A method for accelerating the fatigue test of a crankshaft

Abstract

The present invention discloses a crankshaft accelerated fatigue test method, comprising the following steps: Step 1: Establishing an empirical model of the crankshaft's natural frequency and cycle number, wherein the empirical model is a double exponential model; Step 2: Simplifying the established empirical model to establish a Kalman filter system observation model for predicting the crankshaft's remaining fatigue life; and Step 3: Predicting the crankshaft's remaining fatigue life using the UKF system observation model. The present invention utilizes an improved Kalman filter remaining life prediction method that can be applied to crankshaft accelerated fatigue testing. Furthermore, the present invention utilizes minimal experimental data, and the predicted results are close to the actual results. Only the first portion of the experiment is required to predict the actual results, reducing both experimental costs and experimental time, resulting in excellent economical practicality.

Description

Technical Field

[0001] The invention relates to the technical field of crankshaft testing, in particular to a crankshaft accelerated fatigue testing method. Background Art

[0002] The crankshaft is one of the key components in the engine structure. Its geometric parameters are directly related to the overall size of the entire engine, and are also directly related to its service life and reliability. If the crankshaft is damaged, it will have a great impact and damage to other engine components. During the normal operation of the engine, due to the long-term repeated alternating loads of the turbine and cylinder, it will suffer fatigue and wear, causing it to fail. If the crankshaft is seriously damaged, it is likely to cause engine damage or even serious traffic accidents. Therefore, evaluating the remaining service life of the crankshaft has become an important issue. The fatigue reliability of the crankshaft is an important performance indicator currently pursued by engines. Therefore, in actual production and use, the impact of fatigue on the remaining service life of the crankshaft is crucial.

[0003] There are various methods for testing crankshaft bending fatigue. Resonant devices designed based on vibration principles have been widely used in actual testing. This testing method can apply bending loads to the crankshaft at a certain load level, but its disadvantages are high testing costs and long test cycles. Therefore, when performing crankshaft fatigue testing, how to accelerate this testing process, achieve prediction of its remaining life, and determine its fatigue limit load based on this is of great significance for improving the working performance of the crankshaft. In actual engineering, the test steps of a resonant crankshaft bending fatigue testing device include calibration, loading, and analysis. The loading process is time-consuming and costly. The accelerated fatigue testing method of the present invention mainly starts with this step. In actual engineering, methods such as particle filtering, Kalman filtering, linear minimum mean square error meter, echo state network, and adaptive neural-fuzzy inference are generally used to predict the remaining life. These methods have their own advantages and disadvantages and scope of application. Among them, the Kalman filter (KF) algorithm has the advantage that only the measurement value information of the previous moment is required for calculation, which is easy to perform iterative calculations in real time. Moreover, KF is the optimal filtering method for linear Gaussian systems.

[0004] Unscented Kalman Filter (UKF) uses unscented transform (UT) to deal with the nonlinear transfer problem of mean and covariance. The main idea of unscented transform is that "it is easier to approximate probability distribution than to approximate nonlinear function". UT changes the calculation of mean and covariance, approximates probability distribution through a set of points (sigma points) determined by mean and covariance, and estimates mean and covariance by selecting appropriate weights. UKF has higher estimation accuracy and meets the application requirements of nonlinear filtering and control with various complex requirements. The basic principle of UT transformation is as follows: Assume a nonlinear system y = f(x), where x is an n-dimensional state vector, and its average value is If the variance is Px, then 2n+1 Sigma points Xi can be constructed through UT transformation, and the corresponding weights Wi of Xi can be constructed at the same time, thereby obtaining the statistical characteristics of y.

[0005] In the article "Research on Remaining Life and Crack Fault Detection of Cracked Crankshafts in CNG Engines" published in 2016, Xiao Xiang (Southwest Petroleum University) studied the fatigue crack growth curve of the crankshaft. The study showed that the crankshaft crack growth rate is divided into three stages: A, B, and C. Area A is the initial stable crack growth zone, area B is the stable crack growth zone, and area C is the rapid crack growth zone, corresponding to the low, medium, and high rate regions respectively. Summary of the Invention

[0006] Purpose of the invention: The present invention provides a crankshaft accelerated fatigue test method. Based on the known crankshaft natural frequency experimental data, the present invention uses the Kalman filter algorithm to establish a corresponding life prediction model, predicts the remaining life of the crankshaft and analyzes the accuracy of the prediction results. Then, in order to address the problem of large errors in the prediction of the Kalman filter algorithm, the sample space of the data is improved.

[0007] Technical solution: A crankshaft accelerated fatigue test method includes the following steps:

[0008] Step 1: Establish an empirical model of crankshaft natural frequency and cycle number, the empirical model is a double exponential model:

[0009] y=a exp(bx)+c exp(dx)

[0010] Where y represents the natural frequency of the crankshaft, x represents the number of cycles, and a, b, c, and d are unknowns;

[0011] Step 2: Simplify the established empirical model and establish a Kalman filter system observation model for predicting the remaining fatigue life of the crankshaft. The state space equation of the UKF system observation model is as follows:

[0012] Z(k+1)=(c(k)*exp(d(k)*(t-1))*(1-exp(b(k)-d(k)))) / (1-exp(b(k)))+a+v(k)

[0013] Where Z(k+1) is the observation value at the current moment, α is the empirical value of the system's natural frequency decay; V(k) is the process noise, both of which satisfy the standard normal distribution with a mean of 0 and a variance of σw;

[0014] Step 3: Predict the remaining fatigue life of the crankshaft through the UKF system observation model.

[0015] Furthermore, the steps for obtaining the empirical model are as follows:

[0016] 1) The crankshaft is subjected to a cyclic test with a load on a crankshaft fatigue test bench to obtain experimental data on the number of cycles at which its natural frequency drops to failure and the decrease in the natural frequency value with increasing cycle number;

[0017] 2) According to the natural frequency obtained from the experiment, the law of change of the crankshaft natural frequency and the principle of minimum fitting error, the experimental data are fitted nonlinearly and the double exponential model is selected as the empirical model.

[0018] Furthermore, the step of acquiring the empirical model also includes data processing, specifically: in step 1), the natural frequency data obtained based on the experiment is removed from the data in the initial stable expansion region.

[0019] Furthermore, the principle of minimum fitting error is:

[0020] The root mean square (RMSE) and the coefficient of determination (R-square) are introduced to judge the quality of the experimental data fitting:

[0021]

[0022]

[0023] Where y i represents the i-th true value, is the average value of the original real data, is the model prediction value, m is the number of original data points;

[0024] The smaller the RMSE value, the better the model performance and the better the fitting effect; the value range of R-square is [0,1]. The closer the R-square is to 1, the better the fitting effect is, and the closer it is to 0, the greater the deviation of the fitting result.

[0025] Furthermore, the specific steps of step 2 are as follows:

[0026] 1) For a discrete-time nonlinear system consisting of a random variable with Gaussian white noise W(k) and an observation variable Z with Gaussian white noise V(k), it can be described as:

[0027]

[0028] Where f is the nonlinear state equation function, c is the nonlinear observation equation function;

[0029] 2) Assuming that w(k) has a covariance matrix Q and v(k) has a covariance matrix R; based on the decreasing characteristics of the natural frequency and the double exponential model, the UKF state model can be expressed as follows:

[0030] δ(k+1|k)=δ(k)+w(k) In the formula, δ(k)=[b(k) c(k) d(k)] T represents the estimated value of the natural frequency drop model parameter after the previous moment, and δ(k+1|k) represents the state prediction value at the current moment;

[0031] 3) Based on the double exponential model, the state space equation of the UKF system observation model for predicting the remaining fatigue life of the crankshaft is established:

[0032] Z(k+1)=(c(k)*exp(d(k)*(t-1))*(1-exp(b(k)-d(k)))) / (1-exp(b(k)))+α+v(k)

[0033] Z(k+1) is the observation value at the current moment, α is the empirical value of the system's natural frequency decay; V(k) is the process noise, which all satisfy the standard normal distribution with mean 0 and variance σw; b(k), c(k), and d(k) are the parameters of the state-space equation.

[0034] Furthermore, the specific steps of step three are as follows:

[0035] The UKF iterative update estimates the optimal parameters, and the basic steps of the unscented Kalman filter algorithm for the predicted value δ of the natural frequency at different times k are as follows:

[0036] (1) Use the state estimate X(k) at time k and its error covariance matrix to calculate 2n+1 sigma points:

[0037]

[0038] Where λ is the scale factor and n is the dimension of the state variable;

[0039] (2) Calculate the corresponding weight of the sigma point:

[0040]

[0041] Where i represents the number of sigma points, ω m represents the weight of the mean, ω c represents the weight of the mean;

[0042] λ=α 2 +(n+k)-n is a scaling parameter used to reduce the prediction error, and k is a parameter to be selected to ensure that the matrix (n+λ)P is a semi-positive definite matrix;

[0043] (3) Using the two formulas in (1) and (2), we can find:

[0044]

[0045] (4) These 2n+1 sigma points are nonlinearly mapped to:

[0046] δ (i) (k+1|k)=f[k,δ (i) (k|k)]

[0047] (5) The one-step prediction and covariance matrix of the system state are:

[0048]

[0049]

[0050] (6) Based on the one-step prediction value, UT transformation is used again to generate a new Sigma point set, as shown below:

[0051]

[0052] (7) Substitute the Sigma point predicted by the above formula into the observation prediction equation, and obtain the mean and covariance of the system observation through weighted summation:

[0053]

[0054] (8) The observed predicted values of the Sigma points are obtained from step (7), and the mean and covariance of the system prediction are obtained by weighted summation:

[0055]

[0056]

[0057]

[0058] (9) Calculate the Kalman gain matrix K:

[0059]

[0060] (10) Finally, calculate the state update and covariance update of the system:

[0061]

[0062]

[0063] (11) Use the parameters identified by UKF to predict the natural frequency.

[0064] Beneficial Effects: The present invention adopts an improved Kalman filter remaining life prediction method, which can be applied to the crankshaft accelerated fatigue method. In addition, the experimental data used is small, and the predicted results are close to the actual results. Only the first part of the experiment needs to be performed to predict the actual results. This reduces the experimental cost and the experimental time, and has good economic practicality. This is also meaningful for the use of daily engineering parts. The failure point of the parts can be predicted in advance, and replacement is carried out in time to avoid affecting industrial production. At the same time, the predicted number of crankshaft cycle loads can also be used as actual crankshaft fatigue test data for statistical analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart of predicting the natural frequency of a crankshaft using the unscented Kalman filter algorithm in the present invention;

[0066] Figure 2 This is a diagram showing the predicted and actual measured values obtained by applying Kalman filtering to the data when the crankshaft natural frequency drops 0.3Hz from the initial value without removing the initial stable expansion zone;

[0067] Figure 3 This is a diagram showing the predicted and actual measured values obtained by applying Kalman filtering to the data when the crankshaft natural frequency drops 0.5Hz from the initial value without removing the initial stable expansion zone;

[0068] Figure 4 This is a diagram showing the predicted and actual measured values obtained by applying Kalman filtering to the data when the crankshaft natural frequency drops 0.7Hz from the initial value without removing the initial stable expansion zone;

[0069] Figure 5 Schematic diagram of the predicted and actual measured values after removing the data in the initial stable expansion zone and applying Kalman filtering to the data when the crankshaft natural frequency drops 0.5Hz from the initial value; DETAILED DESCRIPTION

[0070] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0071] Example 1

[0072] A crankshaft accelerated fatigue test method comprises the following steps:

[0073] Step 1: Establish an empirical model of crankshaft natural frequency and cycle number:

[0074] 1) Cyclic testing of a crankshaft with a load on a crankshaft fatigue test bench to determine the number of cycles required for its natural frequency to drop to failure. Four tests were conducted on the same crankshaft to obtain experimental data showing that the natural frequency decreases with increasing cycle number.

[0075] 2) According to the experimentally obtained natural frequency, the law of crankshaft natural frequency change and the principle of minimum fitting error, an appropriate empirical model is selected to perform nonlinear fitting. Commonly used methods include polynomial fitting, Gaussian fitting, exponential fitting, etc.

[0076] The principle of minimum fitting error is as follows: when selecting a model, the fitting phenomenon is taken into consideration, and RMSE (root mean square) and R-square (coefficient of determination) are introduced to judge the quality of the fitting of experimental data:

[0077]

[0078]

[0079] Where y i represents the i-th true value, is the average value of the original real data, is the model prediction value, m is the number of original data points;

[0080] The smaller the RMSE value, the better the model performance and the better the fitting effect. The value range of R-square is [0,1]. The closer the R-square is to 1, the better the fitting effect is, and the closer it is to 0, the greater the deviation of the fitting result. The fitting results are shown in Table 1:

[0081] Table 1 Fitting results

[0082]

[0083] By not comparing the fitting effects of different formulas, the empirical model selected is the double exponential model:

[0084] y=a exp(bx)+c exp(dx)

[0085] Where y represents the natural frequency of the crankshaft, x represents the number of cycles, and a, b, c, and d are unknowns.

[0086] Step 2: Simplify the established empirical model and establish an unscented Kalman filter system observation model for predicting the remaining fatigue life of the crankshaft; specifically:

[0087] 1) For a discrete-time nonlinear system consisting of a random variable with Gaussian white noise W(k) and an observation variable Z with Gaussian white noise V(k), it can be described as:

[0088]

[0089] Where f is the nonlinear state equation function, c is the nonlinear observation equation function;

[0090] 2) Assuming that w(k) has a covariance matrix Q and v(k) has a covariance matrix R; based on the decreasing characteristics of the natural frequency and the double exponential model, the UKF state model can be expressed as follows:

[0091] δ(k+1|k)=δ(k)+w(k)

[0092] In the formula, δ(k)=[b(k) c(k) d(k)] T represents the estimated value of the natural frequency drop model parameter after the previous moment, and δ(k+1|k) represents the state prediction value at the current moment;

[0093] 3) Establish the state space equation of the UKF system observation model for predicting the remaining fatigue life of the crankshaft:

[0094] Z(k+1)=(c(k)*exp(d(k)*(tl))*(l-exp(b(k)-d(k)))) / (l-exp(b(k)))+α+v(k)

[0095] Z(k+1) is the observation value at the current moment, α is the empirical value of the system's natural frequency decay; V(k) is the process noise, both of which satisfy the standard normal distribution with a mean of 0 and a variance of σw.

[0096] Step 3: Predict the remaining fatigue life of the crankshaft through the UKF system observation model;

[0097] The UKF iterative update estimates the optimal parameters, and the basic steps of the unscented Kalman filter algorithm for the predicted value δ of the natural frequency at different times k are as follows:

[0098] (1) Use the state estimate X(k) at time k and its error covariance matrix to calculate 2n+1 sigma points:

[0099]

[0100] Where λ is the scale factor and n is the dimension of the state variable;

[0101] (2) Calculate the corresponding weight of the sigma point:

[0102]

[0103] Where i represents the number of sigma points, ω m represents the weight of the mean, ω c represents the weight of the mean;

[0104] λ=α 2 +(n+k)-n is a scaling parameter used to reduce the prediction error, and k is a parameter to be selected to ensure that the matrix (n+λ)P is a semi-positive definite matrix;

[0105] (3) Using the two formulas in (1) and (2), we can find:

[0106]

[0107] (4) These 2n+1 sigma points are nonlinearly mapped to:

[0108] δ (i) (k+1|k)=f[k,δ (i) (k|k)]

[0109] (5) The one-step prediction and covariance matrix of the system state are:

[0110]

[0111]

[0112] (6) Based on the one-step prediction value, UT transformation is used again to generate a new Sigma point set, as shown below:

[0113]

[0114] (7) Substitute the Sigma point predicted by the above formula into the observation prediction equation, and obtain the mean and covariance of the system observation through weighted summation:

[0115]

[0116] (8) The observed predicted values of the Sigma points are obtained from step (7), and the mean and covariance of the system prediction are obtained by weighted summation:

[0117]

[0118]

[0119]

[0120] (9) Calculate the Kalman gain matrix K:

[0121]

[0122] (10) Finally, calculate the state update and covariance update of the system:

[0123]

[0124]

[0125] (11) Use the parameters identified by UKF to predict the natural frequency.

[0126] The entire data fitting and prediction process is simulated by Matlab. The prediction process is as follows: Figure 1 As shown:

[0127] It is generally believed that after the crankshaft's natural frequency drops by 1Hz, the downward trend increases significantly, and this point is therefore identified as the crankshaft failure point. Therefore, test data from the crankshaft's natural frequency at the beginning of cyclic loading to the time when the crankshaft's natural frequency drops by 0.3Hz, 0.5Hz, and 0.7Hz after a certain number of cyclic loadings are applied is selected. Using the Kalman filter algorithm, we predict the number of loads applied at the time of crankshaft failure.

[0128] Depending on the selected data sample space, the parameters in the state space equation are also different. These parameters are obtained by nonlinear fitting the selected data through a double exponential model. Based on these parameters, a general code is selected to use the above UKF system observation model to predict the remaining fatigue life of the crankshaft;

[0129] 1) When the frequency of the data used decreases by 0.3Hz, the parameters and RMS values are shown in Tables 2 and 3:

[0130] Table 2 State space equation parameters (initial drop 0.3Hz)

[0131]

[0132] Table 3 Root mean square error (initial drop 0.3Hz)

[0133]

[0134] 2) When the frequency of the data used decreases by 0.5 Hz, the parameters and RMS values are shown in Tables 4 and 5:

[0135] Table 4 State space equation parameters (initial drop 0.5Hz)

[0136]

[0137] Table 5 Root mean square error (initial drop 0.5Hz)

[0138]

[0139]

[0140] 3) When the frequency of the data used decreases by 0.7 Hz, the parameters and RMS values are shown in Tables 6 and 7:

[0141] Table 6 State space equation parameters (initial drop 0.7 Hz)

[0142]

[0143] Table 7 Root mean square error (initial drop 0.7Hz)

[0144]

[0145] The prediction results are as follows Figure 2-Figure 4 As shown, Figure 2 This is the prediction result of the first prediction. The data when the crankshaft natural frequency drops 0.3Hz from the initial value is selected for prediction by Kalman filtering. Figure 2 (A), (B), (C), and (D) correspond to the first to fourth groups of data respectively; Figure 3 This is the prediction result of the second prediction. The data when the crankshaft natural frequency drops 0.5Hz from the initial value is selected for prediction by Kalman filtering. Figure 3 (A), (B), (C), and (D) correspond to the first to fourth groups of data respectively; Figure 4 This is the prediction result of the third prediction. The data when the crankshaft natural frequency drops 0.7Hz from the initial value is selected for Kalman filtering prediction. Figure 4 (A), (B), (C), and (D) correspond to the first to fourth groups of data respectively; Figure 2-Figure 4 The prediction results show that the prediction results of these four data sets all conform to the rules. The data selected for these four data sets were initially predicted when the initial frequency dropped by 0.3Hz. Due to the small amount of data, the predicted remaining crankshaft life differed significantly from the actual crankshaft life, resulting in a large error. When the data when the initial frequency dropped by 0.7Hz was selected for prediction, the prediction results had smaller errors than the two previous predictions (dropping to 0.3Hz and 0.5Hz). This shows that the accuracy of the prediction results is related to the amount of data. However, there are also certain errors in the second set of data, indicating that changing the amount of data can only reduce the prediction error to a certain extent. This prediction method still has the problem of inaccurate prediction of some data. Using a frequency drop of 0.3Hz can save about 30% of the test time, and using a frequency drop of 0.7Hz can save 15% of the test time.

[0146] The direct use of Kalman filtering to predict the remaining life of the crankshaft has some data inaccurate prediction problems, which needs further improvement. The depth, location and number of crankshaft cracks have a great influence on the crankshaft natural frequency.

[0147] Example 2

[0148] The crankshaft crack growth rate is divided into three stages: A, B, and C. Zone A is the initial stable growth zone of the crack, zone B is the stable crack growth zone, and zone C is the rapid crack growth zone, corresponding to the low, medium, and high rate zones respectively. When the bi-exponential model is used to fit these three different zones directly, the fitting effect is not ideal. Because the data of the early crack in the initial stable growth zone does not conform to the fitting curve very well, including these data in the fitting will cause a large error in the fitting result. When fitted into a hyperbolic exponential model, the root mean square error (RMSE) of the fitting result is large, and the fitting result is not ideal. Therefore, you can choose to improve the sample space of the experimental data, discard the first part of the data, select the middle part of the data, and then fit it. Use the goodness of fit value R for the re-fitted data. 2 The root mean square error (RMSE) is used to evaluate the quality of the fitting.

[0149] Therefore, based on the data of Example 1, the crankshaft is subjected to a cyclic test by loading a load on a crankshaft fatigue test bench in step one, and the natural frequency data obtained is fitted after removing the data in the initial stable expansion zone. Then, the Kalman filter algorithm is used to predict the remaining life of the crankshaft.

[0150] Specific experimental process:

[0151] 1) The experimental data were processed as follows: the first group discarded the data before 46.10 Hz and selected the frequency range from 46.10 Hz to 45.59 Hz; the second group discarded the data before 46.17 Hz and selected the frequency range from 46.17 Hz to 45.67 Hz; the third group discarded the data before 46.13 Hz and selected the frequency range from 46.13 Hz to 45.63 Hz; the fourth group discarded the data before 46.163 Hz and selected the frequency range from 46.163 Hz to 45.663 Hz. In all cases, the natural frequency dropped by 0.5 Hz from the beginning.

[0152] The results after refitting are shown in Table 8:

[0153] Table 8 Fitting results of processed data

[0154]

[0155] By comparing the fitting results of the unreduced data (Table 1), when the goodness of fit value R 2 When evaluated, the two fit results were similar, both very close to 1, indicating that the accuracy of the two fits was similar when compared using the goodness-of-fit value. When evaluated using the root mean square (RMSE), it can be seen that the fit result is significantly lower than the fit result without data reduction (Table 1). The smaller the RMSE value, the more accurate the fit result, indicating that the fit result after data reduction (Table 8) is better than the fit result without data reduction (Table 1).

[0156] 2) Fit the four sets of data in Table 7 to obtain the parameter values of the state space equation. The parameter values and root mean square errors of the four sets of equations are shown in Tables 9 and 10:

[0157] Table 9 State equation parameters (down 0.5Hz)

[0158]

[0159] Table 10 Root mean square error (down 0.5Hz)

[0160]

[0161]

[0162] 3) Using Kalman filtering to predict the remaining life of the crankshaft, the data in the range of 0.5Hz decrease in the crankshaft natural frequency is used. The results are as follows: Figure 5 As shown;

[0163] Figure 5 The data selected are all from the range where the crankshaft natural frequency drops by 0.5Hz from the initial value under cyclic load. When compared with the natural frequency of the data without reduction, it is found that the root mean square error of the data is significantly smaller than the root mean square error of the data without reduction. In the four sets of data after data reduction (corresponding to Table 8), Figure 5 (A), (B), (C), and (D) correspond to the first to fourth groups of data in Table 8, respectively. The remaining life curves of the crankshafts predicted by the first and second groups are very close to the actual remaining life curves of the crankshafts. The error of the third group is slightly larger than that of the first and second groups. The life curve predicted by the fourth group is slightly smaller than the actual life curve data. Therefore, when using the predicted remaining life for calculation, it can play a warning role, and it is not much different from the actual life data. The prediction results of these groups of data have errors within 5%, which largely meets the requirements of practical applications.

[0164] The reason why there are still errors in the prediction results is that although the number of data training has been improved and the impact on the Kalman filter estimation results has been improved, there are noise problems in the setting of the initial value of the Kalman filter and the prediction process. Even if filtering is performed, it will still affect the prediction results and cause errors.

[0165] The above experimental results indicate that the improved Kalman filter remaining life prediction method can be applied to crankshaft accelerated fatigue testing. Furthermore, minimal experimental data is required; using only data from the 0.5Hz range within the crankshaft's natural frequency, the number of crankshaft load cycles to failure can be predicted in advance. The predicted results closely match the actual results, requiring only the initial set of experiments to predict the actual results. This reduces both experimental costs and experimental time, demonstrating excellent economic practicality. This approach is also valuable for the use of everyday engineering components, enabling early prediction of component failure points and timely replacement to prevent disruptions to industrial production. Furthermore, the predicted number of crankshaft load cycles can be used as actual crankshaft fatigue test data for statistical analysis.

[0166] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A crankshaft accelerated fatigue test method, characterized in that: The steps include: Step 1: Establish an empirical model of crankshaft natural frequency and cycle number, the empirical model is a double exponential model: ； Where y represents the natural frequency of the crankshaft, x represents the number of cycles, and a, b, c, and d are unknowns. In step 1, when establishing the empirical model, the principle of minimizing the fitting error used in data processing is: The root mean square (RMSE) and the coefficient of determination (R-square) are introduced to judge the quality of the experimental data fitting: ； In the formula, yi represents the i-th true value, is the average value of the original real data, is the model prediction value, m is the number of original data points; The smaller the RMSE value, the better the model performance and the better the fitting effect. The value range of R-square is [0, 1]. The closer the R-square is to 1, the better the fitting effect is, and the closer it is to 0, the greater the deviation of the fitting result. Step 2: Simplify the established empirical model and establish a Kalman filter system observation model for predicting the remaining fatigue life of the crankshaft. The state space equation of the UKF system observation model is as follows: ； Where Z(k+1) is the observation value at the current moment, α is the empirical value of the system's natural frequency decay; V(k) is the process noise, both of which satisfy the standard normal distribution with a mean of 0 and a variance of σw. The specific steps of step 2 are as follows: 1) For a discrete-time nonlinear system consisting of a random variable with Gaussian white noise W (k) and an observation variable Z with Gaussian white noise V(k), it can be described as: ； Where f is the nonlinear state equation function, c is the nonlinear observation equation function; 2) Assume that w(k) has a covariance matrix Q and v(k) has a covariance matrix R; based on the decreasing characteristics of the natural frequency and the double exponential model, the UKF state model is expressed as follows: ； Where, It represents the estimated value of the natural frequency drop model parameter after the last moment, Indicates the current state prediction value; 3) Based on the double exponential model, the state space equation of the UKF system observation model for predicting the remaining fatigue life of the crankshaft is established: ； Z(k+ 1) is the observed value at the current moment, α is the empirical value of the system's natural frequency decay; V(k) is the process noise, which all satisfy the standard normal distribution with mean 0 and variance σw; b(k), c(k), and d(k) are the parameters of the state-space equation; Step 3: Predict the remaining fatigue life of the crankshaft through the UKF system observation model.

2. A crankshaft accelerated fatigue test method according to claim 1, characterized in that: In step 1, the steps for obtaining the empirical model are as follows: 1) The crankshaft is subjected to a cyclic test with a load on a crankshaft fatigue test bench to obtain experimental data on the number of cycles at which its natural frequency drops to failure and the decrease in the natural frequency value with increasing cycle number; 2) According to the experimental natural frequency, the law of crankshaft natural frequency change and the principle of minimum fitting error, the experimental data are fitted nonlinearly, and the double exponential model is selected as the empirical model.

3. The crankshaft accelerated fatigue test method according to claim 2, characterized in that: In the step 1, the step of acquiring the empirical model also includes data processing, specifically: in step 1), the natural frequency data obtained from the experiment is removed from the data in the initial stable expansion region.

4. The crankshaft accelerated fatigue test method according to claim 1, characterized in that: The specific steps of step three are as follows: Perform UKF iterative update to estimate the optimal parameters, and the steps of the unscented Kalman filter algorithm for the predicted value δ of the natural frequency at different times k are as follows: (1) Use the state estimate X(k) at time k and its error covariance matrix to calculate 2n+1 sigma points: ； Where λ is the scale factor, n is the dimension of the state variable; (2) Calculate the corresponding weight of the sigma point: ； In the formula, i represents the number of sigma points, ωm represents the weight of the mean, represents the weight of the mean; λ = α2 +(n+k)-n is a scaling parameter used to reduce the prediction error, and k is a parameter to be selected to ensure that the matrix (n+λ)P is a semi-positive matrix; (3) Using the two formulas in (1) and (2), find: ； (4) These 2n+1 sigma points are transformed into: ； (5) The one-step prediction and covariance matrix of the system state are: ； (6) Based on the one-step prediction value, UT transformation is used again to generate a new Sigma point set, as shown below: ； (7) Substitute the Sigma point predicted by the above formula into the observation prediction equation, and obtain the military mean and covariance of the system observation through weighted summation: ； (8) The observed predicted value of the Sigma point is obtained from step (7), and the mean and covariance of the system prediction are obtained by weighted summation: ； (9) Calculate the Kalman gain matrix K: ； (10) Finally, calculate the state update and covariance update of the system: ； (11) Use the parameters identified by UKF to predict the natural frequency.

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