A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization

Abstract

A kind of nuclear function bandwidth optimization mechanical structure load extrapolation algorithm device, comprising: data processing model, data clustering model, load extrapolation model;The present application is clustered according to data density, and the bandwidth of different clusters is respectively obtained according to the result of clustering when carrying out kernel density estimation, to solve the problem of global fixed bandwidth, improve the accuracy of load extrapolation.The mean, standard deviation and maximum of the extrapolated load are more close to the test load, and the corresponding error is less than the fixed bandwidth method.The distribution of the extrapolated load data and the measured load data has high similarity, can effectively simulate the data distribution characteristics and rules of measured load, prove the feasibility of the extrapolation device.The pseudo-damage ratio of the present application is lower than the fixed bandwidth method, and has high consistency with the original load.

Description

Technical Field

[0001] This invention relates to the field of vehicle durability testing, and more specifically to a mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization. Background Technology

[0002] During the research and development phase, automobiles undergo extensive full-vehicle durability road tests at proving grounds. Collecting load signals from these tests on public roads is a crucial input for developing vehicle durability road test standards. While the design life of a vehicle is typically 240,000 to 300,000 kilometers, load signal collection on public roads is often limited by time and cost, typically only covering tens of thousands of kilometers. Therefore, the collected load signals from public roads need to be extrapolated to estimate the load signals over the vehicle's entire lifespan, enabling more reasonable application in developing vehicle durability road test specifications.

[0003] Obtaining user road load spectra is helpful for developing vehicle fatigue durability and optimizing the structure of key components. However, obtaining user road load spectra is limited by time and cost, making full-process load time history testing impossible. Therefore, reasonable and effective load extrapolation is needed from the obtained user road load time histories. Extrapolation methods include time-domain extrapolation and rainflow matrix extrapolation. Time-domain extrapolation preserves the load time sequence and is suitable for stationary loads; however, it is computationally intensive when the load exhibits non-stationarity. Rainflow matrix extrapolation, while not preserving the load time sequence, has lower computational cost and is applicable to both stationary and non-stationary loads, making it valuable for engineering applications. Due to the complexity of road conditions and the large proportion of non-stationary loads, rainflow matrix extrapolation is suitable. The extrapolated loads are a crucial basis for subsequent load spectrum compilation; the accuracy of the extrapolation directly affects the accuracy of the compiled load spectrum.

[0004] Studies have shown that bandwidth is the main factor affecting kernel density estimation and an important value affecting the accuracy of kernel density estimation. When the data distribution varies greatly, using a fixed bandwidth will cause a large error. Summary of the Invention

[0005] The purpose of this invention is to provide a mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, comprising: a data processing model, a data clustering model, and a load extrapolation model.

[0006] The data processing model is used to preprocess vehicle load data to obtain preprocessed load data.

[0007] The data clustering model is used to perform cluster analysis on the preprocessed load data to obtain clustered load data.

[0008] The load extrapolation model uses kernel density estimation to estimate the probability of clustered load data and uses Monte Carlo simulation to extrapolate the load and determine the load signal of the vehicle during its life cycle.

[0009] Furthermore, the preprocessing includes deburring, drift correction, signal resampling, and rainflow matrix filtering.

[0010] Furthermore, the deburring identification formula is as follows:

[0011]

[0012] In the formula, x i Given the load data, if equation (1) holds, then x i This is glitch data.

[0013] Among them, the mean The standard deviation σ is shown below:

[0014]

[0015]

[0016] In the formula, i is the load data index and n is the number of load data.

[0017] Furthermore, the drift correction steps are as follows:

[0018] s11 uses a K-order polynomial U i By fitting the measured load data, the trend term is obtained as shown below:

[0019]

[0020] In the formula, i is the load data index, k is the order index, and K is the number of orders. k represents the k-th order coefficient of the polynomial. h is the sampling interval. U i Let be the trend term for the i-th load data.

[0021] Based on the least squares method, s12 defines the error function between the estimated value and the measured value as follows:

[0022]

[0023] In the formula, E(h) is the error function between the estimated value and the measured value. n is the number of load data points. i is the measured value of the i-th load data.

[0024] s13 solves the error function by partial derivatives to obtain the coefficients of each term of the trend term, and then obtains the load data after drift correction.

[0025] The formula for calculating the error function using partial derivatives is as follows:

[0026]

[0027] In the formula, j is the order index, j = 0, 1, 2, ..., K.

[0028] Furthermore, the rainflow matrix filtering involves counting rainflows in the load data and filtering load cycles that are less than a% of the maximum load cycle amplitude, where a is an integer.

[0029] Furthermore, the step of performing cluster analysis on the preprocessed load data to obtain clustered load data includes:

[0030] s21 calculates the distance between load data, constructs a distance distribution matrix, and sets column index K0 = 1.

[0031] s22 sorts the elements of each row of the distance distribution matrix in ascending order to obtain the K0-nearest neighbor distance vector of all load data.

[0032] s23 calculates the K0-nearest neighbor distance vector average And let the average value As candidate Eps parameters, they are stored in the sets Eps and MinPts.

[0033] s24 calculates the number of Eps neighborhood objects corresponding to the candidate Eps parameters and calculates the expected value of the number of Eps neighborhood objects.

[0034] Let the mathematical expectation value The MinPts parameter, which serves as the neighborhood density threshold for the load data, is stored in the set Eps, MinPts.

[0035] s25 Determine whether K0 = n is true. If yes, proceed to step s26. If no, set K0 = K0 + 1 and return to step s22.

[0036] s26 sequentially selects the Eps parameter and the MinPts parameter from the sets Eps and MinPts, and uses the DBSCAN algorithm to perform cluster analysis on the preprocessed load data to obtain the number of clusters generated by different Eps parameters and MinPts parameters.

[0037] If the number of clusters generated is the same multiple times consecutively, the clustering result tends to be stable, and the corresponding number of clusters is the optimal number of clusters, and the corresponding MinPts parameter is the optimal MinPts parameter.

[0038] Step s27 returns the remaining payload data after clustering to step s21 until all payload data has been clustered.

[0039] Furthermore, the distance distribution matrix is ​​shown below:

[0040] D n×n ={Dist(i,p)|1≤i≤n,1≤p≤n} (7)

[0041] In the formula, i and p are both load data indices, and n is the number of load data. D n×n Let be the distance distribution matrix. Dist(i,p) is the distance from the i-th load data point to the p-th load data point.

[0042] Furthermore, the K0-nearest neighbor distance vector It consists of all elements in the sorted distance distribution matrix located in column K0.

[0043] Furthermore, the formula for calculating the probability of solving the clustered payload data using the kernel density estimation method is as follows:

[0044]

[0045] In the formula, f(x,y) represents the probability distribution of the load data. i is the load data index. n is the number of load data points. (x i ,y i Let be the i-th load data. K(·) is the kernel function. x ,h y All values ​​represent the global bandwidth. (x, y) represents the payload data to be calculated.

[0046] Furthermore, the formula for calculating the bandwidth is as follows:

[0047] h ROT =0.9Cn -1 / 5 (9)

[0048] In the formula, h ROT Where is the bandwidth. n is the number of payload data.

[0049] The intermediate parameter C is shown below:

[0050] C=min{σ,IQR / 1.34} (10)

[0051] In the formula, σ is the standard deviation of the load data sample. IQR is the standard interquartile range of the load data.

[0052] The technical effects of this invention are undeniable. This invention can accurately simulate the load signals of a vehicle on public roads and estimate the load signals of the vehicle throughout its entire life cycle. This can be more reasonably applied to the formulation of vehicle durability road test specifications, thereby contributing to the development of vehicle fatigue durability and the structural optimization of key components.

[0053] This invention performs clustering based on data density, and calculates the bandwidth of different clusters based on the clustering results when estimating kernel density, thereby solving the problem of global fixed bandwidth and improving the accuracy of load extrapolation.

[0054] The extrapolated load of this invention has a mean, standard deviation and maximum value that are closer to the test load, and the corresponding errors are all smaller than those of the fixed bandwidth method.

[0055] The extrapolated load data of this invention has a high degree of similarity to the distribution of the measured load data, which can effectively simulate the data distribution characteristics and patterns of the measured load, proving the feasibility of the extrapolation device of this invention.

[0056] The pseudo-damage ratio of this invention is lower than that of the fixed bandwidth method, and it has a high degree of consistency with the original load. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the present invention;

[0058] Figure 2 This is a schematic diagram of the vertical load at the wheel center;

[0059] Figure 3 This is a schematic diagram of the load cyclic average amplitude matrix;

[0060] Figure 4 This is a schematic diagram of the clustered data;

[0061] Figure 5 This is a schematic diagram comparing the frequency of the mean amplitude values ​​of the measured load and the extrapolated load data; Figure 5 (a) is a schematic diagram of the load cyclic amplitude; Figure 5 (b) is a schematic diagram of the load cycle mean. Detailed Implementation

[0062] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0063] Example 1:

[0064] See Figures 1 to 5A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization includes: a data processing model, a data clustering model, and a load extrapolation model.

[0065] The data processing model is used to preprocess vehicle load data to obtain preprocessed load data.

[0066] The data clustering model is used to perform cluster analysis on the preprocessed load data to obtain clustered load data.

[0067] The load extrapolation model uses kernel density estimation to estimate the probability of clustered load data and uses Monte Carlo simulation to extrapolate the load and determine the load signal of the vehicle during its life cycle.

[0068] Example 2:

[0069] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization is described in Example 1. Further, the preprocessing includes deburring, drift correction, signal resampling, and rainflow matrix filtering.

[0070] Example 3:

[0071] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of Embodiments 1 and 2, and further, the deburring identification formula is as follows:

[0072]

[0073] In the formula, x i Given the load data, if equation (1) holds, then x i This is glitch data.

[0074] Among them, the mean The standard deviation σ is shown below:

[0075]

[0076]

[0077] In the formula, i is the load data index and n is the number of load data.

[0078] Example 4:

[0079] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of Embodiments 1 to 3, and further, the drift correction steps are as follows:

[0080] s11 uses a K-order polynomial U i By fitting the measured load data, the trend term is obtained as shown below:

[0081]

[0082] In the formula, i is the load data index, k is the order index, and K is the number of orders. k represents the k-th order coefficient of the polynomial. h is the sampling interval. U i Let be the trend term for the i-th load data.

[0083] Based on the least squares method, s12 defines the error function between the estimated value and the measured value as follows:

[0084]

[0085] In the formula, E(h) is the error function between the estimated value and the measured value. n is the number of load data points. i This represents the measured value of the i-th load data.

[0086] s13 solves the error function by partial derivatives to obtain the coefficients of each term of the trend term, and then obtains the load data after drift correction.

[0087] The formula for calculating the error function using partial derivatives is as follows:

[0088]

[0089] In the formula, j is the order index, j = 0, 1, 2, ..., K.

[0090] Example 5:

[0091] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of embodiments 1 to 4. Further, the rainflow matrix filtering is to count the rainflows in the load data and filter the load cycles that are less than the maximum load cycle amplitude a%, where a is an integer.

[0092] Example 6:

[0093] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of embodiments 1 to 5, further comprising the step of performing cluster analysis on the preprocessed load data to obtain clustered load data, including:

[0094] s21 calculates the distance between load data, constructs a distance distribution matrix, and sets column index K0 = 1.

[0095] s22 sorts the elements of each row of the distance distribution matrix in ascending order to obtain the K0-nearest neighbor distance vector of all load data.

[0096] s23 calculates the K0-nearest neighbor distance vector average And let the average value As candidate Eps parameters, they are stored in the sets Eps and MinPts.

[0097] s24 calculates the number of Eps neighborhood objects corresponding to the candidate Eps parameters and calculates the expected value of the number of Eps neighborhood objects.

[0098] Let the mathematical expectation value The MinPts parameter, which serves as the neighborhood density threshold for the load data, is stored in the set Eps, MinPts.

[0099] s25 Determine whether K0 = n is true. If yes, proceed to step s26. If no, set K0 = K0 + 1 and return to step s22.

[0100] s26 sequentially selects the Eps parameter and the MinPts parameter from the sets Eps and MinPts, and uses the DBSCAN algorithm to perform cluster analysis on the preprocessed load data to obtain the number of clusters generated by different Eps parameters and MinPts parameters.

[0101] If the number of clusters generated is the same multiple times consecutively, the clustering result tends to be stable, and the corresponding number of clusters is the optimal number of clusters, and the corresponding MinPts parameter is the optimal MinPts parameter.

[0102] Step s27 returns the remaining payload data after clustering to step s21 until all payload data has been clustered.

[0103] Example 7:

[0104] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of Embodiments 1 to 6, and further, the distance distribution matrix is ​​as follows:

[0105] D n×n ={Dist(i,p)|1≤i≤n,1≤p≤n} (7)

[0106] In the formula, i and p are both load data indices, and n is the number of load data. D n×n Let be the distance distribution matrix. Dist(i,p) is the distance from the i-th load data point to the p-th load data point.

[0107] Example 8:

[0108] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of Embodiments 1 to 7, further, the K0-nearest neighbor distance vector It consists of all elements in the sorted distance distribution matrix located in column K0.

[0109] Example 9:

[0110] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization is provided. The main technical contents are described in any one of Embodiments 1 to 8. Further, the calculation formula for the probability of solving the kernel density estimation of the clustered load data using the kernel density estimation method is as follows:

[0111]

[0112] In the formula, f(x,y) represents the probability distribution of the load data. i is the load data index. n is the number of load data points. (x i ,y i Let be the i-th load data. K(·) is the kernel function. x ,h y All values ​​represent the global bandwidth. (x, y) represents the payload data to be calculated.

[0113] Example 10:

[0114] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of embodiments 1 to 9, and further, the calculation formula of the bandwidth is as follows:

[0115] h ROT =0.9Cn -1 / 5 (9)

[0116] In the formula, h ROT Where is the bandwidth. n is the number of payload data.

[0117] The intermediate parameter C is shown below:

[0118] C=min{σ,IQR / 1.34} (10)

[0119] In the formula, σ is the standard deviation of the load data sample. IQR is the standard interquartile range of the load data.

[0120] Example 11:

[0121] See Figures 1 to 5 A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization includes: a data processing model, a data clustering model, and a load extrapolation model.

[0122] The data processing model is used to preprocess vehicle load data to obtain preprocessed load data.

[0123] The data clustering model is used to perform cluster analysis on the preprocessed load data to obtain clustered load data.

[0124] The load extrapolation model uses kernel density estimation to estimate the probability of clustered load data and uses Monte Carlo simulation to extrapolate the load and determine the load signal of the vehicle during its life cycle.

[0125] Example 12:

[0126] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization is described in Example 11. Further, the preprocessing includes deburring, drift correction, signal resampling, and rainflow matrix filtering.

[0127] To ensure the accuracy of the collected data, the sampling frequency of the test was set to 1000Hz, which resulted in a large amount of data and low data processing efficiency. In addition, the frequency of the road load signal is below 50Hz, so it is necessary to resample the original load spectrum.

[0128] Example 13:

[0129] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of Embodiments 11 to 12, and further, the deburring identification formula is as follows:

[0130]

[0131] In the formula, x i Given the load data, if equation (1) holds, then x i This is glitch data.

[0132] Among them, the mean The standard deviation σ is shown below:

[0133]

[0134]

[0135] In the formula, i is the load data index and n is the number of load data.

[0136] Example 14:

[0137] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization is disclosed in any one of Examples 11 to 13. Furthermore, during load acquisition tests on test tracks and user roads, changes in ambient temperature or humidity, as well as thermal deformation of the vehicle itself, can cause data drift, affecting subsequent data analysis results. Therefore, it is necessary to correct the distorted data. In engineering practice, the least squares method is commonly used for drift correction. The least squares method can eliminate both linear baseline offsets and trend terms with high-order polynomials. This paper, based on the least squares principle, uses a second-order polynomial to fit the trend term of the drift signal. Subtracting the trend term from the measured data achieves drift signal correction. The drift correction steps are as follows:

[0138] s11 uses a K-order polynomial U i By fitting the measured load data, the trend term is obtained as shown below:

[0139]

[0140] In the formula, i is the load data index, k is the order index, and K is the number of orders. k represents the k-th order coefficient of the polynomial. h is the sampling interval. U i Let be the trend term for the i-th load data.

[0141] Based on the least squares method, s12 defines the error function between the estimated value and the measured value as follows:

[0142]

[0143] In the formula, E(h) is the error function between the estimated value and the measured value. n is the number of load data points. i is the measured value of the i-th load data.

[0144] After simplification, we can obtain K+1 equations.

[0145]

[0146] Trend item U n The coefficients b k Related to order K, let but

[0147] When K=0

[0148] b0 = N -1 ∑u n

[0149] When K=1,

[0150]

[0151] When K=2

[0152]

[0153] s13 solves the error function by partial derivatives to obtain the coefficients of each term of the trend term, and then obtains the load data after drift correction.

[0154] The formula for calculating the error function using partial derivatives is as follows:

[0155]

[0156] In the formula, j is the order index, j = 0, 1, 2, ..., K.

[0157] Example 15:

[0158] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of embodiments 11 to 14. Further, the rainflow matrix filtering is to count the rainflows in the load data and filter the load cycles that are less than 10% of the maximum load cycle amplitude.

[0159] Example 16:

[0160] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of embodiments 11 to 15, further comprising the step of performing cluster analysis on the preprocessed load data to obtain clustered load data, including:

[0161] s21 calculates the distance between load data, constructs a distance distribution matrix, and sets column index K0 = 1.

[0162] s22 sorts the elements of each row of the distance distribution matrix in ascending order to obtain the K0-nearest neighbor distance vector of all load data.

[0163] s23 calculates the K0-nearest neighbor distance vector average And let the average value As candidate Eps parameters, they are stored in the sets Eps and MinPts.

[0164] s24 calculates the number of Eps neighborhood objects corresponding to the candidate Eps parameters and calculates the expected value of the number of Eps neighborhood objects.

[0165] Let the mathematical expectation value The MinPts parameter, which serves as the neighborhood density threshold for the load data, is stored in the set Eps, MinPts.

[0166] s25 Determine whether K0 = n is true. If yes, proceed to step s26. If no, set K0 = K0 + 1 and return to step s22.

[0167] s26 sequentially selects the Eps parameter and the MinPts parameter from the sets Eps and MinPts, and uses the DBSCAN algorithm to perform cluster analysis on the preprocessed load data to obtain the number of clusters generated by different Eps parameters and MinPts parameters.

[0168] If the number of clusters generated is the same four times in a row, the clustering result tends to be stable, and the corresponding number of clusters is the optimal number of clusters, and the corresponding MinPts parameter is the optimal MinPts parameter.

[0169] Step s27 returns the remaining payload data after clustering to step s21 until all payload data has been clustered.

[0170] Example 17:

[0171] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of Embodiments 11 to 16, and further, the distance distribution matrix is ​​as follows:

[0172] D n×n ={Dist(i,p)|1≤i≤n,1≤p≤n} (7)

[0173] In the formula, i and p are both load data indices, and n is the number of load data. D n×n Let be the distance distribution matrix. Dist(i,p) is the distance from the i-th load data point to the p-th load data point.

[0174] Example 18:

[0175] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of embodiments 11 to 17, further, the K0-nearest neighbor distance vector It consists of all elements in the sorted distance distribution matrix located in column K0.

[0176] Example 19:

[0177] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization is provided. The main technical details are described in any one of Examples 11 to 18. Furthermore, the kernel density estimation method can more accurately reflect the actual distribution of data and avoid potential biases in parameter estimation. The rainflow counting matrix contains information on load cycle amplitude and load cycle mean. Its extrapolation is a two-dimensional problem. The formula for calculating the probability of solving the kernel density estimation problem using the kernel density estimation method on the clustered load data is as follows:

[0178]

[0179] In the formula, f(x,y) represents the probability distribution of the load data. i is the load data index. n is the number of load data points. (x i ,y i Let be the i-th load data. K(·) is the kernel function, which has a global integral of 1 and is essentially a probability density function, taking the existing data points (x) as the basis for the load data. i ,y i Centered on h x ,h y This is an algorithm for estimating the probability density of the influence radius. x ,h y All values ​​represent the global bandwidth. (x, y) represents the payload data to be calculated.

[0180] Example 20:

[0181] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, the main technical contents of which are described in any one of Embodiments 11 to 19, and further, the calculation formula of the bandwidth is as follows:

[0182] h ROT =0.9Cn -1 / 5 (9)

[0183] In the formula, h ROT Where is the bandwidth. n is the number of payload data.

[0184] The intermediate parameter C is shown below:

[0185] C=min{σ,IQR / 1.34} (10)

[0186] In the formula, σ is the standard deviation of the load data sample. IQR is the standard interquartile range of the load data.

[0187] Example 21:

[0188] A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization is provided. The main technical contents are described in any one of Embodiments 11 to 20. Furthermore, the vehicle load extrapolation algorithm device also includes a result verification model.

[0189] The result verification model is used to verify the load extrapolation effect of the vehicle load extrapolation algorithm device.

[0190] To verify the effectiveness and accuracy of the proposed method, it is compared with the traditional kernel density estimation load extrapolation based on fixed bandwidth. The evaluation is conducted from three aspects: statistical parameters, goodness of fit, and spurious damage.

[0191] 1. The mean, standard deviation, and maximum value of the statistical parameters are selected as the criteria for judging the measured load and extrapolated load of this vehicle model.

[0192] 2. The original load data and extrapolated load data were statistically analyzed using the rainflow counting method, and the load cycle amplitude-load cycle cumulative frequency curve of the original load was compared with that of the fixed bandwidth kernel density estimation extrapolation.

[0193] 3. Using spurious impairments to compare the spurious impairment ratio of the proposed method with that of a fixed bandwidth.

[0194] Example 22:

[0195] See Figures 1 to 5 A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization mainly includes the following:

[0196] 1. Establish a data processing model

[0197] (1) Deburring

[0198] For glitch signals in the measured load data, the Rheinda criterion is used for data glitch identification. For the measured load point x i Let i = 1, 2, 3, ..., n, and its mean is... and standard deviation σ is

[0199]

[0200]

[0201] like At that time, it was believed that x i This is glitch data.

[0202] (2) Drift correction

[0203] During load acquisition tests on test tracks and user roads, changes in ambient temperature or humidity, as well as the thermal deformation of the vehicle itself, can cause data drift, affecting subsequent data analysis results. Therefore, it is necessary to correct the distorted data. In engineering practice, the least squares method is commonly used for drift correction. The least squares method can eliminate both linear baseline offsets and trend terms with high-order polynomials. This paper, based on the least squares principle, uses a second-order polynomial to fit the trend term of the drift signal. Subtracting the trend term from the measured data corrects the drift signal. The basic principle is as follows:

[0204] Let {u n} represents the measured load points n = 1, 2, ..., N with a sampling interval of h, using a K-order polynomial U n Fitting trend term,

[0205]

[0206] In the formula, b k U represents the coefficients of the polynomial. n The set of points is u n Estimation of polynomial elements. Based on the least squares principle, define the error function between the estimated and measured values.

[0207]

[0208] Find b for E(h) respectively j The partial derivatives of j = 0, 1, 2, ..., K, set to zero, are:

[0209]

[0210] After simplification, we can obtain K+1 equations.

[0211]

[0212] Trend item U n The coefficients b k Related to order K, let but

[0213] When K=0

[0214] b0 = N -1 ∑u n

[0215] When K=1,

[0216]

[0217] When K=2

[0218]

[0219] (3) Signal resampling

[0220] To ensure the accuracy of the collected data, the sampling frequency of the test was set to 1000 Hz, which resulted in a large amount of data and low data processing efficiency. In addition, the frequency of the road load signal is below 50 Hz, so it is necessary to resample the original load spectrum.

[0221] (4) Rainflow matrix filtering

[0222] Rainflow counts are performed on the processed data, and load cycles that are less than 10% of the maximum load cycle amplitude are filtered.

[0223] 2. Establish a data clustering model

[0224] Step 1: Calculate the distance distribution matrix of dataset D, i.e.

[0225] D n×n ={Dist(i,j)|1≤i≤n,1≤j≤n}

[0226] In the formula, D n×n Let D be an n×n real symmetric matrix; n is the number of objects contained in dataset D; Dist(i,j) is the distance from the i-th object to the j-th object in dataset D.

[0227] Step 2: For the distance matrix D n×n Sort each row of elements in ascending order. The distance vector D0 formed by the elements in the first column represents the distance from the object to itself. The elements in the Kth (1≤K≤n)th column form the K-nearest neighbor distance vector D for all data points. K .

[0228] Step 3: Calculate the average of each column of the sorted matrix, thus obtaining vector D. K average And use it as a candidate Eps parameter. Represented as:

[0229]

[0230] Step 4: For a list of n Eps parameters, calculate the number of Eps neighborhood objects corresponding to each Eps parameter, and calculate its expected value, which serves as the neighborhood density threshold MinPts parameter for dataset D, expressed as:

[0231]

[0232] In the formula: P i For Eps K The number of neighboring objects, where n is the total number of objects in dataset D.

[0233] Step 5: Select elements from sets Eps and MinPts sequentially as candidate Eps and MinPts parameters, and input them into the DBSCAN algorithm to perform cluster analysis on the dataset, obtaining the number of clusters generated for different Eps and MinPts parameters. When the number of clusters generated is the same for four consecutive times, the clustering result is considered to be stable, and this number of clusters N is denoted as the optimal number of clusters. The corresponding MinPts parameter is then the optimal MinPts parameter.

[0234] Step 6: Repeat steps 1-5 using the remaining data after clustering until the data clustering is complete.

[0235] 3. Establish a load extrapolation model

[0236] The formula for calculating the bandwidth h using the thumb method in the kernel density estimation model based on the Gaussian kernel function is as follows:

[0237] h ROT =0.9Cn -1 / 5

[0238] C = min{σ, IQR / 1.34}

[0239] In the formula: n is the number of sample points; σ is the sample standard deviation; IQR is the standard interquartile range of the data.

[0240] Kernel density estimation can more accurately reflect the actual distribution of data and avoid potential biases in parameter estimation. The rainflow counting matrix contains information on load cycle amplitude and load cycle mean; its extrapolation is a two-dimensional problem. The expression for two-dimensional kernel density estimation is as follows:

[0241]

[0242] In the formula: n is the number of data points; (x i ,y i ) represents the i-th data point; h x ,h y K is the global bandwidth; K(·) is the kernel function, which has a global integral of 1 and is essentially a probability density function, based on the existing data points (x). i ,y i Centered on h x ,h y This is an algorithm for estimating the probability density of the influence radius.

[0243] The kernel density estimation formula is used to estimate the probability of the clustered data. Finally, Monte Carlo simulation is used to extrapolate the load.

[0244] 4. Establish a results verification model

[0245] To verify the effectiveness and accuracy of the proposed method, it is compared with the traditional kernel density estimation load extrapolation based on fixed bandwidth. The evaluation is conducted from three aspects: statistical parameters, goodness of fit, and spurious damage.

[0246] 1) Select the mean, standard deviation and maximum value of the statistical parameters as the evaluation criteria for the measured load and extrapolated load of this vehicle model.

[0247] 2) Use the rainflow counting method to perform dual-parameter statistics on the amplitude of the original load data and the extrapolated load data; compare the load cycle amplitude-load cycle cumulative frequency curve of the original load with the extrapolation by fixed bandwidth kernel density estimation.

[0248] 3) Use spurious damage to compare the spurious damage ratio of the proposed method with that of a fixed bandwidth.

[0249] Example 23:

[0250] See Figures 1 to 5 A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization mainly includes the following:

[0251] Using an electric car as the test object, a durability load spectrum acquisition test was conducted, and wheel center force load signals were collected on a public road in a city.

[0252] The pre-processed measured vertical load signal of the wheel center, such as... Figure 2 As shown.

[0253] Rainflow counting is a widely used statistical method for counting measured load time histories, and it statistically analyzes the amplitude and mean of load cycles, consistent with the inherent characteristics of fatigue loads. For pre-processed load signals, rainflow counting is used to perform statistical counting on the pre-processed measured loads, obtaining the load cycle mean amplitude matrix. Based on the statistical counting results, it can be seen that... Figure 3 As shown.

[0254] For load cycles with amplitudes less than 10% of the maximum load cycle, filtering is performed to significantly reduce the amount of data input required for kernel density estimation, thereby reducing computation time to some extent. The rainflow matrix, after filtering out small load cycles, is statistically counted and used as input for kernel density estimation. The scatter plot of the mean amplitude of the filtered load cycles is then used. Figure 3 As shown.

[0255] The KANN-DBSCAN algorithm was used to perform cluster analysis and bandwidth calculation on the selected data, and the kernel density estimation method was used to extrapolate cyclic loads. Taking the left front wheel as an example, the data was clustered into 4 clusters after KANN-DBSCAN. The Eps and MinPts parameters of each cluster are shown in Table 1. The clustering effect is as follows: Figure 4 As shown in the figure, the bandwidth of each cluster was then calculated, and the calculated bandwidth of each cluster is shown in Table 2.

[0256] Table 1 Clustering parameters

[0257]

[0258] Table 2 Bandwidth of different clusters

[0259]

[0260] Depend on Figure 5 It can be seen that, compared with the fixed-bandwidth extrapolation method, the proposed method can better ensure that the extrapolated load distribution characteristics are consistent with the measured load. The load generated by the fixed-bandwidth method is too concentrated compared with the measured load. The proposed method can more closely approximate the distribution of the measured load during extrapolation and can better extrapolate the extreme load, while the fixed-bandwidth method has a larger deviation in extrapolating the extreme load. The statistical parameters are shown in Table 3.

[0261] Table 3 Statistical Parameters

[0262]

[0263] By calculating and analyzing the correlation between two different distributions, the formula for calculating the correlation coefficient is as follows:

[0264]

[0265] In the formula: Cov(X,Y) is the covariance of variables X and Y, σ x ,σ y It is the standard deviation of the variable.

[0266] The definition of spurious damage ignores the influence of the structure's inherent fatigue characteristics, treating all load signals as generalized stress. Using the standard SN curve, damage accumulation is calculated on the generalized stress according to the solution method for real fatigue damage. Therefore, the numerical value of spurious damage has no specific meaning; generally, the relative magnitude of spurious damage under different load conditions is compared to measure the fatigue strength of the load. Based on the linear accumulation of spurious damage caused by the number of stress cycles on the material according to the SN curve, the expression for spurious damage calculation is as follows:

[0267]

[0268] In the formula: ∑D represents the total damage; n i For materials in S i Number of cycles under load; N i For load S i The number of fatigue life cycles under stress.

[0269] To facilitate comparison of spurious damage, the damage ratio is defined as the ratio of damage caused by the extrapolated load to damage caused by the measured load. A damage ratio closer to 1 indicates that the extrapolation effect is closer to the measured load. Spurious damage was chosen as the standard for comparison in this study. The calculation results of the spurious damage ratio are shown in Table 4.

[0270] Table 4. Pseudo-damage ratio

[0271]

[0272] 1. The extrapolated loads obtained by the proposed method have mean, standard deviation, and maximum values ​​that are closer to the test loads. The errors of the proposed method are 1.4%, 0.1%, and 1.5%, respectively, all of which are smaller than those of the fixed bandwidth method.

[0273] 2. The correlation coefficient of the load cyclic amplitude distribution obtained by the method in this paper is 0.9917, and the correlation coefficient of the load cyclic mean distribution is 0.9900. The correlation coefficient of the load cyclic amplitude distribution obtained by the fixed bandwidth method is 0.9314, and the correlation coefficient of the load cyclic mean distribution is 0.8930. The results show that the extrapolated load data obtained by the method in this paper has a high similarity to the distribution of the measured load data, and can effectively simulate the data distribution characteristics and patterns of the measured load, demonstrating the feasibility of the extrapolation method.

[0274] 3. The extrapolated load of sample 1 obtained by the extrapolation method proposed in this paper has a pseudo-damage ratio of 1.021, which is highly consistent with the original load.

Claims

1. A mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization, characterized in that, include: Data processing model, data clustering model, load extrapolation model; The data processing model is used to preprocess vehicle load data to obtain preprocessed load data. The data clustering model is used to perform cluster analysis on the preprocessed load data to obtain clustered load data. The steps include: s21 calculates the distance between load data, constructs a distance distribution matrix, and sets the column indices... =1; s22 sorts the elements of each row of the distance distribution matrix in ascending order to obtain all load data. -Nearest neighbor distance vector ; s23 calculation -Nearest neighbor distance vector average and let the average value As a candidate Parameters are stored in a collection. , ; s24 finds the candidates Parameters corresponding Count the number of neighboring objects and calculate. Mathematical expectation of the number of neighborhood objects ; Let the mathematical expectation value Neighborhood density threshold for payload data Parameters are stored in a collection. , ; S25 judgment Is it true? If yes, proceed to step s26; otherwise, let... and return to step s22; s26 sequentially from set , Selected from Parameters and The parameters were analyzed using the DBSCAN algorithm to perform clustering analysis on the preprocessed load data, yielding different... Parameters and The number of clusters generated by the parameters; If the number of clusters generated is the same multiple times consecutively, the clustering result tends to stabilize, and the corresponding number of clusters is the optimal number of clusters. Parameters are optimal parameter; s27 returns the remaining payload data after clustering to step s21 until all payload data has been clustered; The load extrapolation model uses kernel density estimation to estimate the probability of clustered load data and uses Monte Carlo simulation to extrapolate the load and determine the load signal of the vehicle during its life cycle.

2. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 1, characterized in that, The preprocessing includes deburring, drift correction, signal resampling, and rainflow matrix filtering.

3. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 2, characterized in that, The deburring identification formula is as follows: （1） In the formula, Given the load data, if equation (1) holds, then For glitch data; Among them, the mean and standard deviation As shown below: （2） （3） In the formula, For load data indexing, This represents the amount of payload data.

4. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 2, characterized in that, The drift correction steps are as follows: s11 uses a K-order polynomial By fitting the measured load data, the trend term is obtained as shown below: （4） In the formula, For load data index; k is the order index, K is the number of orders; The coefficients are the k-th order coefficients of the polynomial; The sampling interval; For the first Trend items for individual load data; Based on the least squares method, s12 defines the error function between the estimated value and the measured value as follows: （5） In the formula, This is the error function between the estimated value and the measured value. The number of payload data; For the first Measured values ​​of each load data; s13 solves the error function by partial derivatives to obtain the coefficients of each term of the trend term, and then obtains the load data after drift correction; The formula for calculating the error function using partial derivatives is as follows: （6） In the formula, j is the order index, j=0,1,2,...,K.

5. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 2, characterized in that, The rainflow matrix filtering involves counting rainflows in the load data and filtering load cycles that are less than a% of the maximum load cycle amplitude, where a is an integer.

6. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 1, characterized in that, The distance distribution matrix is ​​shown below: （7） In the formula, , All are load data indexes. The number of payload data; This is the distance distribution matrix; For the first The load data to the first Distance of each load data point.

7. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 1, characterized in that, The -Nearest neighbor distance vector It is the distance distribution matrix after sorting that is located at the th It consists of all the elements of the column.

8. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 1, characterized in that, The formula for calculating the probability of solving the kernel density estimation problem using the kernel density estimation method on the clustered payload data is as follows: （8） In the formula, The probability distribution of the load data; Index the load data; The number of payload data; For the first One load data; For kernel functions; All are global bandwidth; The data represents the load to be calculated.

9. The mechanical structure load extrapolation algorithm device with kernel function bandwidth optimization according to claim 8, characterized in that, The formula for calculating the bandwidth is as follows: （9） In the formula, For bandwidth; The number of payload data; Among them, intermediate parameters As shown below: （10） In the formula, The standard deviation of the load data samples; The standard interquartile range for load data.

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