A long short-term memory neural network-based degradation prediction method for close nut

Abstract

The application aims at the problem of long time consumption and high cost of locking performance test of closing nut for aircraft structure assembly connection, and provides a closing nut degradation prediction method based on long and short time memory neural network, first, the early degradation data of the locking torque of the closing nut is obtained by carrying out the locking performance test of the closing nut; second, based on the locking performance degradation mechanism of the closing nut, a double variable correlation model of the locking torque of the closing nut is established; then, a long and short time memory neural network model with double variable input is established; finally, the early test data of the locking torque is learned by using the established neural network model, and the locking performance degradation trend of the closing nut in the future test time is predicted. Combined with engineering practice, the model is simple to build, the end-to-end model structure is easy to optimize and train, expert experience is not needed, and the method is scientific and normative.

Description

Technical Field

[0001] This invention proposes a method for predicting the locking performance of a constricting nut, specifically a method based on the tightening torque of the screw-in and tightening torques. This method automatically learns the patterns in early locking performance test data to quickly and accurately predict the future degradation trend of the locking performance of the constricting nut, effectively shortening the locking performance test time and product delivery cycle. It involves a degradation prediction model based on a long short-term memory neural network using bivariate locking torque input, and is applicable to the field of constricting nut processing and manufacturing technology. Background Technology

[0002] In the assembly process of modern aircraft, bolts and nut fasteners are widely used as a connection method. They are the basic components for assembling aircraft structural parts. However, once the locking performance of the nut fastener deteriorates, it will lose its ability to fit bolts with thread deviations. The critical connection parts of the aircraft body will also be unable to withstand repeated impacts and vibrations, directly threatening the safety of the aircraft body. Therefore, the locking performance of the nut fastener is of paramount importance.

[0003] The fit between a tightening nut and a threaded bolt primarily relies on the frictional torque generated between the tightening nut's structural plastic deformation and the threaded pair, thus creating the locking torque. This connection structure facilitates repeated disassembly and reassembly; however, the locking torque of the tightening nut typically degrades and decays gradually during repeated use. Especially under harsh conditions involving prolonged vibration, impact, load variations, and significant temperature fluctuations in aircraft, the locking torque of the tightening nut exhibits a substantial decrease, potentially leading to inherent safety hazards and even flight accidents. Therefore, accurately predicting the degradation trend of the tightening torque of tightening nuts is of significant engineering and practical importance. However, the degradation mechanism of tightening nuts is complex, exhibiting a rapid early degradation rate followed by a slower rate in the later stages. Specifically, with increasing screwing-in and unscrewing cycles, the surface coating of the tightening nut suffers early damage, increasing surface roughness and the coefficient of friction, resulting in a larger locking torque. However, with repeated screwing-in and unscrewing, the surface coating gradually wears down, reducing surface roughness and the coefficient of friction, thus decreasing the locking torque. Furthermore, under the influence of multiple factors such as the closing method, closing amount, and locking section wall thickness, the degradation decay pattern and degradation decay magnitude of different closing nuts also show significant differences.

[0004] In actual manufacturing processes, the locking performance of a nut is typically described by its tightening torque. The tightening torque is obtained through testing and compared with a standard value to determine the nut's degradation state. However, this test requires continuous, uninterrupted testing and repeated measurements of the tightening and loosening torques to accurately determine its degradation status. This time-consuming and labor-intensive testing significantly impacts production schedules and delivery times. Considering that both the tightening and loosening torques jointly characterize the degradation state of the nut, this patent proposes a method for predicting the degradation of nut locking performance based on a bivariate input long short-term memory neural network. Through bivariate correlation analysis, the trend relationship between the tightening and loosening torques is clarified. The bivariate input long short-term memory neural network is used to uncover the commonalities between the two torques. With only a small amount of early test data, it can automatically learn and accurately predict the degradation trend of the nut in the future. This patent can effectively shorten the testing time for the locking performance of the closing nut, reduce the reliance on expert knowledge for the analysis of test results, and quickly and accurately predict the degradation trend of the locking performance of the closing nut. Summary of the Invention

[0005] (1) Objective of this invention: This invention addresses the problem of excessively long testing time and high cost in testing the locking performance of locking nuts used in the assembly and connection of aircraft structural components. It provides a method for predicting the locking performance of locking nuts based on a bivariate input long short-term memory neural network. First, it obtains early degradation data of the tightening torque (both screwing in and screwing out) by conducting locking performance tests on locking nuts. Second, based on the mechanism of locking performance degradation, a bivariate correlation model of the tightening torque (both screwing in and screwing out) is established. Then, a bivariate input long short-term memory neural network model is established. Finally, the established neural network model is used to learn the early test data of the tightening torque (both screwing in and screwing out) to predict the future trend of locking performance degradation over the testing period.

[0006] (2) Technical Solution: Based on the above methods and ideas, this invention provides a method for predicting the degradation of locking performance of a closing nut based on a bivariate long short-term memory neural network. The specific implementation steps are as follows:

[0007] Step 1: Obtain test data on the degradation of the locking performance of the closing nut.

[0008] First, prepare a threaded mandrel and a closing nut in good condition. Tighten the threaded mandrel and closing nut together and measure the tightening torque during the tightening and rotation process. Compare this torque with the standard value to confirm that the tightening torque does not exceed the maximum value specified in the standard. Then, using the same threaded mandrel and the same closing nut, perform a cyclic tightening and loosening test, measuring and recording the tightening torque during each cycle. For each closing nut, assuming measurement and recording at each time point t in chronological order, and a test duration of N (i.e., a total of N measurements), a time-series data set of tightening torque is obtained. The measured tightening torque X is recorded. in for

[0009]

[0010] Similarly, record the tightening torque X. ot for

[0011]

[0012] After the test is completed, the degradation state of the nut is marked according to the standard values. If the measured tightening torque does not exceed the maximum value specified in the standard, and the measured loosening torque is not lower than the minimum value specified in the standard, the nut is deemed qualified; otherwise, it is deemed unqualified.

[0013] Step 2: Correlation analysis of the degradation trend of tightening torque during screwing in and screwing out

[0014] First, calculate the correlation between the tightening and loosening torques. The correlation between two variables of the same individual is commonly measured by the Pearson correlation coefficient. Let ρ be the overall Pearson correlation coefficient between the two variables. Then, the tightening torque X... in and tightening torque X ot The correlation between them can be expressed as

[0015]

[0016] Where cov(·) is X in and X ot covariance, σ in and σ ot For X in and X ot Standard deviation, μ in and μ ot For X in and X ot The mean.

[0017] Furthermore, by calculating the estimated values ​​of the sample covariance and standard deviation using the torque data obtained from the tightening performance test of the locking nut, the sample Pearson correlation coefficient r can be obtained, specifically expressed as...

[0018]

[0019] in, and These are the sample average values ​​of the tightening torque for screwing in and screwing out, respectively.

[0020] Secondly, hypothesis testing of the correlation coefficient is performed. As a calculated statistic, the correlation coefficient also has sampling error; therefore, the estimated value of r cannot be used alone to judge the relationship between two variables X. in and X ot The correlation between the two variables is unknown. Even if r≠0, there may be a case where ρ=0, in which case there is no linear correlation between the two variables. Therefore, the following hypothesis test is constructed:

[0021] Null hypothesis H0: ρ = 0, that is, the two variables X in and X ot There is no significant linear correlation between them;

[0022] Alternative hypothesis H1: ρ ≠ 0, that is, the two variables X in and X ot There is a significant linear correlation between them.

[0023] For hypothesis testing of the correlation coefficient, the following statistic T can be constructed, expressed as follows:

[0024]

[0025] in, α is the standard deviation of the correlation coefficient. This statistic follows a student distribution with N-1 degrees of freedom. Given a significance level α, the T-value is calculated using formula (5), and the P-value can be obtained from a table. Compare the P-value with the given significance level α. If the value is less than α, the null hypothesis H0 is rejected, and the alternative hypothesis H1 is accepted, meaning that there is a significant linear correlation between the two variables. If the value is greater than α, the null hypothesis H0 is accepted, and the alternative hypothesis H1 is rejected, meaning that there is no linear correlation between the two variables.

[0026] Step 3: Establish a bivariate input Long Short-Term Memory Neural Network Model

[0027] Long Short-Term Memory (LSTM) neural networks excel at handling prediction tasks involving temporal information. The model structure of an LTM neural network typically consists of one or more LTM modules, each containing multiple gating structures to control the cell state and regulate the flow of temporal information at different times. Specifically, a complete LTM module contains three sequentially related gating structures: a forget gate, an input gate, and an output gate. To construct an LTM neural network, it is necessary to first define the three gating structures and clarify the current cell state. The construction of the LTM neural network model is as follows:

[0028] First, define the prediction task and input data. For time-series locking torque data, set the sliding window of the time series to τ, that is, divide the locking torque data with a test duration of N into bivariate data samples X with a duration of τ and an interval of 1. i , represented as

[0029]

[0030] Where 1≤t≤N, t represents the start time of the torque data, and t+τ represents the end time of the torque data. Therefore, data with a test duration of N can be divided into N-τ data samples, which are then used to construct the training dataset D={X1,X2,…,X… N-τ For the prediction task, the time step is set to 1, meaning the Long Short-Term Memory (LSTM) neural network model only predicts the tightening torque value at the next moment. Therefore, each data sample X... t This corresponds to a real data label Y of length τ. t Since the prediction task is to accurately predict the value of the tightening torque, then Y t Represented as

[0031]

[0032] Given an X t The Long Short-Term Memory (LSTM) neural network model will provide a value close to Y. t Predicted value

[0033] Next, we construct the gating structure for the forget gate, input gate, and output gate. The forget gate is used to selectively discard feature information from the previous time step, and its output is f. t The formula is expressed as follows:

[0034] f t =σ(z) f，t )=σ(W f ·x t +U f ·h t-1 +bf (6)

[0035] in, Given the bivariate input data at time t, h t-1 Let W be the hidden layer state at time t-1. f and U f All are learning parameters for the forget gate, b f Let z be the bias term, · be the matrix product, and σ be the sigmoid nonlinear activation function that maps the output of the forget gate to the range [0, 1]. For ease of notation, let z be defined as... f，t =W f ·x t +U f ·h t-1 +b f , representing the input characteristics of the nonlinear activation function σ.

[0036] For input gate i t In essence, it is used to control the input information at the current moment, determining x. t and h t-1 The input information is required. Similar to the forget gate structure, the output i of the input gate... t It can be represented as

[0037] i t =σ(z) i，t )=σ(W i ·X t +U i ·h t-1 +b i (7)

[0038] W i and U i All of these are the learning parameters of the input gate, b i For the bias term, z i，t =W i ·X t +U i ·h t-1 +b i , representing the input characteristics of the nonlinear activation function σ, and the output range of the output gate is also between [0, 1]. The output gate is used to determine X. t and h t-1 The information that needs to be output is the output of the output gate. t It can be represented as

[0039] o t =σ(z) o，t )=σ(W o ·x t +U o ·h t-1+b o (8)

[0040] W o and U o All of these are the learning parameters for the output gate, b o For the bias term, z o，t =W o ·x t +U o ·h t-1 +b o , representing the input characteristics of the nonlinear activation function σ.

[0041] Secondly, the current cell state and predicted output value can be defined using three gating structures. t and h t-1 Some information will be retained to define the cell's immediate state at the current time t. It can be represented as

[0042]

[0043] Among them, W c and U c All are learning parameters, b c is the bias term. tanh is a non-linear activation function that modulates the instantaneous state value between [-1, 1]. This non-linear activation function can effectively prevent gradient explosion and gradient vanishing. Furthermore, due to the combined effect of the forget gate and the input gate, the Long Short-Term Memory (LSTM) neural network model can selectively retain the cell state c at time t-1. t-1 and real-time cell state The current cell state c at time t t Ultimately, it can be represented as

[0044]

[0045] Among them, f t and i t Let be the output of the forget gate and the input gate, and ⊙ be the element-wise product. Due to the modulating effect of the output gate, the hidden layer output at time t can be expressed as:

[0046] h t =o t ⊙tanh(c t (11)

[0047] Among them, o t This is the output of the output gate. Thus, the structural definition of a Long Short-Term Memory (LSTM) module is complete. Finally, through an output layer, the model's prediction at time t can be expressed as...

[0048]

[0049] Where V and b are both learned parameters of the output layer, z t =h t ·V+b represents the input features of the nonlinear activation function σ. These are the predicted values ​​from the Long Short-Term Memory (LSTM) neural network model. This completes the definition of the LSM neural network model.

[0050] Step 4: Training and optimization of the Long Short-Term Memory Neural Network Model and prediction of locking performance degradation.

[0051] Training and optimizing a Long Short-Term Memory (LSTM) neural network model involves constructing the objective function and updating the weights. First, the objective function for the prediction task is constructed. Assuming... Let X be the objective function of the Long Short-Term Memory (LSTM) neural network model. In the prediction task, the root mean square (RMS) function is used as the objective function. For a bivariate data sample X... i In other words, at any time t within its sliding window τ loss function The formula is expressed as

[0052]

[0053] Then, backpropagation is used to calculate the model's error at unknown learning parameters. Assuming we are currently at time t, and the Long Short-Term Memory (LSTM) module is located at layer l of the model, the backpropagation error at this module mainly comes from two parts: one part is the error backpropagated from layer l at time t+1. The other part is the error back propagated from the (l+1)th layer at time t. When the activation function of the output layer is the Softmax function, according to the chain rule of derivative calculation, at time t, It can be represented as

[0054]

[0055] Where V represents the learning parameters of the output layer. t and These are all relevant features of the l-th hidden layer in the Long Short-Term Memory neural network model, z t These are the input features of the Softmax function, while This represents the output characteristic of the Softmax function. During the derivative calculation, For the objective function For z t The first derivative, For z t for The first derivative. If time t is the last time point of the observed time series, then At time t, the hidden layer output h in the Long Short-Term Memory neural network model t The total error at is

[0056]

[0057] in, loss function For h t The first derivative.

[0058] Next, the input error of each gating structure can be calculated, as follows:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] Therefore, at time t, the learning parameters {W} of the Long Short-Term Memory Neural Network Model o，t U o，t b o，t The error of} is

[0065]

[0066]

[0067]

[0068] in, This represents the symbol for derivative calculation.

[0069] For a bivariate data sample X i Extending the above equation from any time t to a sliding window τ, the learning parameters {W} of the Long Short-Term Memory Neural Network Model are... o U o b o The total error is defined as the sum of the errors at all times within the sliding window τ, expressed as:

[0070]

[0071]

[0072]

[0073] Similarly, the learning parameters {W} of the Long Short-Term Memory neural network model c U c b c The total error of} is

[0074]

[0075]

[0076]

[0077] The learning parameters {W} of the Long Short-Term Memory Neural Network Model i U i b i The total error of} is

[0078]

[0079]

[0080]

[0081] The learning parameters {W} of the Long Short-Term Memory Neural Network Model f U f b f The total error of} is

[0082]

[0083]

[0084]

[0085] Thus, a bivariate sample X is completed. i The backpropagation error at layer l is calculated. Similarly, the backpropagation error of the Long Short-Term Memory (LSTM) neural network model at time t-1 is calculated. and the backpropagation error of layer l-1 They can be represented as

[0086]

[0087]

[0088] according to and The learning parameters of the Long Short-Term Memory Neural Network model at time t-1 and the backpropagation error of the l-1th layer can be derived.

[0089] Finally, stochastic gradient descent is used to update the learning parameters W of the l-th layer in the Long Short-Term Memory (LSTM) neural network model on the training dataset. To reduce computational overhead, B samples are randomly drawn from the training data D in each iteration, and their mean is used as the mean value. The estimated value is used to update the model weights, and the formula is as follows:

[0090]

[0091] in, This indicates that for a bivariate data sample X i The error of the root mean square loss function, ← represents parameter update, η is the learning rate used to control the update magnitude of W in iterations, and B is the number of samples adopted in batch training. At this point, the learning parameters {W} of the Long Short-Term Memory Neural Network model... c U o b o The update process of} can be represented as

[0092]

[0093]

[0094]

[0095] The learning parameters {W} of the Long Short-Term Memory Neural Network Model c U c b c The update process of} can be represented as

[0096]

[0097]

[0098]

[0099] The learning parameters {W} of the Long Short-Term Memory Neural Network Model i U i b i The update process of} can be represented as

[0100]

[0101]

[0102]

[0103] The learning parameters {W} of the Long Short-Term Memory Neural Network Model f U f b fThe update process of} can be represented as

[0104]

[0105]

[0106]

[0107] Therefore, repeated sampling without repetition is performed. The [·] symbol represents the rounding operation, which continues until all training samples within the training sample have been covered, thus completing one model training cycle.

[0108] Repeating the above steps allows for iterative updates of the unknown parameters in the Long Short-Term Memory (LSTM) neural network, enabling multiple model training iterations. During training, a stopping criterion is typically set, or simply a certain number of iterations is introduced to obtain a trained predictive model, which can then be used for trend prediction on a test set. After training, to verify the model's predictive performance, a univariate input LSTM neural network is used as a comparison method, and its prediction results are obtained on the test set. The percentage decrease in the root mean square error (RMSE) is used as the evaluation metric for predictive performance, expressed as...

[0109]

[0110] in, The value of the root mean square loss function for the proposed bivariate input long short-term memory neural network model is given by [the value of the loss function]. The root mean square loss function of a long short-term memory neural network model with univariate input is a numerical value that intuitively reflects the degree of reduction in the model's prediction error.

[0111] Based on the early test data of the tightening torque of the locking nut, the above steps are used to integrate the bivariate degradation trend correlation of the tightening torque and the locking torque. Using a bivariate input long short-term memory neural network model, accurate prediction of the locking performance of the locking nut in the future is achieved. This prediction method conforms to the general law of the degradation of the locking performance of the locking nut, ensuring the accuracy of the model, and is easy to implement in engineering. It solves the engineering problem of time-consuming and labor-intensive locking performance testing of locking nuts, shortening the testing time of the locking performance of locking nuts and the product delivery cycle.

[0112] (3) Advantages:

[0113] This invention proposes a method for predicting the degradation of locking performance of a closed nut using a bivariate long short-term memory neural network, which has the following advantages:

[0114] ① This invention starts from the decay and degradation mechanism of the locking performance of the closing nut, and constructs a bivariate input long short-term memory neural network model based on the bivariate trend correlation of the tightening torque and tightening torque. It accurately predicts the degradation trend of the locking performance of the closing nut in the future, and solves the production technology problems of long test time for the locking performance of closing nuts, reliance on expert experience for degradation trend analysis, and easy delay in delivery cycle.

[0115] ② The prediction method proposed in this invention is combined with engineering practice, the model is simple to build, adopts an end-to-end model structure, is easy to optimize and train, does not require the intervention of expert experience, is easy for engineering technicians to apply, and the method is standardized and scientific. Attached Figure Description

[0116] Figure 1 This is a flowchart of the method described in this invention.

[0117] Figure 2 This is a schematic diagram of the long short-term memory neural network model constructed by the method described in this invention.

[0118] Figure 3 This is a structural diagram of the content gating unit of a long short-term memory neural network model.

[0119] Figures 4a-4f This is a curve of the tightening torque for screwing in and out of the nut that is deemed a qualified product in this invention. Figure 4a This is the locking torque curve of the qualified closing nut numbered #1.

[0120] Figure 4b This is the locking torque curve of the qualified closing nut numbered #2.

[0121] Figure 4c This is the locking torque curve of the qualified closing nut, number #3.

[0122] Figure 4d This is the tightening torque curve of the qualified closing nut, number #4.

[0123] Figure 4e This is the tightening torque curve of the qualified closing nut, number #5.

[0124] Figure 4f This is the tightening torque curve of the qualified closing nut, number #6.

[0125] Figures 5a-5h This is a torque curve of tightening and loosening for the closing nuts that are deemed defective in this invention. Figure 5a This is the tightening torque curve of the defective closing nut, number #1.

[0126] Figure 5bThis is the tightening torque curve of the defective closing nut, number #2.

[0127] Figure 5c This is the tightening torque curve of the defective closing nut, number #3.

[0128] Figure 5d This is the tightening torque curve of the defective closing nut, number #4.

[0129] Figure 5e This is the tightening torque curve of the defective closing nut, number #5.

[0130] Figure 5f This is the tightening torque curve of the defective closing nut, number #6.

[0131] Figure 5g This is the tightening torque curve of the defective closing nut, number #7.

[0132] Figure 5h This is the tightening torque curve of the defective closing nut, number #8. Detailed Implementation

[0133] This invention discloses a method for predicting the degradation of locking performance of a closing nut based on a bivariate long short-term memory neural network, the flowchart of which is shown below. Figure 1 As shown, the constructed bivariate long short-term memory neural network is as follows: Figure 2 As shown, the Long Short-Term Memory (LSTM) module is as follows: Figure 3 As shown.

[0134] The following section uses the example of predicting the locking performance of a certain type of aircraft's locking nut to provide a detailed explanation of the features of this invention.

[0135] In the locking performance degradation test of the closing nuts, the same test conditions were used to test the locking performance degradation of six different models (0159, 0100, 4174, A286, 0405, and T2105). First, the current locking performance was tested using a threaded mandrel, measuring the tightening torque of the closing nut at that moment. The measured value must not exceed the standard maximum value of 3.4 N / m. Then, using the same threaded mandrel, 1500 cycles of testing were continuously performed on the same closing nut for 24 hours. One cycle was defined as one complete tightening and loosening process. In each cycle, the measured tightening torque must not exceed the standard maximum value, and the measured loosening torque must not be less than the standard minimum value of 0.39 N / m. During the test, if the tightening torque does not exceed the maximum value specified in the standard, and the tightening torque is not lower than the minimum value specified in the standard, the nut is deemed to be qualified; otherwise, it is deemed to be unqualified.

[0136] This invention proposes a method for predicting the locking performance of a closing nut based on a bivariate long short-term memory neural network. The specific execution steps are as follows:

[0137] Step 1: Obtain test data on the degradation of the locking performance of the closing nut.

[0138] The test examined the locking performance degradation of six different types of locking nuts, obtaining a total of 14 sets of test data. This includes degradation test data for 8 sets of qualified locking nuts and 6 sets for 6 sets of unqualified locking nuts. The test data for qualified locking nuts, as shown in the table below, are included in the 14 sets of locking torque test data for tightening and loosening. Figures 4a-4f As shown, where, Figure 4a This is the tightening torque curve of the qualified closing nut, numbered #1. Figure 4b This is the tightening torque curve of the qualified closing nut, number #2. Figure 4c This is the tightening torque curve of the qualified closing nut, number #3. Figure 4d This is the tightening torque curve of the qualified closing nut, number #4. Figure 4e This is the tightening torque curve of the qualified closing nut, number #5. Figure 4f This is the tightening torque curve for the qualified tightening nut, number #6. The test data for the unqualified tightening nut is as follows: Figures 5a-5h As shown, where, Figure 5a This is the tightening torque curve of the defective closing nut, number #1. Figure 5b This is the tightening torque curve of the defective closing nut, number #2. Figure 5cThis is the tightening torque curve of the defective closing nut, number #3. Figure 5d This is the tightening torque curve of the defective closing nut, number #4. Figure 5e This is the tightening torque curve of the defective closing nut, number #5. Figure 5f This is the tightening torque curve of the defective closing nut, number #6. Figure 5g This is the tightening torque curve of the defective closing nut, number #7. Figure 5h This is the tightening torque curve of the defective closing nut, number #8.

[0139] Step 2: Correlation analysis of the degradation trend between screwing in and screwing out locking torques

[0140] First, the correlation coefficient between the tightening and loosening torques was calculated. For any type of nut, the first 70% of the 1500 tightening torque data points measured over 24 consecutive hours were defined as known early degradation data. Therefore, in the degradation prediction task, only the early degradation data were known, and the correlation coefficients for these data were calculated according to the correlation coefficient calculation formula. The specific calculation results for the 14 sets of nut degradation test data are shown in Table 1. From the calculated Pearson correlation coefficients, it can be seen that in all test data, regardless of the specific nut model, the tightening and loosening torques are strongly correlated.

[0141] Table 1. Pearson correlation coefficients for early degradation data of the closing nut.

[0142] Sample number 1 2 3 4 5 6 7 Correlation coefficient 0.9648 0.9885 0.9845 0.9111 0.9077 0.3019 0.8492 sample 8 9 10 11 12 13 14 Correlation coefficient number 0.4642 0.9446 0.9862 0.9060 0.9174 0.9405 0.8004

[0143] Next, a significance test of the correlation coefficient was performed. A significance level α of 0.05 was selected, and the calculated P-values ​​are shown in Table 2. In the results, the P-values ​​for all samples were significantly smaller than the significance level α = 0.05. Therefore, the null hypothesis was rejected, and the alternative hypothesis was accepted, indicating a strong trend correlation between the tightening and loosening torques.

[0144] Table 2. Significance test results for early degradation data of the closing nut.

[0145]

[0146]

[0147] Step 3: Establish a bivariate input Long Short-Term Memory Neural Network Model

[0148] First, the input data for the model is determined. In the prediction model for the degradation of the locking performance of the tightening nut, the bivariate tightening torque (both screw-in and screw-out torques) is used as the input data. The sliding window τ of the input data is 20, meaning that in each iteration of training, 20 consecutive pairs of measured values ​​of the tightening torque (both screw-in and screw-out torques) are used. To predict the measurement value at the next moment. Among them, Indicates the range of variation of a variable.

[0149] Next, a Long Short-Term Memory (LSTM) module is built. This method uses a LSM module, which is built using the PyTorch framework. An LSM module is defined by calling the `nn.LSTM(·)` class in the framework. Furthermore, by specifying the values ​​of the variables contained in the `nn.LSTM(·)` class, the LSM module is instantiated, thus completing the construction of the LSM module in the model. Specifically, for the `nn.LSTM(·)` class, the hidden layer `h` of each gate structure in its forget gate, input gate, and output gate has a dimension of 128, meaning the dimensions of each parameter are... To prevent overfitting, a dropout layer is added after the long short-term memory module. Its function is to randomly ignore 20% of the hidden layer neurons in each batch of iterative training to alleviate overfitting.

[0150] Then, after the Long Short-Term Memory (LSTM) module, a fully connected layer is added as the output layer. Its input is the output value of the LSM module, and its output is the predicted value of the locking torque at the current moment. Similarly, an output layer can be defined by calling the `nn.Linear(·)` class. Given that the output layer has a dimension of 128, instantiating the output layer completes the construction of the output layer in the model. Specifically, the dimensions of each parameter of the output layer are... Thus, the definition and construction of the model are completed.

[0151] Step 4: Model training and optimization, and prediction of locking torque in future time.

[0152] After the model is built, it is necessary to clarify the data input process, the objective function for model training, and the training optimization methods to obtain a well-trained prediction model.

[0153] First, define the training and testing datasets. Taking the locking performance test data of any type of locking nut as an example, regardless of the tightening torque, the first 70% of the locking torque data measured over 24 consecutive hours is defined as early degradation data, used to form the training set and train the model, while the latter 30% is defined as degradation data at future moments, used to form the test set and test the model performance.

[0154] Secondly, the optimization method of the model is clarified. In the prediction task, the root mean square function is used as the loss function to represent the difference between the model's predicted value and the actual value. Stochastic gradient descent is employed to optimize the learning parameters of the gating units in the model. During iterative training, the batch training sample size B is 64, meaning that for each training iteration, two groups of bivariate training samples with a window length of 20 data points are randomly selected. Specifically, during the initial model training, the learning parameters of the gating units are randomly initialized to obtain initial values ​​for the first prediction. Subsequently, the learning rate η during the stochastic gradient descent process is set to 0.001, and the learning parameters of the gating units are continuously updated during each batch of training.

[0155] Then, the termination strategy for optimized training was defined. The model was set to undergo 2000 training iterations on the training set, and an early stopping mechanism was implemented during training. Specifically, after each iteration, the model was immediately tested on the test dataset. If no improvement in prediction performance was achieved on the test dataset for 10 consecutive iterations, the iterative training of the model was immediately stopped; otherwise, iterative training continued until the set number of iterations was reached. The test results of the model are shown in Table 3. It can be seen that the correlation coefficients of the tightening and loosening torque test data are relatively large, indicating a strong correlation in their degradation trends. Compared to the univariate long short-term memory neural network, the bivariate long short-term memory neural network achieved significant performance improvements in all 13 test tasks, and can better predict the degradation trend of the locking performance of the closing nut.

[0156] Table 3 Model Prediction Results

[0157]

[0158] In summary, this invention takes the locking nuts used in the assembly of structural components of a certain type of aircraft as the research object. The proposed bivariate input long short-term memory neural network model accurately and quickly predicts the locking torque of locking nuts of multiple models, achieving the goal of accurately predicting the future locking performance degradation trend of locking nuts and shortening the test time of locking torque. Furthermore, the model is simple and convenient to build and train, adopting an end-to-end model structure that only requires given data as input. The prediction process does not involve the intervention of expert experience, making it easy for engineering technicians to apply.

Claims

1. A method for predicting the degradation of a taper nut based on a long short-term memory neural network, characterized in that, The steps are as follows: Step 1: Obtain test data on the degradation of the locking performance of the closing nut: First, prepare a threaded mandrel and a closing nut in good condition. Tighten the threaded mandrel and the closing nut together and measure the tightening torque during the tightening and rotation process. Compare this tightening torque with the standard value to confirm that the tightening torque does not exceed the maximum value specified in the standard. Then, using the same threaded mandrel and the same closing nut, perform a tightening and loosening cycle test, measuring and recording the tightening torque during each cycle. After the test is completed, the degradation state of the nut is marked according to the standard value. If the measured tightening torque does not exceed the maximum value specified in the standard and the measured tightening torque is not lower than the minimum value specified in the standard, the nut is deemed to be qualified. Otherwise, the nut is deemed to be unqualified. Step 2: Correlation analysis of the degradation trend of tightening torque during screwing in and screwing out: First, calculate the correlation between the tightening and loosening torques; second, perform hypothesis testing on the correlation coefficient. Step 3: Establish a bivariate input long short-term memory neural network model: A complete Long Short-Term Memory (LSTM) module contains three sequentially related gating structures: the forget gate, the input gate, and the output gate. To construct an LSM neural network, it is necessary to first define the three gating structures and clarify the current cell state. First, the prediction task and input data must be defined. Second, the cell state and predicted output value at the current moment are defined using the three gating structures. Step 4: Training and optimization of the Long Short-Term Memory Neural Network Model and prediction of locking performance degradation: The training and optimization of a Long Short-Term Memory (LSTM) neural network model includes objective function construction and weight update. First, the objective function for the prediction task is constructed. Then, backpropagation is used to calculate the error values ​​of the model at unknown learning parameters. Next, the input errors of each gating structure are calculated. Finally, stochastic gradient descent is used on the training dataset to optimize the LSM model. Layer learning parameters Update; In step one, for each closing nut, according to the time sequence, at each moment... Measure and record once; the test duration is [duration missing]. That is, a total of N measurements are performed to obtain a set of time series data of the locking torque; among them, the measured screwing-in locking torque is recorded. for: (1) Similarly, record the tightening torque. for: (2) In step two, the correlation between two variables of the same individual is measured using the Pearson correlation coefficient, denoted as the overall Pearson correlation coefficient between the two variables. Then tighten to the locking torque. and tightening torque The correlation between them is expressed as: (3) in, for and covariance, and for and standard deviation and for and The mean; Based on the torque data obtained from the tightening performance test of the locking nut, the estimated values ​​of the sample covariance and standard deviation were calculated, and the sample Pearson correlation coefficient was obtained. Specifically, it is expressed as: (4) in, and These are the sample average values ​​of the tightening torque for screwing in and screwing out, respectively; In step two, the following hypothesis test is constructed: Null hypothesis That is, two variables and There is no significant linear correlation between them; Alternative Hypothesis That is, two variables and There is a significant linear correlation between them; For hypothesis testing of the correlation coefficient, the following statistic is constructed. It is represented as follows: (5) in, The standard deviation of the correlation coefficient; this statistic follows a sequence with degrees of freedom. The student distribution, given a significance level. Calculate using formula (5) Value, obtained by looking up a table. Value; will Values ​​and given significance levels Compare, if its value is less than Then reject the null hypothesis. Accept the alternative hypothesis This means that a significant linear correlation is considered to exist between the two variables; if its value is greater than 1, it indicates a significant linear correlation. Then accept the null hypothesis. Reject the alternative hypothesis This means that there is no linear correlation between the two variables.

2. The method for predicting the degradation of a taper nut based on a long short-term memory neural network according to claim 1, characterized in that: In step three, the Long Short-Term Memory (LSTM) neural network model is constructed as follows: First, define the prediction task and input data; for time-series locking torque data, set the sliding window of the time series to... The duration of the upcoming test is The locking torque data is divided into time periods. Bivariate data samples with an interval of 1 time point , is represented as: (6) in, This is the starting time for the torque data. This represents the last moment of the torque data; therefore, the test duration is... The data was divided into... These data samples are used to construct the training dataset. For the prediction task, the time step is set to 1, meaning the Long Short-Term Memory (LSTM) neural network model only predicts the tightening torque value at the next moment; thus, each data sample Corresponding to a length of Real data labels Because the prediction task is to accurately predict the value of the tightening torque, then Represented as: (6) Given a The Long Short-Term Memory (LSTM) neural network model will provide a close approximation. Predicted value .

3. The method for predicting the degradation of a taper nut based on a long short-term memory neural network according to claim 2, characterized in that: In step three, a gating structure consisting of a forget gate, an input gate, and an output gate is constructed; the forget gate is used to selectively discard feature information from the previous time step, and its output is... The formula is expressed as follows: (6) in, For the present Bivariate input data at time 10:

00. for The hidden state at any given moment. and These are all learning parameters for the forgetting gate. For bias terms, For matrix multiplication, for A non-linear activation function maps the output of the forget gate to... Between; for ease of symbolic representation, defined , representing a nonlinear activation function Input features; For the output of the input gate In other words, the input information used to control the current moment determines... and The input gate requires specific information; similar to the forget gate structure, the output of the input gate... Represented as: (7) and These are all learning parameters for the input gate. For bias terms, , representing a nonlinear activation function The input characteristics also affect the output range of the output gate. Between; while the output gate is used to determine and The information that needs to be output, the output of the output gate Represented as: (8) and These are all learning parameters for the output gate. For bias terms, , representing a nonlinear activation function Input features.

4. The method for predicting the degradation of a taper nut based on a long short-term memory neural network according to claim 3, characterized in that: In step three, the cell state and predicted output value at the current moment are defined using three gating structures; and Some information will be retained to define the cell in the current context. real-time status , is represented as: (9) in, and All are learning parameters. For bias terms; As a nonlinear activation function, it modulates the instantaneous state numerically. In this context, the nonlinear activation function can prevent gradient explosion and gradient vanishing; furthermore, due to the combined regulatory effect of the forget gate and the input gate, the Long Short-Term Memory (LSTM) neural network model selectively retains... Cellular state at any given moment and real-time cell state ,current Cellular state at any given moment The final representation is: (10) in, and The outputs of the forget gate and the input gate, It is an element-wise product; due to the control effect of the output gate, the current... The hidden layer output at time step 1 is represented as: (11) in, This is the output of the output gate; thus, the structural definition of a Long Short-Term Memory (LSTM) module is completed; finally, through an output layer, the model at time t... The prediction results are expressed as follows: (12) in, and These are all learned parameters for the output layer. , representing a nonlinear activation function Input features, These are the predicted values ​​of the Long Short-Term Memory (LSTM) neural network model; thus, the definition of the LSM neural network model is completed.

5. The method for predicting the degradation of a taper nut based on a long short-term memory neural network according to claim 4, characterized in that: In step four, the objective function for the prediction task is constructed; let... The objective function for the Long Short-Term Memory (LSTM) neural network model is the root mean square (RMS) function in the prediction task; for a bivariate data sample... In terms of its sliding window any inner Loss function at time step The formula is expressed as: (13) Then, backpropagation is used to calculate the model's error at unknown learning parameters; assuming the current state is... At time, and, the Long Short-Term Memory module is located in the model's... If the layer is such that the backpropagation error at that module originates from two parts, one part comes from... The first moment Errors propagated back from the layer The other part is from The first moment Errors propagated back from the layer When the activation function of the output layer is When dealing with functions, according to the chain rule for derivative calculation, in At that moment, Represented as: (14) in, These are the learning parameters for the output layer; and All are the first in the Long Short-Term Memory neural network model Relevant features of hidden layers for The input characteristics of the function, and for The output characteristics of the function; in the differentiation calculation, For the objective function for The first derivative, for for The first derivative; if If time is the last time point of the observed time series, then At this time, in At any given moment, the hidden layer output in the Long Short-Term Memory neural network model The total error at this point is: (15) in, loss function for The first derivative.

6. The method for predicting the degradation of a taper nut based on a long short-term memory neural network according to claim 5, characterized in that: In step four, the input error of each gating structure is calculated, as follows: ； (19) ； (17) ； (18) ； (19) ； (20) Therefore, in Learning parameters of the Long Short-Term Memory neural network model at time The error is: (21) (22) (23) in, Indicates the symbol for derivative calculation; For a bivariate data sample Transform the above expression from any Time extends to sliding window The above refers to the learning parameters of the Long Short-Term Memory neural network model. The total error is defined as the sliding window. The sum of errors at all times within the interval is expressed as: (24) (25) (26) Similarly, the learning parameters of the Long Short-Term Memory neural network model The total error is: (27) (28) (29) Learning parameters of a Long Short-Term Memory (LSTM) neural network model The total error is: (30) (31) (32) Learning parameters of a Long Short-Term Memory (LSTM) neural network model The total error is: (33) (34) (35) Thus, a bivariate sample is completed. In the The calculation of backpropagation error in layers; similarly, the calculation of backpropagation error in long short-term memory neural network models. Backpropagation error at time and the Backpropagation error of layer , respectively represented as ； (36) ； . (37) according to and The learning parameters of the Long Short-Term Memory (LSTM) neural network model are derived. Time and the Backpropagation error of the layer.

7. The method for predicting the degradation of a taper nut based on a long short-term memory neural network according to claim 6, characterized in that: In step four, to reduce computational overhead, in each iteration update, data is randomly selected from the training data. Extraction A sample of ... The estimated value is used to update the model weights, and the formula is as follows: (38) in, This indicates that for a bivariate data sample The error of the root mean square loss function, This indicates a parameter update. It is the learning rate, used to control the learning rate during iteration. The update range, This refers to the number of samples used in batch training; at this point, the learning parameters of the Long Short-Term Memory neural network model... The update process is represented as: (39) , (40) (41) Learning parameters of a Long Short-Term Memory (LSTM) neural network model The update process is represented as: (42) (43) (44) Learning parameters of a Long Short-Term Memory (LSTM) neural network model The update process is represented as: (45) (46) (47) Learning parameters of a Long Short-Term Memory (LSTM) neural network model The update process is represented as: (48) (49) (50) Therefore, repeated sampling without repetition is performed. Second-rate, This indicates a rounding operation, which continues until all training samples within the training sample have been covered, completing one round of model training.

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