Error change trend partition calibration-based nonlinear error correction method for eddy current displacement sensor

Abstract

The invention belongs to the technical field of detection, and discloses a nonlinear error correction method based on error change trend partition calibration for an eddy current displacement sensor. The method comprises the steps of firstly analyzing a corresponding relation between a displacement value and output voltage, and drawing an output characteristic curve of a sensor; distinguishing an error change trend according to a local extreme value, carrying out interval partitioning on an error change curve, training each partition, constructing a partition training set, constructing a correction model covering the full range of the sensor, and realizing error correction of high-precision measurement of the eddy current displacement sensor; and finally, the measured displacement value is obtained through the linear relation between the output voltage and the displacement value. According to the method, the linearity error, the sensitivity error, the return stroke error and the zero drift error after correction are greatly reduced, and the method is simple, easy to operate and high in real-time performance. Through reasonable segmentation, the complexity of curve fitting is reduced, the correction efficiency of the non-linear error of the eddy current sensor is improved, and the measurement precision is improved.

Description

Technical Field

[0001] The invention belongs to the field of detection technology and relates to a correction model establishment method for improving the calibration accuracy of an output characteristic curve of an eddy current sensor. Background Art

[0002] Eddy current sensor is a high-precision sensor that uses the eddy current effect for non-contact non-destructive testing. It is mainly used to accurately measure the displacement, distance, position and vibration of conductive targets. It can accurately capture the tiny displacement changes between the measured metal conductor and the probe end face. It has the characteristics of high precision and good real-time performance. It has become a popular method in the field of high-precision micro-displacement detection and is widely used in micro-displacement detection and damage detection in industrial automation, machinery manufacturing, aerospace, shipbuilding, railways, automobiles, medical and other fields.

[0003] However, one of the main problems faced by eddy current sensors in measuring small displacements is nonlinear error, which is affected by factors such as temperature fluctuations and electromagnetic interference, and exhibits significant nonlinear characteristics under different ranges. At present, the methods to overcome this challenge mainly include hardware compensation methods that physically adjust or improve sensor hardware to reduce sensor measurement errors, and software compensation methods that mathematically process sensor output data and adjust algorithms to reduce sensor measurement errors.

[0004] Feng et al. proposed a temperature self-compensation method for eddy current displacement sensor in the article "Ultrastable and highly sensitive eddy current displacement sensor using self-temperature compensation" published in the journal "Sensors and Actuators A: Physical". This method improves the circuit of the eddy current sensor, decouples the impedance into resistance and inductance through bridge design, and uses resistance change to calibrate the effect of temperature on inductance, effectively reducing thermal drift. However, this method has high design cost, high difficulty, and complex design process, and only compensates for errors caused by temperature, and has limited ability to correct nonlinear errors and suppress random noise.

[0005] In 2011, Miao Enming et al. published a study on error correction technology of eddy current sensors in the 21st issue of the Journal of Mechanical Engineering of China. A software compensation method based on the autoregressive distributed lag (ADL) model was proposed to improve the measurement accuracy of eddy current sensors. A sophisticated error correction model was used in the paper to improve the nonlinear error correction capability of the sensor, but the model complexity of this method is high, it relies on a large amount of experimental data, and the calibration efficiency is low. In addition, Wu Yulong et al. published a study on error analysis and suppression methods of absolute linear displacement sensors based on eddy current effect in the 3rd issue of the Journal of Instrument Technology and Sensors in 2024. The method based on mechanism modeling was used to compensate for the measurement error of eddy current sensors. For the errors that may be generated in the manufacturing, installation and electrical signal processing of eddy current sensors, a variety of effective error suppression methods such as signal compensation and spatial phase shift were proposed. These methods divide the errors into different frequencies according to the error generation mechanism and suppress them in a targeted manner. This can reduce the error of the sensor and improve the measurement accuracy. However, the calibration process is very complicated, and it is easy to over-correct or under-correct complex error situations.

[0006] In summary, for the hardware compensation method, this method involves in-depth transformation of the internal hardware circuit, and its design process is complicated, the implementation cycle is long, and it is accompanied by high costs and great technical challenges. In addition, the compensation efficiency of this method in dealing with random errors is relatively limited. In contrast, the software compensation method shows significant advantages: it does not require in-depth understanding of the specific principles of the internal circuit of the hardware, and only compensates by analyzing the output data of the sensor and its corresponding measurement indicators. This process is theoretically simpler and more efficient. However, most of the previous software compensation technologies use a single error correction model to compensate for the error under the full range of eddy current. The displacement error in the actual measurement process of the eddy current sensor has a variety of changing trends. A single correction model is difficult to cover the correction problem of the full range. Even if some complex models can correct the error of the full range, it is also necessary to carry out complex and detailed modeling and repeated training of a large amount of experimental data. The process is cumbersome and the training cost is high. When faced with complex and changeable error situations, this method may have problems of over-correction or under-correction. Summary of the invention

[0007] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and invent a nonlinear error correction method for eddy current sensors based on error change trend partition calibration, which divides the full-scale error into multiple sub-areas, and uses an independent model for correction in each area, thereby reducing the complexity of each model, reducing the amount of training data and complexity of a single model, speeding up the model training process, and improving the correction efficiency. At the same time, through targeted training and local optimization, the correction capability of nonlinear errors is improved.

[0008] The technical solution of the present invention:

[0009] A nonlinear error correction method for eddy current displacement sensors based on error change trend partition calibration, firstly, a series of experiments are carried out, with the help of a high-precision displacement platform and a computer, to accurately record and analyze the corresponding relationship between the displacement value and the output voltage of the eddy current sensor during the measurement process, so as to draw the output characteristic curve of the sensor; then, the error change is segmented using the K-means clustering method, and a training data set suitable for each segment is generated; then, the technology in each partition is targetedly trained through machine learning technology, and a partition training set is constructed to construct an accurate correction model covering the full range of the sensor, so as to realize the error correction of high-precision measurement of eddy current displacement sensors, and finally the measured displacement value is obtained through the linear relationship between the output voltage and the displacement value. The specific steps are as follows:

[0010] Step 1: Matching measurement of displacement-output voltage characteristic curve

[0011] Build an eddy current displacement sensor calibration experimental system; first, make the probe end face of the eddy current displacement sensor fully fit with the calibration material to determine the zero point position of the eddy current displacement sensor measurement; then use a linear high-precision displacement platform to drive the calibration material to perform a small displacement, and then the acquisition system collects the voltage data of the eddy current displacement sensor;

[0012] Step 2: Partition the calibration data and training set based on the error change trend

[0013] By statistically analyzing multiple groups of eddy current displacement sensor calibration data, K-means clustering is used for eddy current displacement sensor error segmentation.

[0014] First calculate the measured voltage value U ai With the theoretical voltage value U ti The error e is obtained, an appropriate number of clusters K is selected, and K data points are randomly selected as the initial cluster centers μ j (j=1,2,…,K), assign data points to clusters,

[0015]

[0016] Assign each data point to the cluster center that is closest to it:

[0017]

[0018] For each cluster j, update the cluster center μ i is the mean of all data points in the cluster:

[0019]

[0020] Among them, C jis the number of data points in cluster j; the operation of assigning data points to clusters and updating cluster centers is repeated until the change in cluster center is less than the set threshold;

[0021] Finally, different clusters of voltage measurement errors are found, and the full-scale measurement errors are partitioned according to the boundaries of each cluster. Assuming there are k partitions, the training set D can be expressed as

[0022]

[0023] Step 3: Establishment of partition correction model

[0024] To solve U ai with U ti For each range region, a separate neural network model is trained. Assuming that a neural network model is used to correct the error in the kth range region, the calculation of the hidden layer neurons is as follows:

[0025]

[0026] Among them, h j is the output of the jth hidden layer neuron, is the weight of the jth neuron from the input layer to the hidden layer, is the bias of the jth neuron, σ is the activation function;

[0027] The calculation from the hidden layer to the output layer is as follows:

[0028]

[0029] in, is the predicted output of the network, is the weight from the jth neuron in the hidden layer to the output layer, b (2) is the bias of the output layer;

[0030] The mean square error (MSE) is used as the loss function to train the neural network model for each region. The loss function is:

[0031]

[0032] Where N is the number of samples, is the network prediction value of the i-th sample, y i is the true error compensation value of the i-th sample;

[0033] Use gradient descent to update weights and biases:

[0034]

[0035] Where η is the learning rate, is the gradient of the loss function with respect to weights and biases;

[0036] Finally, the full-range partition correction model of the eddy current displacement sensor measurement error is constructed as follows:

[0037]

[0038] In the formula, g k represents the error correction model of the kth partition, n represents the amount of training data, U ai Indicates the measured voltage, that is, the input data; U ti Indicates the ideal voltage, i.e. output data;

[0039] The full-range error correction model of the eddy current displacement sensor is established through the above steps;

[0040] Step 4: Voltage Correction and Displacement Calculation

[0041] When the eddy current sensor is measuring online, the acquisition system collects voltage in real time and determines the measured voltage U ai The correction area is substituted into formula (8) to calculate the corrected ideal voltage value, and the corrected ideal displacement value is finally calculated through the voltage displacement conversion coefficient.

[0042] The beneficial effects of the present invention are as follows: the method greatly reduces the error between the corrected displacement measurement value of the eddy current displacement sensor and the standard displacement measurement value, and compared with other software compensation methods, it reduces the complexity of the fitting curve through reasonable segmentation, improves the correction efficiency of the nonlinear error of the eddy current sensor, and improves the measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of the eddy current sensor calibration test system.

[0044] Figure 2 This is a flow chart of the correction process of the nonlinear measurement error of the eddy current displacement sensor.

[0045] Figure 3 This is the correction result diagram of the output characteristic curve of the eddy current displacement sensor in a certain experimental measurement. DETAILED DESCRIPTION

[0046] The specific implementation of the present invention is described in detail below in combination with the technical scheme and the accompanying drawings.

[0047] Figure 1The schematic diagram of the full-scale partition correction experimental system for the measurement error of the eddy current displacement sensor is shown in the figure. The NI acquisition system 1 on the computer is connected to the displacement platform controller 2, and the displacement platform controller is connected to the high-precision displacement high-precision displacement platform. The computer NI acquisition system can send instructions to the high-precision displacement platform 3 through the displacement platform controller to make a small movement. The calibration material 4 is attached to the high-precision displacement platform 3, and the sensor 5 is attached to the fixture near the calibration material 4. The NI acquisition system 1 on the computer sends a displacement movement instruction to the displacement platform controller 2 to guide the high-precision displacement platform 3 to drive the calibration material 4 to move horizontally; the eddy current displacement sensor 5 senses the displacement change and outputs the voltage value, and the computer NI acquisition system 1 performs acquisition to complete the matching measurement of the displacement-output voltage characteristic curve. Through the optimization of sensitivity and linearity, the model of high-precision calibration of the eddy current displacement sensor is established, and the measured value is corrected using the corrected model.

[0048] Figure 2 This is a schematic diagram of the full-scale partition correction process of the eddy current displacement sensor measurement error. The entire optimization process is mainly divided into four steps, namely, the matching measurement of the displacement-output voltage characteristic curve, the partitioning of the calibration data and the training set based on the error change trend, the establishment of the partition correction model, and the calculation of the ideal voltage value. The specific steps of the method are as follows:

[0049] Step 1: Matching measurement of displacement-output voltage characteristic curve

[0050] First, the sensor probe end face is fully fitted with the calibration material to determine the zero value of the sensor measurement; secondly, the PI linear high-precision displacement platform (PI, M-521.DD1, repeatability 0.1μm) is used in the experiment to drive the calibration plane to perform a small displacement, in which the slide movement interval is set to 0.1mm, and the distance change range is 0-4mm. The eddy current sensor 3 senses the change of displacement x and converts it into a voltage change u. Then, the NI acquisition system is used to collect the voltage data of the eddy current displacement sensor to complete the matching measurement of the displacement-output voltage characteristic curve x=0, 0.1, 0.2, 0.3,…, 3.9, 4.0, u∈[-1,1]. The experiment is repeated back and forth to obtain multiple sets of calibration data.

[0051] Step 2: Partition the calibration data and training set based on the error change trend

[0052] First calculate the measured voltage value U ai With the theoretical voltage value U ti The error e is obtained, and an appropriate number of clusters K is selected. Here, 3 is selected. Three data points are randomly selected as the initial cluster centers μ j(j=1,2,…,K), assign data points to clusters, assign each data point to the nearest cluster center, and for each cluster j, update the cluster center μ i is the mean of all data points in the cluster until it is less than the threshold.

[0053] The measurement value of one sensor can be divided into three sections according to the error, then k = 3. The three partitions are named as the first partition, the middle partition, and the last partition. The partition training set is constructed by formula (1), and its training set D can be expressed as.

[0054]

[0055] Where U ai Indicates the measured voltage, that is, the input data; U ti Represents the ideal voltage, that is, the output data.

[0056] Step 3: Establishment of partition correction model

[0057] To solve U ai with U ti For each range region, a separate neural network model is trained. Assuming that we use a neural network model to correct the error in the k-th range region, the calculation of the hidden layer neurons is as follows:

[0058]

[0059] Among them, h j is the output of the jth hidden layer neuron, is the weight of the jth neuron from the input layer to the hidden layer, is the bias of the jth neuron and σ is the activation function.

[0060] The calculation from the hidden layer to the output layer is as follows:

[0061]

[0062] in, is the predicted output of the network, is the weight from the jth neuron in the hidden layer to the output layer, b (2) is the bias of the output layer.

[0063] The mean square error (MSE) is used as the loss function to train the model for each region. The loss function is:

[0064]

[0065] Where N is the number of samples, is the network prediction value of the i-th sample, y iis the true error compensation value of the i-th sample.

[0066] Use gradient descent to update weights and biases:

[0067]

[0068] Where η is the learning rate, is the gradient of the loss function with respect to the weights and biases.

[0069] Finally, the full-range partition correction model of the eddy current displacement sensor measurement error is constructed as follows:

[0070]

[0071] In the formula, g k represents the error correction model of the kth partition, n represents the amount of training data, U ai Indicates the measured voltage, that is, the input data; U ti Represents the ideal voltage, that is, the output data.

[0072] The above steps complete the establishment of the full-range error correction model of the eddy current displacement sensor.

[0073] Step 4: Voltage Correction and Displacement Calculation

[0074] When the sensor is measuring online, the NI system collects the voltage U in real time. i , the measured voltage data obtained during a certain measurement process is shown in the following table:

[0075] Table 1 Displacement measurement values ​​of a certain eddy current sensor

[0076]

[0077] Determine the correction area to which the voltage belongs, and call the model of the correction area to which the voltage belongs to calculate the corrected voltage value. The corrected voltage value is shown in the following table:

[0078] Table 2 Correction value of displacement measurement of a certain eddy current sensor

[0079]

[0080] By multiplying the voltage value by the voltage displacement conversion coefficient 0.4, the corrected ideal displacement value is finally obtained, completing the correction and measurement process.

Claims

1. A nonlinear error correction method for an eddy current displacement sensor based on error change trend partition calibration, characterized in that: The specific steps are as follows: Step 1: Matching measurement of displacement-output voltage characteristic curve Build an eddy current displacement sensor calibration experimental system; first, make the probe end face of the eddy current displacement sensor fully fit with the calibration material to determine the zero point position of the eddy current displacement sensor measurement; then use a linear high-precision displacement platform to drive the calibration material to perform a small displacement, and then the acquisition system collects the voltage data of the eddy current displacement sensor; Step 2: Partition the calibration data and training set based on the error change trend By statistically analyzing multiple groups of eddy current displacement sensor calibration data, K-means clustering is used for eddy current displacement sensor error segmentation. First calculate the measured voltage value U ai With the theoretical voltage value U ti The error e is obtained, an appropriate number of clusters K is selected, and K data points are randomly selected as the initial cluster centers μ j (j=1,2,…,K), assign data points to clusters, Assign each data point to the cluster center that is closest to it: For each cluster j, update the cluster center μ i is the mean of all data points in the cluster: Among them, C j is the number of data points in cluster j; the operation of assigning data points to clusters and updating cluster centers is repeated until the change in cluster center is less than the set threshold; Finally, different clusters of voltage measurement errors are found, and the full-scale measurement errors are partitioned according to the boundaries of each cluster. Assuming there are k partitions, the training set D can be expressed as Step 3: Establishment of partition correction model To solve U ai with U ti For each range region, a separate neural network model is trained. Assuming that a neural network model is used to correct the error in the kth range region, the calculation of the hidden layer neurons is as follows: Among them, h j is the output of the jth hidden layer neuron, is the weight of the jth neuron from the input layer to the hidden layer, is the bias of the jth neuron, σ is the activation function; The calculation from the hidden layer to the output layer is as follows: in, is the predicted output of the network, is the weight from the jth neuron in the hidden layer to the output layer, b (2) is the bias of the output layer; The mean square error (MSE) is used as the loss function to train the neural network model for each region. The loss function is: Where N is the number of samples, is the network prediction value of the i-th sample, y i is the true error compensation value of the i-th sample; Use gradient descent to update weights and biases: Where η is the learning rate, is the gradient of the loss function with respect to weights and biases; Finally, the full-range partition correction model of the eddy current displacement sensor measurement error is constructed as follows: In the formula, g k represents the error correction model of the kth partition, n represents the amount of training data, U ai Indicates the measured voltage, that is, the input data; U ti Indicates the ideal voltage, i.e. output data; The full-range error correction model of the eddy current displacement sensor is established through the above steps; Step 4: Voltage Correction and Displacement Calculation When the eddy current sensor is measuring online, the acquisition system collects voltage in real time and determines the measured voltage U ai The correction area is substituted into formula (8) to calculate the corrected ideal voltage value, and the corrected ideal displacement value is finally calculated through the voltage displacement conversion coefficient.

Images