Ultrasonic bolt pre-tightening state discrimination method based on empirical wavelet transform and random forest

Abstract

The invention belongs to the technical field of mechanical engineering and structural health monitoring, and particularly relates to an ultrasonic bolt pre-tightening state judgment method based on empirical wavelet transform and random forest. The invention provides an ultrasonic bolt pre-tightening state judgment method based on empirical wavelet transform and random forest. The method comprises the following steps: step 1, acquiring ultrasonic echo signals of a bolt in different stress states, and marking the signals according to the stress states during acquisition; environment temperature and bolt medium temperature are extracted to serve as input of a follow-up model; step 2, carrying out adaptive filtering processing on the collected original ultrasonic echo signal to optimize the signal quality, and removing noise and irrelevant frequency components; and 3, taking the data obtained in the step 2 as the input of empirical wavelet transform (EWT).

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical engineering and structural health monitoring, and in particular relates to an ultrasonic bolt pre-tightening state determination method based on empirical wavelet transform and random forest. Background Art

[0002] At present, the detection methods of bolt stress mainly include ultrasonic detection method, strain gauge method, Raman spectroscopy and X-ray diffraction method. Ultrasonic detection method has been widely used in the industrial field because of its simple operation and low cost. It can quickly perform non-destructive detection on a large area of ​​the material without special surface treatment. This technology relies on the acoustic elastic effect and can monitor the changes in the stress state inside the material in real time. From the theoretical analysis of the acoustic elastic effect, it can be seen that as the stress increases, the wave speed of ultrasonic longitudinal and transverse waves and longitudinal waves changes continuously, and the propagation time in the bolt also changes accordingly. This method mainly evaluates the stress state of the bolt by measuring the acoustic time difference, thereby ensuring the reliability and safety of the mechanical structure.

[0003] However, the ultrasonic stress detection method is limited in accuracy and stability by many factors, especially when the ambient temperature changes, the diversity of bolt material properties, and different operating conditions. Under variable temperature conditions, the relationship between the wave velocity and stress response of the material becomes complicated, which increases the uncertainty of the detection results. In addition, conventional stress detection only estimates stress by measuring the change in wave velocity, and the accuracy of judging the stress state of the bolt is relatively low. Therefore, in response to these challenges, further optimizing ultrasonic detection technology and improving its application accuracy and reliability in complex environments are the focus of current research.

[0004] Xiang Boran, Zhou Lijun and others disclosed in their invention patent CN114235240A "a temperature compensation method and detection system for ultrasonic stress detection of in-service high-strength bolts". The system includes an ultrasonic probe auxiliary positioner, a connecting cable, and a bolt stress measuring instrument with integrated ultrasonic transceiver and processing algorithms. By measuring the acoustic time values ​​of transverse and longitudinal waves, the system can detect and accurately compensate the axial force of high-strength bolts in real time, which is particularly suitable for axial force measurement in temperature-fluctuating environments, ensuring the safety and reliability of structural connections. However, the method lacks accuracy in processing signals in complex noise environments, and may not be flexible enough in dealing with dynamic temperature changes.

[0005] In 2022, Ai Jianbo, Sun Guocai and others disclosed in the invention patent CN115452338A "a wind turbine tower flange bolt connection status detection system and detection method". The system includes a displacement monitoring device, a data acquisition instrument and a central processing unit for monitoring the relative displacement and stress value of the flange bolts. The system measures the displacement of the bolts through a displacement monitoring device located in the flange through-hole, and uses a handheld electromagnetic ultrasonic dual-wave stress detector to detect the bolt stress, and further ensures the accuracy of the bolt status detection through a correction algorithm. The system allows necessary tightening adjustments based on the detected bolt stress to ensure the structural safety of the wind turbine. However, its system does not take into account the impact of temperature on stress measurement, and may not be effective in adaptability in complex environments. Summary of the invention

[0006] The present invention aims at the above problems and provides a method for distinguishing the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest.

[0007] To achieve the above object, the present invention adopts the following technical solution, which includes the following steps:

[0008] Step 1: Collect ultrasonic echo signals of bolts under different stress states, and mark the signals according to the stress state at the time of acquisition; extract the ambient temperature and the bolt medium temperature as input for subsequent models;

[0009] Step 2: Adaptively filter the collected raw ultrasonic echo signal to optimize signal quality and remove noise and irrelevant frequency components;

[0010] Step 3: The data obtained in step 2 is used as the input of the empirical wavelet transform (EWT). Through EWT, the stress data of each sample is decomposed into a series of intrinsic mode functions (IMFs).

[0011] Step 4: Extract the time domain features related to the bolt stress state from multiple IMFs and residuals, and use the ambient temperature and bolt medium temperature as input data;

[0012] Step 5: Use random forest RF as the classification model to select and train the data.

[0013] As a preferred solution, in step 1 of the present invention, the ultrasonic echo signals of the bolts under different stress states are collected by using Murata MA40S4S / R series piezoelectric sensors.

[0014] As another preferred embodiment, in step 1 of the present invention, different stress states include too loose, too tight and normal.

[0015] As another preferred solution, in step 2 of the present invention, an adaptive filtering method is adopted.

[0016] As another preferred solution, the present invention uses an adaptive filtering method, which first processes the ultrasonic echo signal through a finite impulse response (FIR) filter to optimize noise suppression in the signal and extract signal features. The FIR filter formula is expressed as:

[0017]

[0018] Among them, x(tn) is the input signal, that is, the ultrasonic echo data, y(t) is the output signal after filtering, and h n is the coefficient of the adaptive filter, and N is the length of the filter. h is adjusted by the adaptive algorithm n , to minimize prediction errors and ensure the accuracy of signal processing.

[0019] As another preferred embodiment, the formula of step 3 of the present invention is:

[0020]

[0021] IMF i (t) is the nth intrinsic mode function; r(t) is the remaining signal, i.e., the residual, which contains the undecomposed part of the original signal. F can be regarded as the stress wave velocity distribution with a high degree of match between the measured data and the model prediction data after filtering by the FIR filter.

[0022] As another preferred embodiment, the spectrum analysis of each IMF of the present invention is described by its power spectral density (PSD):

[0023] PSD(f)=|F{IMF i (0)}| 2

[0024] Where F represents Fourier transform and f is frequency. The noise level of each IMF is analyzed through its PSD, and the high-frequency component is an indicator of noise. The standard deviation, mean, and kurtosis are used to evaluate whether each IMF is noisy. After determining which IMFs are noisy, they are removed from the data set. Finally, by linearly superimposing the remaining IMFs, a new signal is reconstructed to accurately describe the behavior of the bolt under different stress states.

[0025] As another preferred solution, in step 4 of the present invention, the ambient temperature and the bolt medium temperature are first averaged (for example, taking two temperatures 10 times and calculating the average value), then normalized, and then input into the model.

[0026] As another preferred solution, step 4 of the present invention finds the local maximum and minimum values ​​of the data, constructs the upper and lower envelopes through these extreme values, and then calculates the mean of the envelope to gradually extract the components that meet the IMF conditions; this includes obtaining the energy E i , dominant frequency f dom,i and envelope characteristics M i Energy E i That is, the energy of each IMF represents the intensity of the signal at different frequencies and is used to distinguish stress states; the energy E i For each intrinsic mode function IMF i Calculated using the following formula:

[0027] E i =∫|IMF i (t)| 2 dt

[0028] In bolt stress testing, each IMF i The energy of a bolt is the integral of the square of its signal amplitude, which reflects the energy intensity in this frequency band and is a key indicator for identifying different stress states (such as too loose, too tight or normal). By analyzing the energy distribution of each IMF, we can more accurately determine the actual physical state of the bolt in operation, thus playing a vital role in maintenance and safety monitoring;

[0029] Dominant frequency f dom,i It is determined by calculating the power spectral density (PSD) of the IMF and finding the frequency of the maximum value:

[0030]

[0031] Where F represents Fourier transform;

[0032] The envelope characteristic reflects the amplitude change of the signal. The upper and lower bounds of the envelope are constructed by finding the local maximum and minimum values ​​of the IMF; the mean value of the envelope M i (t) is expressed as:

[0033]

[0034] Where E upper (t) and E lower (t) are the upper and lower envelopes, respectively; the mean of the envelopes provides smooth information about the signal amplitude variation.

[0035] As another preferred solution, step 5 of the present invention predicts by constructing multiple decision trees, which is suitable for identifying the stress state of bolts. The training data set of each decision tree is obtained by random sampling (bootstrap sampling) from the original bolt detection data set. Each tree independently classifies the stress data instance of the bolt, and the final classification result is determined by the prediction results of all trees through majority voting or average; the mathematical expression is as follows:

[0036]

[0037] in is the final prediction result, indicating the stress state of the bolt (such as too loose, too tight or normal), T i (x) is the prediction result of the i-th tree for sample x (i.e., a set of inspection data of bolts), and the mode function indicates to select the most common prediction result among all decision trees;

[0038] In the process of building each decision tree, not only are samples randomly selected (bootstrap sampling), that is, random forests sample the bolt inspection data set with replacement to form multiple different training subsets (i.e., predicted values), each of which is used to train a decision tree; features are also randomly selected, and only a random subset of features is considered at each split point. This method improves the adaptability and robustness of the model to different manifestations of bolt stress states, making the prediction results more accurate and with better generalization ability; it can be expressed by the following formula:

[0039] S=arg min j∈S,s G(Q,j,s)

[0040] Where j is the index of a feature, selected from a random subset S of features, s is the split point in the decision tree, G(Q,j,s) is the split criterion function based on feature j and split point s, and Q represents the node data set before splitting;

[0041] As another preferred solution, step 5 of the present invention uses part of the data for model training and the remaining data for cross-validation.

[0042] As another preferred solution, step 5 of the present invention uses 70% of the data for model training, and the remaining 30% of the data is used for cross-validation; through the random forest algorithm, stratification is first performed according to the importance score of the features given by each tree, and each validation subset comprehensively covers samples of different feature levels; after each round of cross-validation, the model parameters are adjusted using grid search according to the validation results until the model performance reaches the preset standard; and finally the average performance index of the model is calculated.

[0043] Secondly, the model parameters of the present invention include the number of trees and the maximum depth of the trees.

[0044] In addition, the average performance indicators described in the present invention include accuracy, recall rate and F1 score.

[0045] The invention has beneficial effects.

[0046] Aiming at the limitations of existing ultrasonic bolt stress detection methods in accuracy and stability, especially the uncertainty under variable temperature conditions, the present invention proposes an ultrasonic bolt stress detection method based on empirical wavelet transform (EWT) and random forest (RF). The present invention combines empirical wavelet transform, random forest and ultrasonic detection technology, and judges the characteristics of bolt stress state through more targeted time-frequency signal analysis technology and machine learning technology to improve the accuracy and reliability of classification.

[0047] The present invention combines empirical wavelet transform (EWT), random forest (RF) and ultrasonic detection technology to achieve more accurate detection of bolt stress state under changing environmental conditions and different bolt material properties. In addition, the original ultrasonic signal is adaptively filtered by means of FIR filter, and the ultrasonic signal is analyzed in the time domain by EWT. By selecting appropriate parameter tuning (such as the number of trees, the maximum depth of the tree), the results are more accurate than the existing state judgment methods. The temperature factor is also incorporated into the fusion judgment to avoid the interference of temperature on the classification judgment results. By extracting high-quality features from complex stress signals, the sensitivity and accuracy of the system are significantly improved, while the probability of misjudgment is reduced, providing a new and effective means for accurate detection of bolt tightening in industrial applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods. The protection scope of the present invention is not limited to the following description.

[0049] Figure 1 The present invention is a flow chart of the ultrasonic bolt pre-tightening state determination method based on empirical wavelet transform and random forest.

[0050] Figure 2 This is a model diagram of ultrasonic bolt pre-tightening state discrimination based on empirical wavelet transform and random forest in the present invention.

[0051] Figure 3 This is a flow chart of the random forest algorithm of the present invention. DETAILED DESCRIPTION

[0052] As shown in the figure, data collection is first performed. Ultrasonic echo signals of bolts under different stress states are collected through ultrasonic acquisition equipment to support subsequent data processing and model training. Bolt tightening states are usually divided into three types: too loose, too tight and normal. In order to distinguish these three bolt tightening states, two stress critical values ​​calibrated by the bolts are usually used. The too loose, too tight and normal states are quantified by two specific stress critical values, which have been calibrated by the manufacturer during the bolt manufacturing process. The specific usage method is as follows: Use ultrasonic equipment to collect and record the echo signals of the bolts under these three preset stress states. The basis for determining each state is the comparison result with the stress critical value marked by the manufacturer, where the first critical value is used to distinguish between the too loose state and the normal state, and the second critical value is used to distinguish between the normal state and the overtightened state.

[0053] In actual operation, the ultrasonic signals emitted by the bolts are collected and labeled according to their state at the time of collection (too loose, too tight or normal). These labeled ultrasonic signal data will then be used for supervised machine learning to improve the accuracy and efficiency of tightening state identification. At the same time, the ambient temperature and the bolt medium temperature are extracted as inputs for subsequent models.

[0054] When using adaptive filtering technology to process ultrasonic data of bolts, it is first necessary to design an initial filter model based on the ultrasonic data. This model usually includes a finite impulse response (FIR) filter, which optimizes the frequency response of the signal according to a preset standard.

[0055] Subsequently, ultrasonic waves are emitted at different positions and angles to collect the returned echo data. These collected raw echo data are processed through FIR filters to reduce noise and improve signal quality.

[0056] Next, the filtered data is compared with the expected signal under ideal conditions, and the coefficients of the filter are adjusted through an adaptive filtering algorithm to minimize the error between the actual data and the expected data. This adaptive process is repeated repeatedly, and each iteration optimizes the filter response and gradually improves the accuracy of signal processing.

[0057] After data collection, the data is preprocessed. First, the FIR filter technology is applied to these raw data to filter the collected ultrasonic data. The FIR filter formula is expressed as:

[0058]

[0059] Among them, x(tn) is the input signal, that is, the ultrasonic echo data, y(t) is the output signal after filtering, and h nis the coefficient of the adaptive filter, and N is the length of the filter. h is adjusted by the adaptive algorithm n , to minimize prediction errors and ensure the accuracy of signal processing.

[0060] The improved signal obtained from the FIR filter is used as the input of the EWT. At this time, the signal has been optimized to better reflect the real physical state and reduce the influence of noise and other interference. Through EWT, the stress data of each sample is decomposed into a series of intrinsic mode functions (IMF). The formula is:

[0061]

[0062] Where x(t) is the input signal filtered by the FIR filter, IMF i (t) is the i-th intrinsic mode function, and r(t) is the remaining signal, i.e., the residual, which contains the undecomposed part of the original signal.

[0063] In the ultrasonic signal measured by the present invention, other background reflection signals are mixed, so the present invention needs to decompose the signal into multiple signals, and then take out the one required by the present invention for processing. Usually, the first few IMFs contain higher frequency components, which may contain noise. Those IMFs that are obviously noise (such as those containing high-frequency noise or low-amplitude signals) are removed. The spectrum analysis of each IMF can be described by its power spectral density (PSD):

[0064] PSD(f)=|F{IMF i (0)}| 2

[0065] Where F represents the Fourier transform and f is the frequency. This can help identify and remove IMFs containing high frequency noise. i After removing the noisy IMF, the remaining IMF is reconstructed into a new signal, retaining the useful frequency components and signal characteristics. Therefore, the EWT method has a noise reduction effect compared with other bolt ultrasonic testing methods, and can decompose the signal by automatically and adaptively determining the frequency band boundary of the signal.

[0066] The denoised IMF represents the different frequency components in the signal and provides the local time domain characteristics of the signal. Next, it is necessary to extract the time domain characteristics related to the bolt stress state from the multiple IMFs and residuals obtained by decomposition. Find the local maximum and minimum values ​​of the data, build the upper and lower envelopes through these extreme values, and then calculate the mean of the envelope to gradually extract the components that meet the IMF conditions. This includes obtaining the energy E i , dominant frequency f dom,iand envelope characteristics M i Energy, i.e. the energy of each IMF, represents the intensity of the signal at different frequencies and can be used to distinguish stress states. Energy E i For each intrinsic mode function IMF i It can be calculated using the following formula:

[0067] E i =∫|IMF i (t)| 2 dt

[0068] This shows that each IMF i The energy is the integral of the square of its signal amplitude, reflecting the energy intensity in the corresponding frequency band.

[0069] The frequency is the dominant frequency of each IMF, which is determined by calculating the power spectral density (PSD) of the IMF and finding the frequency of the maximum value:

[0070]

[0071] Where F represents the Fourier transform. This can help determine the dominant frequency components of each IMF.

[0072] In addition, the signal envelope characteristic reflects the amplitude change of the signal and may also be related to the stress state. The upper and lower bounds of the envelope can be constructed by finding the local maximum and minimum of the IMF. The mean value Mi(t) of the envelope can be expressed as:

[0073]

[0074] Where E upper (t) and E lower (t) are the upper envelope and the lower envelope, respectively. The mean of the envelope provides smooth information about the signal amplitude change, which is helpful for further analysis. These analysis steps transform the ultrasound signal data of each sample into a set of fine features with labels, providing multidimensional and accurate input for model training, significantly enhancing the performance and reliability of the prediction model.

[0075] After completing the data preprocessing and feature extraction, the next step of the present invention is to perform model selection and training to ensure that the stress state of the bolt can be accurately predicted. After selecting the features, the present invention selects random forest (RF) as the classification model. RF naturally handles nonlinear problems without the need for additional transformations or complex parameter tuning. Random forest improves the accuracy and stability of prediction by building multiple decision trees and synthesizing their results, and performs well for data sets containing complex interactive features.

[0076] Random forests make predictions by building multiple decision trees. The training data set for each decision tree is obtained by random sampling (bootstrap sampling) from the original data set, a process usually called bagging. Each tree classifies the instance independently, and the final classification result is determined by the prediction results of all trees through majority voting or average. The mathematical expression is as follows:

[0077]

[0078] in is the final prediction result, T i (x) is the prediction result of the i-th tree for sample x, and the mode function indicates to select the most common prediction result among all decision trees.

[0079] In the construction process of each decision tree, random forest not only randomly extracts samples, but also randomly selects features, which further enhances the generalization ability of the model and reduces overfitting. At each split point, only a random subset of features is considered. This can be expressed by the following formula:

[0080] S=arg min j∈S,s G(Q,j,s)

[0081] Where j is the index of a feature, selected from a random subset S of features, s is the split point in the decision tree, G(Q,j,s) is a split criterion function based on feature j and split point s, such as Gini impurity or information gain, which quantifies the increase in the "purity" of the node after the split, and Q represents the node dataset before the split.

[0082] This process is to train the random forest (RF) model through samples of multidimensional features, and finally build an efficient three-classification model. First, the multidimensional time domain features (i.e., energy, frequency, envelope), ambient temperature, and bolt medium temperature extracted from each IMF are used as the input of the model. Due to the different measurement scales of the features, the magnitude and distribution of the features are also very different. The present invention performs minimum-maximum normalization processing and scales the features to between 0 and 1, which can help the random forest model learn and generalize more effectively. At the same time, considering the influence of temperature on the accuracy of stress detection, in addition to the time domain features, ambient temperature and medium temperature are added as additional input features, because temperature may affect the stress state of the bolt.

[0083] During the model training process, the present invention uses part of the data set for training and the rest of the data for cross-validation. Cross-validation is a statistical method used to evaluate and improve the predictive performance of the model and ensure the generalization ability of the model on unseen data. The present invention uses part of the training set data for cross-validation. By repeatedly splitting the data and performing training and validation respectively, the present invention can calculate the average performance indicators of the model, such as accuracy, recall rate, and F1 score. This systematic approach ensures the reliability and effectiveness of the model under various working conditions.

[0084] During the model training process, the present invention uses 70% of the data for model training to ensure that there is enough data to support the learning process; the remaining 30% of the data is used for cross-validation. Unlike the traditional cross-validation method, the present invention adopts a stratified sampling technique based on feature importance. Through the random forest algorithm, the present invention first conducts a preliminary assessment of the importance of all features. Based on this assessment, the data is stratified according to feature importance to ensure that each validation subset comprehensively covers samples at different feature levels. This method can more accurately evaluate the model's processing capabilities and stability for various types of data.

[0085] In addition, the present invention also incorporates an iterative optimization process. After each round of cross-validation, the present invention adjusts the model parameters (including the number of trees, the maximum depth of the trees) according to the results of the validation. This iterative optimization process continues until the model performance reaches the preset standard or further improvement becomes minimal. Finally, the average performance indicators of the model are calculated, including accuracy, recall rate and F1 score.

[0086] Finally, the above technology is implemented in the actual system. According to the input ultrasonic signal and temperature data, the system outputs three states of bolt stress, namely, too loose, normal, and too tight.

[0087] The invention is particularly suitable for real-time stress and preload detection and evaluation of high-strength bolts in industrial applications.

[0088] The present invention proposes an ultrasonic bolt stress detection method based on empirical wavelet transform (EWT) and random forest (RF), which improves the detection accuracy and system stability of the bolt stress state through fine signal processing and random forest machine learning technology. The following are the advantages and effects of the present invention:

[0089] First, before performing EWT time-frequency analysis on the ultrasonic echo signal, the present invention filters the original signal through adaptive filtering technology to ensure the clarity and availability of the signal, providing a high-quality data basis for subsequent structural analysis and integrity assessment.

[0090] Next, the ultrasonic signals of the bolts under different stress states were preprocessed by EWT to effectively separate the intrinsic mode functions (IMFs) in the signals. This decomposition method can identify and remove high-frequency noise components in the signal, retaining the signal components that are more critical to the stress state determination. Through this processing, not only the signal-to-noise ratio of the signal is improved, but also the accuracy and reliability of subsequent feature extraction are enhanced.

[0091] Secondly, the present invention uses random forest (RF) as a classification model to analyze the time domain features extracted from IMF and the collected ambient temperature and medium temperature. The random forest model effectively distinguishes the three states of loose, normal and overtightened bolts by constructing multiple decision trees and integrating their results. This integrated learning method not only improves the accuracy of classification, but also enhances the adaptability and generalization of the model to new variables by averaging the prediction results on multiple decision trees. Each decision tree uses randomly selected features and sample subsets during the training process, which helps the model capture complex relationships in the multidimensional feature space and reduce the risk of overfitting. The final output is a combination of the prediction results of each tree, thereby ensuring effective distinction between different stress states.

[0092] In addition, the present invention takes into account the impact of temperature changes on bolt stress detection, introduces temperature as an influencing factor and integrates it into the model. This innovation makes the system more accurate and stable under variable temperature conditions. By real-time monitoring of temperature changes and adjusting the classification model, the interference of environmental factors on the detection results is reduced, so that the system can maintain a high level of performance under various environmental conditions.

[0093] In terms of application, the system of the present invention does not need to rely on professional operators to interpret data. After collecting various ultrasonic echo signals, the system automatically completes signal processing, feature extraction, model input and stress state determination. This increase in automation significantly reduces the complexity of operation and the possibility of human error, making the detection process faster and more accurate.

[0094] Finally, the method of the present invention provides a reliable technical means, which is applicable to various industrial occasions, such as aerospace, automobile manufacturing and bridge construction, and provides a solid technical guarantee for the safety of bolt tightening. By continuously monitoring the stress state of the bolt, potential safety risks can be discovered in time, accidents caused by bolt failure can be avoided, and the long-term stability and safety of the structure can be ensured.

[0095] The present invention proposes an ultrasonic bolt stress detection method based on empirical wavelet transform (EWT) and random forest (RF). The method uses advanced signal processing and machine learning techniques to improve the accuracy and stability of ultrasonic detection of bolt stress state, especially under temperature variation conditions.

[0096] The equipment used in the present invention includes an ultrasonic transmitting and receiving system (Murata MA40S4S / R series piezoelectric sensor), a signal processing unit (including Analog Devices AD620 instrument amplifier, Texas Instruments ADS1115 analog to digital converter), a computer analysis system (using a Raspberry Pi processor), and a temperature sensing device (Dallas Semiconductor DS18B20 digital temperature sensor). The ultrasonic transmitting and receiving system is responsible for transmitting ultrasonic waves and receiving reflected waves, which will vary according to the different stress states of the bolt. The signal processing unit includes an amplifier and a filter for enhancing the received ultrasonic signal and filtering out noise. The computer analysis system is loaded with software and an operating environment for performing adaptive filtering technology (FIR), empirical wavelet transform (EWT) and random forest (RF) algorithms. The temperature sensor is used to record the temperature of the test environment and the bolt itself, because changes in temperature may affect the propagation characteristics of the ultrasonic wave and the physical state of the bolt.

[0097] In the specific operation, the ultrasonic echo signal of the bolt is first collected by the ultrasonic transmitting and receiving system under different stress states (too loose, too tight and normal). Then, these signals are sent to the signal processing unit for preliminary processing, including amplification and filtering. The processed signals are sent to the computer analysis system, where the signals are first further optimized and reconstructed through the full waveform inversion technology to more accurately simulate the stress wave velocity distribution in the bolt.

[0098] The optimized signal is then transformed by empirical wavelet transform to decompose the signal into multiple intrinsic mode functions (IMFs) and a residual signal. These IMFs are used to extract key features from the signal, such as frequency, energy, and time domain characteristics. Based on these features, the random forest (RF) algorithm is used to classify and predict the stress state of the bolt. Random forest effectively distinguishes different stress states by constructing multiple decision trees and voting or averaging the prediction results from each tree.

[0099] Finally, the system outputs the stress state of the bolt (too loose, normal, overtightened) based on the data processed and analyzed.

[0100] This embodiment shows how the present invention effectively combines advanced signal processing technology and machine learning algorithms in actual operation to solve the accuracy and stability problems of bolt stress state detection under variable temperature conditions in the prior art. Through this method, the reliability and accuracy of bolt tightening detection can be significantly improved, the misjudgment rate can be reduced, and solid technical support can be provided for the application of bolt tightening technology.

[0101] Example

[0102] Step 1: Dataset division:

[0103] From the original ultrasonic signal data sequence (x1, x2, ..., x p ,…,x m ), select the first p data as the training set, that is, (x1, x2, …, x p ), the remaining data (x p+1 ,…,x m ) as the validation set. Each data point includes an ultrasonic signal and its corresponding ambient temperature and material temperature values.

[0104] Step 2: Data preprocessing and decomposition:

[0105] The original training data is processed by adaptive filtering, and then the filtered data is decomposed using the empirical wavelet transform (EWT) in combination with the ambient temperature and material temperature data. The training set (x1, x2, ..., xp) is decomposed into k+1 parts, and the results are output from high to low frequency, recorded as EWT1~EWT k+1 Among them, EWT1 is the high frequency part, which mainly contains noise, and the rest is EWT2 to EWT k+1 , where EWT k+1 is a low-frequency trend term used for denoising and reconstructing signals.

[0106] Step 3: Feature extraction and random forest training:

[0107] Convert each decomposed part EWT1 to EWT k+1 Combined with the corresponding ambient temperature and material temperature into a feature vector, these features are normalized to the maximum and minimum, and then trained using the random forest algorithm. The Gini coefficient of each feature is calculated in the random forest to evaluate its importance, and the future value of each part is predicted, recorded as EWT1 predicted value to EWT k+1 Predicted value.

[0108] Step 4: Inverse wavelet reconstruction and model evaluation:

[0109] The predicted value is reconstructed using the inverse wavelet reconstruction algorithm to synthesize the final prediction result. The reconstructed signal is compared with the validation set (x p+1 ,…,x m ) were compared to evaluate the prediction accuracy and effect of the model.

[0110] Step 5: Verification of validation set performance:

[0111] Use the model obtained in step 4 to predict the validation set data to verify the model's generalization ability for unknown data. The prediction performance of the model can be quantified by calculating the error between the prediction and the actual data (such as the mean square error MSE).

[0112] It can be understood that the above specific description of the present invention is only used to illustrate the present invention and is not limited to the technical solutions described in the embodiments of the present invention. Those skilled in the art should understand that the present invention can still be modified or replaced by equivalents to achieve the same technical effects; as long as the use requirements are met, they are within the protection scope of the present invention.

Claims

1. The ultrasonic bolt preload state identification method based on empirical wavelet transform and random forest includes the following steps: Step 1: Collect ultrasonic echo signals of bolts under different stress states, and mark the signals according to the stress state at the time of acquisition; extract the ambient temperature and the bolt medium temperature as input for subsequent models; Step 2: Adaptively filter the collected raw ultrasonic echo signal to optimize signal quality and remove noise and irrelevant frequency components; Step 3: The data obtained in step 2 is used as the input of the empirical wavelet transform. Through EWT, the stress data of each sample is decomposed into a series of intrinsic mode functions IMFs; Step 4: Extract the time domain features related to the bolt stress state from multiple IMFs and residuals, and use the ambient temperature and bolt medium temperature as input data; Step 5: Use random forest RF as the classification model to select and train the data.

2. According to claim 1, the method for distinguishing the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest is characterized in that In step 1, different stress states include too loose, too tight and normal.

3. According to claim 1, the method for determining the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest is characterized in that The ultrasonic echo signal is processed by a finite impulse response filter to optimize the noise suppression in the signal and extract the signal features; the FIR filter formula is expressed as: Among them, x(tn) is the input signal, that is, the ultrasonic echo data, y(t) is the output signal after filtering, and h n is the coefficient of the adaptive filter, N is the length of the filter; h is adjusted by the adaptive algorithm n , to minimize prediction errors and ensure the accuracy of signal processing.

4. According to claim 1, the method for distinguishing the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest is characterized in that The formula of step 3 is: IMF i (t) is the i-th intrinsic mode function; r(t) is the residual signal, which contains the undecomposed part of the original signal; x F (t) is considered as the stress wave velocity distribution with a high degree of match between the measured data and the model prediction data after filtering by the FIR filter.

5. According to claim 1, the method for determining the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest is characterized in that The spectral analysis of each of the IMFs is described by its power spectral density: PSD(f)=|F{IMF i (0)}| 2 Where F represents Fourier transform and f is frequency. The noise level of each IMF is analyzed through its PSD, and the high-frequency component is an indicator of noise. The standard deviation, mean, and kurtosis are used to evaluate whether each IMF is noisy. After determining which IMFs are noisy, they are removed from the data set. Finally, a new signal is reconstructed by linearly superimposing the remaining IMFs to accurately describe the behavior of the bolt under different stress states.

6. According to claim 1, the method for determining the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest is characterized in that In step 4, the ambient temperature and the bolt medium temperature are first averaged, then normalized, and then input into the model.

7. According to claim 1, the method for determining the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest is characterized in that Step 4 finds the local maximum and minimum values ​​of the data, constructs the upper and lower envelopes through these extreme values, and then calculates the mean of the envelope to gradually extract the components that meet the IMF conditions; this includes obtaining the energy E i , dominant frequency f dom，i and envelope characteristics M i Energy E i That is, the energy of each IMF represents the intensity of the signal at different frequencies and is used to distinguish stress states; the energy E i For each intrinsic mode function IMF i Calculated using the following formula: E i =∫|IMF i (t)| 2 dt In bolt stress testing, each IMF i The energy is the integral of the square of its signal amplitude, reflecting the energy intensity in this frequency band, and is a key indicator for identifying different stress states. By analyzing the energy distribution of each IMF, the actual physical state of the bolt during operation can be determined. Dominant frequency f dom，i It is determined by calculating the power spectral density of the IMF and finding the frequency at which the maximum value occurs: Where F represents Fourier transform; The envelope characteristic reflects the amplitude change of the signal. The upper and lower bounds of the envelope are constructed by finding the local maximum and minimum values ​​of the IMF; the mean value of the envelope M i (t) is expressed as: Where E upper (t) and E lower (t) are the upper and lower envelopes, respectively; the mean of the envelopes provides smooth information about the signal amplitude variation.

8. According to claim 1, the method for determining the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest is characterized in that Step 5 is to make predictions by constructing multiple decision trees, which is suitable for identifying the stress state of bolts. The training data set of each decision tree is obtained by random sampling from the original bolt detection data set. Each tree independently classifies the stress data instances of the bolts, and the final classification result is determined by the prediction results of all trees through majority voting or average. The mathematical expression is as follows: in is the final prediction result, which indicates the stress state of the bolt, T i (x) is the prediction result of the i-th tree for sample x, and the mode function indicates to select the most common prediction result among all decision trees; In the process of building each decision tree, not only samples are randomly selected, that is, random forest samples the bolt detection data set with replacement to form multiple different training subsets, each subset is used to train a decision tree; features are also randomly selected, and only a random subset of features is considered at each split point; it can be expressed as the following formula: S=arg min j∈S,s G(Q,j,s) Where j is the index of a feature selected from a random subset S of features, s is the split point in the decision tree, G(Q, j, s) is the split criterion function based on feature j and split point s, and Q represents the node data set before splitting.

9. The method for determining the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest according to claim 1 is characterized in that In step 5, part of the data is used for model training, and the rest of the data is used for cross-validation.

10. The method for determining the pre-tightening state of ultrasonic bolts based on empirical wavelet transform and random forest according to claim 1 is characterized in that The step 5 uses 70% of the data for model training, and the remaining 30% of the data is used for cross-validation; through the random forest algorithm, stratification is first performed according to the importance score of the features given by each tree, and each validation subset comprehensively covers samples at different feature levels; after each round of cross-validation, the model parameters are adjusted using grid search according to the validation results until the model performance reaches the preset standard; and finally the average performance index of the model is calculated.

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