A quantitative calibration method for sensitivity coefficient of intelligent sensor

Abstract

The application relates to the technical field of intelligent sensor calibration and characteristic parameter quantification, and discloses a sensitivity coefficient quantitative calibration method of an intelligent sensor. Original output voltages are collected in sequence at different inclination positions and direct current bias is removed, a multilayer exponential smoothing kernel is adaptively constructed based on the maximum span and the minimum adjacent difference of the voltage sequence, and the signal is subjected to multiscale smoothing; the gradient of each layer of the smoothed voltage sequence is extracted by adopting central difference and end point difference respectively, and the maximum gradient and the corresponding inclination value are extracted in each layer as the local sensitivity; the sensitivities of the layers are arithmetically averaged to obtain the comprehensive sensitivity coefficient; finally, the prediction output and the real inclination residual are calculated by combining the verification data, and whether the calibration is qualified is judged according to the preset root mean square error threshold value; when the calibration is unqualified, sample points are supplemented or the smoothing parameter is adjusted to perform iteration.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent sensor calibration and characteristic parameter quantification, in particular to a sensitivity coefficient quantitative calibration method of an intelligent sensor. BACKGROUND

[0002] With the rapid development of automation, intelligent manufacturing, Internet of Things and other fields, intelligent sensors have been widely used in industrial control, structural health monitoring, intelligent equipment, mobile terminals and other occasions. As an important type of intelligent sensors, tilt sensors can detect and feedback the posture or tilt angle information of objects in real time, and are the core components in key links such as intelligent robots, precision instruments and civil engineering monitoring. The sensitivity coefficient of the sensor, i.e. the proportional coefficient between the output change of the sensor and the change of the measured physical quantity, is one of the core indicators for measuring the performance and accuracy of the sensor.

[0003] In actual application process, due to the differences in manufacturing process, installation conditions, environmental factors and other factors of the sensor, the output characteristics of the same type of sensor have certain dispersion. In order to ensure the high precision and stability of the system, it is usually necessary to quantitatively calibrate each sensor to obtain its true sensitivity coefficient. However, the commonly used sensitivity calibration methods at present mostly rely on classical data processing techniques such as linear fitting and least squares method, which are often sensitive to abnormal points and noise interference, and have limited adaptability to data distribution; some existing schemes also have problems such as high dependence on artificial experience or parameter selection, lack of physical interpretation, etc., which affect the reliability and consistency of the calibration. In addition, with the improvement of application requirements, the demand for on-site automation, batch calibration and unattended calibration is growing, and higher requirements are put forward for the autonomy, intelligence and generalization ability of the calibration algorithm.

[0004] Therefore, the present application aims to provide a sensitivity coefficient quantitative calibration method of an intelligent sensor. First, the original voltage signal collected is preprocessed to eliminate DC bias and noise interference; then a multi-level smoothing operator is adaptively constructed to suppress data jitter through exponential weighted smoothing; then the gradient is accurately calculated and the most significant change point is extracted as a local sensitivity index under each scale; then all local indicators are fused to obtain the comprehensive sensitivity; finally, the calibration result is determined by the root mean square error based on the verification set and iteratively optimized if necessary. SUMMARY

[0005] The present application provides a sensitivity coefficient quantitative calibration method of an intelligent sensor, which solves the problems mentioned in the background.

[0006] The present application provides the following technical solutions: a sensitivity coefficient quantitative calibration method of an intelligent sensor, comprising:

[0007] S1, sequentially collecting original output voltages and corresponding inclination values of the intelligent inclination sensor to be calibrated at different inclination positions, and calculating a direct current component of the original output voltage sequence to obtain a bias-corrected voltage value sequence after deviation removal processing;

[0008] S2, adaptively determining a smoothing scale layer number based on a maximum span of inclination and a minimum adjacent difference of the preprocessed data, and constructing an exponential smoothing kernel radius of each smoothing scale according to a geometric equal ratio principle;

[0009] S3, for each smoothing scale, an exponential weighting method is used to calculate the original voltage signal to obtain a smoothed voltage sequence under the corresponding scale;

[0010] S4, for the smoothed voltage sequence under each smoothing scale, the central difference method is used to calculate the gradient at the internal measuring point, and the forward difference method and the backward difference method are used to calculate the gradient at the boundary measuring point, respectively, to obtain a complete gradient sequence under each smoothing scale;

[0011] S5, in the gradient sequence corresponding to each smoothing scale, the maximum gradient value and the corresponding inclination position are extracted, which are marked as the local gradient extreme point under the smoothing scale;

[0012] S6, the maximum gradient value corresponding to the local gradient extreme point of each smoothing scale layer is defined as the local sensitivity coefficient of the layer;

[0013] S7, the local sensitivity coefficients of all smoothing scale layers are arithmetically averaged to obtain a final comprehensive sensitivity coefficient;

[0014] S8, calculating the residual error between the predicted output and the true inclination based on the verification data set, and determining whether the calibration is qualified according to a preset root mean square error threshold, and if not, supplementing sampling points or adjusting the smoothing parameters and then re-calibrating.

[0015] Optionally, the original output voltage and the corresponding inclination value of the intelligent inclination sensor to be calibrated are sequentially collected at different inclination positions, and the direct current component of the original output voltage sequence is calculated to obtain a bias-corrected voltage value sequence after deviation removal processing, specifically including:

[0016] S101, sequentially collecting group calibration data according to inclination from small to large, and satisfying :

[0017] , ; wherein, is the data point number; is the inclination measurement value; is the original output voltage corresponding to the inclination.

[0018] S102, for any adjacent data points, if only keep the smaller number of measuring points , delete the larger number of measuring points ; wherein, is the nominal resolution of the sensor;

[0019] After deletion, the remaining measuring points must be renumbered in ascending order, repeat the above judgment until all adjacent measuring points meet ;

[0020] If the final remaining measuring point number is greater than or equal to 3, continue to the next step; if less than 3, reacquire or supplement data and return to step S101;

[0021] Get the final measuring point, denoted as , update the number of measuring points ;

[0022] S103, calculate the DC component of the voltage and perform the offset processing, specifically as follows:

[0023] , ; wherein, is the arithmetic mean of all original voltages; is the output voltage after removing the DC bias;

[0024] The preprocessed data set is .

[0025] Optionally, the maximum span and minimum adjacent difference of the inclination angle based on the preprocessed data are used to adaptively determine the number of smoothing scales, and the exponential smoothing kernel radius of each smoothing scale is constructed according to the geometric equal ratio principle, specifically including:

[0026] Calculate the inclination angle value range and the minimum adjacent difference, specifically:

[0027] , ; wherein, is the maximum span of the inclination angle of all collected data points; is the minimum value of the inclination angle difference of all adjacent data points;

[0028] Determine the number of smoothing scales: ; wherein, is the total number of smoothing scales;

[0029] Based on the geometric equal ratio principle, construct layers of smoothing scales, specifically:

[0030] ; wherein, is the first layer smoothing scale index, and the value range is is the scale layer number, and the value range is to .

[0031] Optionally, for each smoothing scale, the original voltage signal is smoothed by using an exponential weighting method to obtain a smoothed voltage sequence under the corresponding scale, specifically including:

[0032] For each smoothing scale and each data point , the smoothing calculation is performed in the following way:

[0033] ; wherein, is the smoothed voltage value of the th data point under the th smoothing scale; is the measurement point sequence number traversed during smoothing kernel weighting; is an exponential function, .

[0034] Optionally, the smoothed voltage sequence under each smoothing scale is calculated by using a central difference method for internal measurement points and a forward difference method and a backward difference method for boundary measurement points to obtain a complete gradient sequence under each smoothing scale, specifically including:

[0035] For internal data points, i.e. , the gradient is calculated by using a central difference method:

[0036] ; wherein, is the gradient of the th data point under the th smoothing scale;

[0037] For boundary data points, the gradient is calculated by using a forward difference method and a backward difference method:

[0038] , .

[0039] Optionally, in the gradient sequence corresponding to each smoothing scale, the maximum gradient value and the corresponding dip angle position are extracted, which are marked as the local gradient extreme point under the smoothing scale, specifically including:

[0040] For each smoothing scale , the maximum gradient position and the corresponding gradient value are determined:

[0041] , , ; wherein, is the serial number of the point where the maximum gradient of the first layer is located; is the serial number of the point where the maximum gradient of the first layer is located; is the maximum gradient value of the first layer; is the maximum gradient value of the first layer; is the inclination angle of the maximum gradient point of the first layer.

[0042] Optionally, the maximum gradient value corresponding to the local gradient extreme point of each smoothing scale layer is defined as the local sensitivity coefficient of the layer, specifically including:

[0043] The maximum gradient value of each smoothing scale is directly defined as the sensitivity coefficient under the scale:

[0044] , ; wherein, is the sensitivity coefficient under the smoothing scale of the first layer. is the sensitivity coefficient under the smoothing scale of the first layer.

[0045] Optionally, the local sensitivity coefficients of all smoothing scale layers are arithmetically averaged to obtain the final comprehensive sensitivity coefficient, specifically including:

[0046] The sensitivity coefficients under all scales are arithmetically averaged to obtain the final sensitivity coefficient:

[0047] ; wherein, is the final output inclination sensor comprehensive sensitivity coefficient.

[0048] Optionally, the residual between the predicted output and the true inclination is calculated based on the verification data set, and it is judged whether the calibration is qualified according to the preset root mean square error threshold, and if not, the sampling points are supplemented or the smoothing parameters are adjusted to re-calibrate, specifically including:

[0049] Set the number of verification data points and the error threshold ;

[0050] Collect and arrange in ascending order group verification data, get , ; wherein, is the serial number of the verification data point; is the serial number of the verification data point; is the true inclination of the first verification point; is the true inclination of the first verification point; is the original output voltage of the first verification point;

[0051] The verification data is de-biased and the predicted output is calculated:

[0052] ,​ ; wherein, is the de-meaned voltage of the th validation point; is the de-meaned voltage of the th validation point predicted by the final sensitivity and the inclination ;

[0053] the output prediction residual and the root mean square error of the th validation point are calculated:

[0054] , ; and

[0055] a judgment is made according to the root mean square error and an error threshold value:

[0056] if , the calibration is qualified, and the final sensitivity is outputted;

[0057] if , the calibration is unqualified, and the calibration point should be supplemented or the smoothing scale parameter should be adjusted, and then the calibration is re-implemented from step S1.

[0058] The present application has the following beneficial effects:

[0059] 1. The sensor output is sequentially collected at multiple angle positions, and the measurement data is organized in ascending order, so that the subsequent difference and calculation process is based on an ordered and continuous signal sequence. At the same time, the DC component of the voltage signal is removed and combined with arithmetic average filtering, which effectively removes the baseline offset and random noise of the measurement system. Compared with the traditional method of directly using the original output value, the pre-processing of the present application can more reliably eliminate invalid data and stabilize the signal baseline, overcome the deviation caused by DC drift in the measurement process, and focus the subsequent smoothing and gradient calculation on the true signal change component, thereby improving the accuracy and repeatability of the sensitivity estimation.

[0060] 2. According to the distribution characteristics of different experimental data, the scheme dynamically determines the number of smoothing layers according to the maximum inclination span and the minimum adjacent difference, and constructs the multi-layer smoothing kernel radius according to the geometric equal ratio principle, realizing multi-level signal smoothing from local to global. Compared with the traditional method of fixed number of layers or fixed radius, the present scheme can adaptively adjust according to the data amount and distribution characteristics, effectively balance the smoothing details and calculation efficiency, reduce the subjectivity of smoothing level selection, make the signal accurately reflect the internal change characteristics at each scale, and thus improve the flexibility and stability of the calibration process.

[0061] 3. Based on the kernel parameters of each smoothing scale, an exponentially weighted smoothing operation is performed on the debiased voltage signal to suppress the influence of long-distance noise by dynamically attenuating the weights. Compared with simple moving average or fixed window filtering, exponential weighting can balance signal smoothing and local response, reducing information loss caused by windowing effects. This method can adaptively balance noise suppression and trend preservation at different smoothing scales, achieving multi-level smoothing from microscopic local to macroscopic overall, providing a cleaner and more coherent signal foundation for subsequent gradient extremum localization.

[0062] 4. The scheme employs central difference to calculate gradients within the smooth voltage sequence, and forward and backward differences at the beginning and end boundaries respectively, ensuring that each data point has a defined gradient value. Compared to using only central difference or other approximate difference methods, this strategy avoids the problems of missing or distorted gradients at boundaries, while guaranteeing the highest accuracy in gradient calculations within the sequence. This design makes the gradient sequence consistent throughout the entire range, improving the ability to capture signal change rates and laying a solid foundation for sensitive point localization.

[0063] 5. In the gradient sequence corresponding to each smooth scale, the scheme extracts the maximum gradient and its corresponding tilt angle position by scanning all data points, and identifies this position as the most sensitive operating point of the sensor. Compared with the traditional method of directly using the overall maximum slope or selecting points in a fixed interval, multi-scale gradient extremum extraction can not only discover the true peak value of the signal change at different scales, but also avoid the deviation caused by noise or outliers at a single scale, making the local sensitivity index more representative and stable, and thus more accurately reflecting the sensor's response capability at various levels.

[0064] 6. This scheme directly defines the maximum gradient value extracted at each smoothing level as the local sensitivity coefficient at that scale, without the need for additional fitting or interpolation. Unlike methods that require fitting curves or constructing complex response models, directly using the gradient extremum as the sensitivity index not only simplifies the calculation process but also provides physical interpretability. It can intuitively reflect the sensor's response capability to tilt angle changes at different smoothing levels, avoids the accumulation of model errors, and improves the transparency and traceability of the calibration process.

[0065] 7. For the local sensitivity coefficients at all smooth scales, the scheme uses an arithmetic mean to fuse them into the final comprehensive sensitivity coefficient. Compared with the method of simply selecting the maximum or minimum value, the arithmetic mean can balance the contribution of each level to the sensitivity estimation, overcome the distortion or bias that may occur at a single scale, and obtain a more comprehensive and stable sensitivity characterization value. In addition, this fusion method is simple to understand and easy to implement, providing a reliable calibration output for engineering applications.

[0066] 8. Finally, the scheme introduces an independent validation dataset. The calibration effect is determined by calculating the root mean square error between the predicted tilt angle output and the true value. If necessary, additional sampling points are added or smoothing parameters are adjusted before iterating again. Unlike traditional one-time calibration or methods that rely solely on single error evaluation, this design establishes a closed-loop feedback mechanism. This mechanism can adaptively optimize the calibration process in an engineering environment, ensuring that the output sensitivity meets accuracy requirements while maintaining efficiency, effectively improving the reliability and applicability of the calibration results. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0068] 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.

[0069] Example, refer to Figure 1 A method for quantitatively calibrating the sensitivity coefficient of a smart sensor, comprising:

[0070] S1. The original output voltage and corresponding tilt angle value of the smart tilt sensor to be calibrated are collected sequentially at different tilt angle positions, and the DC component of the original output voltage sequence is calculated. The bias is then processed to obtain the voltage value sequence after bias correction.

[0071] S2. Based on the maximum span of the tilt angle and the minimum adjacent difference of the preprocessed data, the number of smoothing scale layers is adaptively determined, and the exponential smoothing kernel radius of each smoothing scale is constructed according to the geometric proportionality principle.

[0072] S3. For each smoothing scale, the original voltage signal is smoothed using an exponential weighting method to obtain the smoothed voltage sequence at the corresponding scale.

[0073] S4. For the smoothed voltage sequence at each smoothing scale, the gradient is calculated using the central difference method at the internal measurement points and the gradient is calculated using the forward difference method and the backward difference method at the boundary measurement points, respectively, to obtain the complete gradient sequence at each smoothing scale.

[0074] S5. In the gradient sequence corresponding to each smoothing scale, extract the maximum gradient value and its corresponding tilt angle position, and mark it as the local gradient extreme point under that smoothing scale.

[0075] S6. Define the maximum gradient value corresponding to the local gradient extreme point of each smooth scale layer as the local sensitivity coefficient of that layer.

[0076] S7. Perform an arithmetic average of the local sensitivity coefficients of all smooth scale layers to obtain the final comprehensive sensitivity coefficient.

[0077] S8. Calculate the residual between the predicted output and the true tilt angle based on the validation dataset, and determine whether the calibration is qualified according to the preset root mean square error threshold. If it is not qualified, supplement the sampling points or adjust the smoothing parameters and recalibrate.

[0078] This paper reveals a complete quantitative calibration process for the sensitivity coefficient of an intelligent tilt sensor, characterized by a closed-loop system encompassing signal preprocessing, multi-scale smoothing, precise gradient calculation, extreme value extraction, index fusion, and result verification and iterative optimization. By acquiring raw voltages at different tilt angles and performing denoising and DC bias correction, and then adaptively constructing multi-layer smoothing scales based on the maximum tilt angle span and minimum adjacent difference of the data, the influence of baseline drift and random noise in the measurement system can be effectively eliminated. Subsequently, exponential weighted smoothing is applied to the preprocessed signals to suppress noise while preserving the true trend. At each scale, the internal and boundary gradients are accurately calculated, and the maximum gradient value is extracted as a local sensitivity index. Finally, the arithmetic mean of all indices is calculated, and iterative optimization is performed in conjunction with the error judgment of the validation set. These steps solve the problems of traditional single-scale or one-time smoothing methods, which easily lose details, are sensitive to noise and outliers, and lack adaptive verification mechanisms. They improve calibration accuracy and robustness, achieve multi-level characterization of sensor sensitivity features, and, by introducing closed-loop verification and parameter iteration, ensure the repeatability and engineering reliability of the calibration results. Compared to existing technologies, this solution innovatively combines adaptive multi-scale with exponential smoothing, and is supplemented with complete verification feedback, filling the gap in the industry for insufficient sensitivity quantization and feedback-free optimization mechanisms in high-noise environments.

[0079] The process involves sequentially acquiring the original output voltage and corresponding tilt angle values ​​at different tilt angle positions of the intelligent tilt sensor to be calibrated, calculating the DC component of the original output voltage sequence, and performing debiasing processing to obtain a bias-corrected voltage value sequence, specifically including:

[0080] S101. Collect data sequentially according to the tilt angle from smallest to largest. The calibration data is set and meets the requirements. :

[0081] , ;in, For data point sequence numbers; For the first One tilt angle measurement value; For the first The original output voltage corresponding to each tilt angle;

[0082] The original measurement data are organized in ascending order of tilt angle to ensure that subsequent algorithms such as adjacent difference and scale construction are based on an ordered and complete data sequence.

[0083] S102. For any adjacent data points, if Then only the measuring points with smaller numbers are retained. Delete the measuring points with larger numbers. ;in, This refers to the sensor's nominal resolution.

[0084] After deletion, the remaining measuring points must be renumbered in ascending order, and the above judgment must be repeated until all adjacent measuring points meet the requirements. ;

[0085] If the final number of remaining measurement points is greater than or equal to 3, proceed to the next step; if it is less than 3, data needs to be collected again or supplemented before returning to step S101.

[0086] Obtain the final measurement point, denoted as... Update the number of measurement points ;

[0087] Eliminate invalid or redundant measurement points and ensure that the distance between adjacent data points is not less than the sensor resolution, so that the adjacent difference and subsequent smoothing are more stable and reliable.

[0088] S103. Calculate the DC component of the voltage and perform debiasing processing, as follows:

[0089] , ;in, This is the arithmetic mean of all the original voltages; The output voltage after removing DC bias;

[0090] The preprocessed dataset is obtained as follows ;

[0091] Eliminating the DC baseline offset of the measurement system allows subsequent smoothing and gradient calculations to focus on the signal variation components, thereby improving the accuracy of sensitivity calculations.

[0092] The data acquisition and preprocessing process was further refined, with particular emphasis on acquiring data point by point in ascending order of tilt angle and removing redundant measurement points below the resolution, as well as performing arithmetic mean filtering and DC bias elimination on the remaining points. By removing overly dense or invalid data points according to the principle of orderly and equidistant distribution during the raw signal acquisition stage, error amplification caused by excessively dense or unevenly spaced measurement points during subsequent differential operations and multi-scale smoothing is avoided. At the same time, baseline correction and local averaging filtering are performed on the signal to reduce the offset and high-frequency noise of the measurement system. This solves the pain point of existing technologies that ignore the rationality of measurement point distribution during the data preprocessing stage, leading to jitter and misjudgment in subsequent gradient calculations; it ensures the integrity and stability of the input data sequence, provides a reliable foundation for multi-scale processing, and reduces the impact of outliers on the overall calibration accuracy, making subsequent smoothing and gradient analysis more focused on real signal fluctuations, thereby improving the accuracy and repeatability of sensitivity calculation. Unlike traditional methods that only perform simple noise reduction or uniform filtering, this scheme controls both sampling density and baseline bias, taking into account both stability and precision, reflecting a profound innovation in data quality management.

[0093] The method adaptively determines the number of smoothing scale layers based on the maximum span of the tilt angle and the minimum adjacent difference of the preprocessed data, and constructs the exponential smoothing kernel radius for each smoothing scale according to the geometric proportionality principle, specifically including:

[0094] The calculation of the range of tilt angle values ​​and the minimum adjacent difference is as follows:

[0095] , ;in, The maximum span of the tilt angle for all collected data points; It represents the minimum tilt angle difference among all adjacent data points; it quantifies the data distribution characteristics and provides data support for the adaptive construction of multi-scale smoothing kernel parameters.

[0096] Determine the number of smoothing scale layers: ;in, To smooth the total number of scale layers; the number of scale layers is adaptively set according to the amount of data, ensuring both detailed characterization and computational efficiency;

[0097] Based on the principle of geometric proportionality, construct The layer smoothing scale is as follows:

[0098] ;in, For the first Layer smoothing exponent kernel radius; This is the scale layer number, and its value range is... to It generates an exponential kernel scale that increases progressively from local to global levels, achieving multi-level signal smoothing and capturing trend features in different ranges.

[0099] The adaptive construction of multi-scale smoothing parameters is described in detail. This includes quantifying data distribution characteristics based on the dip angle span and minimum neighbor difference, adaptively determining the number of smoothing layers, and generating an exponentially increasing kernel radius layer by layer according to a geometric proportionality principle. This mechanism solves the problem of over-smoothing or under-smoothing that can easily occur in existing methods that use fixed layers or empirical parameters under different data volumes and distribution scenarios. When the data span is large and rich in detail, the number of smoothing layers can be dynamically increased to capture macroscopic trends; when the neighbor difference is small, the scale can be refined to characterize local changes. This balances computational efficiency with signal detail preservation, ensuring the smoothing process is neither too coarse nor overly sensitive, thus improving the adaptability and generalization ability of multi-scale processing. Compared to traditional techniques that manually set or fix kernel parameters once, this scheme avoids reliance on human empirical parameters by quantifying data distribution and automatically generating geometric series kernel parameters, enhancing the method's intelligence and universality, and ensuring efficient and stable multi-scale smoothing in various application scenarios.

[0100] For each smoothing scale, an exponential weighting method is used to smooth the original voltage signal to obtain a smoothed voltage sequence at the corresponding scale, specifically including:

[0101] For each smoothing scale and each data point The smoothing calculation is performed in the following manner:

[0102] ;in, For the first Layer smoothing scale Smoothed voltage values ​​for each data point; The sequence number of the measurement points traversed during the smoothing kernel weighting; It is an exponential function. For debiasing voltage By applying an exponentially weighted kernel average, noise suppression and signal trend extraction are achieved at various scales.

[0103] This paper proposes a technique for smoothing preprocessed voltage signals using exponential weighting at each smoothing scale. By assigning weights to adjacent data points within the weighting kernel according to an exponential function and accumulating them, smoothed voltage sequences at each scale are obtained. This step addresses the shortcomings of traditional simple moving averages in smoothing, such as insufficient ability to suppress boundary abrupt changes and noise, and the tendency to introduce delays and information loss. Exponential weighting balances rapid response to nearest-neighbor data with effective suppression of distant noise, preserving trend characteristics while reducing high-frequency jitter at different scales. The multi-scale smoothing effect is more flexible and natural, more accurately reflecting the sensor's true response to tilt angle changes, and providing a high-quality input sequence for subsequent gradient extraction. Furthermore, compared to existing techniques relying solely on fixed windows and equal-weighted filtering, the exponential weighting design in this scheme enhances the convergence speed and local optimization capability of the smoothing operator, improving the overall performance of signal processing.

[0104] The process involves calculating the gradient of the smoothed voltage sequence at each smoothing scale using the central difference method at internal measurement points and the forward difference method and backward difference method at boundary measurement points, respectively, to obtain the complete gradient sequence at each smoothing scale. Specifically, this includes:

[0105] For internal data points, i.e. The gradient is calculated using the central difference method:

[0106] ;in, For the first The data point at the th th Gradient at the layer smoothing scale; local rate of change of internal points is accurately extracted by the difference between adjacent smoothing values ​​on both sides, providing accurate information for sensitivity extremum location;

[0107] For boundary data points, the gradient is calculated using forward differencing and backward differencing methods:

[0108] , The endpoints use first-order differences to ensure that the gradient of the entire data sequence is defined and to avoid index out-of-bounds errors.

[0109] In the gradient calculation stage, a strategy combining central difference at internal measurement points with forward or backward difference at boundary measurement points is employed to ensure accurate gradient values ​​are obtained at all locations. This step overcomes the shortcomings of existing methods that rely solely on central difference, which cannot handle boundary issues at the beginning and end of the sequence or suffer from gradient loss or distortion due to amplified boundary errors. Central difference guarantees the second-order accuracy advantage of extracting the rate of change at internal points, while first-order difference avoids out-of-bounds errors at the boundaries. The benefits are that the entire gradient sequence is coherent and complete, all measurement points can participate in subsequent extreme value extraction, there is no need to discard boundary data, and all sampling information is utilized to the maximum extent, improving the accuracy of sensitivity analysis and data utilization. Compared to single difference methods, this scheme takes into account both boundary conditions and internal accuracy, exhibiting better versatility and reliability.

[0110] The step of extracting the maximum gradient value and its corresponding tilt angle position from the gradient sequence corresponding to each smoothing scale, and marking them as local gradient extrema points at that smoothing scale, specifically includes:

[0111] For each smoothing scale Determine the location of the maximum gradient and the corresponding gradient value:

[0112] , , ;in, For the first The sequence number of the measurement point where the layer gradient maximum is located; For the first The maximum gradient value of the layer; For the first The tilt angle of the maximum gradient point at each layer; the location of the most significant signal change at each layer scale, and the most sensitive operating point of the sensor.

[0113] By scanning the complete gradient sequence at each smooth scale, the maximum gradient value and its corresponding tilt angle are extracted as markers of local gradient extrema. This approach solves the problem in existing technologies where the overall slope selection is easily affected by local noise or outliers, making it difficult to accurately locate the most sensitive operating point. By locating the maximum gradient at each scale, the peak response under relaxation conditions at different scales can be captured. The obtained local sensitivity index is highly representative and robust to the most sensitive section of the sensor, while avoiding misjudgments caused by a single scale, thus improving the comprehensiveness of sensitivity characterization. Unlike traditional one-time peak detection, this scheme completes multiple screenings before multi-scale fusion, improving the accuracy and stability of sensitivity assessment.

[0114] The step of defining the maximum gradient value corresponding to the local gradient extremum point of each smoothing scale layer as the local sensitivity coefficient of that layer specifically includes:

[0115] The maximum gradient value at each smoothing scale is directly defined as the sensitivity coefficient at that scale:

[0116] , ;in, For the first Sensitivity coefficients at the layer smoothing scale; using the maximum gradient at each scale as the layer sensitivity reflects the signal's response capability at different feature levels, eliminating the need for refitting and providing a clear physical interpretation.

[0117] The local gradient extrema at each smoothing scale are directly defined as the sensitivity coefficient of that layer, eliminating the need for additional fitting or model transformation. This step addresses the common problems in existing technologies, such as the susceptibility of complex curve fitting processes to model assumption biases, high computational cost, and poor interpretability. By directly using physically meaningful gradient extrema as the sensitivity index, subsequent processing is simplified while maintaining the transparency of the measurement process. The sensitivity coefficient has direct physical meaning, is easy to verify and trace, and reduces algorithm complexity, making the calibration process more efficient. Compared to traditional methods that require multiple iterative fitting, this approach eliminates the need for additional model training, reducing computational overhead and improving the reliability of engineering applications.

[0118] The arithmetic averaging of the local sensitivity coefficients of all smooth scale layers to obtain the final comprehensive sensitivity coefficient specifically includes:

[0119] The final sensitivity coefficient is obtained by taking the arithmetic mean of the sensitivity coefficients across all scales.

[0120] ;in, This is the final output of the tilt sensor's overall sensitivity coefficient; by fusing responses from all scales, a calibration coefficient is obtained that reflects the sensor's true sensitivity characteristics as a whole, preventing distortion at a single scale.

[0121] The final comprehensive sensitivity coefficient is obtained by arithmetically averaging the local sensitivity coefficients across all smooth scales. This fusion method addresses the potential distortion or deviation from the true response that may occur with single-scale sensitivity indices. The arithmetic average balances the contribution of each scale to the overall measurement, achieving a comprehensive reflection of the sensor's response capabilities at different feature levels. The advantage is that the comprehensive sensitivity coefficient more closely approximates the sensor's true performance, suppressing fluctuations caused by anomalies at a particular scale while maintaining the stability and consistency of the results. Compared to more complex methods such as directly selecting extreme values ​​or weighted averaging, this scheme combines simplicity and reliability, meeting the dual requirements of speed and accuracy in engineering applications.

[0122] Calculating the residual between the predicted output and the true inclination angle based on the validation dataset, and judging whether the calibration is qualified according to the preset root mean square error threshold. When it is unqualified, supplementing sampling points or adjusting the smoothing parameters and then re - calibrating, specifically including:

[0123] Setting the number of validation data points and the error threshold ; Defining the test range and objectives, and providing a quantitative criterion to ensure the practical usability of the calibration result;

[0124] The error threshold is the only quantitative standard for judging whether the sensitivity calibration result of this time is qualified. It represents the maximum allowable error between the model prediction value and the actual validation data through the root mean square error . When , it means that the calibrated sensitivity coefficient can meet the accuracy requirements and the calibration passes; if , it is determined that the calibration is unqualified, and data needs to be supplemented or parameters adjusted to re - calibrate. The setting of this threshold directly determines the reliability of the sensitivity coefficient output and the lower limit of the quality of engineering applications. If takes a smaller value, only a very close to the ideal calibration result will be judged as qualified. This can maximize the accuracy of the sensitivity coefficient, but at the same time will greatly increase the probability of unqualified, resulting in multiple repeated acquisitions and calculations, increasing the complexity and time cost of the calibration process, and is prone to repeated rework in the case of large actual noise and environmental disturbances. If takes a larger value, more calibration results may be judged as qualified. Although it improves the passing rate and calibration efficiency, it may cover up model errors and outliers, thus reducing the accuracy and reliability of the actual measurement and control of the system and affecting the subsequent engineering application effect. Reasonably setting can improve the calibration efficiency on the basis of ensuring the sensor output accuracy, making the process neither too strict nor lacking in rigor, and balancing the engineering reality and technical requirements. The basis for the value of the error threshold: Sensor resolution and linearity: Key indicators such as resolution, linearity or factory error provided by the sensor manufacturer can be referred to, and the set error range should not exceed its allowable range. Actual application requirements: Different thresholds should be set according to the tolerance of the inclination measurement error in the final application scenario. For example, high - precision industrial measurement and structural monitoring have stricter requirements for error tolerance, while high - fault - tolerance occasions can be appropriately relaxed. System error analysis: Considering the comprehensive effects of noise, environmental temperature, assembly, etc., reasonably select the maximum tolerance error that can accommodate these factors. Suggestions for the value of the error threshold: General suggestion: Set to one - thousandth to one - hundredth of the sensor range. For example, for an inclination sensor with a range of , it is recommended that takes a value between and Between. High-precision applications: such as aerospace, precision measurement, etc., are recommended. Less than the manufacturer's stated resolution or linearity error. For typical industrial applications: refer to the product manual for the maximum permissible error and allow for appropriate adjustments. Actual adjustments: During batch calibration or on-site calibration, optimization can be gradually achieved through statistical analysis of the distribution of calibration results. The settings achieve a dynamic balance between optimal pass rate and application accuracy.

[0125] Collect and sort in ascending order Group validation data, obtained , ;in, To verify the data point sequence number; For the first The true inclination angle of each verification point; For the first The original output voltage of each verification point; the verification set is organized in ascending order to maintain the same data structure and order as the calibration set;

[0126] The validation data is debiased and the prediction output is calculated:

[0127] , ;in, For the first The average voltage of each verification point; For the first Each verification point is determined by the final sensitivity. and tilt angle Predicted output voltage; establish a prediction model using calibrated sensitivity and compare it with the actual debiasing voltage;

[0128] Calculate the first Output prediction residuals at each validation point and root mean square error :

[0129] , Quantitatively assess the accuracy of predictions to provide an objective basis for branch decisions;

[0130] The judgment is based on the root mean square error and the error threshold:

[0131] like If the calibration is successful, the final sensitivity will be output. ;

[0132] like If the calibration fails, additional calibration points should be added or the smoothing scale parameters should be adjusted before returning to step S1 to re-perform the calibration.

[0133] The calibration results are determined based on the error threshold, and the iterative direction of the improved solution is provided to ensure the closed loop and repeatability of the process.

[0134] By introducing an independent validation dataset and a preset error threshold, the calibration results are objectively judged, and recalibration is performed after supplementary sampling or parameter adjustment when unqualified, forming a closed-loop optimization mechanism. This step solves the problems of traditional one-time calibration processes, which cannot guarantee the consistency of results across different datasets and field environments, and lack feedback for adjustment. The use of validation sets and the setting of error thresholds can quantify calibration quality and guide the dynamic adjustment of the calibration scheme. The benefits are that it ensures the reliability and stability of the final sensitivity coefficient in practical application scenarios, while providing clear optimization directions and criteria, avoiding blindly repeating calibration or excessively relaxing standards. Compared with existing processes that lack iterative verification mechanisms, this scheme achieves repeatability and adaptability of the calibration process through controllable error assessment and branch decision-making, improving the reliability and engineering usability of the final measurement performance.

[0135] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0136] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for quantitatively calibrating the sensitivity coefficient of an intelligent sensor, characterized in that, include: S1. The original output voltage and corresponding tilt angle value of the smart tilt sensor to be calibrated are collected sequentially at different tilt angle positions, and the DC component of the original output voltage sequence is calculated. The bias is then processed to obtain the voltage value sequence after bias correction. S2. Based on the maximum span of the tilt angle and the minimum adjacent difference of the preprocessed data, the number of smoothing scale layers is adaptively determined, and the exponential smoothing kernel radius of each smoothing scale is constructed according to the geometric proportionality principle. S3. For each smoothing scale, the original voltage signal is smoothed using an exponential weighting method to obtain the smoothed voltage sequence at the corresponding scale. S4. For the smoothed voltage sequence at each smoothing scale, the gradient is calculated using the central difference method at the internal measurement points and the gradient is calculated using the forward difference method and the backward difference method at the boundary measurement points, respectively, to obtain the complete gradient sequence at each smoothing scale. S5. In the gradient sequence corresponding to each smoothing scale, extract the maximum gradient value and its corresponding tilt angle position, and mark it as the local gradient extreme point under that smoothing scale. S6. Define the maximum gradient value corresponding to the local gradient extreme point of each smooth scale layer as the local sensitivity coefficient of that layer. S7. Perform an arithmetic average of the local sensitivity coefficients of all smooth scale layers to obtain the final comprehensive sensitivity coefficient. S8. Calculate the residual between the predicted output and the true tilt angle based on the validation dataset, and determine whether the calibration is qualified according to the preset root mean square error threshold. If it is not qualified, supplement the sampling points or adjust the smoothing parameters and recalibrate.

2. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 1, characterized in that, The process involves sequentially acquiring the original output voltage and corresponding tilt angle values ​​at different tilt angle positions of the intelligent tilt sensor to be calibrated, calculating the DC component of the original output voltage sequence, and performing debiasing processing to obtain a bias-corrected voltage value sequence, specifically including: S101. Collect data sequentially according to the tilt angle from smallest to largest. The calibration data is set and meets the requirements. : , ;in, For data point sequence numbers; For the first One tilt angle measurement value; For the first The original output voltage corresponding to each tilt angle; S102. For any adjacent data points, if Then only the measuring points with smaller numbers are retained. Delete the measuring points with larger numbers. ;in, This refers to the sensor's nominal resolution. After deletion, the remaining measuring points must be renumbered in ascending order, and the above judgment must be repeated until all adjacent measuring points meet the requirements. ; If the final number of remaining measurement points is greater than or equal to 3, proceed to the next step; if it is less than 3, data needs to be collected again or supplemented before returning to step S101. Obtain the final measurement point, denoted as... Update the number of measurement points ; S103. Calculate the DC component of the voltage and perform debiasing processing, as follows: , ;in, This is the arithmetic mean of all the original voltages; The output voltage after removing DC bias; The preprocessed dataset is obtained as follows .

3. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 2, characterized in that, The method adaptively determines the number of smoothing scale layers based on the maximum span of the tilt angle and the minimum adjacent difference of the preprocessed data, and constructs the exponential smoothing kernel radius for each smoothing scale according to the geometric proportionality principle, specifically including: The calculation of the range of tilt angle values ​​and the minimum adjacent difference is as follows: , ;in, The maximum span of the tilt angle for all collected data points; It is the minimum value among all adjacent data points of tilt angle difference; Determine the number of smoothing scale layers: ;in, This represents the total number of smooth scale layers; Based on the principle of geometric proportionality, construct The layer smoothing scale is as follows: ;in, For the first Layer smoothing exponent kernel radius; This is the scale layer number, and its value range is... to .

4. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 3, characterized in that, For each smoothing scale, an exponential weighting method is used to smooth the original voltage signal to obtain a smoothed voltage sequence at the corresponding scale, specifically including: For each smoothing scale and each data point The smoothing calculation is performed in the following manner: ;in, For the first Layer smoothing scale Smoothed voltage values ​​for each data point; The sequence number of the measurement points traversed during the smoothing kernel weighting; It is an exponential function. .

5. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 4, characterized in that, The process involves calculating the gradient of the smoothed voltage sequence at each smoothing scale using the central difference method at internal measurement points and the forward difference method and backward difference method at boundary measurement points, respectively, to obtain the complete gradient sequence at each smoothing scale. Specifically, this includes: For internal data points, i.e. The gradient is calculated using the central difference method: ;in, For the first The data point at the th th Gradient at the layer smoothing scale; For boundary data points, the gradient is calculated using forward differencing and backward differencing methods: ， 。 6. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 5, characterized in that, The step of extracting the maximum gradient value and its corresponding tilt angle position from the gradient sequence corresponding to each smoothing scale, and marking them as local gradient extrema points at that smoothing scale, specifically includes: For each smoothing scale Determine the location of the maximum gradient and the corresponding gradient value: , , ;in, For the first The sequence number of the measurement point where the layer gradient maximum is located; For the first The maximum gradient value of the layer; For the first The tilt angle of the point with the maximum gradient below the layer.

7. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 6, characterized in that, The step of defining the maximum gradient value corresponding to the local gradient extremum point of each smoothing scale layer as the local sensitivity coefficient of that layer specifically includes: The maximum gradient value at each smoothing scale is directly defined as the sensitivity coefficient at that scale: , ;in, For the first Sensitivity coefficient at the layer smoothing scale.

8. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 7, characterized in that, The arithmetic averaging of the local sensitivity coefficients of all smooth scale layers to obtain the final comprehensive sensitivity coefficient specifically includes: The final sensitivity coefficient is obtained by taking the arithmetic mean of the sensitivity coefficients across all scales. ;in, This is the final output of the tilt sensor's overall sensitivity coefficient.

9. The method for quantitatively calibrating the sensitivity coefficient of a smart sensor according to claim 8, characterized in that, The process involves calculating the residual between the predicted output and the true tilt angle based on the validation dataset, and determining whether the calibration is qualified according to a preset root mean square error threshold. If the calibration is unqualified, additional sampling points are added or the smoothing parameters are adjusted before recalibration. This process specifically includes: Set the number of verification data points and error threshold ; Collect and sort in ascending order Group validation data, obtained , ;in, To verify the data point sequence number; For the first The true inclination angle of each verification point; For the first Original output voltage at each verification point; The validation data is debiased and the prediction output is calculated: , ;in, For the first The average voltage of each verification point; For the first Each verification point is determined by the final sensitivity. and tilt angle Predicted output voltage; Calculate the first Output prediction residuals at each validation point and root mean square error : ， ； The judgment is based on the root mean square error and the error threshold: like If the calibration is successful, the final sensitivity will be output. ; like If the calibration fails, additional calibration points should be added or the smoothing scale parameters should be adjusted before returning to step S1 to re-perform the calibration.

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