LVDT sensor precision correction method based on machine learning

Abstract

The invention discloses an LVDT sensor precision correction method based on machine learning, and relates to the technical field of LVDT sensors. The method comprises the following steps: collecting an LVDT sensor response signal and a disturbance source parameter; obtaining a sub-band of an LVDT sensor response signal through a multi-level wavelet packet decomposition algorithm, calculating a sub-band energy index and a sub-band energy entropy, and obtaining an energy concentration index in combination with the maximum value of the sub-band energy index and the sub-band energy entropy; obtaining a sub-band peak factor through peak analysis, and obtaining a sub-band comprehensive peak index in combination with the sub-band energy index; clustering response signal features of the combination of the energy concentration index and the sub-band comprehensive peak index through a KMEANS algorithm to obtain a response signal cluster, and adding an interference feature tag through a disturbance parameter; constructing a sensor precision error prediction model; and collecting an LVDT original signal in real time and inputting the LVDT original signal into the sensor precision error prediction model of the corresponding interference label to obtain an LVDT signal error result, thereby realizing precision correction.

Description

Technical Field

[0001] The present invention relates to the technical field of LVDT sensors, and specifically provides a method for correcting the accuracy of an LVDT sensor based on machine learning. Background Art

[0002] In the fields of industrial automation, aerospace, and precision machining, linear variable differential transformer (LVDT) sensors are widely used for real-time measurement of displacement and position due to their high precision, long lifespan, and strong anti-interference ability. With the growing demand for intelligent manufacturing and precision control, LVDT sensors need to maintain stable output under complex working conditions such as high-frequency vibration, multi-axis disturbance, and electromagnetic noise, which poses higher requirements for the dynamic accuracy and anti-interference ability of the sensors. However, existing technologies generally adopt static calibration or error compensation methods based on fixed filtering, making it difficult to meet the real-time accuracy correction requirements in dynamic disturbance environments. With the complication of application scenarios, such as strong vibration, electromagnetic noise interference, and drastic temperature changes in industrial sites and other harsh working conditions, the measurement accuracy of LVDT sensors is easily affected by various disturbance sources, resulting in problems such as non-linear distortion, zero drift, and amplitude deviation of the output signal, severely restricting its reliable application in high-precision measurement scenarios.

[0003] Existing technologies suppress high-frequency noise through low-pass filtering, making it difficult to meet the real-time accuracy correction requirements in dynamic disturbance environments, resulting in insufficient error prediction accuracy in dynamic disturbance environments. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technologies, the present invention provides a method for correcting the accuracy of an LVDT sensor based on machine learning, which solves the problem that existing technologies suppress high-frequency noise through low-pass filtering, making it difficult to meet the real-time accuracy correction requirements in dynamic disturbance environments, resulting in insufficient error prediction accuracy in dynamic disturbance environments.

[0005] To achieve the above objectives, the present invention is realized through the following technical solutions: A method for correcting the accuracy of an LVDT sensor based on machine learning, comprising the following steps: Step S1: By adding different disturbance sources to the LVDT sensor, an LVDT sensor disturbance dataset is obtained, and the LVDT sensor disturbance dataset includes: the response signal of the LVDT sensor and the disturbance source parameters; Step S2: Decompose the frequency of the LVDT sensor response signal through a multi-level wavelet packet decomposition algorithm to obtain a wavelet coefficient sequence of the sub-bands of the LVDT sensor response signal, and calculate the sub-band energy index through the wavelet coefficient sequence; Calculate the sub-band energy entropy by calculating the entropy value of the sub-band energy index; Calculate the energy concentration index by combining the maximum value of the sub-band energy index and the sub-band energy entropy; Step S3: By performing peak analysis on the wavelet coefficient sequence, obtain the sub-band peak factor; by combining the sub-band peak factor and the sub-band energy index, calculate the sub-band comprehensive peak index; by combining the sub-band comprehensive peak index and the energy concentration index, obtain the LVDT response signal feature; Step S4: Cluster the LVDT response signal features through the KMEANS algorithm to obtain the response signal clustering clusters, and by statistically analyzing the disturbance source parameters of each clustering cluster in the response signal clustering clusters, obtain the interference feature labels of the clustering clusters; Step S5: According to the interference feature labels, construct a sensor accuracy error prediction model corresponding to the interference feature labels; collect the LVDT original measurement signals in real time, calculate the LVDT response signal features of the LVDT original measurement signals, input the LVDT response signal features into the response signal clustering clusters to obtain the interference feature labels of the LVDT original measurement signals; then input the LVDT original measurement signals into the sensor accuracy error prediction model corresponding to the interference feature labels to obtain the signal error result of the LVDT; Step S6: By combining the LVDT response signal features of the LVDT original measurement signals and the signal error result of the LVDT, calculate the correction result of the LVDT signal to achieve the accuracy correction of the LVDT sensor.

[0006] Preferably, the frequency decomposition of the LVDT sensor response signal through the multi-level wavelet packet decomposition algorithm to obtain the wavelet coefficient sequence of the sub-bands of the LVDT sensor response signal, and calculating the sub-band energy index through the wavelet coefficient sequence includes the following specific steps: Through the low-pass filtering and high-pass filtering of the multi-level wavelet transform, use the LVDT sensor response signal x[n] as the original input of the 0th layer of the multi-level wavelet transform, where 0 < n < N, and N is the total number of sampling points of the LVDT sensor response signal; The low-frequency coefficient of the Lth layer of decomposition is: ; represents the value of the low-frequency coefficient of the Lth layer of decomposition of the LVDT sensor response signal at the jth position, j is the position index of the low-frequency coefficient of the Lth layer of decomposition, 0 j < , represents the nth sampling point of the LVDT sensor response signal, N is the total number of sampling points of the LVDT sensor response signal, represents the low-pass filter coefficient, represents the low-frequency coefficient of the (L - 1)th layer; The high-frequency coefficient of the Lth layer of decomposition is: ; represents the value of the high-frequency coefficient after the L-th layer decomposition of the LVDT sensor response signal at the j-th position, where j is the position index of the high-frequency coefficient after the L-th layer decomposition, 0 j < , represents the n-th sampling point of the LVDT sensor response signal, and N is the total number of sampling points of the LVDT sensor response signal, represents the high-pass filter coefficient, represents the high-frequency coefficient of the (L - 1)-th layer

[0007] Continue to decompose the coefficients of each layer, and finally obtain a sequence of wavelet coefficients of ={ , }, i = 1, 2,... , where L is the number of layers; Then the energy index of each sub-band is: ; where, is the energy index of the i-th sub-band, N represents, and N is the total number of sampling points of the LVDT sensor response signal, represents the sequence of wavelet coefficients of the i-th sub-band, and n is the index of the n-th value in the sequence of wavelet coefficients of the sub-band, represents the total number of sub-bands generated when the decomposition layer is L, and L is the decomposition layer.

[0008] Preferably, the sub-band energy entropy is obtained by calculating the entropy value of the sub-band energy index, including the following steps: The sub-band energy entropy is obtained by calculating the entropy value of the sub-band energy index: ; where H is the sub-band energy entropy, represents the total number of sub-bands generated when the decomposition layer is L, and L is the decomposition layer, is the energy index of the i-th sub-band.

[0009] Preferably, the energy concentration index is calculated by combining the maximum value of the sub-band energy index and the sub-band energy entropy, including the following steps: The energy concentration index is calculated by combining the maximum value of the sub-band energy index and the sub-band energy entropy: ; where, is the energy concentration index, and H is the sub-band energy entropy, represents the maximum value of the sub - band energy index, and max() is the function for taking the maximum value.

[0010] Preferably, obtaining the sub - band peak factor by performing peak analysis on the wavelet coefficient sequence includes the following specific steps: Performing peak analysis on the wavelet coefficient sequence of the sub - band of the LVDT sensor response signal to obtain the sub - band peak factor. For the wavelet coefficient sequence of each sub - band perform wavelet reconstruction to obtain the reconstructed signal sequence of this sub - band , representing the reconstructed signal of the i - th sub - band; Performing peak analysis on the reconstructed signal sequence of the i - th sub - band to obtain the sub - band peak factor: ; where is the i - th sub - band peak factor, represents the reconstructed signal sequence of the i - th sub - band, N represents the total number of sampling points of the reconstructed signal sequence, and n is the index of the n - th value in the wavelet coefficient sequence of the i - th sub - band.

[0011] Preferably, calculating the sub - band comprehensive peak index by combining the sub - band peak factor and the sub - band energy index includes the following specific steps: Calculating the sub - band comprehensive peak index by combining the sub - band peak factor and the sub - band energy index: ; where Q is the sub - band comprehensive peak index, L is the number of layers, i represents the index of the i - th sub - band, is the i - th sub - band peak factor, is the i - th sub - band energy index.

[0012] Preferably, obtaining the LVDT response signal feature by combining the sub - band comprehensive peak index and the energy concentration index includes the following specific steps: Obtaining the LVDT response signal feature T by combining the sub - band comprehensive peak index and the energy concentration index, T = , Q], where is the energy concentration index and Q is the comprehensive peak index.

[0013] Preferably, constructing the sensor accuracy error prediction model corresponding to the interference feature label includes the following specific steps: The interference feature label The corresponding sensor accuracy error prediction model structure includes: an input layer, a convolution module, a fully - connected regression layer, a fully - connected layer, and an output layer; The input layer receives the LVDT sensor response signal and the standard displacement input; Convolution module: First-layer convolution: One-dimensional convolution operation is adopted, with 64 convolution kernels of width 3, a stride of 1, and the ReLU activation function. After convolution, the input generates a feature map with 64 channels. Residual connection: A skip connection is introduced after the second-layer convolution, and the output of the first-layer convolution is directly added to the output of the second layer; Recurrent module: Bidirectional LSTM layer: A bidirectional long short-term memory network is adopted, with 32 hidden units set in each direction to capture the temporal dependencies of the signal before and after. Fully connected regression layer: The temporal features output by the LSTM layer are flattened into a one-dimensional vector; Fully connected layer: The features are mapped through two fully connected networks. The first layer has 256 neurons, with the ReLU activation function, and Dropout is added to prevent overfitting; The output layer has 1 linear neuron, directly regressing to predict the error value Δy; Output layer: The output layer directly generates the error prediction value, in millimeters, aligned with the sensor range; The loss function is: ; wherein, is the loss function of the sensor accuracy error prediction model, N represents the total number of signal sampling points, n represents the nth signal sampling point, represents the error value of the nth sampling point of the predicted LVDT sensor response signal and the standard displacement, represents the error value of the nth sampling point of the actual LVDT sensor response signal and the standard displacement.

[0014] Preferably, inputting the LVDT original measurement signal into the sensor accuracy error prediction model corresponding to the interference feature label to obtain the signal error result of the LVDT includes the following specific steps: Inputting the LVDT original measurement signal into the sensor accuracy error prediction model corresponding to the interference feature label to obtain the signal error result of the LVDT: ; wherein, represents the error value of the nth sampling point of the predicted LVDT original measurement signal input and the standard displacement, represents the sensor accuracy error prediction model with the interference feature label of , represents the LVDT original measurement signal, and n represents the nth signal sampling point.

[0015] Preferably, the corrected result of the LVDT signal is calculated by combining the LVDT response signal characteristics of the original LVDT measurement signal and the signal error result of the LVDT, and the specific steps are as follows: The corrected result of the LVDT signal is obtained by combining the original measurement output of the LVDT and the signal error result of the LVDT: ; wherein, represents the corrected result of the nth sampling point of the LVDT signal, n represents the nth sampling point of the signal, represents the value of the nth sampling point of the original measurement output of the LVDT, represents the error value of the nth sampling point of the predicted input of the LVDT original measurement signal and the standard displacement, represents the interference characteristic label of the LVDT original measurement signal and and the energy concentration index in the response signal characteristics is the dynamic weight coefficient, is the interference characteristic label, is the energy concentration index of the original measurement output of the LVDT, is the attenuation factor, which controls the attenuation rate of the compensation amount with respect to the original measurement output of the LVDT ;

[0016] Beneficial effects The present invention provides a method for correcting the accuracy of an LVDT sensor based on machine learning, having the following beneficial effects: (1) By combining the maximum value of the sub-band energy index and the sub-band energy entropy to calculate the energy concentration index, the concentration of signal energy distribution and the complexity of perturbation can be comprehensively quantified. This method can not only accurately identify the dominant perturbation frequency band, but also evaluate the uniformity of energy distribution through the entropy value, so as to distinguish between single interference and composite interference scenarios. For example, the combination of a high energy index and a low entropy value indicates that the signal is dominated by a single strong perturbation, while a low energy index and a high entropy value reflect complex multi-source interference, which provides a key basis for the targeted construction of subsequent error models and effectively improves the robustness of perturbation feature extraction.

[0017] (2) By combining the sub-band peak factor and the sub-band energy index to calculate the comprehensive peak index, the problem that the instantaneous impact characteristics in the traditional method are easily interfered by low-energy noise is solved. The peak factor captures the instantaneous impact intensity of the signal in the frequency band, and the energy index gives it a weight, suppressing the noise interference in the non-dominant frequency band. For example, significant peaks in high-energy frequency bands can be strengthened as key features, while random spikes in low-energy frequency bands are weakened, thus significantly improving the sensitivity and identification accuracy of core interference features such as impact and harmonic distortion, and avoiding misjudgment and missed detection.

[0018] (3) By combining the response signal characteristics of the original LVDT measurement signal with the results of real-time predicted signal errors, precise error compensation in a dynamic disturbance environment is achieved. Its core advantages are as follows: Through dynamic weight coefficients and non-linear attenuation factors, the system can adaptively adjust the compensation intensity according to the interference type and energy distribution characteristics - strengthening the correction under strong dominant interference to eliminate systematic deviations, while suppressing the risk of overcompensation in weak and scattered interference, which not only solves the overcompensation or undercompensation problems of traditional linear correction but also avoids the secondary distortion of high-amplitude signals; Secondly, through frequency band energy analysis and clustering label recognition, this method accurately distinguishes multi-source interferences such as periodic vibrations and random noises, and optimizes the compensation strategy accordingly, significantly improving the anti-interference ability of the sensor under complex working conditions such as multi-axis vibration and electromagnetic noise; Finally, through the closed-loop mechanism of real-time error prediction and dynamic correction, errors such as non-linear distortion and zero drift are effectively eliminated, ensuring the high stability and measurement accuracy of the LVDT signal, providing a highly reliable data basis for scenarios such as intelligent manufacturing and precision control. Description of the Drawings

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0020] Figure 1 It is a flowchart of the steps of a method for correcting the accuracy of an LVDT sensor based on machine learning proposed by the present invention; Figure 2 It is a hierarchical diagram of the steps of a method for correcting the accuracy of an LVDT sensor based on machine learning proposed by the present invention; Detailed Embodiments

[0021] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0022] Please refer to Figure 1-2 , the present invention provides a technical solution: a method for correcting the accuracy of an LVDT sensor based on machine learning.

[0023] Step S1: By adding different disturbance sources to the LVDT sensor, a disturbance dataset of the LVDT sensor is obtained. The LVDT sensor disturbance dataset includes: the response signal of the LVDT sensor and the disturbance source parameters.

[0024] The specific steps to construct a disturbance dataset by applying different disturbance sources to the LVDT sensor are as follows: Build a disturbance experiment platform with multi-parameter regulation capabilities. This platform needs to support the precise control of physical disturbances such as vibration frequency, amplitude, direction, and random pulses. Rigidly fix the LVDT sensor on the platform surface to ensure that its output signal only reflects the disturbance characteristics applied by the platform and avoid interference from other environmental noises. Preset multiple groups of disturbance condition combinations, including but not limited to low-frequency and high-frequency sinusoidal vibrations, periodic impacts of different amplitudes, vibration excitations in multi-dimensional directions (such as axial and radial), and random pulse sequences. For each group of conditions, the parameters of the disturbance source need to be clearly recorded, such as key indicators like vibration frequency, amplitude, direction angle, pulse intensity, and timing.

[0025] In the data acquisition stage, through a multi-channel synchronous sampling system, the response signal of the LVDT sensor and the disturbance parameters generated by the platform are recorded in real time. During the acquisition process, it is necessary to ensure that the timestamps are strictly aligned to ensure that each sensor response sample forms a one-to-one mapping relationship with the corresponding disturbance parameter. For example, when applying a 10 Hz sinusoidal vibration, the system synchronously records the continuous output curve of the LVDT within the complete cycle of this vibration and labels the parameter tags such as its frequency and amplitude. For the random pulse scenario, it is necessary to capture the transient response signal of the pulse event and associate the intensity and trigger time information of the pulse.

[0026] Finally, the collected raw data is stored and preprocessed in a structured manner. The data storage format needs to include the response signal of the LVDT sensor, the disturbance type classification label such as "axial 5 Hz sinusoidal vibration", and the numerical matrix of specific disturbance parameters. At the same time, through data cleaning, invalid samples caused by sensor transient saturation or abnormal platform jitter are removed to ensure the integrity and consistency of the dataset. The structured dataset formed in this step not only contains the dynamic response characteristics of the sensor under disturbances but also completely retains the physical characteristics of the disturbance source, providing a highly reliable data basis for subsequent interference mode analysis, feature encoding, and error modeling.

[0027] Step S2: Decompose the response signal of the LVDT sensor in frequency through a multi-level wavelet packet decomposition algorithm to obtain the wavelet coefficient sequence of the sub-bands of the LVDT sensor response signal, and calculate the sub-band energy index through the wavelet coefficient sequence; calculate the sub-band energy entropy by calculating the entropy value of the sub-band energy index; calculate the energy concentration index by combining the maximum value of the sub-band energy index and the sub-band energy entropy.

[0028] The frequency decomposition of the LVDT sensor response signal is carried out by a multi-level wavelet packet decomposition algorithm, and the sub-band energy index is calculated. The specific steps are as follows: First, preprocess the original signal of the sensor, such as removing the DC bias, to eliminate the influence of zero drift; then select a suitable wavelet basis, such as the db4 wavelet, and determine the decomposition level, and decompose the signal layer by layer into low-frequency and high-frequency components to form a tree structure containing sub-bands, and each sub-band corresponds to a unique frequency interval, such as 0 - 625 Hz, 625 - 1250 Hz, etc.; then extract the wavelet packet coefficients of each sub-band, and obtain the sub-band energy index by calculating the sum of the squares of the coefficients, which reflects the total signal energy in this frequency band; finally, obtain the energy indices of all sub-bands, providing a quantitative basis for subsequent analysis of the energy distribution characteristics of each frequency band.

[0029] Through the low-pass filtering and high-pass filtering of the multi-level wavelet transform, the LVDT sensor response signal x[n] is used as the original input of the 0th layer of the multi-level wavelet transform, where 0 < n < N, and N is the total number of sampling points of the LVDT sensor response signal; The low-frequency coefficient of the Lth layer of decomposition is: ; represents the value of the low-frequency coefficient of the Lth layer of decomposition of the LVDT sensor response signal at the jth position, where j is the position index of the low-frequency coefficient after the Lth layer of decomposition, 0 j < , represents the nth sampling point of the LVDT sensor response signal, N is the total number of sampling points of the LVDT sensor response signal, represents the low-pass filter coefficient, represents the low-frequency coefficient of the (L - 1)th layer.

[0030] The high-frequency coefficient of the Lth layer of decomposition is: ; represents the value of the high-frequency coefficient of the Lth layer of decomposition of the LVDT sensor response signal at the jth position, where j is the position index of the high-frequency coefficient after the Lth layer of decomposition, 0 j < , represents the nth sampling point of the LVDT sensor response signal, N is the total number of sampling points of the LVDT sensor response signal, represents the high-pass filter coefficient, represents the high-frequency coefficient of the (L - 1)th layer.

[0031] Continue to decompose the coefficients of each layer, and finally obtain a sequence of wavelet coefficients of sub-bands ={ , , i = 1, 2,... , where L is the number of layers.

[0032] Then the energy index of each sub - band is: ; Where is the energy index of the i - th sub - band, N represents the total number of samples of the LVDT sensor response signal, represents the wavelet coefficient sequence of the i - th sub - band, and n is the index of the n - th value in the wavelet coefficient sequence of the sub - band, represents the total number of sub - bands generated when the decomposition level is L, and L is the decomposition level.

[0033] By calculating the entropy value of the sub - band energy index, the sub - band energy entropy is obtained: ; Where H is the sub - band energy entropy, represents the total number of sub - bands generated when the decomposition level is L, and L is the decomposition level, is the energy index of the i - th sub - band.

[0034] By combining the maximum value of the sub - band energy index and the sub - band energy entropy, the energy concentration index is calculated: ; Where is the energy concentration index, H is the sub - band energy entropy, represents the maximum value of the sub - band energy index, and max() is the maximum value function.

[0035] The energy concentration index is calculated by combining the maximum value of the sub-band energy index and the sub-band energy entropy, which can effectively reflect the distribution of the signal in different frequency components. The maximum value of the sub-band energy index represents the energy intensity of the LVDT sensor response signal in a certain frequency band, which can reveal the importance of the disturbance in this frequency band. The sub-band energy entropy measures whether the energy distribution within this frequency band is uniform. The higher the entropy value, the more dispersed the energy distribution of the signal, and the more complex the disturbance of the system. On the contrary, the lower the entropy value, the more concentrated the energy distribution, and the simpler the system disturbance. By combining the maximum value of the sub-band energy index and the sub-band energy entropy to calculate the energy concentration index, the influence degree and complexity of the disturbance source on the signal can be comprehensively evaluated. If the energy index of a certain frequency band is large and its energy entropy is low, it means that the signal in this frequency band is relatively concentrated, and it is a frequency component with clear disturbance characteristics. On the contrary, it indicates that the signal is affected by various complex interferences. The energy concentration index not only helps to identify the main disturbance source, but also can evaluate the stability of the signal, and further provide a more accurate basis for subsequent error correction and the construction of the interference model.

[0036] Step S3: By performing peak analysis on the wavelet coefficient sequence, the sub-band peak factor is obtained; by combining the sub-band peak factor and the sub-band energy index, the sub-band comprehensive peak index is calculated; by combining the sub-band comprehensive peak index and the energy concentration index, the LVDT response signal characteristics are obtained.

[0037] Peak analysis is performed on the wavelet coefficient sequence of the sub-band of the LVDT sensor response signal to obtain the sub-band peak factor. For the wavelet coefficient sequence of each sub-band perform wavelet reconstruction to obtain the reconstructed signal sequence of this sub-band , representing the reconstructed signal of the i-th sub-band.

[0038] Peak analysis is performed on the reconstructed signal sequence of the i-th sub-band to obtain the sub-band peak factor: ; where is the i-th sub-band peak factor, represents the reconstructed signal sequence of the i-th sub-band, N represents the total number of samples of the reconstructed signal sequence, and n is the index of the n-th value in the wavelet coefficient sequence of the i-th sub-band.

[0039] By combining the sub-band peak factor and the sub-band energy index, the sub-band comprehensive peak index is calculated: ; where Q is the sub-band comprehensive peak index, L is the number of layers, i represents the index of the i-th sub-band, is the i-th sub-band peak factor, is the energy index of the i-th sub-band.

[0040] It should be noted that by combining the sub-band peak factor and the sub-band energy index to calculate the sub-band comprehensive peak index, the sub-band peak factor reflects the instantaneous impact intensity of the signal within a specific frequency band, while the sub-band energy index reflects the contribution degree of this frequency band to the overall energy of the signal. The combination of the two can construct a composite evaluation index that combines feature sensitivity and frequency band importance. It can not only suppress the interference of accidental impacts in low-energy frequency bands through the energy index, avoiding misjudging noise spikes as effective features, but also enhance the expression of impact features in high-energy dominant frequency bands with the help of energy weights, significantly improving the recognition ability of core fault features.

[0041] By combining the sub-band comprehensive peak index and the energy concentration index, the LVDT response signal feature T is obtained, T = , Q], where is the energy concentration index, and Q is the comprehensive peak index.

[0042] It should be noted that by combining the sub-band comprehensive peak index and the energy concentration index, the characteristics of the LVDT sensor response signal are obtained. The sub-band comprehensive peak index can reflect the main peak position and intensity within each frequency band, thereby capturing the main energy distribution of the signal in different frequency ranges. The energy concentration index measures whether the energy distribution of the signal within a specific frequency band is concentrated, and can reveal the local characteristics of the signal, especially the concentration degree in the high-energy region. By combining the sub-band comprehensive peak index and the energy concentration index, the comprehensive peak index can identify significant features in the signal, such as strong interference or mutations, while the energy concentration index can reveal the stability of the signal and the distribution pattern of the spectrum. This combination can not only improve the comprehensive understanding of the essence of the signal, but also effectively distinguish different types of signals and interference patterns, thus playing an important role in subsequent interference recognition, error prediction, and signal optimization.

[0043] Step S4: Cluster the LVDT response signal features through the KMEANS algorithm to obtain the response signal clustering clusters, and statistically analyze the disturbance source parameters of each clustering cluster in the response signal clustering clusters to obtain the interference feature labels of the clustering clusters.

[0044] The LVDT response signal features interfered by different groups of disturbance source parameters are combined into an LVDT response signal feature set, and the LVDT response signal feature set is standardized by Z-score so that the mean of each feature is 0 and the variance is 1, avoiding the influence of magnitude differences on the clustering results.

[0045] Cluster the LVDT response signal feature set using the KMEANS algorithm. Determine the optimal number of clusters \(k\) through the elbow method. Initialize the cluster centers using the KMEANS algorithm. The specific steps are as follows: Randomly initialize \(k\) cluster centers and enter the iterative process. For each sample in the LVDT response signal feature set, assign the sample to the nearest cluster center according to the distance between its feature vector and the current cluster center. Euclidean distance is usually used to measure the distance between the sample and the centroid. All samples are assigned to a cluster according to the nearest centroid. After the assignment is completed, recalculate the centroid of each cluster. The position of the cluster center is the average position of all samples within the cluster, and the updated centroid becomes the reference for the next round of iteration. Continue the iteration until the change in the cluster center is small enough or the preset number of iterations is reached.

[0046] After the KMEANS algorithm iteration is completed, the response signal cluster is obtained, with \(k\) clusters of the response signal cluster: , ,..., , which represents the \(k\)th response signal cluster.

[0047] It should be noted that each cluster represents a type of LVDT sensor response signal with similar characteristics.

[0048] By statistically analyzing the disturbance source parameters in each cluster of the response signal cluster, the interference feature labels of the cluster are obtained: For each cluster in the response signal cluster, extract the disturbance source parameters corresponding to all samples within the cluster, including the original experimental setting parameters such as vibration frequency, amplitude, direction (such as the X-axis or Z-axis), and disturbance type (sine or random pulse).

[0049] Perform a frequency statistics on the disturbance parameters of each cluster, and calculate the distribution ratios of each parameter (frequency, amplitude, direction, type). According to the statistical results, determine the dominant parameter combination in each cluster. For example, if 90% of the samples in a cluster are "X-axis direction, 5 Hz, sine vibration", then the interference feature label of the response signal cluster is "X-5Hz-sine". If the parameter distribution is relatively dispersed, such as a wide frequency range, then combine the parameters with the highest frequency of occurrence. For example, in the cluster, the direction with the most occurrences is the X-axis direction, the vibration with the most occurrences is 10 Hz, and the amplitude type with the most occurrences is sine vibration, then the interference feature label of the response signal cluster is "X-10-sine".

[0050] Finally, , ,..., add the corresponding interference feature labels to the \(k\) clusters: , ,..., , represents the interference feature label of the k-th clustering cluster.

[0051] Step S5: According to the interference feature label, construct a sensor accuracy error prediction model corresponding to the interference feature label; collect the LVDT raw measurement signal in real time, calculate the LVDT response signal feature of the LVDT raw measurement signal, input the LVDT response signal feature into the response signal clustering cluster to obtain the interference feature label of the LVDT raw measurement signal; then input the LVDT raw measurement signal into the sensor accuracy error prediction model corresponding to the interference feature label to obtain the signal error result of the LVDT.

[0052] According to the interference feature label, construct a sensor accuracy error prediction model corresponding to the interference feature label, and construct a set of sensor accuracy error prediction models for different interference types. Each model adopts the same network structure framework, using a residual-enhanced convolutional recurrent hybrid network to balance the local feature extraction ability and the time series modeling ability. For each type of interference feature label, use its corresponding LVDT sensor response signal and standard displacement input as the input-output pair of supervised learning to train and generate the corresponding sensor accuracy error prediction model. All models form an error prediction model library with an interference feature label index. The structure design of the model library has scalability and combinability: when a new interference type is discovered later, a new sub-model can be formed through additional training and dynamically mounted to the model library.

[0053] Interference feature label The corresponding sensor accuracy error prediction model structure includes: an input layer, a convolutional module, a fully connected regression layer, a loop connection layer, and an output layer.

[0054] The input layer receives the LVDT sensor response signal and the standard displacement input.

[0055] It should be noted that the standard displacement input is the true displacement value obtained through a high-precision displacement sensor or a calibration device.

[0056] Convolutional module: First layer convolution: Use one-dimensional convolution operation, configure 64 convolution kernels with a width of 3, a step size of 1, and a ReLU activation function. After convolution, the input generates a feature map with 64 channels to capture local signal fluctuations (such as pulses, harmonic components). Residual connection: Introduce a skip connection after the second layer of convolution, and directly add the output of the first layer of convolution to the output of the second layer. The specific implementation is as follows: If the dimensions of the input and output do not match, adjust the number of input channels through 1×1 convolution. The residual structure alleviates the problem of gradient disappearance and enhances the training stability of the deep network. Max pooling: The pooling window size is 2 and the step size is 2, compressing the length of the feature map to , reduce the computational complexity.

[0057] Recurrent module: Bidirectional LSTM layer: The bidirectional long short-term memory network is adopted, with 32 hidden units set in each direction to capture the temporal dependencies of the signal before and after. For example, the forward LSTM learns historical information, and the backward LSTM learns future context, and finally the bidirectional outputs are concatenated.

[0058] Fully connected regression layer: Flatten the features, and flatten the temporal features output by the LSTM layer into a one-dimensional vector.

[0059] Fully connected layer: Map the features through a two-layer fully connected network. The first layer has 256 neurons (activated by ReLU), and Dropout (dropout rate 0.3) is added to prevent overfitting; the output layer is a single linear neuron that directly regresses and predicts the error value Δy.

[0060] Output layer: The output layer directly generates the error prediction value, with the unit of millimeters, aligned with the sensor range. For example, the predicted error range can be set as Δy ∈ [−0.5, 0.5] mm.

[0061] The loss function is: ; where is the loss function of the sensor accuracy error prediction model, N represents the total number of signal sampling points, n represents the nth signal sampling point, represents the error value of the nth sampling point of the predicted LVDT sensor response signal and the standard displacement, represents the error value of the nth sampling point of the actual LVDT sensor response signal and the standard displacement.

[0062] Collect the LVDT raw measurement signals in real time and calculate the features of the LVDT response signals. The calculation of the LVDT response signal features is the same as that in steps S2 to S3. Input the LVDT response signal features into the response signal clustering clusters, assign the LVDT raw measurement signal to the nearest clustering cluster, and obtain the interference feature label corresponding to the clustering cluster.

[0063] Then input the LVDT raw measurement signal into the sensor accuracy error prediction model corresponding to the interference feature label to obtain the signal error result of the LVDT: ; where represents the error value of the nth sampling point of the predicted LVDT raw measurement signal input and the standard displacement, represents the sensor accuracy error prediction model with the interference feature label , represents the LVDT raw measurement signal, and n represents the nth sampling point of the signal.

[0064] Step S6: Calculate the corrected result of the LVDT signal by combining the LVDT response signal characteristics of the LVDT original measurement signal and the signal error result of the LVDT, so as to realize the accuracy correction of the LVDT sensor.

[0065] By combining the original measurement output of the LVDT and the signal error result of the LVDT, the corrected result of the LVDT signal is obtained: ; where represents the corrected result of the nth sampling point of the LVDT signal, n represents the nth sampling point of the signal, represents the value of the nth sampling point of the original measurement output of the LVDT, represents the error value of the nth sampling point of the predicted LVDT original measurement signal input and the standard displacement, represents the interference characteristic label of the LVDT original measurement signal as and the energy concentration index in the response signal characteristic is the dynamic weight coefficient, is the interference characteristic label, is the energy concentration index of the original measurement output of the LVDT, is the attenuation factor, which controls the attenuation rate of the compensation amount with respect to the original measurement output of the LVDT.

[0066] It should be noted that represents the interference characteristic label of the LVDT original measurement signal as and the energy concentration index in the response signal characteristic is the dynamic weight coefficient. When the interference characteristic label indicates a strong dominant interference, if has a high value, it means that the interference is clear and the energy is significant. At this time, will be increased to 1.2, for example, to strengthen the compensation to eliminate the systematic error. If has a medium value (partial energy concentration), then remains at the standard value (such as 1.0) to balance the correction strength and stability. When the interference characteristic label indicates a weak and scattered interference (such as background noise), even if has a medium or low value (scattered energy), will be decreased (such as 0.8) to avoid amplifying the noise due to overcompensation.

[0067] By combining the energy concentration index in the LVDT original measurement signal and its response signal characteristics with the real-time predicted error results, the system can dynamically identify the type of interference and quantify its impact on the signal, thereby achieving accurate error compensation. Through the analysis of frequency band energy distribution and instantaneous impact characteristics, different interference sources such as periodic vibration and random noise can be distinguished, and the compensation strategy can be adjusted in a targeted manner to avoid over-compensation or under-compensation problems caused by traditional linear correction; secondly, the introduction of a nonlinear attenuation mechanism can not only strengthen the correction strength under strong interference to eliminate systematic deviations, but also suppress the risk of secondary distortion of high-amplitude signals to ensure the stability of the signal dynamic range.

[0068] This paper proposes a LVDT sensor accuracy correction method based on machine learning. By integrating multi-level frequency band analysis, clustering modeling and dynamic error prediction technology, high-precision real-time correction of sensor signals in complex disturbance environments is achieved. This method innovatively constructs composite features such as energy concentration index and comprehensive peak index, combines KMEANS clustering and residual enhanced neural network model, dynamically associates signal features with interference types, and significantly improves the anti-interference ability and measurement accuracy of LVDT sensors in dynamic disturbance scenarios.

[0069] By combining the maximum value of the sub-band energy index and the sub-band energy entropy to calculate the energy concentration index, the concentration of the signal energy distribution and the complexity of the disturbance can be comprehensively quantified. This method can not only accurately identify the dominant disturbance frequency band, but also evaluate the uniformity of the energy distribution through the entropy value, thereby distinguishing between single interference and complex interference scenarios. For example, the combination of a high energy index and a low entropy value indicates that the signal is dominated by a single strong disturbance, while a low energy index and a high entropy value reflect complex multi-source interference. This provides a key basis for the targeted construction of the subsequent error model and effectively improves the robustness of disturbance feature extraction.

[0070] By combining the sub-band peak factor and the sub-band energy index to calculate the comprehensive peak index, the problem of instantaneous impact features being easily interfered by low-energy noise in traditional methods is solved. The peak factor captures the instantaneous impact strength of the signal in the frequency band, while the energy index gives it a weight, suppressing the noise interference of non-dominant frequency bands. For example, significant peaks in high-energy frequency bands can be strengthened as key features, while random spikes in low-energy frequency bands are weakened, thereby significantly improving the sensitivity and recognition accuracy of core interference features (such as impact and harmonic distortion), avoiding misjudgment and missed detection.

[0071] This paper realizes accurate error compensation in a dynamic disturbance environment by combining the response signal characteristics of the LVDT original measurement signal with the real-time predicted signal error results. Its core advantage is that through the dynamic weight coefficient and nonlinear attenuation factor, the system can adaptively adjust the compensation strength according to the interference type and energy distribution characteristics - strengthening the correction under strong dominant interference to eliminate systematic deviations, and suppressing the risk of overcompensation in weak dispersed interference, which not only solves the over-compensation or under-compensation problem of traditional linear correction, but also avoids the secondary distortion of high-amplitude signals; secondly, this method accurately distinguishes multi-source interference such as periodic vibration and random noise through frequency band energy analysis and cluster label recognition, and optimizes the compensation strategy in a targeted manner, significantly improving the anti-interference ability of the sensor under complex working conditions (such as multi-axis vibration and electromagnetic noise); finally, through the closed-loop mechanism of real-time error prediction and dynamic correction, nonlinear distortion, zero drift and other errors are effectively eliminated, ensuring the high stability and measurement accuracy of the LVDT signal, and providing a highly reliable data foundation for scenarios such as intelligent manufacturing and precision control.

[0072] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions. The sentence "includes an element defined by ... does not exclude the existence of other identical elements in the process, method, article or device including the element".

[0073] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calibrating the accuracy of an LVDT sensor based on machine learning, characterized in that: It includes the following steps: Step S1: By adding different disturbance sources to the LVDT sensor, an LVDT sensor disturbance data set is obtained, and the LVDT sensor disturbance data set includes: the LVDT sensor response signal and the disturbance source parameters; Step S2: The LVDT sensor response signal is decomposed in frequency by a multi-level wavelet packet decomposition algorithm to obtain a wavelet coefficient sequence of the sub-bands of the LVDT sensor response signal, and the sub-band energy index is calculated through the wavelet coefficient sequence; the sub-band energy entropy is obtained by calculating the entropy value of the sub-band energy index; by combining the maximum value of the sub-band energy index and the sub-band energy entropy, the energy concentration index is calculated; Step S3: By performing peak analysis on the wavelet coefficient sequence, the sub-band peak factor is obtained; by combining the sub-band peak factor and the sub-band energy index, the sub-band comprehensive peak index is calculated; by combining the sub-band comprehensive peak index and the energy concentration index, the LVDT response signal feature is obtained; Step S4: The LVDT response signal features are clustered by the KMEANS algorithm to obtain a response signal clustering cluster, and the disturbance source parameters of each clustering cluster in the response signal clustering cluster are statistically analyzed to obtain the interference feature label of the clustering cluster; Step S5: According to the interference feature label, a sensor accuracy error prediction model corresponding to the interference feature label is constructed; the LVDT original measurement signal is collected in real time, the LVDT response signal feature of the LVDT original measurement signal is calculated, and the LVDT response signal feature is input into the response signal clustering cluster to obtain the interference feature label of the LVDT original measurement signal; then the LVDT original measurement signal is input into the sensor accuracy error prediction model corresponding to the interference feature label to obtain the signal error result of the LVDT; Step S6: By combining the LVDT response signal feature of the LVDT original measurement signal and the signal error result of the LVDT, the correction result of the LVDT signal is calculated to realize the accuracy correction of the LVDT sensor.

2. The method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 1, wherein: The step of decomposing the LVDT sensor response signal in frequency by a multi-level wavelet packet decomposition algorithm to obtain a wavelet coefficient sequence of the sub-bands of the LVDT sensor response signal and calculating the sub-band energy index through the wavelet coefficient sequence includes the following specific steps: Through the low-pass filtering and high-pass filtering of the multi-level wavelet transform, the LVDT sensor response signal x[n] is used as the original input of the 0th layer of the multi-level wavelet transform, where 0 < n < N and N is the total number of sampling points of the LVDT sensor response signal; The low-frequency coefficient of the Lth layer decomposition is: ； represents the value of the low-frequency coefficient after the L-th layer decomposition of the LVDT sensor response signal at the j-th position, where j is the position index of the low-frequency coefficient after the L-th layer decomposition, 0 j < , represents the n-th sampling point of the LVDT sensor response signal, and N is the total number of sampling points of the LVDT sensor response signal represents the low-pass filter coefficient represents the low-frequency coefficient of the (L - 1)-th layer The high-frequency coefficient of the Lth layer decomposition is: ； represents the value of the high-frequency coefficient after the L-th layer decomposition of the LVDT sensor response signal at the j-th position, where j is the position index of the high-frequency coefficient after the L-th layer decomposition, 0 j < , represents the n-th sampling point of the LVDT sensor response signal, and N is the total number of sampling points of the LVDT sensor response signal represents the high-pass filter coefficient represents the high-frequency coefficient of the (L - 1)-th layer Continue to decompose the coefficients of each layer, and finally obtain the wavelet coefficient sequences of sub-bands ={ , }, i = 1, 2,... , where L is the number of layers; Then the energy index of each sub-band is: ； Wherein, is the energy index of the i-th sub-band, N represents that N is the total number of sampling points of the LVDT sensor response signal, represents the wavelet coefficient sequence of the i-th sub-band, and n is the index of the n-th value in the wavelet coefficient sequence of the sub-band, represents the total number of sub-bands generated when the decomposition level is L, and L is the decomposition level.

3. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 2, characterized in that: The step of obtaining the sub-band energy entropy by calculating the entropy value of the sub-band energy index includes the following steps: The sub-band energy entropy is obtained by calculating the entropy value of the sub-band energy index: ； where H is the sub-band energy entropy, represents the total number of sub-bands generated when the decomposition level is L, and L is the decomposition level, is the energy index of the i-th sub-band.

4. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 3, characterized in that: The step of calculating the energy concentration index by combining the maximum value of the sub-band energy index and the sub-band energy entropy includes the following steps: The energy concentration index is calculated by combining the maximum value of the sub-band energy index and the sub-band energy entropy: ； Among them, is the energy concentration index, H is the energy entropy of the sub-band, represents the maximum value of the sub-band energy index, and max() is the maximum value function.

5. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 4, characterized in that: The sub-band peak factor is obtained by performing peak analysis on the wavelet coefficient sequence, including the following specific steps: Peak analysis is performed on the wavelet coefficient sequence of the sub-band of the response signal of the LVDT sensor to obtain the peak factor of the sub-band. For the wavelet coefficient sequence of each sub-band wavelet reconstruction is carried out to obtain the reconstructed signal sequence of this sub-band , which represents the reconstructed signal of the i-th sub-band; Peak analysis is performed on the reconstructed signal sequence of the sub-band of the i-th sub-band to obtain the sub-band peak factor: ； Among them, is the peak factor of the i-th sub-band, represents the reconstructed signal sequence of the i-th sub-band. N represents the total number of sampling points of the reconstructed signal sequence, and n is the index of the n-th value in the wavelet coefficient sequence of the i-th sub-band.

6. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 5, characterized in that: The sub-band comprehensive peak index is calculated by combining the sub-band peak factor and the sub-band energy index, including the following specific steps: The sub-band comprehensive peak index is calculated by combining the sub-band peak factor and the sub-band energy index: ； Among them, Q is the sub-band comprehensive peak index, L is the number of layers, i represents the index of the i-th sub-band, is the peak factor of the i-th sub-band, is the energy index of the i-th sub-band.

7. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 6, characterized in that: The LVDT response signal feature is obtained by combining the sub-band comprehensive peak index and the energy concentration index, including the following specific steps: By combining the sub-band comprehensive peak index and the energy concentration index, the LVDT response signal feature T is obtained, where T = , Q], where is the energy concentration index and Q is the comprehensive peak index.

8. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 7, characterized in that: The sensor accuracy error prediction model corresponding to the interference feature label is constructed, including the following specific steps: Interference feature label The corresponding sensor accuracy error prediction model structure includes: an input layer, a convolutional module, a fully connected regression layer, a fully connected layer, and an output layer; The input layer receives the LVDT sensor response signal and the standard displacement input; Convolution module: First-layer convolution: One-dimensional convolution operation is adopted, with 64 convolution kernels of width 3, a stride of 1, and a ReLU activation function. After convolution, the input generates a feature map with 64 channels. Residual connection: A skip connection is introduced after the second-layer convolution, and the output of the first-layer convolution is directly added to the output of the second layer; Recurrent module: Bidirectional LSTM layer: A bidirectional long short-term memory network is adopted, with 32 hidden units set in each direction to capture the temporal dependencies of the signal before and after. Fully connected regression layer: The temporal features output by the LSTM layer are flattened into a one-dimensional vector; Fully connected layer: The features are mapped through a two-layer fully connected network. The first layer has 256 neurons and a ReLU activation function, and Dropout is added to prevent overfitting; The output layer is a single linear neuron that directly regresses and predicts the error value Δy; Output layer: The output layer directly generates the error prediction value, in millimeters, aligned with the sensor range; The loss function is: ； Among them, is the loss function of the sensor accuracy error prediction model. N represents the total number of signal sampling points, and n represents the nth signal sampling point. represents the error value of the predicted LVDT sensor response signal and the nth sampling point of the standard displacement. represents the error value of the actual LVDT sensor response signal and the nth sampling point of the standard displacement.

9. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 8, characterized in that: The LVDT raw measurement signal is input into the sensor accuracy error prediction model corresponding to the interference feature label to obtain the signal error result of the LVDT, including the following specific steps: The LVDT raw measurement signal is input into the sensor accuracy error prediction model corresponding to the interference feature label to obtain the signal error result of the LVDT: ； Among them, represents the error value between the predicted original measurement signal input of the LVDT and the nth sampling point of the standard displacement, represents that the interference feature label is the sensor accuracy error prediction model, represents the original measurement signal of the LVDT, and n represents the nth sampling point of the signal.

10. A method for calibrating the accuracy of an LVDT sensor based on machine learning according to claim 9, characterized in that: The corrected result of the LVDT signal is calculated by combining the LVDT response signal feature of the LVDT raw measurement signal and the signal error result of the LVDT, including the following specific steps: The corrected result of the LVDT signal is obtained by combining the original measurement output of the LVDT and the signal error result of the LVDT: ； Among them, represents the correction result of the nth sampling point of the LVDT signal, where n represents the nth sampling point of the signal, represents the value of the nth sampling point of the original measurement output of the LVDT, represents the error value of the nth sampling point between the predicted input of the LVDT original measurement signal and the standard displacement, represents the interference feature label of the LVDT original measurement signal and the energy concentration index in the response signal feature is the dynamic weight coefficient, is the interference feature label, is the energy concentration index of the original measurement output of the LVDT, is the attenuation factor, which controls the attenuation rate of the compensation amount with respect to the original measurement output of the LVDT of the LVDT.

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