Quantitative calibration method for sensitivity coefficient of intelligent sensor

Abstract

The invention 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 sequentially collected at different inclination angle positions, direct current bias is removed, a multi-layer exponential smoothing kernel is adaptively constructed based on the maximum span and the minimum adjacent difference of a voltage sequence, and multi-scale smoothing is carried out on signals; respectively extracting the gradient of the smooth voltage sequence of each layer by adopting central difference and endpoint difference, and extracting the maximum gradient and the corresponding dip angle value in each layer as local sensitivity; arithmetically averaging the sensitivity of each layer to obtain a comprehensive sensitivity coefficient; and finally, combining verification data to calculate a prediction output and a real dip angle residual error, judging whether calibration is qualified or not according to a preset root-mean-square error threshold value, and if the calibration is unqualified, supplementing sampling points or adjusting smoothing parameters and then carrying out iterative execution.

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, performing smoothing calculation on the original voltage signal in an exponential weighting manner to obtain a smoothed voltage sequence under the corresponding scale;

[0010] S4, calculating the gradient at the internal measuring point using the central difference method, and calculating the gradient at the boundary measuring point using the forward difference method and the backward difference method respectively, to obtain a complete gradient sequence under each smoothing scale;

[0011] S5, in the gradient sequence corresponding to each smoothing scale, extracting the maximum gradient value and the inclination position corresponding thereto, and marking it as a local gradient extreme point under the smoothing scale;

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

[0013] S7, performing arithmetic average processing on the local sensitivity coefficients of all smoothing scale layers 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 intelligent inclination sensor to be calibrated sequentially collects original output voltages and corresponding inclination values at different inclination positions, and calculates a direct current component of the original output voltage sequence 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 a 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 parameters of each smooth scale kernel, an exponential weighted smoothing operation is performed on the de-biased voltage signal to dynamically attenuate the influence of remote noise. Compared with simple moving average or fixed window filtering, exponential weighting can balance signal smoothing and local response, reducing information loss caused by window effect. This method can adaptively balance noise suppression and trend preservation at different smoothing scales, achieving multi-level smoothing from micro-local to macro-global, and providing a purer and more coherent signal basis for subsequent gradient extremum positioning.

[0062] 4、 The scheme uses central difference to calculate the gradient at the internal position of the smoothed voltage sequence, and uses forward difference and backward difference at the beginning and end boundaries respectively, ensuring that each data point has a defined gradient value. Compared with using only central difference or other approximate difference methods, this strategy can avoid the problem of missing or distorted gradient values at the boundary data, while ensuring the highest accuracy of gradient calculation at internal positions. This design makes the gradient sequence consistent throughout the range, improving the ability to capture signal change rates and laying a solid foundation for sensitive point positioning.

[0063] 5、 In the gradient sequence corresponding to each smoothing scale, the scheme extracts the maximum gradient and its corresponding inclination position by scanning all data points, and identifies this position as the most sensitive working point of the sensor. Compared with traditional methods that directly use the overall maximum slope or fixed interval selection, using multi-scale gradient extremum extraction can not only find the true change peak of the signal at different scales, but also avoid deviations caused by noise or abnormal points at a single scale, making the local sensitivity index more representative and stable, and thus more accurately reflecting the response ability of the sensor at each level.

[0064] 6、 This scheme directly defines the maximum gradient value extracted at each smoothing level as the local sensitivity coefficient at that scale, without additional fitting or interpolation processing. Unlike methods that require curve fitting or complex response modeling, directly using gradient extremum as a sensitivity index not only simplifies the calculation process, but also has physical interpretability, which can intuitively reflect the response ability of the sensor to inclination changes at different smoothing levels, avoiding model error accumulation and improving the transparency and traceability of the calibration process.

[0065] 7、 For the local sensitivity coefficients of all smoothing scales, the scheme uses arithmetic mean fusion to obtain the final comprehensive sensitivity coefficient. Compared with simply selecting the maximum or minimum value, arithmetic mean can balance the contribution of each level to sensitivity estimation, overcome distortion or bias that may occur at a single scale, and obtain a more comprehensive and stable sensitivity representation 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 verification data set to determine the calibration effect by calculating the root mean square error of the predicted inclination output and the true value, and if necessary, additional sampling points or adjustment of the smoothing parameter is re-iterated. Unlike the traditional one-time calibration or only relying on single error evaluation, the design establishes a closed-loop feedback mechanism, which can adaptively optimize the calibration process in the engineering environment, ensure the output sensitivity while meeting the accuracy requirements, and effectively improve the reliability and applicability of the calibration results. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 The flowchart of the present application is shown. DETAILED DESCRIPTION

[0068] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0069] Embodiments, refer to Figure 1 A quantitative calibration method for sensitivity coefficient of intelligent sensor, comprising:

[0070] S1, the original output voltage and the corresponding inclination value of the intelligent inclination sensor to be calibrated are collected in sequence at different inclination positions, and the direct current component of the original output voltage sequence is calculated, and the bias corrected voltage value sequence is obtained after the bias is removed;

[0071] S2, based on the inclination maximum span and the minimum adjacent difference of the preprocessed data, the smoothing scale layer is adaptively determined, and the exponential smoothing kernel radius of each smoothing scale is constructed according to the geometric equal ratio principle;

[0072] S3, for each smoothing scale, the original voltage signal is smoothed and calculated by using exponential weighting method, and the smoothed voltage sequence under the corresponding scale is obtained;

[0073] S4, for the smoothed voltage sequence under each smoothing scale, the gradient is calculated by using central difference method at internal measuring points, and the gradient is calculated by using forward difference method and backward difference method at boundary measuring points, respectively, to obtain the complete gradient sequence under each smoothing scale;

[0074] S5, in the gradient sequence corresponding to each smoothing scale, the maximum gradient value and the inclination position corresponding to the maximum gradient value are extracted, which are marked as the local gradient extreme point under the smoothing scale;

[0075] 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;

[0076] S7, arithmetically average the local sensitivity coefficients of all smooth scale layers to obtain a final comprehensive sensitivity coefficient;

[0077] S8, calculate the residual between the predicted output and the true inclination based on the verification data set, and determine whether the calibration is qualified according to a preset root mean square error threshold, and if not, supplement the sampling points or adjust the smoothing parameters and then re-perform the calibration.

[0078] A complete intelligent inclination sensor sensitivity coefficient quantitative calibration process is disclosed, which is characterized by a closed-loop system from signal preprocessing to multi-scale smoothing, accurate gradient calculation, extreme value extraction, index fusion, and result verification and iterative optimization. By collecting the original voltage at different inclination positions and performing denoising and DC bias correction, and then adaptively constructing multiple smooth scales based on the maximum inclination span and the minimum adjacent difference of the data, the influence of the baseline drift and random noise of the measurement system can be effectively eliminated; then, the preprocessed signal is applied with exponential weighted smoothing, which can suppress noise while retaining the true trend; the internal and boundary gradients are accurately calculated at each scale, and the maximum gradient value is extracted as the local sensitivity index; finally, all indexes are arithmetically averaged and combined with the error determination of the verification set to perform iterative optimization. Through these steps, the problems of traditional single scale or one-time smoothing, such as easy to lose details, sensitive to noise and abnormal points, and lack of adaptive verification mechanism, are solved; the calibration accuracy and robustness are improved, the multi-level characterization of the sensor sensitivity characteristics is realized, and the repeatability and engineering reliability of the calibration results are guaranteed by introducing closed-loop verification and parameter iteration. Compared with the prior art, the scheme innovatively combines adaptive multi-scale and exponential smoothing, and is supplemented by complete verification feedback, filling the gap in the industry in the lack of sensitivity quantization and feedback optimization mechanism in high-noise environments.

[0079] The intelligent inclination sensor to be calibrated sequentially collects original output voltages and corresponding inclination values at different inclination positions, and calculates the DC component of the original output voltage sequence, and performs bias correction to obtain a voltage value sequence after bias correction, specifically including:

[0080] S101, sequentially collect inclination from small to large group calibration data, and satisfy :

[0081] , ; wherein, is the data point number; is the inclination measurement value of the th; is the original output voltage corresponding to the inclination of the th;

[0082] The original measurement data is organized in ascending order of inclination to ensure that subsequent adjacent difference, scale construction and other algorithms are based on ordered and complete data sequences;

[0083] 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;

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

[0085] If the final number of remaining measuring points 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;

[0086] Get the final measuring point, denoted as , update the number of measuring points ;

[0087] Eliminate invalid or redundant measuring points to ensure that the distance between adjacent data points is not less than the resolution of the sensor, making the adjacent difference and subsequent smoothing more stable and reliable;

[0088] S103, calculate the direct current component of the voltage and perform the offset processing, as follows:

[0089] , ; wherein, is the arithmetic mean of all original voltages; is the output voltage after removing the direct current bias;

[0090] The preprocessed data set is ;

[0091] Eliminate the direct current baseline offset of the measurement system, so that subsequent smoothing and gradient operation focus on signal change components, and improve the sensitivity calculation accuracy.

[0092] Further refine the data acquisition and preprocessing process, especially emphasize the resolution of the redundant points according to the dip angle ascending point by point collection and elimination, and the arithmetic average filtering and DC bias elimination of the remaining points. By eliminating the dense or invalid data points according to the ordered and equidistant principle in the original signal acquisition stage, the error amplification caused by the too dense or uneven spacing of the measuring points in the subsequent difference operation and multi-scale smoothing process is avoided; At the same time, the baseline correction and local average filtering are performed on the signal, which reduces the offset and high frequency noise of the measurement system. In this way, the pain points of the prior art in the data preprocessing stage are solved, that is, the rationality of the measuring point distribution is ignored, which leads to the jitter and misjudgment of the subsequent gradient calculation; Ensure the integrity and stability of the input data sequence, provide a reliable foundation for multi-scale processing, and reduce the influence of abnormal points on the overall calibration accuracy, so that the subsequent smoothing and gradient analysis are more focused on the true signal fluctuation, thereby improving the accuracy and repeatability of the sensitivity calculation. Unlike the traditional simple denoising or uniform filtering, the present scheme controls the sampling density and baseline bias in two dimensions, taking into account stability and precision, and embodies the in-depth innovation of data quality management.

[0093] The maximum span of the dip angle and the minimum adjacent difference 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:

[0094] The dip angle value range and the minimum adjacent difference are calculated, specifically:

[0095] , ; wherein, is the maximum span of the dip angle of all collected data points; is the minimum value in the dip angle difference of all adjacent data points; quantifying data distribution characteristics provides data support for adaptively constructing multi-scale smoothing kernel parameters;

[0096] Determine the number of smoothing scales: ; wherein, is the total number of smoothing scales; the number of scales is adaptively set according to the data volume, which takes into account the calculation efficiency while ensuring detail description;

[0097] Based on the geometric equal ratio principle, the layer smoothing scale is constructed, specifically:

[0098] ; wherein, is the exponential kernel radius of the layer smoothing; is the scale layer number, the value range is to ; Generate an exponential kernel scale that increases layer by layer from local to global, realize multi-level signal smoothing, and capture trend characteristics in different ranges.

[0099] The adaptive construction of multi-scale smoothing parameters is described in detail, including adaptive determination of the number of smoothing layers based on the inclination span and minimum adjacent difference quantization data distribution characteristics, and generation of exponentially increasing kernel radii according to the geometric equal ratio principle. Through this mechanism, the problem of over-smoothing or insufficient smoothing of existing fixed number of layers or empirical parameter construction methods in different data volume and distribution scenarios is solved; when the data span is large and the details are rich, the number of smoothing layers can be dynamically increased to capture macro trends; when the adjacent difference is small, the scale can be refined to depict local changes. Balancing the calculation efficiency and signal detail preservation, the smoothing process is neither too rough nor overly sensitive, improving the adaptability and generalization ability of multi-scale processing. Compared with traditional artificial setting or one-time fixed kernel parameter technology, the scheme generates geometric series kernel parameters by quantifying data distribution, avoiding the dependence on human experience parameters, enhancing the intelligence and universality of the method, and ensuring efficient and stable multi-scale smoothing in various application scenarios.

[0100] For each smoothing scale, the original voltage signal is smoothed by using an exponential weighting method 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 way:

[0102] ; wherein, is the smoothed voltage value of the th data point at the th smoothing scale; is the measurement point sequence number traversed during smoothing kernel weighting; is an exponential function, ; the exponential weighting kernel average is applied to the de-biased voltage to achieve noise suppression and signal trend extraction at each scale.

[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] The center difference of internal measuring points and the forward or backward difference of boundary measuring points are combined in the gradient calculation link to ensure that accurate gradient values can be obtained at all positions. Through this step, the disadvantages of the prior art, such as the inability to process boundary points at the beginning and end of a sequence or the amplification of boundary errors, which leads to the absence or distortion of gradients, are solved. The center difference ensures the second-order precision advantage of the change rate extraction of internal points, and the first-order difference can avoid the out-of-bound situation at the boundary. The advantage is that the entire gradient sequence is coherent and complete, all measuring points can participate in subsequent extreme value extraction, boundary data does not need to be discarded, all sampling information is maximally utilized, and the accuracy and data utilization rate of sensitivity analysis are improved. Compared with a single difference method, the present scheme takes into account the boundary condition and internal precision, and has better universality and reliability.

[0110] The maximum gradient value and the corresponding inclination position in the gradient sequence corresponding to each smoothing scale are extracted, and are marked as the local gradient extreme point under the smoothing scale, and specifically include:

[0111] For each smoothing scale , the maximum gradient position and the corresponding gradient value are determined:

[0112] , , ; wherein, is the measuring point sequence number of the maximum gradient of the first layer; is the maximum gradient value of the first layer; is the inclination of the maximum gradient point under the first layer. The most significant position of signal change under each scale is located, and the most sensitive working point of the sensor is extracted.

[0113] By scanning the complete gradient sequence under each smoothing scale, the maximum gradient value and the corresponding inclination position are extracted as the local gradient extreme point mark. Through this measure, the problem that the commonly used overall slope selection point in the prior art is easily affected by local noise or abnormal points and is difficult to accurately locate the most sensitive working point is solved. Locating the maximum gradient under each scale can capture the peak response under the relaxation state of different scales. The obtained local sensitivity index has high representativeness and robustness for the most sensitive section of the sensor, avoids misjudgment caused by a single scale, and improves the comprehensiveness of the sensitivity characterization. Unlike the traditional one-time peak detection, the present scheme completes multiple screening before multi-scale fusion, and improves the accuracy and stability of the sensitivity evaluation.

[0114] 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, and specifically includes:

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

[0116] , ; wherein, is the sensitivity coefficient at the smooth scale of the i-th layer; the maximum gradient of each scale is taken as the layer sensitivity, which reflects the response ability of the signal at different feature levels, without the need for further fitting, and the physical interpretation is clear. The local gradient extreme value at each smooth scale is directly defined as the layer sensitivity coefficient, without additional fitting or model conversion. Through this step, the problem that the complex curve fitting process in the prior art is easily affected by model assumption deviation, has large calculation amount and poor interpretability is solved; the gradient extreme value with clear physical meaning is directly taken as the sensitivity index, which simplifies the subsequent processing and maintains the transparency of the measurement process. The sensitivity coefficient has a direct physical meaning, is easy to verify and trace, reduces the algorithm complexity, and makes the calibration process more efficient. Compared with the traditional method which needs multiple iterations of fitting, the present scheme does not need additional model training, reduces the calculation overhead and improves the reliability of engineering application.

[0117] The local sensitivity coefficients of all smooth scale layers are arithmetically averaged to obtain the final comprehensive sensitivity coefficient, specifically including:

[0118] The sensitivity coefficients at all scales are arithmetically averaged to obtain the final sensitivity coefficient:

[0119]

[0120] ; wherein, is the final output comprehensive sensitivity coefficient of the tilt angle sensor; the sensitivity coefficients of all scales are fused to obtain a calibration coefficient that reflects the real sensitivity characteristics of the sensor, preventing distortion of a single scale. The local sensitivity coefficients of all smooth scales are arithmetically averaged to obtain the final comprehensive sensitivity coefficient. Through this fusion mode, the problem of distortion or deviation from the real response that may occur in a single scale sensitivity index is solved; the arithmetic average balances the contribution of each scale to the overall measurement, and realizes the comprehensive reflection of the response ability of the sensor at different feature levels. The advantage is that the comprehensive sensitivity coefficient is closer to the real performance of the sensor, can suppress fluctuations caused by an abnormal scale, and at the same time maintains the stability and consistency of the result. Compared with the complex method of directly selecting the extreme value or weighted average, the present scheme has the advantages of simplicity and reliability, and meets the dual needs of speed and accuracy in engineering application.

[0121]

[0122] ​The residual of the predicted output based on the verification data set and the true inclination angle is calculated, and whether the calibration is qualified is judged according to a preset root mean square error threshold, and when unqualified, supplementary sampling points or adjustment of the smoothing parameter is carried out to re-calibrate, and specifically comprising:

[0123] Set the number of verification data points And the error threshold ; define the test range and target, and provide quantitative criteria to ensure the practical availability of the calibration results;

[0124] Error threshold is the only quantitative standard for determining whether the sensitivity calibration result is qualified. It represents the maximum allowed error between the model prediction value and the actual verification data measured by the root mean square error . When , it means that the calibrated sensitivity coefficient can meet the accuracy requirement, and the calibration is passed; if , it is determined that the calibration is unqualified, and it needs to be re-calibrated by supplementing data or adjusting parameters. The setting of the threshold directly determines the reliability of the sensitivity coefficient output and the lower limit of the quality of the engineering application. If , the value is small, only the calibration result very close to the ideal one will be judged as qualified. In this way, the accuracy of the sensitivity coefficient can be maximized, but at the same time, the probability of unqualified will be greatly increased, resulting in repeated collection and calculation, increasing the complexity and time cost of the calibration process, and in the case of actual noise and environmental disturbance, it is easy to cause repeated rework. If , the value is large, more calibration results can be judged as qualified, although the pass rate and calibration efficiency are improved, but the model error and abnormal points may be covered up, thereby reducing the accuracy and reliability of the actual measurement and control of the system, affecting the effect of subsequent engineering application. Reasonable setting of can improve the calibration efficiency on the basis of ensuring the accuracy of the sensor output, so that the process is neither too strict nor too rigorous, balancing the engineering practice and technical demand. The value of the error threshold is based on: sensor resolution and linearity: refer to the resolution, linearity or factory error of the sensor provided by the sensor manufacturer, and set it to be not more than the allowed error range. Actual application demand: different threshold values should be set according to the tolerance of the inclination measurement error in the final application scenario. For example, high-precision industrial measurement and structure monitoring require more stringent error tolerance, and high-fault-tolerant occasions can be appropriately relaxed. System error analysis: combined with noise, environmental temperature, assembly and other comprehensive influences, the maximum tolerance error that can accommodate these factors is reasonably selected. The value of the error threshold is recommended: generally recommended: set to one thousandth to one percent of the sensor range. For example, for an inclination sensor with a range of , it is recommended that be set to to High precision applications: such as aerospace, precision measurement, etc. It is recommended to less than the manufacturer's stated resolution or linear error. General industrial applications: can refer to the maximum allowable error in the product manual, and appropriately relax . Actual adjustment: in the process of batch calibration or on-site calibration, the distribution of calibration results can be gradually optimized Set, realize the dynamic balance of optimal pass rate and application accuracy.

[0125] Collect and arrange in ascending order Group verification data, get , ; wherein, is the verification data point number; is the true inclination of the first verification point; is the original output voltage of the first verification point; Organize the verification set in ascending order, maintain the same data structure and order as the calibration set;

[0126] Debias the verification data and calculate the predicted output:

[0127] , ; wherein, is the debiased voltage of the first verification point; is the output voltage of the first verification point predicted by the final sensitivity and inclination ; Use the calibration sensitivity to establish a prediction model and compare it with the actual debiased voltage;

[0128] Calculate the output prediction residual and root mean square error of the first verification point:

[0129] , ; Quantitative evaluation of prediction accuracy provides an objective basis for branch decision-making;

[0130] According to the root mean square error and the error threshold:

[0131] If , the calibration is qualified, and the final sensitivity is output;

[0132] If , the calibration is not qualified, and the calibration points should be supplemented or the smoothing scale parameter should be adjusted before returning to step S1 to re-implement the calibration;

[0133] The calibration result is determined based on the error threshold value, and an iterative direction of the perfect scheme is provided to ensure the process closed loop and repeatability.

[0134] By introducing an independent verification data set and a preset error threshold value, the calibration result is objectively determined, and when it is unqualified, the sampling is supplemented or the parameters are adjusted for re-calibration, forming a closed loop optimization mechanism. Through this step, the problem that the consistency of the result in different data sets and field environments cannot be guaranteed in the traditional one-time calibration process and the lack of feedback adjustment are solved; the use of the verification set and the setting of the error threshold value can quantify the calibration quality and guide the dynamic adjustment of the calibration scheme. The advantage is to ensure the reliability and stability of the final sensitivity coefficient in the actual application scene, while providing a clear optimization direction and criterion, avoiding blind repeated calibration or excessive relaxation of standards. Compared with the existing process lacking iterative checking mechanism, the present scheme realizes the repeatability and adaptability of the calibration process through controllable error evaluation and branch decision, and improves the reliability and engineering usability of the final measurement performance.

[0135] It should be noted that, in this text, 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 that there is any such actual relationship or order between these entities or operations. Moreover, the terms "include", "contain" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or equipment including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or equipment.

[0136] The above is only the preferred embodiment of the present application, and it should be noted that for ordinary skilled in the art, without departing from the technical principles of the present application, a number of improvements and refinements can be made, which should also be considered as the protection scope of the present application.

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 then 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 an intelligent 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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