Micro-force intelligent calibration and high-precision resolving method and system based on data driving

Abstract

The invention discloses a micro-force intelligent calibration and high-precision resolving method and system based on data driving, and the method comprises the steps: carrying out the loading experiment of a micro-force measurement device through a high-precision standard force source, and constructing a calibration data set; the GPR model is trained by using the training set with the capacitance value variation as an input feature and the standard force value as an output label, and the GPR model is selected as a final model based on the comprehensive performance evaluation indexes on the verification set; performing performance evaluation on the final model based on a test set of whole-course isolation and storage to obtain unbiased estimation of generalization performance; deploying the final model for actual measurement, collecting capacitance value variation caused by to-be-measured micro force, inputting the capacitance value variation into the model, calculating to obtain a force value measurement result, and synchronously outputting synthetic standard uncertainty of the measurement result; the self output performance is monitored in real time, and a decision basis is provided for predictive maintenance and model updating. According to the invention, high-precision and high-reliability measurement can be carried out on the micro force from milliNewton to micro Newton magnitude.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and in particular to a data-driven intelligent calibration and high-precision calculation method and system for micro-force. Background Technology

[0002] High-precision and high-reliability measurement of minute forces ranging from millineutons to micronewtons is a core requirement in cutting-edge fields such as precision manufacturing, biomedical engineering, and micro-nano technology. However, achieving this goal has long been hampered by a fundamental contradiction between measurement accuracy, environmental robustness, operational complexity, and manufacturing cost.

[0003] Existing technologies have formed three fragmented technical paths: "hardware precision," "process automation," and "algorithm evaluation." These three paths either pursue ultimate hardware performance at the expense of cost and robustness, focus on offline process automation and post-evaluation, or focus on the macroscopic performance evaluation of the algorithm model itself. Together, they result in a technological gap: the lack of a technical solution that can be embedded within terminal devices to achieve "integrated measurement and evaluation." Its shortcomings are mainly reflected in the following aspects: I. Users cannot obtain the immediate reliability of the results in a single real-time measurement; II. Intelligent methods have not been deeply integrated with physical measurement itself, failing to empower the measurement terminal; III. There is a lack of an engineering solution that balances high precision, high robustness, low cost, and ease of use. Summary of the Invention

[0004] Purpose of the invention: This invention provides a data-driven intelligent calibration and high-precision calculation method and system for micro-forces, which can perform high-precision and high-reliability measurement of micro-forces ranging from millineutons to micronewtons.

[0005] Technical solution: The present invention provides a data-driven intelligent calibration and high-precision solution method for micro-force, comprising the following steps:

[0006] Step 1: Using a high-precision standard force source, perform a loading experiment on a micro-force measuring device, and simultaneously collect the standard force value F and the change in capacitance value. Construct a calibration dataset;

[0007] Step 2: Divide the calibration dataset into training, validation, and test sets, based on the change in capacitance values. Using the standard force value F as the output label and the probabilistic framework of the Gaussian process regression (GPR) model as the input feature, the GPR model is trained using the training set and selected as the final model based on the comprehensive performance evaluation index on the validation set.

[0008] Step 3: Perform a one-time performance evaluation on the final model based on the test set that is isolated and sealed throughout the process to obtain an unbiased estimate of its generalization performance;

[0009] Step 4: Deploy the final model in actual measurement. For the micro-force to be measured, collect the original sensor readings caused by it and input them into the model. Solve to obtain the force measurement result and simultaneously output the combined standard uncertainty U of the measurement result and the final force value F. 最终 =[Measured value] ± U;

[0010] Step 5: Monitor its own output performance in real time. By tracking the changing trend of the synthetic standard uncertainty U or periodically using standard samples for verification and calculating the relative error, when the performance index is detected to deviate continuously and exceed the preset threshold, it will automatically send a maintenance prompt signal to the user, thereby providing a basis for decision-making for predictive maintenance and model updates.

[0011] Further, in step 1, the micro-force measuring device includes an outer frame, a lever support, a lever, a fulcrum, a fixed pulley support, a first fixed pulley, a second fixed pulley, a force input end, a force measuring disk, a hanging rope, a motion output end, a traction rope, a counterweight, a first wire, a second wire, an inner cylinder, an outer cylinder, and a standard force source; the lever support is fixed to the bottom of the outer frame via its base, the lever is rotatably supported on the lever support via its fulcrum, the fixed pulley support is fixed to the top of the outer frame, and the first and second fixed pulleys are installed on the fixed pulley support in a tangential position, one above the other and the other to the left and right. One end of the lever is the force input end, used to connect the force to be measured. The force measuring disk is vertically suspended from the force input end by a hanging rope. A standard force source is applied to the force measuring disk step by step. The other end of the lever is the motion output end. One end of the traction rope is fixed to the motion output end, and then passes around the first fixed pulley and the second fixed pulley in sequence. The other end of the traction rope is connected to the counterweight, and then connected to the inner cylinder of the coaxial cylindrical capacitor through the first wire. The outer cylinder of the capacitor is fixed to the bottom of the outer frame and connected to the second wire. The free ends of the first wire and the second wire are respectively connected to the corresponding interfaces of the capacitance measuring instrument to measure the change in capacitance value.

[0012] Furthermore, in step 1, a standard force source is applied step by step on the force measuring plate, and a series of capacitance value changes are collected simultaneously. Construct a dataset { (} using the standard force value F. , ), ( , ), ... , ( , )},in, For the first The change in capacitance value For the first A standard force value.

[0013] Furthermore, in step 2, the GPR model is defined as follows: the force value F is the change in capacitance value. The function follows a Gaussian process, i.e. , For any function, For Gaussian processes, and Let m be the change in any two input capacitance values. ) is the mean function, which is set as a constant function and is taken as the average value of the training set force values; The covariance function, also known as the kernel function, measures the change in any two capacitance values. and The similarity between the values ​​determines the correlation of their corresponding output force values. The covariance function is the sum of the squared exponential kernel function and the white noise kernel function, specifically:

[0014]

[0015] Among them, the squared exponential kernel function White noise kernel function , Where l is the signal variance and l is the length scale. For noise variance, This refers to the Kronecker delta function.

[0016] Furthermore, the GPR model is trained using the training set, which is to determine the hyperparameters of the covariance function. To find the optimal value, we use the method of maximizing the marginal likelihood function to optimize the hyperparameters and solve the optimization problem. ,in, For conditional probabilities, x is an input vector consisting of the capacitance differences of all training samples, and y is an output vector consisting of the corresponding standard force values. Specifically, , .

[0017] Furthermore, based on the comprehensive performance evaluation metrics on the validation set, the GPR model was selected as the final model. This was applied to a newly measured model that had not been used during training. The trained GPR model provides a Gaussian distribution prediction based on its probabilistic framework, the distribution being determined by the predicted mean. That is, the force estimation point and the prediction variance. The common description is as follows:

[0018]

[0019]

[0020] Where I is the identity matrix; y is the noise variance; y is the standard force vector of the training set; The selected kernel function indicates that the kernel function will be used to compute the input points. Covariance with itself; It is the covariance matrix between training data points; yes The covariance vector among all training points; the square root of the predicted variance. The model is defined in Standard uncertainty of prediction at point This indicates that the GPR model can provide point-to-point confidence assessment.

[0021] Furthermore, in step 3, a one-time performance evaluation is performed on the final model based on the fully isolated and archived test set to obtain an unbiased estimate of its generalization performance. The evaluation metrics include the coefficient of determination R. 2 Root mean square error (RMSE) and mean relative error The coefficient of determination R² = 0.9935, the root mean square error RMSE = 0.000155N, and the mean relative error... .

[0022] Furthermore, in step 4, the synthesized standard uncertainty U is the standard uncertainty u introduced by the sensor readings. c Statistical standard uncertainty u of multiple measurements p and the standard uncertainty u introduced by the model prediction m Synthesized to obtain:

[0023]

[0024] Let u be the sensitivity system number, and let u be the standard uncertainty introduced by the model prediction. m The root mean square error value obtained when the final model is evaluated on the test set.

[0025] Accordingly, a data-driven intelligent calibration and high-precision solution system for micro-force includes: a data acquisition unit, a data processing unit, an output unit, and a performance self-monitoring unit;

[0026] The data acquisition unit uses a high-precision standard force source to perform a loading experiment on a micro-force measuring device, simultaneously acquiring a series of standard force values ​​F and corresponding capacitance changes. Construct a calibration dataset;

[0027] The data processing unit divides the calibration dataset into training, validation, and test sets, based on the change in capacitance value. Using the standard force value F as the output label and the GPR model as the input feature, the model is trained using the training set. The GPR model is selected as the final model based on the comprehensive performance evaluation index on the validation set. The final model is then evaluated once using the test set that is completely isolated and sealed throughout the process to obtain an unbiased estimate of its generalization performance.

[0028] The output unit synchronously outputs the combined standard uncertainty U of the measurement results and the final force value F. 最终 =[Measured value] ±U;

[0029] The performance self-monitoring unit monitors its own output performance in real time. By tracking the changing trend of the synthetic standard uncertainty U or periodically using standard samples for verification and calculating the relative error, it automatically sends a maintenance prompt signal to the user when the performance index is detected to deviate continuously and exceed the preset threshold, thereby providing a basis for decision-making for predictive maintenance and model updates.

[0030] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) In terms of accuracy and cost, data-driven intelligent calibration significantly reduces the dependence on high-precision machining and special materials, effectively solving the traditional contradiction between high precision and high cost; (2) In terms of ease of operation, the integrated intelligent calibration process greatly simplifies the complexity of equipment calibration and use, and users do not need to have profound metrology knowledge to complete high-precision measurements, reducing the professional requirements and training costs for operators; (3) In terms of environmental robustness, through global learning and compensation of complex system errors, the resistance to environmental interference such as temperature drift and micro-vibration is greatly improved, enabling the device to maintain stable and reliable measurement performance in non-ideal field environments, greatly reducing the threshold of the use environment; (4) In terms of uncertainty assessment method, machine learning and measurement uncertainty propagation law are innovatively deeply integrated, realizing the intelligent and automated uncertainty assessment, and the sensitivity coefficient is automatically learned by the model. This avoids the complexity of traditional manual differentiation; the optimal calculation method is adopted for different model characteristics, and the model prediction performance (RMSE) is directly engineered into uncertainty components, providing more stable evaluation results; (5) In terms of information output dimension, the measurement results have achieved an essential leap, from providing "point estimate" values ​​to synchronously outputting "interval estimate" values ​​containing "synthetic standard uncertainty", in the form of F = X ± U, providing a quantifiable and real-time reliable basis for high-risk decision-making. By outputting the synthetic standard uncertainty U in real time, the system has the ability to "self-diagnose" its performance for the first time. This uncertainty can be used as a judgment indicator of the system's health status. When environmental changes or equipment aging lead to performance degradation, the U value will increase abnormally, thereby issuing an early warning to the user and prompting maintenance or calibration. This has achieved a fundamental leap from passive use to active warning of the measurement equipment, laying a solid foundation for its predictive maintenance and full life cycle reliability management. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0032] Figure 2 This is a schematic diagram of the micro-force measuring device of the present invention.

[0033] Figure 3 This is a graph showing the unbiased performance evaluation index parameters of the GPR model of this invention on the test set.

[0034] Figure 4 The figure shows the intelligent solution of standard uncertainty under the GPR model of this invention.

[0035] Figure 5 This is a diagram showing the intelligent output result of the GPR model of the present invention for a test force value in the test set.

[0036] Among them, 1. External frame; 2. Lever support; 3. Lever; 4. Fulcrum; 5. Fixed pulley support; 6a. First fixed pulley; 6b. Second fixed pulley; 7. Force input end; 8. Force measuring plate; 9. Hanging rope; 10. Motion output end; 11. Traction rope; 12. Counterweight; 13a. First conductor; 13b. Second conductor; 14. Inner cylinder; 15. Outer cylinder; 16. Standard force source. Detailed Implementation

[0037] like Figure 1 As shown, a data-driven intelligent calibration and high-precision solution method for micro-force includes the following steps:

[0038] Step 1: Using a high-precision standard force source, a loading experiment is conducted on a micro-force measuring device, and a series of standard force values ​​F and corresponding capacitance changes are collected simultaneously. Construct a calibration dataset;

[0039] Step 2: Divide the calibration dataset into training, validation, and test sets, based on the change in capacitance values. Using the standard force value F as the output label and the probabilistic framework of the Gaussian process regression (GPR) model as the input feature, the GPR model is trained using the training set and selected as the final model based on the comprehensive performance evaluation index on the validation set.

[0040] Step 3: Perform a one-time performance evaluation on the final model based on the test set that is isolated and sealed throughout the process to obtain an unbiased estimate of its generalization performance;

[0041] Step 4: Deploy the final model in actual measurement. For the micro-force to be measured, collect the original sensor readings caused by it and input them into the model. Solve to obtain the force measurement result and simultaneously output the combined standard uncertainty U of the measurement result and the final force value F. 最终 =[Measured value] ± U;

[0042] Step 5: Monitor its own output performance in real time. By tracking the changing trend of the synthetic standard uncertainty U or periodically using standard samples for verification and calculating the relative error, when the performance index is detected to deviate continuously and exceed the preset threshold, it will automatically send a maintenance prompt signal to the user, thereby providing a basis for decision-making for predictive maintenance and model updates.

[0043] like Figure 2As shown, the micro-force measuring device includes an outer frame 1, a lever support 2, a lever 3, a fulcrum 4, a fixed pulley support 5, a first fixed pulley 6a, a second fixed pulley 6b, a force input end 7, a force measuring disc 8, a hanging rope 9, a motion output end 10, a traction rope 11, a counterweight 12, a first wire 13a, a second wire 13b, an inner cylinder 14, an outer cylinder 15, and a standard force source 16. The lever support 2 is fixed to the bottom of the outer frame 1 via its base. The lever 3 is rotatably supported on the lever support 2 via its fulcrum 4. The fixed pulley support 5 is fixed to the top of the outer frame 1. The first fixed pulley 6a and the second fixed pulley 6b are installed on the fixed pulley support 5 in a tangential position, one above the other and the other to the left and right. The force input end 7 is used to connect the force to be measured. The force measuring disk 8 is vertically suspended from the force input end 7 by the hanging rope 9. The standard force source 16 is applied to the force measuring disk 8 step by step. The other end of the lever 3 is the motion output end 10. One end of the traction rope 11 is fixed to the motion output end 10, and then passes through the first fixed pulley 6a and the second fixed pulley 6b in sequence. The other end of the traction rope 11 is connected to the counterweight 12, and then connected to the inner cylinder 14 of the coaxial cylindrical capacitor through the first wire 13a. The outer cylinder 15 of the capacitor is fixed to the bottom of the outer frame 1 and connected to the second wire 13b. The free ends of the first wire 13a and the second wire 13b are respectively connected to the corresponding interfaces of the capacitance measuring instrument to measure the change in capacitance value.

[0044] The design principle of the micro-force measuring device is to provide a highly linear signal sensing foundation. Its signal chain of "micro-force-displacement-capacitance change" has good inherent linearity, providing a "clean" input source for subsequent model construction and solution. The micro-force measuring device extensively uses common materials and simple processes, such as acrylic cylinders, copper foil tape, aluminum from aluminum cans, fishing line, and hot melt adhesive fixing, demonstrating the core advantage of this invention that it is not sensitive to hardware processing precision.

[0045] In step 1, a standard force source is applied step by step on the force measuring plate, and a series of capacitance changes are collected simultaneously. Construct a dataset { (} using the standard force value F. , ), ( , ), ... , ( , )},in, For the first The change in capacitance value For the first A standard force value.

[0046] In step 2, measurement initialization: The meter used to measure the capacitance value is a VICTOR 6013 digital capacitance meter. Based on theoretical derivation, the theoretical maximum capacitance of the coaxial cylindrical capacitor in the prototype is less than 30pF; therefore, a 200pF range is selected. This range has a resolution of 0.1pF, an accuracy of ±(0.5% + 7), and an operating temperature range of (23±5)℃. During measurement, the two probes of the capacitance meter are connected to the two measurement interfaces on the frame, respectively. A suitable range (such as the 200pF range) is selected and zeroed. Then, once the lever system is stable in a horizontal equilibrium position, the capacitance meter reading is recorded as the initial capacitance value C0.

[0047] A series of known force values ​​are applied to the input end of the lever, and the changes in capacitance are recorded simultaneously. Using the change in capacitance as a characteristic and the corresponding applied force as a label, a total of 140 valid data pairs were obtained.

[0048] The known force is the weight of tiny objects of known mass. These tiny objects consist of standard weights with masses of 10mg, 20mg, 50mg, 100mg, 200mg, 500mg, and 1g; 50 precision stainless steel balls with a diameter of 2.50mm (each ball's mass is measured to be 0.06g by an electronic balance); and several pieces of modeling clay weighed by the electronic balance. The electronic balance is a Wante disc balance with an accuracy of 0.01g and a lifting capacity of 0.03g. Various gravitational loads are generated by combining these tiny objects (gravitational acceleration g is taken as 9.8m / s²). 2 (The same below) is loaded onto the force measuring plate, and the corresponding capacitance value is measured by a digital capacitance meter. 140 sets of data are collected to construct the dataset.

[0049] Strictly adhering to machine learning standards, the 140 datasets were divided into training, validation, and test sets. Ten datasets were randomly selected as the final test set and were isolated and archived throughout the model development process, never to be used. The remaining 130 datasets were divided into training and validation sets at a ratio of 70% and 30%, respectively. The training set consisted of 91 datasets (used for model training), the validation set of 39 datasets (used for model selection), and the test set of 10 datasets (used for final unbiased evaluation).

[0050] The GPR model was determined as the final optimal model due to its best overall accuracy (highest R², lowest RMSE) and best performance uniformity (most stable BinnedRMSE).

[0051] The GPR model is defined by its mean function and covariance function (kernel function). In a specific embodiment of the invention, the input is the change in capacitance value. The output is the force value F. The mean function is set to a constant function and is taken as the average of the force values ​​in the training set.

[0052] The choice of kernel function is crucial to model performance. This is especially important considering the change in capacitance during micro-force measurements. The physical mapping relationship between the standard force value F and the standard force value is smooth and continuous. This invention uses the Squared Exponential (SE) kernel function as the dominant kernel function. In a specific embodiment of this invention, its mathematical form is: ,in, is the signal variance, controlling the range of fluctuation of the function value; l is the length scale, controlling the smoothness of the function's variation. This kernel function can generate infinitely smooth function samples, and is related to the change in the microforce (F)-capacitance value (...). The mapping relationship should have highly matched physical characteristics.

[0053] To further improve the model's robustness under complex conditions, the squared exponential kernel can be added to a white noise kernel function to form the final covariance function:

[0054]

[0055] Among them, white noise kernel , For noise variance, This is the Kronecker delta function. This combination can simultaneously model the smoothing trend of the data and the random noise present in the measurement.

[0056] The length scale *l* defines the correlation scale of the change in capacitance difference. For any two measurement points, as long as their difference... The force value is smaller than the length scale l. and They have a strong correlation, where 1≤ and ≤ ,and ≠ The model can make high-confidence predictions; otherwise, the uncertainty of the model's predictions increases. The length scale is not only used to characterize the characteristics of the current measurement system, but also to provide a quantitative basis for the iterative optimization of the measurement system. That is, the resolution of the capacitive sensor should be significantly better than this parameter, and the data point interval of the calibration experiment should be reasonably planned on this basis to ensure the reliability of the model's predictions throughout the entire measurement range. It is the standard deviation of the signal, and its square. It is the signal variance, which defines the range of force value variation expected by the model; It is the standard deviation of noise, and its square. Noise variance is used to quantify the level of random error in the observed data. The optimal combination of signal variance and noise variance determines the model's trade-off between trend and noise in the data. Furthermore, The Kronecker delta function is a fixed mathematical component of the kernel function, defined as follows: This function ensures that the white noise kernel contributes variance only at the same input point and is the standard mathematical construct of the kernel function.

[0057] The training process of the model is based on the calibration dataset ( F) By maximizing the marginal likelihood function, the optimal hyperparameter θ is found, thereby determining the specific form of the covariance function and updating the prior Gaussian process to a posterior Gaussian process for prediction. Specifically, the method of maximizing the marginal likelihood function is used for hyperparameter optimization to solve the optimization problem: Here, x is the input vector composed of the capacitance differences of all training samples, and y is the output vector composed of the corresponding standard force values. Specifically, , The optimization process is completed automatically using numerical optimization algorithms such as the conjugate gradient method, ultimately yielding the optimal combination of hyperparameters. This completely confirms the trained GPR model. In this embodiment, based on the training set data, the optimal hyperparameter combination is as follows: length scale l = 6.63 pF, signal standard deviation... Noise standard deviation The length scale indicates that the effective dynamic range of this micro-force measurement system has a characteristic scale of approximately 6.63 pF, providing a key parameter for sensor range selection and signal conditioning circuit design. For example, based on this parameter, when designing a similar micro-force measurement system with higher performance requirements, this length scale can be used for quantitative design: the resolution of the capacitance sensor in the new system should be better than l / 10 ≈ 0.66 pF, and the data point interval of the calibration experiment should be set to approximately l / 2 ≈ 3.3 pF to ensure that the model can effectively learn the complete force-capacitance mapping relationship. The signal standard deviation and noise standard deviation values ​​indicate that the optimized signal standard deviation is significantly greater than the noise standard deviation, and the model identifies that the data has a high signal-to-noise ratio. The main component of the force value change is a systematic signal rather than random noise, thus ensuring that the model can reliably learn the force-capacitance mapping relationship from the calibration data.

[0058] For a newly measured value that was not used during training A trained GPR model, based on its probabilistic framework, will provide a Gaussian distribution prediction. This distribution is determined by the predicted mean. (i.e., force estimation point) and prediction variance Common description. Its calculation formula is:

[0059]

[0060]

[0061] Where I is the identity matrix; y is the noise variance; y is the standard force vector of the training set; The selected kernel function indicates that the kernel function will be used to compute the input points. Covariance with itself; It is the covariance matrix between training data points; yes The covariance vector between all training points.

[0062] Theoretically, the square root of the prediction variance The model is defined in Standard uncertainty of prediction at point This demonstrates the theoretical advantage of the GPR model in providing point-to-point confidence assessment, a unique advantage compared to deterministic models. However, precisely because of this, the value is dynamic and varies for different... The values ​​differ, with smaller values ​​in densely populated regions of the training data and larger values ​​in sparse regions. In other words, if the measurement point happens to fall within a sparse region of the training data... It can suddenly increase, causing the combined uncertainty U value in the final force value (measured value ± U) to fluctuate wildly. This may occur when two measurements are taken under the same conditions but the uncertainties are different, or it may be too optimistic. In data-intensive areas, its value may be too small, underestimating the systematic model bias.

[0063] Therefore, due to the requirements of full-range stability and engineering practicality, this invention does not directly use the above-mentioned theory to predict variance. Instead, it innovatively uses the root mean square error (RMSE) obtained by a one-time evaluation of the model on a test set that is isolated and sealed throughout the entire process as the standard uncertainty component introduced by the model prediction. .

[0064] A final evaluation of the selected GPR model was performed using a fully sealed test set (10 datasets). Based on the prediction results, the following calculations were performed: Figure 3 The final performance indicators shown represent the actual performance level achievable by the method described in this invention: coefficient of determination R² = 0.9935, root mean square error RMSE = 0.000155N, and mean relative error. .

[0065] The results based on the independent test set fully demonstrate that the GPR model selected by this invention has excellent and reliable generalization ability, and strongly proves that the intelligent calibration method of this invention can achieve high-precision and high-stability micro-force measurement.

[0066] To comprehensively characterize the reliability of measurement results, this invention not only focuses on prediction accuracy but also innovatively introduces a complete measurement uncertainty evaluation system based on intelligent calibration, providing a "quantifiable reliability" index for each measurement result. The method for synthesizing and evaluating the measurement uncertainty is as follows:

[0067]

[0068] The sensitivity coefficient is defined in this invention as the calibration function F = f( The derivative of the capacitance value reflects the gain of the micro-force measurement system, i.e., the conversion efficiency of the capacitance change into the applied force value, and is measured in N / pF. This coefficient is automatically learned by the model through a data-driven calibration process. In a preferred embodiment, for the GPR model, its value is the local derivative of the function at a specific operating point.

[0069] To account for the uncertainty introduced by the capacitance meter reading, this invention uses a VICTOR 6013 digital capacitance meter with a minimum reading division of 0.1 pF. Therefore, the uncertainty caused by its reading is... .

[0070] This is a statistical uncertainty introduced by multiple measurements. For a conservative assessment, this invention calculates the uncertainty based on repeatable measurements of the three force value intervals with the highest data point density in the calibration dataset, and takes the maximum value as a fixed value for the synthesis formula. This ensures the reliability of the output uncertainty of the device at any measurement point. For example, a loaded mass value of 0.36g corresponds to seven capacitance difference data points, thus the sample standard deviation is calculated to be s = 0.269pF. .

[0071] It is the uncertainty associated with the prediction model, which is the RMSE value of the model on the test set, for the GPR model selected above. .

[0072] When using the optimized model to predict the force to be measured, simply input the relevant data in the prescribed format according to the system prompts to calculate the uncertainty. Figure 4 The intelligent solution of uncertainty is presented, and the combined standard uncertainty is calculated based on the above analysis. This uncertainty applies to all measurements within the measurement range.

[0073] In practice, the system is first deployed by embedding the trained GPR model into the system, which then receives real-time changes in capacitance values. The model directly calculates the force value. ), and simultaneously output the combined standard uncertainty (U). Figure 5 A practical application example is given: The capacitance value changes when a sample mass of 0.46g is applied (corresponding to a standard force of 0.004508N). Taking the case of -2.0pF as an example, the final measurement result should be characterized as follows:

[0074] F = 0.004410N ± 0.000215N (Relative error Er = 2.2%)

[0075] This representation not only provides the measured value, but also elevates the measurement result from "point estimation" to "interval estimation", providing users with quantifiable reliability indicators and greatly enhancing the practical value of the measurement result.

[0076] The above prediction and uncertainty assessment processes are all completed automatically by the system. For example... Figure 5 As shown, users only need to input the change in capacitance value, and the system can simultaneously output the predictive power value and its uncertainty. The entire model training and evaluation process takes about 8 seconds and is completed on a Lenovo ThinkPad T14 (configuration: Intel Core i7-10510U CPU@1.80GHz, 16GB RAM). After training, prediction and uncertainty assessment can be performed in real time.

[0077] Accordingly, a data-driven intelligent calibration and high-precision solution system for micro-force includes: a data acquisition unit, a data processing unit, an output unit, and a performance self-monitoring unit;

[0078] The data acquisition unit uses a high-precision standard force source to perform a loading experiment on a micro-force measuring device, simultaneously acquiring the standard force value F and the change in capacitance value. Construct a calibration dataset;

[0079] The data processing unit divides the calibration dataset into training, validation, and test sets, based on the change in capacitance value. Using the standard force value F as the output label and the GPR model as the input feature, the model is trained using the training set. The GPR model is selected as the final model based on the comprehensive performance evaluation index on the validation set. The final model is then evaluated once using the test set that is completely isolated and sealed throughout the process to obtain an unbiased estimate of its generalization performance.

[0080] The output unit synchronously outputs the combined standard uncertainty U of the measurement results and the final force value F. 最终 =[Measured value] ±U;

[0081] The performance self-monitoring unit monitors its own output performance in real time. By tracking the changing trend of the synthetic standard uncertainty U or periodically using standard samples for verification and calculating the relative error, it automatically sends a maintenance prompt signal to the user when the performance index is detected to deviate continuously and exceed the preset threshold, thereby providing a basis for decision-making for predictive maintenance and model updates.

Claims

1. A data-driven intelligent calibration and high-precision solution method for micro-forces, characterized in that, Includes the following steps: Step 1: Using a high-precision standard force source, a loading experiment is conducted on a micro-force measuring device, and a series of standard force values ​​F and capacitance changes are collected simultaneously. Construct a calibration dataset; Step 2: Divide the calibration dataset into training, validation, and test sets, based on the change in capacitance values. Using the standard force value F as the output label and the Gaussian process regression (GPR) model as the input feature, the GPR model is trained using the training set, and the final model is selected based on the comprehensive performance evaluation index on the validation set. Step 3: Perform a one-time performance evaluation on the final model based on the test set that is isolated and sealed throughout the process to obtain an unbiased estimate of its generalization performance; Step 4: Deploy the final model for actual measurement. For the micro-force to be measured, collect the change in capacitance caused by it and input it into the final model. Solve for the force measurement result and simultaneously output the combined standard uncertainty U of the measurement result and the final force value F. 最终 =[Measured value] ± U; Step 5: Monitor its own output performance in real time. By tracking the changing trend of the synthetic standard uncertainty U or periodically using standard samples for verification and calculating the relative error, when the performance index is detected to deviate continuously and exceed the preset threshold, it will automatically send a maintenance prompt signal to the user, thereby providing a basis for decision-making for predictive maintenance and model updates.

2. The data-driven intelligent calibration and high-precision solution method for micro-force as described in claim 1, characterized in that, In step 1, the micro-force measuring device includes an outer frame, a lever support, a lever, a fulcrum, a fixed pulley support, a first fixed pulley, a second fixed pulley, a force input end, a force measuring disk, a hanging rope, a motion output end, a traction rope, a counterweight, a first wire, a second wire, an inner cylinder, an outer cylinder, and a standard force source. The lever support is fixed to the bottom of the outer frame via its base. The lever is rotatably supported on the lever support via its fulcrum. The fixed pulley support is fixed to the top of the outer frame. The first and second fixed pulleys are installed on the fixed pulley support in a tangential relationship, one above the other and the other below, and left and right. One end of the lever is the force input end, used to connect the force to be measured. The force measuring plate is vertically suspended from the force input end by a hanging rope. A standard force source is applied to the force measuring plate step by step. The other end of the lever is the motion output end. One end of the traction rope is fixed to the motion output end, and then passes around the first and second fixed pulleys in sequence. The other end of the traction rope is connected to the counterweight, and then connected to the inner cylinder of the coaxial cylindrical capacitor through the first wire. The outer cylinder of the capacitor is fixed to the bottom of the outer frame and connected to the second wire. The free ends of the first and second wires are respectively connected to the corresponding interfaces of the capacitance measuring instrument to measure the change in capacitance value.

3. The data-driven intelligent calibration and high-precision solution method for micro-force as described in claim 1, characterized in that, In step 1, a standard force source is applied step by step on the force measuring plate, and a series of capacitance changes are collected simultaneously. Construct a dataset { (} using the standard force value F. , ), ( , ), ... , ( , )},in, For the first The change in capacitance value For the first A standard force value.

4. The data-driven intelligent calibration and high-precision solution method for micro-force as described in claim 1, characterized in that, In step 2, the GPR model is defined as follows: the force value F is the change in capacitance value. The function follows a Gaussian process, i.e. , For any function, For Gaussian processes, and Let m be the change in any two input capacitance values. ) is the mean function, which is set as a constant function and is taken as the average value of the training set force values; The covariance function, also known as the kernel function, measures the change in any two capacitance values. and The similarity between the values ​​determines the correlation of their corresponding output force values. The covariance function is the sum of the squared exponential kernel function and the white noise kernel function, specifically: , Among them, the squared exponential kernel function White noise kernel function , Where l is the signal variance and l is the length scale. For noise variance, This refers to the Kronecker delta function.

5. The data-driven intelligent calibration and high-precision solution method for micro-force as described in claim 4, characterized in that, Training the GPR model using the training set is equivalent to training the hyperparameters of the covariance function. To find the optimal value, we use the method of maximizing the marginal likelihood function to optimize the hyperparameters and solve the optimization problem. ,in, For conditional probabilities, x is an input vector consisting of the capacitance differences of all training samples, and y is an output vector consisting of the corresponding standard force values. Specifically, , .

6. The data-driven intelligent calibration and high-precision solution method for micro-force as described in claim 5, characterized in that, Based on the comprehensive performance evaluation metrics on the validation set, the GPR model was selected as the final model. This was done for a newly measured model that had not been used during training. The trained GPR model provides a Gaussian distribution prediction based on its probabilistic framework, the distribution being determined by the predicted mean. That is, the force estimation point and the prediction variance. The common description is as follows: , , Where I is the identity matrix; y is the noise variance; y is the standard force vector of the training set; The selected kernel function indicates that the kernel function will be used to compute the input points. Covariance with itself; It is the covariance matrix between training data points; yes The covariance vector among all training points; the square root of the predicted variance. The model is defined in Standard uncertainty of prediction at point This indicates that the GPR model can provide point-to-point confidence assessment.

7. The data-driven intelligent calibration and high-precision solution method for micro-force as described in claim 1, characterized in that, In step 3, a one-time performance evaluation is performed on the final model based on the fully isolated and archived test set to obtain an unbiased estimate of its generalization performance. The evaluation metrics include the coefficient of determination R. 2 Root mean square error (RMSE) and mean relative error .

8. The data-driven intelligent calibration and high-precision solution method for micro-force as described in claim 1, characterized in that, In step 4, the combined standard uncertainty U is the standard uncertainty u introduced by the sensor readings. c Statistical standard uncertainty u of multiple measurements p and the standard uncertainty u introduced by the model prediction m Synthesized to obtain: , Let u be the sensitivity system number, and let u be the standard uncertainty introduced by the model prediction. m This is the root mean square error value obtained when the final model is evaluated on the test set.

9. A system for implementing the data-driven intelligent micro-force calibration and high-precision solution method as described in claim 1, characterized in that, include: Data acquisition unit, data processing unit, output unit, and performance self-monitoring unit; The data acquisition unit uses a high-precision standard force source to perform a loading experiment on a micro-force measuring device, simultaneously acquiring a series of standard force values ​​F and corresponding capacitance changes. Construct a calibration dataset; The data processing unit divides the calibration dataset into training, validation, and test sets, based on the change in capacitance value. Using the standard force value F as the output label and the GPR model as the input feature, the model is trained using the training set. The GPR model is selected as the final model based on the comprehensive performance evaluation index on the validation set. The final model is then evaluated once using the test set that is completely isolated and sealed throughout the process to obtain an unbiased estimate of its generalization performance. The output unit synchronously outputs the combined standard uncertainty U of the measurement results and the final force value F. 最终 =[Measured value] ± U; The performance self-monitoring unit monitors its own output performance in real time. By tracking the changing trend of the synthetic standard uncertainty U or periodically using standard samples for verification and calculating the relative error, it automatically sends a maintenance prompt signal to the user when the performance index is detected to deviate continuously and exceed the preset threshold, thereby providing a basis for decision-making for predictive maintenance and model updates.

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