bridge's aging equipment is generated and pushed to the operation and maintenance platform to guide precise resource allocation. This early warning allows the operation and maintenance team to intervene in advance, avoiding the risk of misjudgment due to inaccurate data.

[0135] Working principle: Miniature temperature, humidity, and vibration sensors are structurally embedded in the inclinometer hardware platform. Basic calibration parameters are obtained by completing the factory-level static calibration of each sensor. In a constant temperature and humidity laboratory, the integrated system is fixed on a high-precision inclinometer reference platform. Standard inclinometer positions covering the entire range are sequentially set, and the system waits for environmental and output steady-state conditions. Simultaneously, the system captures the original inclinometer signal environmental parameters and equipment status. Millisecond-level data synchronization is achieved through timestamp alignment and interpolation compensation. Noise outliers are eliminated using sliding window filtering and statistical criteria. Frequency domain analysis is performed on the vibration data to mark interference periods. A spatiotemporal correlation mapping table of standard inclinometer values, inclinometer output, and environmental parameters is constructed. Data confidence is graded based on synchronization accuracy, environmental stability, and signal-to-noise ratio. High-reliability samples are selected to form a structured reference database.

[0136] Based on synchronous data, the tilt measurement error sequence is calculated, and the original environmental parameters are integrated to derive dynamic features such as temperature change rate and vibration statistics. A multi-dimensional environmental feature matrix is ​​constructed and standardized. Error-aware weighted covariance analysis is used to highlight the impact of high-error samples on interference patterns. The main components of the dominant environmental interference are extracted through eigenvalue decomposition. The component load vector is analyzed to map mathematical components to interpretable physical interference mechanisms such as temperature change rate and low-frequency vibration coupling. The dynamic correlation strength between each component and the error sequence is calculated. The influence weight of the components on the tilt error is comprehensively evaluated by combining the variance contribution rate and correlation coefficient. This is then mapped back to the relative weights of the original environmental feature generation parameters to extract the dominant environmental factors and form a structured dynamic error feature parameter set. Based on the dynamic... Error feature parameters are selected to screen a subset of core environmental features. Original environmental parameters with corresponding timestamps are extracted from the benchmark database to generate dynamic features and form a structured input vector. A lightweight fully connected neural network architecture is designed with input layer matching feature dimensions, hidden layer configured with an appropriate number of neurons and activation functions, and output layer directly predicting compensation values. The total number of parameters is strictly controlled to meet the real-time inference requirements of edge devices. Sensor thermodynamic and physical prior constraints are embedded in the loss function to ensure that the compensation direction conforms to physical laws. Small noise is applied to high-confidence data to enhance robustness, and the dataset is divided into layers according to environmental conditions. A dynamic weight allocation strategy is adopted to focus training resources on high-interference conditions. A high-precision initial AI compensation model is generated through iterative training and multi-dimensional verification by the optimizer.

[0137] The trained AI compensation model and standardized parameters are loaded, and a pre-allocated circular buffer stores historical data for dynamic feature calculation. Real-time synchronization is achieved by capturing the original tilt angle value and performing timestamp alignment verification with environmental parameters, generating standardized feature vectors to input into the model, outputting compensation values, and calculating the post-compensation tilt angle. Simultaneously, the standardized deviation of current environmental features from the training distribution, environmental fluctuation stability, and the physical rationality of the compensation direction are evaluated, and a comprehensive confidence score is generated by fusing these three dimensions. The judgment criteria are dynamically adjusted based on preset thresholds and the aging index fed back by S7, classifying confidence into high, medium, and low levels. At low confidence, a structured trigger package containing root cause identifiers is generated. When the confidence level is determined to be low, the micro-motor status and the safety of the current operating conditions are first verified. If environmental risks exceed the standard, calibration is delayed and the system switches to standby monitoring mode. Triggering root cause identification is used to intelligently plan micro-motion strategies; for example, a center-radial micro-motion strategy is used in scenarios with distribution deviations, and a gradient verification-based micro-motion strategy is used in scenarios with physical violations, driving the sensor to rotate slightly within a safe amplitude. The micro-motion arrival signal is used as the trigger point to synchronously latch the tilt angle output environmental parameters and the motor encoder feedback angle, using the encoder angle as the standard tilt angle change to determine the measurement error under the current operating condition. A virtual environment combination is generated using the benchmark database for data augmentation, and samples are labeled according to quality level. After fine-tuning the model using newly added high-confidence calibration points, the confidence verification calibration effect is re-evaluated. Upon successful calibration, parameters are updated, and a data package is encapsulated and uploaded. Cloud-based secure aggregation of all network nodes is then uploaded. High-confidence dynamically labeled data and low-confidence challenging samples are intelligently weighted and fused based on data quality level and root cause identification, and differential privacy technology is applied to strictly protect the security of the original data. Based on the enhanced training set, an incremental learning and multi-node knowledge transfer strategy is used to retrain the global AI compensation model, focusing on optimizing the model's compensation accuracy, physical law compliance, and cross-environment generalization ability under low-confidence conditions. Cross-node cross-validation and physical constraint verification ensure model reliability. Lightweight encrypted incremental update packages are generated and securely distributed to edge nodes using a batch-based gray-scale release mechanism. The nodes automatically complete model hot replacement and second-level rollback in case of performance verification anomalies. The cloud continuously monitors the performance indicators of the entire network after the update and feeds back the verification results. The system continuously aggregates calibration archives of all network devices throughout their entire lifecycle to construct a multi-dimensional performance degradation index system. It uses sliding window trend analysis and exponentially weighted moving average algorithms to identify the gradual drift and abrupt changes of key indicators, and combines preset stability thresholds to verify system health in real time. When a significant aging trend is detected, it predicts the remaining effective lifespan based on historical degradation curve fitting, and automatically generates graded early warnings and precise maintenance suggestions such as re-inspection cycles and key operating conditions. The dynamically calculated aging index is fed back in real time to the S4 confidence judgment threshold and the S5 micro-motion strategy trigger logic to achieve adaptive optimization of system parameters. At the same time, it generates a heat map of device group aging and a calibration strategy optimization report and pushes it to the operation and maintenance platform to guide preventive maintenance.

[0138] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their likenesses.

[0139] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. A digital calibration method for inclinometers based on intelligent sensors, characterized in that, Includes the following steps: S1. Baseline data fusion is performed by synchronously collecting data from integrated multi-source environmental sensors and an inclinometer; S2. Based on synchronous data, principal component analysis is used to quantify the weight of environmental parameters on the tilt angle output and to extract dynamic error features. S3. Construct a lightweight neural network model using the extracted dynamic error feature parameters and perform initial AI compensation model training. S4. Real-time tilt compensation and confidence assessment are performed using an AI compensation model; S5. Based on low-confidence results, dynamic calibration data is generated by controlling micro-motors to perform triggered self-calibration and data augmentation. S6. By aggregating calibration data and multi-node low-confidence data, cloud-based collaborative model retraining and parameter updates are performed. S7. By analyzing long-term calibration history and performance trends, system stability verification and aging warning are conducted.

2. The inclinometer digital calibration method based on intelligent sensors according to claim 1, characterized in that: In step S1, miniature temperature, humidity, and triaxial vibration sensors are embedded in the inclinometer body in a structured manner on the inclinometer's hardware platform. In a temperature- and humidity-controlled laboratory, the integrated system is fixed on a high-precision inclinometer reference platform. Standard inclinometer positions covering the measurement range are sequentially set, and each point is maintained until the environmental parameters and inclinometer output reach a steady state. The original inclinometer signal, environmental parameter sequence, and equipment operating status are captured synchronously. The environmental conditions, equipment parameters, and data quality indicators are recorded in real time, and instantaneous outliers are eliminated through statistical criteria. Frequency domain analysis is performed on the vibration data to identify and mark external interference periods. The data is classified into confidence levels based on synchronization accuracy, environmental stability, and signal-to-noise ratio, and high-reliability samples are selected. Data packets are stored according to the reference point angle.

3. The inclinometer digital calibration method based on intelligent sensors according to claim 2, characterized in that: In step S2, synchronized data is acquired, and the difference between the original output of the inclinometer and the standard value is calculated point by point based on the inclinometer reference value to form a time-continuous inclinometer measurement error sequence. The synchronously acquired original environmental parameters are integrated, and key dynamic features are derived. A multi-dimensional environmental feature matrix containing static parameters and dynamically derived features is constructed, and the covariance matrix of the standardized environmental feature matrix is ​​calculated. Eigenvalue decomposition is then performed, resulting in: ， In the formula, This represents the error-aware weighted covariance matrix. Let I represent the standardized environmental feature matrix, and let I represent the identity matrix. Represents the error sensitivity coefficient. This represents the construction of a diagonal matrix, where e represents the tilt error sequence; Based on the error-aware weighted covariance matrix, the linear correlation coefficient between the principal component score sequence and the tilt angle error sequence is calculated as follows: ， In the formula, This represents the dynamic correlation strength between the k-th component and the error. express The characteristics of the k-th unit in the data, , This represents the cross-correlation vector between environmental characteristics and errors. Indicates error Norm, This represents the variance of the weight vector w. Indicates the corresponding eigenvalue. Indicates the stability adjustment parameter. Indicates the attenuation intensity. Indicates protection against zero.

4. The inclinometer digital calibration method based on intelligent sensors according to claim 3, characterized in that: In S2, the combined influence weight of each principal component on the tilt angle error is calculated by integrating the variance contribution rate of the principal components and the absolute value of the correlation coefficient, as follows: ， In the formula, This represents the normalized comprehensive influence weight of the k-th principal component on the tilt error, where m represents the number of selected principal components. This represents the dynamic correlation strength between the k-th component and the error. This represents the variance contribution of the k-th principal component after adjustment. The variance contribution of the j-th principal component after adjustment is represented. The contributions of the significant principal components are back-mapped to the original environmental features. For each original parameter, the product of the absolute values ​​of the loadings in all significant principal components and the weights of the principal components is aggregated. The relative weight values ​​of the parameters with respect to the tilt error are generated through normalization. The dominant environmental factors are extracted based on the weight ranking to form a structured dynamic error feature parameter set.

5. The inclinometer digital calibration method based on intelligent sensors according to claim 4, characterized in that: In step S3, dynamic error feature parameters are obtained, a subset of core environmental features with cumulative weight contribution greater than or equal to a threshold is selected, the original environmental parameters with corresponding timestamps are extracted from the benchmark database, and dynamic features are generated according to predefined derivation rules. The filtered features are grouped according to physical logic to form a structured input vector. The tilt error label is calculated by using a fully connected architecture with an input layer, two hidden layers, and an output layer. Small Gaussian noise is applied to the high-confidence benchmark data to simulate short-term fluctuations of the sensor, and stratified sampling is performed according to environmental conditions.

6. The inclinometer digital calibration method based on intelligent sensors according to claim 5, characterized in that: S3, based on the normalized weights of each environmental feature on the tilt angle error. Extract the standardized environmental feature vector from the i-th sample in the benchmark database. Calculate the dynamic weights of the samples ; Preset direction constraints The total loss function is implemented as follows: ， In the formula, L represents the total loss function value. This represents the tilt angle compensation value predicted by the neural network for the i-th sample. Indicates the true tilt error label. Represents the physical constraint strength coefficient. This represents the temperature change of the i-th sample. This represents the thermal drift sensitivity coefficient. Indicates the tolerance threshold.

7. The inclinometer digital calibration method based on intelligent sensors according to claim 6, characterized in that: In step S4, the trained AI compensation model is loaded, and the original tilt angle value at the current moment is synchronously read based on the tilt meter sampling clock. Dynamic features are calculated in real time according to the defined derivation rules; Environmental feature vectors were processed using solidified standardized parameters. Normalization: Input standardized feature vectors into the AI ​​compensation model, and output compensation values. The compensated tilt angle is .

8. The inclinometer digital calibration method based on intelligent sensors according to claim 7, characterized in that: In step S4, the Mahalanobis distance of the current feature in the principal component analysis space is calculated based on the environmental feature vector. Mapping Mahalanobis distance to distribution confidence Calculate the standard deviation of short-term fluctuations of environmental parameters based on a circular buffer. Compare with similar operating conditions in the benchmark library Generate stability confidence The overall confidence level is The overall confidence level is normalized to obtain A preset base threshold Th is used to determine the overall confidence level by comparing it with the base threshold. Generate structured trigger packets and mark data priorities before outputting.

9. The inclinometer digital calibration method based on intelligent sensors according to claim 8, characterized in that: In step S5, the confidence level result is obtained and the status of the micro-motor is verified; the safety of the current working condition is assessed: the vibration intensity is lower than the safety threshold, the tilt angle change rate is stable, and there are no external impact events; if the environmental risk exceeds the standard, the root cause identifier in the trigger packet is analyzed and densely covered in the neighborhood of the current environmental parameters through central radial micro-motion; taking the initial position before micro-motion as the reference zero point, the motor encoder feedback angle is used as the standard tilt angle change at the micro-motion position, and the change of the original output of the inclinometer at the micro-motion position relative to the initial position is compared with the standard tilt angle change and the original output change of the inclinometer to determine the measurement error of the inclinometer under the environmental working condition; based on the current environmental parameters and combined with the distribution of similar working conditions in the benchmark database, a virtual environment combination is generated to enhance the sample quality labeling.

10. The inclinometer digital calibration method based on intelligent sensors according to claim 9, characterized in that: In S6, the cloud securely aggregates high-confidence dynamically labeled data and labeled low-confidence difficult samples uploaded by nodes across the entire network, and performs intelligent weighted fusion based on data quality level and root cause identification. Based on the enhanced training set, the global AI compensation model is collaboratively retrained through incremental learning and multi-node knowledge transfer strategies. The focus is on optimizing the model's compensation accuracy, physical law compliance, and cross-environment generalization ability under low confidence conditions. At the same time, cross-node cross-validation and physical constraint verification are used to ensure the model's reliability. After training, a lightweight encrypted incremental update package is generated and securely distributed to edge nodes using a batch gray-scale release mechanism. The node end automatically completes the hot replacement of the model and effect verification, and rolls back in seconds in case of anomalies. The cloud monitors the confidence improvement rate and compensation residual changes after the network-wide update in real time and feeds the verification results back to the training loop.

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