Ball screw pair pre-tightening force prediction method based on typical sequence and deep learning

Abstract

The application discloses a ball screw pair pre-tightening force prediction method based on typical sequences and deep learning, and is applied to the ball screw pair pre-tightening force prediction technical field.The application proposes a method for predicting the pre-tightening force by using friction torque data based on typical sequences and deep learning.First, the original data of the friction torque of the screw is obtained through a monitoring device, and the typical sequences are extracted through hierarchical clustering and mutual information.Based on the phase space reconstruction of the chaotic time sequence, the typical sequences are taken as the input of the deep network to establish a nonlinear regression model, and the change of the pre-tightening force is predicted and evaluated.The application can better predict the change of the pre-tightening force of the ball screw pair, has higher prediction accuracy and numerical stability in the prediction process, and is suitable for the pre-tightening force prediction of the ball screw pair.

Description

Technical Field

[0001] This invention belongs to the field of ball screw pair performance testing technology, and in particular, it is a method for predicting the preload of ball screw pairs based on typical sequences and deep learning. Background Technology

[0002] Ball screw assemblies are widely used in precision machinery, medical equipment, and aerospace due to their high working accuracy, transmission efficiency, and low maintenance costs. During the manufacturing process, internal clearances are introduced due to manufacturing and equipment errors. During use, axial loads cause contact elastic deformation of the balls and raceways. This leads to backlash errors when the screw reverses, affecting transmission accuracy and reducing axial stiffness. Applying axial preload can effectively solve the clearance problem, reduce ball screw deformation, and improve stiffness. However, over long-term operation, the preload gradually diminishes due to friction, wear, vibration, shock, and environmental changes, which is one of the main reasons for the deterioration of ball screw assembly accuracy.

[0003] When a ball screw pair operates without external load, neglecting the influence of machining errors, the impact between the balls and the reversing device is very small. The frictional torque of the screw, unaffected by axial load, can be approximated as originating entirely from the relative deformation caused by the axial preload. Based on the dynamic preload torque measurement specifications recognized and adopted by well-known manufacturers, and considering that the ball screw frictional torque mainly consists of the dynamic preload torque and the shim frictional torque, which is approximately constant, the frictional torque and preload can be considered to have a linear relationship. Therefore, characterizing the change in screw preload through frictional torque is feasible.

[0004] Measuring preload is one of the effective means of monitoring preload. Preload measurement methods are mainly divided into direct measurement and indirect measurement. However, preload is an internal force of the ball screw pair, which is difficult to measure directly after assembly. Furthermore, direct preload measurement devices are very complex, have strict environmental requirements, and are costly, making them difficult to apply in practical work scenarios. In recent years, with the deepening research on ball screw pairs, some methods have been developed to measure preload decay by measuring physical quantities closely related to the preload. However, due to the wide variety of system structures and the fact that uncertainties and measurement noise during processing are not incorporated into the physical model, accurately extracting vibration signals related to preload becomes a challenge, posing a significant challenge to the application of these methods. Moreover, real-time measurement of preload can only detect preload loss when it occurs. At this point, the working state of the ball screw pair already exhibits insufficient accuracy, meaning irreversible damage has been caused to the final machined part. Therefore, prediction can be applied to preload assessment to anticipate potential preload decay and ensure the working accuracy of the screw.

[0005] Preload prediction methods, similar to remaining life estimation, can be categorized into model-based prediction methods, data-driven prediction methods, and hybrid prediction methods. Currently, research on preload prediction for ball screw pairs is relatively limited, with most studies focusing on predicting preload decay failures. These methods determine the preload decay point based on model analysis using intermediate signals. The analysis process is relatively complex, model parameters are difficult to determine, the judgment results are relatively coarse, and the specific changes in preload cannot be obtained.

[0006] Meanwhile, data-driven prediction methods strike a trade-off between prediction accuracy, complexity, and implementation cost. The ability to collect vast amounts of equipment operation data using multi-sensor systems has spurred the development of data-driven prediction methods. Data-driven machine learning methods primarily focus on identifying patterns in existing observational data and using these patterns to predict future data changes. Combining deep learning algorithms with preload prediction for ball screw pairs, and through theoretical analysis and experimental demonstration, shows that deep learning-based preload prediction can deeply mine information about preload changes, exhibiting relatively more stable prediction accuracy, especially when dealing with large amounts of data. Summary of the Invention

[0007] The purpose of this invention is to provide a ball screw pair preload prediction method based on typical sequences and deep learning, which is applicable to ball screw pair preload prediction and solves the problem of the lack of current ball screw pair preload prediction methods.

[0008] The technical solution to achieve the purpose of this invention is: a method for predicting the preload of a ball screw pair based on typical sequences and deep learning, the method comprising the following steps:

[0009] Step 1: Measure the friction torque sample of the ball screw pair using a ball screw pair friction torque test bench;

[0010] Step 2: Perform hierarchical clustering on the friction torque time series, and remove friction torque time series that do not meet the preset conditions;

[0011] Step 3: Calculate the mutual information between each pair of friction torque time series to form a mutual information symmetric matrix. Based on the descending order of the mutual information, extract the first N friction torque time series as typical series.

[0012] Step 4: Reconstruct the phase space of typical sequences using mutual information and correlation dimension to generate a dataset;

[0013] Step 5: Use the dataset to train a long short-term memory network to obtain a ball screw pair friction torque prediction model;

[0014] Step 6: For the ball screw pair to be predicted, use the prediction model in Step 5 to predict the time series of the friction torque of the ball screw pair, thereby obtaining the preload of the ball screw pair.

[0015] Further, step 1 specifically includes: placing the ball screw pair on a ball screw pair friction torque test bench for testing; stopping the test bench and removing the ball screw pair after the test is completed; and measuring the friction torque of the ball screw pair using the ball screw pair friction torque test bench.

[0016] Furthermore, the hierarchical clustering of the friction torque time series described in step 2 is specifically achieved by analyzing the temporal characteristics of the ball screw pair friction torque, including:

[0017] Step 2-1: Treat each friction torque time series as a separate category;

[0018] Step 2-2: Calculate the dynamic time-normalized distance between the clusters and merge the two closest clusters into one cluster; then repeat this step until the preset number of clusters is met to complete the clustering.

[0019] Further, in step 2-2, the dynamic time warping distance is calculated using the fuzzy differential evolution algorithm, and the calculation formula is as follows:

[0020]

[0021] In the formula, dist avg (A, B) represents the average connection distance between class A and class B, |A| and |B| represent the size of class A and class B, respectively, and X... i and X j D represents elements in class A and class B respectively. Fuzz (X i X j ) represents element X i and X j The fuzzy distance between them, and 1≤i, j≤N, i≠j.

[0022] Furthermore, step 2 involves removing friction torque time series that do not meet the preset conditions, specifically including:

[0023] During the clustering process, it is determined whether the minimum dynamic time-normalized distance between each class and other classes exceeds a preset threshold. If so, the class is deleted.

[0024] If a cluster is found to be a separate cluster, that cluster is removed.

[0025] Furthermore, in step 3, the mutual information between the pairwise friction torque time series is calculated. The specific process includes:

[0026] For a certain friction torque time series {x i The system has a control over variable x. i The average information content is the information entropy of the system, and the formula used is:

[0027]

[0028] In the formula, H(X) represents the information entropy of the random variable X, and P... x (x i ) represents the random variable X taking the value x. i The probability of X occurring at a given time, where n represents the number of possible values ​​for the random variable X;

[0029] For two friction torque time series {x i y j}, and its joint entropy H(X,Y) is:

[0030]

[0031] In the formula, H(X, Y) represents the joint entropy of random variables X and Y, and P x，y (x i y j ) represents the random variable (X, Y) taking the value (x, y). i y j The joint probability distribution function of random variables X and Y is given by n and m, respectively, where n and m represent the number of values ​​that random variables X and Y can take.

[0032] Therefore, the friction torque time series {x i y j The mutual information of} is represented as:

[0033] I(X,Y)=H(X)+H(Y)-H(X,Y)

[0034] In the formula, I(X,Y) represents the mutual information of random variables X and Y, H(X) and H(Y) represent the marginal entropy of random variables X and Y respectively, and H(X,Y) represents the joint entropy of random variables X and Y.

[0035] Furthermore, step 4, which involves reconstructing the phase space of a typical sequence using mutual information and correlation dimension, specifically includes:

[0036] Step 4-1, for each friction torque time series x(t) in the typical sequence j )={x(t1),x(t2),...,x(t q Let q be the data length of the friction torque time series. Using the time delay method, construct M = n - (m - 1)τ m-dimensional phase space vectors. Then, the j-th phase space vector X j for:

[0037] Xj =(x(t) j ), x(t) j +τ), ..., x(t) j +(m-1)τ))j=1,2,...,M

[0038] In the formula, x(t) j ) represents time point t j The observed values ​​on the time scale, where τ represents the time delay;

[0039] The reconstructed trajectory is then:

[0040] X = [X1, X2, ..., X] M ] T

[0041] In the formula, X is an M×m dimensional matrix;

[0042] Step 4-2: Use the reconstructed orbits to complete the phase space reconstruction of typical sequences and generate a dataset;

[0043] If the j-th input sample set is:

[0044] A j =x(t) j ), x(t) j +τ), ..., x(t) j +(m-2)τ)

[0045] In the formula, A j This represents the time series of frictional torque at time point t. j And the vector consisting of the observations after a delay of (m-2) times τ;

[0046] The actual output of the j-th corresponding element is:

[0047] B j =x(t) j +(m-1)τ)

[0048] In the formula, B j This represents the time series of frictional torque at time point t. j Observations on +(m-1)τ;

[0049] Construct the input matrix:

[0050]

[0051] Among them, M 入 It is a (k×(m-1)) dimensional matrix, representing the input matrix consisting of k input samples; Let be the i-th input sample set, and let represent the input vector of the i-th sample. This vector is of length (m-1), where the j-th element represents the friction torque time series at time point t. j +(i-1)τ observations, i = 1, 2, ..., k; k also represents the number of typical sequences;

[0052] Construct the output matrix:

[0053]

[0054] In the formula, M 出 This represents the output matrix in delayed embedding; It is the k-th output sample set, representing the k-th sample at time point t. j Observations on +(i-1)τ;

[0055] The input matrix and the output matrix form a dataset.

[0056] Furthermore, the loss function for the Long Short-Term Memory network in step 5 is:

[0057]

[0058] In the formula, n′ is the number of typical sequences, pre i For the predicted value of the i-th typical sequence, test i Let be the true value of the i-th typical sequence.

[0059] Furthermore, in step 5, during the training of the long short-term memory network, the Adam optimizer is used to optimize the loss function Loss.

[0060] Compared with the prior art, the significant advantages of this invention are:

[0061] 1) This invention analyzes the temporal characteristics of the friction torque of the ball screw pair, performs hierarchical clustering on the friction torque sample sequence of a specific screw, eliminates sequences with large differences due to manufacturing or experimental conditions, and completes the preliminary division of similar sequences, which can initially improve the accuracy of the preload prediction of the ball screw pair.

[0062] 2) This invention calculates the mutual information between sample sequences and extracts sequences with high mutual information as typical sequences. It then further seeks structured relationships between sequences. This approach reduces the impact of redundancy, error accumulation, and lack of correlation information between sequences, effectively sharing domain information (degenerate information) and improving the model's information content. Furthermore, this invention extracts preload sequences with representative characteristics as typical sequences and uses them as input to the neural network, improving the model's quality and prediction accuracy.

[0063] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0064] Figure 1 This is a flowchart of the ball screw pair preload prediction method based on typical sequences and deep learning according to the present invention.

[0065] Figure 2 This is a waveform diagram of the friction torque measurement of the ball screw pair test sample of the present invention.

[0066] Figure 3 This is a schematic diagram of hierarchical clustering of the friction torque timing of the present invention.

[0067] Figure 4 This is a heatmap of mutual information between two types of sequences in this invention, wherein... Figure 4 (a) in the figure is a heatmap of mutual information between class A sequences. Figure 4 (c) in the figure is a heatmap of mutual information between B-type sequences.

[0068] Figure 5 This is a typical sequence waveform diagram extracted in this invention.

[0069] Figure 6 The mutual information I(τ) relationship curves of a typical sequence under different time delays τ are obtained by calculating the mutual information method of this invention.

[0070] Figure 7 The graph shows the relationship between lnC(m, r) and lnr for a typical sequence at different embedding dimensions m, as calculated in this invention.

[0071] Figure 8 A schematic diagram of a long short-term memory network prediction model for a typical sequence. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0073] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0074] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0075] In one embodiment, combined Figure 1 This paper provides a method for predicting the preload of ball screw pairs based on typical sequences and deep learning. The method includes the following steps:

[0076] Step 1: Measure the friction torque sample of the ball screw pair using a ball screw pair friction torque test bench;

[0077] Step 2: Perform hierarchical clustering on the friction torque time series, and remove friction torque time series that do not meet the preset conditions;

[0078] Step 3: Calculate the mutual information between each pair of friction torque time series to form a mutual information symmetric matrix. Based on the descending order of the mutual information, extract the first N friction torque time series as typical series.

[0079] Step 4: Reconstruct the phase space of typical sequences using mutual information and correlation dimension to generate a dataset;

[0080] Step 5: Use the dataset to train a long short-term memory network to obtain a ball screw pair friction torque prediction model;

[0081] Step 6: For the ball screw pair to be predicted, use the prediction model from Step 5 to predict the time series of friction torque of the ball screw pair.

[0082] Further, in one embodiment, step 1 specifically includes: placing the ball screw pair on a ball screw pair friction torque test bench for testing, stopping the test bench and removing the ball screw pair after the test is completed, and measuring the friction torque of the ball screw pair using the ball screw pair friction torque test bench.

[0083] Furthermore, in one embodiment, the hierarchical clustering of the friction torque time series in step 2 is specifically achieved by analyzing the temporal characteristics of the ball screw pair friction torque, specifically including:

[0084] Step 2-1: Treat each friction torque time series as a separate category;

[0085] Step 2-2: Calculate the dynamic time-normalized distance between the clusters and merge the two closest clusters into one cluster; then repeat this step until the preset number of clusters is met to complete the clustering.

[0086] Furthermore, in one embodiment, in step 2-2, the dynamic time warping distance is calculated using a fuzzy differential evolution algorithm, and the calculation formula is as follows:

[0087]

[0088] In the formula, dist avg (A, B) represents the average connection distance between class A and class B, |A| and |B| represent the size of class A and class B, respectively, and X... i and X j D represents elements in class A and class B respectively. Fuzz (X i X j ) represents element X i and X j The fuzzy distance between them, and 1≤i, j≤N, i≠j.

[0089] Furthermore, in one embodiment, step 2, which involves eliminating friction torque time series that do not meet the preset conditions, specifically includes:

[0090] During the clustering process, it is determined whether the minimum dynamic time-normalized distance between each class and other classes exceeds a preset threshold. If so, the class is deleted.

[0091] If a cluster is found to be a separate cluster, that cluster is removed.

[0092] Furthermore, in one embodiment, step 3 involves calculating the mutual information between pairwise friction torque time series, specifically including:

[0093] For a certain friction torque time series {x i The system has a control over variable x. i The average information content is the information entropy of the system, and the formula used is:

[0094]

[0095] In the formula, H(X) represents the information entropy of the random variable X, and P... x (x i ) represents the random variable X taking the value x. i The probability of X occurring at a given time, where n represents the number of possible values ​​for the random variable X;

[0096] For two friction torque time series {x i y j}, and its joint entropy H(X,Y) is:

[0097]

[0098] In the formula, H(X, Y) represents the joint entropy of random variables X and Y, and P x，y (x i y j ) represents the random variable (X, Y) taking the value (x, y). i y j The joint probability distribution function of random variables X and Y is given by n and m, respectively, where n and m represent the number of values ​​that random variables X and Y can take.

[0099] Therefore, the friction torque time series {x i y j The mutual information of} is represented as:

[0100] I(X,Y)=H(X)+H(Y)-H(X,Y)

[0101] In the formula, I(X,Y) represents the mutual information of random variables X and Y, H(X) and H(Y) represent the marginal entropy of random variables X and Y respectively, and H(X,Y) represents the joint entropy of random variables X and Y.

[0102] Furthermore, in one embodiment, step 4, which involves reconstructing the phase space of a typical sequence using mutual information and correlation dimension, specifically includes:

[0103] Step 4-1, for each friction torque time series x(t) in the typical sequence j )={x(t1),x(t2),...,x(t q Let q be the data length of the friction torque time series. Using the time delay method, construct M = n - (m - 1)τ m-dimensional phase space vectors. Then, the j-th phase space vector X j for:

[0104] X j =(x(t) j ), x(t) j +τ), ..., x(t) j +(m-1)τ))j=1,2,...,M

[0105] In the formula, x(t) j ) represents time point t j The observed values ​​on the time scale, where τ represents the time delay;

[0106] The reconstructed trajectory is then:

[0107] X = [X1, X2, ..., X] M ] T

[0108] In the formula, X is an M×m dimensional matrix;

[0109] Step 4-2: Use the reconstructed orbits to complete the phase space reconstruction of typical sequences and generate a dataset;

[0110] If the j-th input sample set is:

[0111] A j =x(t) j ), x(t) j +τ), ..., x(t) j +(m-2)τ)

[0112] In the formula, A j This represents the time series of frictional torque at time point t. j And the vector consisting of the observations after a delay of (m-2) times τ;

[0113] The actual output of the j-th corresponding element is:

[0114] B j =x(t) j +(m-1)τ)

[0115] In the formula, B j This represents the time series of frictional torque at time point t. j Observations on +(m-1)τ;

[0116] Construct the input matrix:

[0117]

[0118] Among them, M 入 It is a (k×(m-1)) dimensional matrix, representing the input matrix consisting of k input samples; Let be the i-th input sample set, and let represent the input vector of the i-th sample. This vector is of length (m-1), where the j-th element represents the friction torque time series at time point t. j +(i-1)τ observations, i = 1, 2, ..., k; k also represents the number of typical sequences;

[0119] Construct the output matrix:

[0120]

[0121] In the formula, M 出 This represents the output matrix in delayed embedding; It is the k-th output sample set, representing the k-th sample at time point t. j Observations on +(i-1)τ;

[0122] The input matrix and the output matrix form a dataset.

[0123] Furthermore, in one embodiment, the loss function of the Long Short-Term Memory network in step 5 is:

[0124]

[0125] In the formula, n′ is the number of typical sequences, pre i For the predicted value of the i-th typical sequence, test i Let be the true value of the i-th typical sequence.

[0126] Furthermore, in one embodiment, during the training of the long short-term memory network in step 5, the Adam optimizer is used to optimize the loss function Loss.

[0127] In one embodiment, a ball screw pair preload prediction system based on typical sequences and deep learning is provided, the system comprising:

[0128] The first module is used to measure the friction torque sample of the ball screw pair using a ball screw pair friction torque test bench;

[0129] The second module is used to perform hierarchical clustering on the friction torque time series, while removing friction torque sample sequences that do not meet the preset conditions.

[0130] The third module is used to calculate the mutual information between each pair of friction torque time series, form a mutual information symmetric matrix, and extract the first N friction torque time series as typical series according to the descending order of mutual information.

[0131] The fourth module is used to reconstruct the phase space of typical sequences using mutual information and correlation dimension, and generate a dataset.

[0132] The fifth module is used to train a long short-term memory network using the dataset to obtain a ball screw pair friction torque prediction model.

[0133] The sixth module is used to predict the time series of the friction torque of the ball screw pair using the ball screw pair friction torque prediction model.

[0134] Specific limitations regarding the ball screw pair preload prediction system based on typical sequences and deep learning can be found in the limitations of the ball screw pair preload prediction method based on typical sequences and deep learning mentioned above, and will not be repeated here. Each module in the aforementioned ball screw pair preload prediction system based on typical sequences and deep learning can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0135] As a specific example, the invention will be further described and verified in detail in one embodiment.

[0136] In this embodiment, the ball screw pair friction torque test bench mainly consists of a servo motor, a triangular chuck, a worktable, a force sensor, and a tailstock. The ball screw pair to be tested is fixed to the machine bed using the triangular chuck and tailstock; the measurement stroke is set to 70% of the length of the ball screw pair, and the test speed is set to 40 r / min; during data processing, the forward and reverse strokes are measured three times each, and the average value is taken as the friction torque of the ball screw pair to be tested.

[0137] We selected GD4010 model lead screw pairs produced by a well-known domestic lead screw manufacturer and conducted a comprehensive performance evaluation experiment on 14 randomly selected lead screws of this model, and collected the temporal changes of friction torque during the process.

[0138] Based on the collected friction torque measurement data of 14 lead screws of model GD4010, and for quantitative comparison, root mean square error and mean absolute error are introduced to measure the prediction results. The corresponding expressions are as follows:

[0139]

[0140]

[0141] The existing friction torque sequences of the 14 lead screws are numbered from 0 to 13. After preprocessing, the timing sequence of torques 0-5 is as follows: Figure 2 As shown.

[0142] Observing the six sequences reveals that sequence number 2 differs significantly in geometric shape from the others. Drawing a dashed line at the point where the frictional torque is 0 as a reference line further confirms that sequence number 2 also differs greatly from the others in both numerical value and its variation. The other five sequences show little difference in geometric shape and numerical magnitude.

[0143] Hierarchical clustering was performed on the 14 sequences for further analysis: Each known friction torque time series was considered as a single class. The dynamic time warping distance (DTW) between sequences was calculated using the DTW distance, and the similarity of the time series shapes was measured by matching mappings. Based on the calculated DTW distance, the two closest classes were merged into one class. The average-linkage was used to measure the distance between classes A and B. This process was repeated until a pre-defined number of clusters was met, completing the clustering process. The results are as follows: Figure 3 As shown. The formula used is:

[0144]

[0145] In the formula, dist avg (A, B) represents the average connection distance between class A and class B, |A| and |B| represent the size of class A and class B, respectively, and X... i and X j D represents elements in class A and class B respectively. Fuzz (X i X j ) represents element X i and X j The fuzzy distance between them, and 1≤i, j≤N, i≠j.

[0146] from Figure 3 It can be observed that sequence number 2 forms a separate cluster and is therefore considered an outlier and removed. Sequences 1, 3, 4, 6, 7, and 8 cluster together and are defined as cluster A. Sequences 0, 5, 9, 10, 11, 12, and 13 cluster together and are defined as cluster B. Since the other sequences besides sequence number 2 still exhibit significant similarity, it is impossible to accurately extract typical sequences. Therefore, the mutual information between sequences in clusters A and B is calculated.

[0147] The measure of the information capacity of an event will depend on the probability distribution p(x), and entropy is defined as follows: If X is a random variable, its probability distribution is:

[0148] p(x) = P(X = x) x∈X

[0149] The entropy H(X) of X is:

[0150]

[0151] For the time series {x i}, define P x (x i ) represents the variable x i The probability of occurrence, then the system's response to variable x i The average information content is the information entropy of the system, and the formula used is:

[0152]

[0153] For two sets of time series {x i y i If we denote P x，y (x i y j ) is the variable x i y j If the joint probability distribution is such that the joint entropy H(X, Y) is:

[0154]

[0155] Therefore, the time series {x} i y i Mutual information I(x) i y j This can be represented as:

[0156] I(X,Y)=H(X)+H(Y)-H(X,Y)

[0157] After clustering, the mutual information between each pair of sequences is calculated to form a symmetric mutual information matrix. Based on the mutual information matrix, sequences with high mutual information are selected to form typical sequences. The mutual information between sequences of classes A and B is as follows: Figure 4 As shown.

[0158] By comparing the heatmaps of mutual information between the two types of sequences, it can be found that sequences 6, 7, and 8 from type A can be extracted to form typical sequences, with an average mutual information of 0.0837 nat. Sequences 5, 10, and 12 from type B can be extracted to form typical sequences, with an average mutual information of 0.0753 nat. Therefore, sequences 6, 7, and 8 were ultimately selected as the typical sequences, as shown below. Figure 5 As shown.

[0159] The Wolf method was used to calculate the maximum Lyapunov exponent of the time series for chaos detection, proving that it possesses a chaotic factor. The phase space of the time series was then reconstructed using mutual information and correlation dimension. Through phase space reconstruction of typical time series, training and prediction sets for the Long Short-Term Memory (LSTM) network were constructed. Training and prediction based on the LTM network were then performed separately on typical sequences 6, 7, and 8.

[0160] For each friction torque time series x(t) in the typical sequence j )={x(t1),x(t2),...,x(t q Let q be the data length of the friction torque time series. Using the time delay method, construct M = n - (m - 1)τ m-dimensional phase space vectors. Then, the j-th phase space vector X j for:

[0161] X j=(x(t) j ), x(t) j +τ), ..., x(t) j +(m-1)τ))j=1,2,...,M

[0162] In the formula, x(t) j ) represents time point t j The observed values ​​on the time scale, where τ represents the time delay;

[0163] The reconstructed trajectory is then:

[0164] X = [X1, X2, ..., X] M ] T

[0165] In the formula, X is an M×m dimensional matrix.

[0166] For a single sequence, to effectively utilize its chaotic properties, the input and output of the Long Short-Term Memory network of the original sequence can be constructed by reconstructing the trajectory. If the input sample set is:

[0167] A j =x(t) j ), x(t) j +τ), ..., x(t) j +(m-2)τ)

[0168] Corresponding output sample set B j for:

[0169] B j =x(t) j +(m-1)τ)

[0170] The mutual information method is used to determine the time delay τ for phase space reconstruction, and the optimal embedding dimension m is identified by the correlation dimension to obtain more accurate experimental results. Specifically, the mutual information method calculates the mutual information I(τ) for typical sequences under different time delays τ, and the curves are shown below. Figure 6 As shown.

[0171] The time corresponding to the first minimum point of the curve is the delay time τ, i.e., τ = 2.

[0172] The correlation dimension is used to determine the phase space reconstruction. A correlation integral table is introduced to prove the probability that the distance between any two phase points in the phase space is less than the neighborhood radius, thus characterizing the degree of phase point clustering. The correlation integral is defined as follows:

[0173]

[0174] In the formula: r is the neighborhood radius, M = N - (m -)τ is the number of phase points in the phase space (N is the total length of the time series). The relationship between lnC(m, r) and lnr is calculated for typical sequences at different embedding dimensions m, as follows: Figure 7 As shown in the figure, the slope of the linear portion of the curve represents the correlation value D(m) when the system embedding dimension is m. When it tends to stabilize, it is the saturated correlation dimension, and at this point, m is the optimal embedding dimension. Therefore, the optimal embedding dimension is finally determined to be m = 12.

[0175] Based on the time delay τ and the embedding dimension m, combined with the dataset construction method, the training set and prediction set of typical sequences can be constructed.

[0176] Each sequence has 900 samples in the training set and 60 samples in the test set. The root mean square error and mean absolute error are calculated. The training dataset for a Long Short-Term Memory (LSTM) recurrent neural network includes three steps:

[0177] S601: Calculate the output value of the model according to the forward calculation formula;

[0178] S602: Calculate the model error based on the defined loss function;

[0179] S603: Repeat step S602 until the model accuracy meets the preset conditions.

[0180] Input and output are accomplished by establishing an input-output matrix. The input matrix is ​​as follows:

[0181]

[0182] In the formula, k represents each number in the typical sequence.

[0183] The output matrix is:

[0184]

[0185] Predictive models such as Figure 8 As shown.

[0186] By ensuring that each sequence's input passes through the same processing kernel, they collectively filter information and optimize weight coefficients, thereby improving the prediction model. The optimization objective of the Long Short-Term Memory (LSTM) network is:

[0187]

[0188] Among them, pre i For the predicted value, test iThe data is set to the true values, and the Adam optimizer is used to optimize the loss. By choosing batch gradient descent and setting a reasonable batch size, training efficiency can be improved without reducing training accuracy. After data normalization, an appropriate batch size is set to divide the training samples, and model training begins. The results are shown in Table 1.

[0189] Table 1 Training Results

[0190]

[0191] In the experiment, since the number of hidden layer nodes in the Long Short-Term Memory network has a significant impact on both training and prediction results, and the setting of the number of hidden layer nodes is related to the input and output dimensions of the network, a large number of experiments were conducted based on the principle that the number of nodes should be between 5 and 32 times the input dimension. The network was constructed by selecting the number of nodes with the highest accuracy to complete the experiment.

[0192] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0193] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the preload of a ball screw pair based on typical sequences and deep learning, characterized in that, The method includes the following steps: Step 1: Measure the friction torque sample of the ball screw pair using a ball screw pair friction torque test bench; Step 2: Perform hierarchical clustering on the friction torque time series, and remove friction torque time series that do not meet the preset conditions; Step 3: Calculate the mutual information between each pair of friction torque time series to form a mutual information symmetric matrix. Based on the descending order of the mutual information, extract the first N friction torque time series as typical series. Step 4: Reconstruct the phase space of typical sequences using mutual information and correlation dimension to generate a dataset; Step 5: Use the dataset to train a long short-term memory network to obtain a ball screw pair friction torque prediction model; Step 6: For the ball screw pair to be predicted, use the prediction model in step 5 to predict the time series of friction torque of the ball screw pair, thereby obtaining the preload of the ball screw pair. Step 3 involves calculating the mutual information between pairwise friction torque time series. The specific process includes: For a certain friction torque time series The system has variables The average information content is the information entropy of the system, and the formula used is: In the formula, H(X) represents the information entropy of the random variable X. This represents the range of values ​​of the random variable X. The probability of X occurring at a given time, where n represents the number of possible values ​​for the random variable X; For two friction torque time series Its joint entropy for: In the formula, H(X,Y) represents the joint entropy of random variables X and Y. This represents the random variable (X,Y) taking values... The joint probability distribution function of X and Y, where n and m represent the number of values ​​that random variables X and Y can take, respectively; Therefore, the time series of friction torque The mutual information is represented as: In the formula, I(X,Y) represents the mutual information of random variables X and Y, H(X) and H(Y) represent the marginal entropy of random variables X and Y respectively, and H(X,Y) represents the joint entropy of random variables X and Y.

2. The method for predicting preload of ball screw pairs based on typical sequences and deep learning according to claim 1, characterized in that, Step 1 specifically includes: placing the ball screw pair on the ball screw pair friction torque test bench for testing, stopping the test bench and removing the ball screw pair after the test is completed, and measuring the friction torque of the ball screw pair using the ball screw pair friction torque test bench.

3. The method for predicting preload of ball screw pairs based on typical sequences and deep learning according to claim 1, characterized in that, Step 2, which involves hierarchical clustering of the friction torque time series, is specifically achieved by analyzing the temporal characteristics of the ball screw pair friction torque. This includes: Step 2-1: Treat each friction torque time series as a separate category; Step 2-2: Calculate the dynamic time-normalized distance between the clusters and merge the two closest clusters into one cluster; then repeat this step until the preset number of clusters is met to complete the clustering.

4. The method for predicting preload of ball screw pairs based on typical sequences and deep learning according to claim 3, characterized in that, In step 2-2, the dynamic time warping distance is calculated using the fuzzy differential evolution algorithm. The calculation formula is as follows: In the formula, This represents the average connection distance between class A and class B. and They represent the sizes of class A and class B, respectively. These represent elements from class A and class B, respectively. Represents element The fuzzy distance between them, and i,j N, i≠j.

5. The method for predicting preload of ball screw pairs based on typical sequences and deep learning according to claim 3, characterized in that, Step 2 involves removing friction torque time series that do not meet the preset conditions, specifically including: During the clustering process, it is determined whether the minimum dynamic time-normalized distance between each class and other classes exceeds a preset threshold. If so, the class is deleted. If a cluster is found to be a separate cluster, that cluster is removed.

6. The method for predicting preload of ball screw pairs based on typical sequences and deep learning according to claim 1, characterized in that, Step 4 describes the reconstruction of the phase space of a typical sequence using mutual information and correlation dimension, specifically including: Step 4-1, for each friction torque time series in the typical sequence q is the data length of the friction torque time series, constructed using the time delay method. If there are m-dimensional phase space vectors, then the j-th phase space vector... for: In the formula, Indicates a point in time The observed values ​​on the time scale, where τ represents the time delay; The reconstructed trajectory is then: In the formula, for 3D matrix; Step 4-2: Use the reconstructed orbits to complete the phase space reconstruction of typical sequences and generate a dataset; If the j-th input sample set is: In the formula, This represents the time series of frictional torque at time point And the vector consisting of the observations after a delay of (m-2) times τ; The actual output of the j-th corresponding element is: In the formula, This represents the time series of frictional torque at time point Observations on; Construct the input matrix: in, It is a (k×(m-1)) dimensional matrix, representing the input matrix consisting of k input samples; Let be the i-th input sample set, and let represent the input vector of the i-th sample. This vector is of length (m-1), where the j-th element represents the friction torque time series at time point . The observed values, i=1,2,...,k; k also represents the number of typical sequences; Construct the output matrix: In the formula, This represents the output matrix in delayed embedding; It is the k-th output sample set, representing the k-th sample at time point. Observations on; The input matrix and the output matrix form a dataset.

7. The method for predicting preload of ball screw pairs based on typical sequences and deep learning according to claim 6, characterized in that, The loss function for the Long Short-Term Memory network in step 5 is: In the formula, The number of typical sequences. Let be the predicted value of the i-th typical sequence. Let be the true value of the i-th typical sequence.

8. The method for predicting preload of ball screw pairs based on typical sequences and deep learning according to claim 7, characterized in that, In step 5, during the training of the Long Short-Term Memory network, the Adam optimizer is used to optimize the loss function Loss.

9. A ball screw pair preload prediction system based on typical sequences and deep learning, based on the method of any one of claims 1 to 8, characterized in that, The system includes: The first module is used to measure the friction torque sample of the ball screw pair using a ball screw pair friction torque test bench; The second module is used to perform hierarchical clustering on the friction torque time series, while removing friction torque sample sequences that do not meet the preset conditions. The third module is used to calculate the mutual information between each pair of friction torque time series, form a mutual information symmetric matrix, and extract the first N friction torque time series as typical series based on the descending order of mutual information. The fourth module is used to reconstruct the phase space of typical sequences using mutual information and correlation dimension, and generate a dataset. The fifth module is used to train a long short-term memory network using the dataset to obtain a ball screw pair friction torque prediction model. The sixth module is used to predict the time series of the friction torque of the ball screw pair using the ball screw pair friction torque prediction model, thereby obtaining the preload of the ball screw pair.

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