Engineering equipment fatigue damage estimation method and device, electronic equipment and storage medium

Abstract

This application provides a method and apparatus, electronic device, and storage medium for estimating fatigue damage of engineering equipment, belonging to the field of state estimation technology. The method includes: dividing the equivalent stress amplitude sequence into a first region and a second region based on a target initial threshold, where the equivalent stress amplitude in the first region is greater than or equal to the target initial threshold, and the equivalent stress amplitude in the second region is less than the target initial threshold; extrapolating the extreme value distribution of the first region to obtain the extrapolated equivalent stress amplitude spectrum of the first region; performing linear extrapolation of the second region to obtain the extrapolated equivalent stress amplitude spectrum of the second region; merging the extrapolated equivalent stress amplitude spectra of the first and second regions to obtain the extrapolated equivalent stress amplitude spectrum; and calculating the cumulative fatigue damage of the engineering equipment based on the extrapolated equivalent stress amplitude spectrum and the stress-life curve using Palmgern-Miner linear cumulative damage calculation. This application can improve the accuracy of stress amplitude spectrum extrapolation and the accuracy of fatigue damage estimation.

Description

Technical Field

[0001] This application belongs to the field of fatigue damage estimation technology, and more specifically, relates to a fatigue damage estimation method and device for engineering equipment, electronic equipment, and storage medium. Background Technology

[0002] Engineering equipment encompasses heavy engineering equipment such as bridge erecting machines, cranes, and excavators. Their main load-bearing structures are continuously subjected to random, alternating equivalent stress amplitudes under complex field conditions. Dynamic response signals refer to the stress and strain time-series data collected by sensors at critical hazardous locations of the equipment. After performing cyclic counting and average stress correction on the dynamic response data, the equivalent stress amplitude can be obtained. The continuous application of numerous equivalent stress cycles of varying magnitudes gradually accumulates fatigue damage. Damage quantification results are the core basis for determining equipment maintenance cycles and managing structural safety. Due to limitations in work sites, testing costs, and the randomness of operating conditions, only short-time domain measured dynamic response data can be collected at engineering sites. To assess fatigue damage throughout the entire service life of the equipment, it is necessary to rely on short-term stress amplitude data to perform stress amplitude spectrum extrapolation.

[0003] Currently, the main methods for extrapolating the equivalent stress amplitude spectrum in the industry are divided into two categories: statistical extrapolation of rainflow and time-domain extrapolation based on extreme value theory. Parametric rainflow extrapolation relies on a preset probability distribution function for fitting extrapolation, while nonparametric rainflow extrapolation and extreme value extrapolation rely on manually defining a threshold value to distinguish between the range of conventional equivalent stress amplitude and extreme equivalent stress amplitude.

[0004] Existing extrapolation techniques generally suffer from a significant drawback: the thresholds used for equivalent stress amplitude partitioning are entirely determined manually by R&D personnel based on their experience. This threshold selection is highly subjective, and unreasonable threshold divisions can directly lead to statistical distortion of equivalent stress amplitudes in high-stress extreme value sections. This causes the extrapolated equivalent stress amplitude spectrum to deviate from the actual long-term service equivalent stress amplitude patterns of the equipment, ultimately resulting in large errors in subsequent fatigue damage calculations and failing to provide accurate data support for equipment operation and maintenance. Therefore, improving the accuracy of equivalent stress amplitude spectrum extrapolation, thereby enhancing the accuracy of fatigue damage estimation, is a problem that needs to be addressed. Summary of the Invention

[0005] The purpose of this application is to provide a method, device, electronic equipment, and storage medium for estimating fatigue damage of engineering equipment, in order to solve the problem in the prior art where the extrapolated equivalent stress amplitude spectrum deviates from the actual long-term service equivalent stress amplitude law of the equipment, resulting in large errors in the subsequent fatigue damage calculation results, and to improve the authenticity of the extrapolated equivalent stress amplitude spectrum, thereby improving the accuracy of fatigue damage estimation.

[0006] A first aspect of this application provides a method for estimating fatigue damage of engineering equipment, comprising: Obtain the dynamic response signal of the dangerous stress area of ​​the engineering equipment, generate the equivalent stress amplitude sequence based on the dynamic response signal, and determine the probability distribution map corresponding to the equivalent stress amplitude sequence; The initial threshold interval is determined based on the probability distribution map, and the initial threshold interval is divided into multiple sub-intervals; the initial equivalent stress amplitude of each sub-interval is used as the initial threshold benchmark, and the target initial threshold is determined based on each initial threshold benchmark. Based on the target initial threshold, the equivalent stress amplitude sequence is divided into a first region and a second region. The equivalent stress amplitude in the first region is greater than or equal to the target initial threshold, and the equivalent stress amplitude in the second region is less than the target initial threshold. The extreme value distribution extrapolation of the first region is used to obtain the extrapolated equivalent stress amplitude spectrum of the first region. The linear extrapolation of the second region is used to obtain the extrapolated equivalent stress amplitude spectrum of the second region. The extrapolated equivalent stress amplitude spectra of the first and second regions are combined to obtain the extrapolated equivalent stress amplitude spectrum. Based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, the cumulative fatigue damage of engineering equipment is calculated using Palmgren-Miner linear cumulative damage.

[0007] A second aspect of this application provides a fatigue damage estimation device for engineering equipment, comprising: The equivalent stress amplitude sequence generation module is used to acquire the dynamic response signal of the dangerous stress area of ​​engineering equipment, generate the equivalent stress amplitude sequence based on the dynamic response signal, and determine the probability distribution map corresponding to the equivalent stress amplitude sequence. The initial threshold determination module is used to determine the initial threshold interval based on the probability distribution map, divide the initial threshold interval into multiple sub-intervals, use the initial equivalent stress amplitude of each sub-interval as the initial threshold benchmark, and determine the target initial threshold based on each initial threshold benchmark. The equivalent stress amplitude extrapolation module is used to divide the equivalent stress amplitude sequence into a first region and a second region based on a target initial threshold. The equivalent stress amplitude in the first region is greater than or equal to the target initial threshold, and the equivalent stress amplitude in the second region is less than the target initial threshold. The extreme value distribution extrapolation is performed on the first region to obtain the extrapolated equivalent stress amplitude spectrum of the first region. Linear extrapolation is performed on the second region to obtain the extrapolated equivalent stress amplitude spectrum of the second region. The extrapolated equivalent stress amplitude spectra of the first region and the extrapolated equivalent stress amplitude spectra of the second region are merged to obtain the extrapolated equivalent stress amplitude spectrum. The cumulative fatigue damage estimation module is used to calculate the cumulative fatigue damage of engineering equipment based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, using Palmgren-Miner linear cumulative damage.

[0008] A third aspect of this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of the above-described fatigue damage estimation method for engineering equipment.

[0009] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described fatigue damage estimation method for engineering equipment.

[0010] The beneficial effects of the fatigue damage estimation method and device for engineering equipment, electronic equipment, and storage medium provided in this application are as follows: This application's embodiments determine a reasonable initial target threshold based on the probability distribution map corresponding to the equivalent stress amplitude sequence, avoiding human intervention and ensuring that the initial target threshold conforms to the objective distribution law of the equivalent stress amplitude. Since the initial target threshold is objectively determined based on the probability distribution map, it can reasonably divide the first and second regions, thus ensuring that a sufficient number of equivalent stress amplitudes from the first region participate in extreme value distribution extrapolation while preventing the equivalent stress amplitudes from the second region from being incorrectly included in the extreme value distribution extrapolation scope. This application's embodiments adopt a zoned differentiated extrapolation mode: for the high-stress first region, extreme value distribution extrapolation is used, utilizing the distribution characteristics of equivalent stress amplitudes greater than or equal to the initial target threshold in the equivalent stress amplitude sequence to accurately capture the distribution of low-frequency, high-risk high stress amplitudes, avoiding the underestimation of extreme values ​​by traditional linear extrapolation; for the low-stress second region, linear extrapolation is used, extending the equivalent stress amplitudes less than the initial target threshold in the equivalent stress amplitude sequence to avoid fitting errors introduced by complex models. By merging the extrapolated equivalent stress amplitude spectra of the first and second regions, the extreme value distribution characteristics of the first region are accurately depicted while retaining the main statistical features of the second region. This fully restores the full-range equivalent stress amplitude characteristics under long-term service conditions, improving the extrapolation accuracy of the equivalent stress amplitude spectrum. Based on this, the Palmgren-Miner linear cumulative damage calculation is applied to the cumulative fatigue damage of the engineering equipment using the extrapolated equivalent stress amplitude spectrum in conjunction with the stress-life curve, making the fatigue damage assessment results more closely match the actual service wear of the equipment. Therefore, this embodiment can improve the extrapolation accuracy of the equivalent stress amplitude spectrum, thereby improving the accuracy of fatigue damage estimation. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 A flowchart illustrating the fatigue damage estimation method for engineering equipment provided in this application embodiment; Figure 2 A schematic diagram of the stress hotspot distribution area of ​​the mobile bridge erecting machine provided in an embodiment of this application; Figure 3 This is a schematic diagram of the power spectral density of the dynamic response signal provided in an embodiment of this application; Figure 4 This is a schematic diagram of the dynamic response signal of the measuring point provided in the embodiments of this application; Figure 5 The stress spectrum processed by the rainflow counting method is provided in the embodiments of this application; Figure 6 The equivalent stress amplitude spectrum of the measuring points provided in the embodiments of this application; Figure 7 A schematic diagram of different k-order empirical average conditional transcendence functions provided for embodiments of this application; Figure 8 A probability distribution diagram of the equivalent stress amplitude spectrum provided in the embodiments of this application; Figure 9 This is a curve showing the extreme value prediction of the equivalent stress amplitude provided in the embodiments of this application; Figure 10 A graph showing the fitting results of the first-order target average conditional transcendence rate function provided for embodiments of this application; Figure 11 This is a schematic diagram of threshold region division provided in an embodiment of this application; Figure 12 The extrapolated load cumulative amplitude-frequency distribution curve provided in the embodiments of this application; Figure 13 The load amplitude-frequency distribution histogram provided in the embodiments of this application; Figure 14 A fatigue damage assessment result diagram provided for an embodiment of this application; Figure 15 A structural block diagram of the fatigue damage estimation device for engineering equipment provided in the embodiments of this application; Figure 16 A schematic block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0013] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0014] To make the objectives, technical solutions, and advantages of this application clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0015] Figure 1 This is a flowchart illustrating a fatigue damage estimation method for engineering equipment provided in an embodiment of this application. The method can be executed by an electronic device and includes: S101: Obtain the dynamic response signal of the dangerous stress area of ​​the engineering equipment, generate the equivalent stress amplitude sequence based on the dynamic response signal, and determine the probability distribution map corresponding to the equivalent stress amplitude sequence.

[0016] In this embodiment, generating an equivalent stress amplitude sequence based on the dynamic response signal includes: Obtain the tensile strength of the target material; the target material is a structural material used to manufacture dangerous stress-bearing parts of engineering equipment. The dynamic response signal is obtained by low-pass filtering. The filtered dynamic response signal is processed by rainflow counting method to obtain multiple sets of stress cycles, which include stress amplitude and stress mean. Based on the tensile strength of the target material, each set of stress cycles is corrected using the Goodman equation to obtain the corresponding equivalent stress amplitude; multiple equivalent stress amplitudes form an equivalent stress amplitude sequence; The Goodman equation is: ; in, This refers to the stress amplitude; This represents the average stress value. The equivalent stress amplitude when the mean is 0; The tensile strength of the target material.

[0017] In this embodiment, the dynamic response signal is the time-varying stress or strain response data generated in the hazardous stress area of ​​the engineering equipment during operation. The equivalent stress amplitude sequence is a data set composed of multiple equivalent stress amplitudes arranged in chronological order. The tensile strength of the target material is the maximum stress value that the target material can withstand before fracture in a tensile test; for example, the tensile strength of the steel used in the curved beam of a bridge erecting machine is 500 MPa. Low-pass filtering is a signal processing method used to filter out high-frequency noise components higher than the cutoff frequency; for example, a low-pass filter with a cutoff frequency of 2 Hz is used to remove high-frequency interference. The filtered dynamic response signal is the stress data that retains the main frequency components after low-pass filtering of the original dynamic response signal. Rainflow counting is a cycle counting method used to decompose the filtered dynamic response signal, from which multiple sets of stress cycles can be extracted. Each set of stress cycles includes a stress amplitude and a stress mean. The stress amplitude is half the fluctuation range from the stress trough to the stress peak in a stress cycle. The stress mean is the average of the stress peak and stress trough values ​​in a stress cycle. The Goodman equation is a mean stress correction formula used to convert asymmetric cyclic stress into equivalent symmetric cyclic stress, thereby obtaining the equivalent stress amplitude. The probability distribution plot is a graphical tool used to determine the distribution characteristics of the equivalent stress amplitude sequence.

[0018] This embodiment first obtains the tensile strength of the target material because the Goodman equation requires the material's inherent parameters as a correction benchmark. Differences in tensile strength between different materials directly affect the calculation results of the equivalent stress amplitude. Low-pass filtering of the dynamic response signal is performed because the measured dynamic response signal contains high-frequency noise components. This noise is not the true mechanical response of the structure; if not filtered out, it will lead to a large number of false small-amplitude cycles being extracted by rainflow counting, interfering with the true statistical characteristics of the equivalent stress amplitude spectrum. Rainflow counting is then used after filtering because the dynamic response signal is a random, non-stationary time history and cannot be directly used for fatigue analysis. Rainflow counting is needed to decompose the complex waveform into several complete stress cycles (i.e., each cycle is characterized by two parameters: stress amplitude and stress mean). Finally, correction is performed using the Goodman equation because the fatigue performance data of materials is usually based on symmetrical cyclic stress measurements, while the stress cycles experienced by structures under actual working conditions are mostly asymmetrical. If the influence of the stress mean is not considered, directly using the stress amplitude for damage estimation will produce a large deviation.

[0019] For example, in this embodiment, the tensile strength of the steel used in the curved beam structure of the bridge erecting machine is obtained by consulting the material certificate or by commissioning a third-party testing agency to conduct a standard tensile test. Next, the dynamic response signal is low-pass filtered. Strain gauges are attached to measuring point seven on the web near the mid-span of the curved beam of the bridge erecting machine, and strain time history data during beam transport is collected at a sampling frequency of 2000Hz. The strain is converted into stress using von Mises theory to obtain the dynamic response signal. Power spectral density analysis is performed on this dynamic response signal to determine that the main frequency range of the excitation energy is within 2Hz. Based on this, a low-pass filter with a cutoff frequency of 2Hz is designed to filter the dynamic response signal, removing high-frequency noise components above 2Hz, resulting in a filtered dynamic response signal. Then, the filtered dynamic response signal is input into a rainflow counting algorithm. This algorithm identifies the peak and trough values ​​in the stress time history using a four-point method, extracting the complete stress cycle from the complex waveform. The processing results in multiple sets of paired data for stress amplitude and stress mean, with each set corresponding to a complete stress cycle. Finally, the Goodman equation is used to correct each set of stress amplitudes and mean stresses. The stress amplitude, mean stress, and tensile strength of the material are obtained and substituted into the Goodman equation to solve for the equivalent stress amplitude. Using the same calculation process, each set of stress amplitudes and mean stresses output by the rainflow counting method is processed sequentially to obtain the corresponding equivalent stress amplitude. Furthermore, an equivalent stress amplitude sequence is formed. All calculated equivalent stress amplitudes are arranged in chronological order to form the equivalent stress amplitude sequence.

[0020] This embodiment effectively filters out high-frequency noise interference, accurately extracts stress cycling characteristics, and uniformly corrects asymmetric cyclic stresses to equivalent symmetric cyclic stresses by sequentially performing low-pass filtering, rainflow counting, and Goodman correction on the dynamic response signal, thereby generating a standardized equivalent stress amplitude sequence. This equivalent stress amplitude sequence eliminates the influence of signal noise and stress mean.

[0021] S102: Determine the initial threshold interval based on the probability distribution map, divide the initial threshold interval into multiple sub-intervals; use the initial equivalent stress amplitude of each sub-interval as the initial threshold benchmark, and determine the target initial threshold based on each initial threshold benchmark.

[0022] In this embodiment, determining the target initial threshold based on each initial threshold benchmark includes: Obtain the initial threshold benchmark for the target sub-interval, and calculate the predicted extreme value corresponding to the initial threshold benchmark; Obtain the predicted extreme value corresponding to the initial threshold benchmark of the previous sub-interval adjacent to the target sub-interval, calculate the absolute value of the difference between the predicted extreme value corresponding to the initial threshold benchmark of the previous sub-interval and the predicted extreme value corresponding to the initial threshold benchmark of the target sub-interval, and obtain the predicted extreme value difference. If the difference between predicted extreme values ​​is greater than or equal to the preset convergence threshold, the process is repeated to obtain the initial threshold benchmark of the next adjacent sub-interval of the target sub-interval, calculate the predicted extreme value corresponding to the initial threshold benchmark, until the preset stopping condition is met, and the initial threshold benchmark that meets the preset stopping condition is taken as the target initial threshold. The preset stopping condition is that the difference between predicted extreme values ​​is less than the preset convergence threshold. The steps for calculating the predicted extreme value corresponding to the initial threshold benchmark include: Determine the target average conditional exceedance function corresponding to this initial threshold benchmark; Based on this initial threshold benchmark, the average conditional exceedance rate corresponding to the initial threshold benchmark is calculated using the corresponding target average conditional exceedance rate function. Based on the average conditional exceedance rate, the cumulative distribution probability corresponding to the initial threshold benchmark is obtained by calculating through the extreme value distribution function. Based on the cumulative distribution probability, the predicted extreme value corresponding to the initial threshold benchmark is obtained by calculating using the quantile function.

[0023] In this embodiment, the initial threshold interval is a continuous numerical range defined by a probability distribution map for selecting target initial thresholds. Sub-intervals are segmented numerical ranges formed by dividing the initial threshold interval at fixed intervals. The initial threshold benchmark is the candidate initial threshold value determined by selecting the starting point of each sub-interval. The predicted extreme value difference is the result of subtracting the predicted extreme values ​​corresponding to adjacent initial threshold benchmarks and taking the absolute value. The average conditional exceedance rate is the average statistical parameter obtained by calculating the target average conditional exceedance rate function. The extreme value distribution function is a computational model constructed based on the average conditional exceedance rate to describe the distribution law of extreme values. The cumulative distribution probability is the distribution probability corresponding to the equivalent stress amplitude output by the extreme value distribution function. The quantile function is a computational model that calculates the corresponding amplitude from the cumulative distribution probability by inversely converting the extreme value distribution function.

[0024] Considering that existing threshold selections often rely on operators' subjective experience, which easily leads to threshold values ​​being too high or too low, resulting in incorrect classification of equivalent stress amplitudes under high and low stress, and affecting the accuracy of subsequent equivalent stress amplitude spectrum extrapolation, this embodiment first uses a probability distribution plot to lock in the initial threshold interval, compressing the overall range of candidate values ​​and reducing redundant computation. Then, the initial threshold interval is split into sub-intervals, and each sub-interval's starting point is used as the initial threshold benchmark. The predicted extreme values ​​are then solved step-by-step using a three-layer function. A convergence criterion is set using the difference between predicted extreme values; optimization stops when the numerical fluctuation meets the convergence requirement, thus completing the initial threshold selection based on the objective changes in the data.

[0025] For example, the equivalent stress amplitude sequence collected from the measuring points of the curved beam of the mobile bridge erecting machine is selected for practical operation. Based on this equivalent stress amplitude sequence, a corresponding probability distribution map is generated. Referring to the data in the probability distribution map, an initial threshold interval of 42MPa to 63MPa is defined. All intervals are divided using 0.5MPa as a fixed interval, resulting in multiple continuously arranged sub-intervals. The initial equivalent stress amplitude of each sub-interval is extracted as the initial threshold benchmark. First, the calculation is performed on the first initial threshold benchmark. The corresponding average conditional exceedance rate is calculated using the target average conditional exceedance rate function. The obtained parameters are substituted into the extreme value distribution function to calculate the corresponding cumulative distribution probability. Then, based on the cumulative distribution probability, the predicted extreme value corresponding to the initial threshold benchmark is calculated using the quantile function. The entire calculation process is repeated for the initial threshold benchmarks corresponding to subsequent sub-intervals. The difference between the predicted extreme values ​​of adjacent sub-intervals is calculated in real time, and continuous iterative optimization is performed until the difference between the predicted extreme values ​​is less than the preset convergence threshold. At this point, the corresponding initial threshold benchmark of 44MPa is determined as the target initial threshold.

[0026] This embodiment automatically determines the initial threshold of the target by defining the range using a probability distribution map and combining it with extreme value convergence rules, eliminating the value errors caused by human experience intervention. It predicts extreme values ​​layer by layer through the average conditional exceedance rate function, extreme value distribution function, and quantile function, ensuring that the extreme value results corresponding to the candidate thresholds are objective and reliable. The equivalent stress amplitude partition boundaries closely match the true distribution of stress amplitudes, and the accuracy of the extrapolated equivalent stress amplitude spectrum formed by partition extrapolation is significantly improved, ultimately effectively improving the calculation accuracy of cumulative fatigue damage in engineering equipment.

[0027] In this embodiment, determining the target average conditional exceedance function corresponding to the initial threshold benchmark includes: The empirical average conditional exceedance rate function is obtained by calculating the equivalent stress amplitude sequence; Based on the exponential form function, and by fitting the equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold benchmark through the empirical average conditional exceedance function, the exponential form average conditional exceedance function is obtained; the values ​​of the parameter combination in the exponential form average conditional exceedance function are unknown, and the parameter combination includes the first parameter, the second parameter, the third parameter, and the fourth parameter; By taking the logarithm of both sides of the exponential form of the average conditional transcendence function, an optimization function is established with the goal of minimizing the sum of squared residuals. The optimal parameter combination is then iteratively fitted based on the Levenberg-Marquardt algorithm and the weighted least squares method. Substituting the optimal parameter combination into the exponential form of the average conditional exceedance function yields the target average conditional exceedance function. The target mean conditional exceedance function is: ; in, The first value in the equivalent stress amplitude sequence that is greater than or equal to the initial threshold baseline. One equivalent stress amplitude, As the initial threshold benchmark, For the first The target average conditional exceedance rate corresponding to each equivalent stress amplitude; , where n is the number of equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold baseline; a k As the first parameter, b k For the second parameter, c k As the third parameter, q k The fourth parameter, a k , b k , c k and q k All are constants.

[0028] In this embodiment, the Average Conditional Exceedance Rate (ACER) function is a function generated based on statistical calculations of the equivalent stress amplitude sequence. The exponential ACER function is an intermediate function obtained by fitting an exponential function, where the value of the parameter combination is unknown. The parameter combination is a set of parameters that aggregate the first, second, third, and fourth parameters. The optimization function is a parameter solution formula built with residual control as the objective. The criterion of minimizing the sum of squared residuals is the criterion for determining the optimization of constraint parameters. The Levenberg-Marquardt algorithm and the weighted least squares method are two different types of parameter iterative optimization algorithms. The optimal parameter combination is the final parameter value that meets the accuracy requirements after iterative optimization. The target ACER function is obtained by substituting the value of the optimal parameter combination into the exponential ACER function.

[0029] The empirical average conditional transcendence rate function is: ; ; in, The first value in the equivalent stress amplitude sequence that is greater than or equal to the initial threshold baseline. One equivalent stress amplitude; For the first The empirical average conditional exceedance rate corresponding to each equivalent stress amplitude; N is the total number of equivalent stress amplitudes in the equivalent stress amplitude sequence. ; For the first The conditional exceedance probability corresponding to each equivalent stress amplitude; Let j be the j-th equivalent stress amplitude in the equivalent stress amplitude sequence. This represents the (j-1)th equivalent stress amplitude in the equivalent stress amplitude sequence. Let be the (j-k+1)th equivalent stress amplitude in the equivalent stress amplitude sequence; k is the conditional correlation order, indicating that the (k-1)th equivalent stress amplitudes before the jth equivalent stress amplitude are related to the jth equivalent stress amplitude, so the statistics start from the (j-(k-1)th)th equivalent stress amplitude.

[0030] The optimized function is: ; in, is the weighting factor for the i-th equivalent stress amplitude, and n is the number of equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold benchmark; It is an exponential form of the average conditional transcendence rate function. The first value in the equivalent stress amplitude sequence that is greater than or equal to the initial threshold baseline. One equivalent stress amplitude, a k As the first parameter, b k For the second parameter, c k As the third parameter, q k The fourth parameter, a k , b k , c k and q k All are constants.

[0031] In this embodiment, the conditional correlation order is a parameter describing the correlation between the current equivalent stress amplitude and several previous equivalent stress amplitudes. Weighting factor This is a coefficient that measures the importance of the i-th equivalent stress magnitude in the fitting process. The optimal parameter combination is the one that minimizes the sum of squared residuals. a k , b k , c k and q k Specific values, such as those in this embodiment. a k The value is 0.0019. bk 38.46 c k For 1.98 and q k It is 0.017.

[0032] This embodiment describes the exponential form of the ACER function. Taking the logarithm of both sides, we get the following formula: ; Given an initial second parameter b k and the initial third parameter c k In this case, let , Then the parameters can be estimated using the weighted linear regression formula. a k and As shown in the formula below: ; ; in, The weighting factor for the i-th equivalent stress amplitude is... , and These represent the upper and lower limits of the 95% confidence interval, respectively. Here is the formula for calculating the confidence interval. n is the number of equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold baseline; k is the conditional correlation order. It is an exponential form of the average conditional transcendence rate function. The first value in the equivalent stress amplitude sequence that is greater than or equal to the initial threshold baseline. One equivalent stress amplitude; for The average value, for The average value.

[0033] Then, an optimization function is established with the goal of minimizing the sum of squared residuals. The values ​​of the parameter combination are updated iteratively using the nonlinear optimization Levenberg-Marquardt algorithm and the weighted least squares method. a k , b k , c k and q k .

[0034]

[0035]

[0036]

[0037] in, , ; This is the weight matrix. The weighting factor for the i-th equivalent stress amplitude is... ; This is a Jacobian matrix with elements of . ; For damping parameters; I It is the identity matrix; t T is the number of iterations; T is the transpose. For the variable iteration increment, Let be the variable matrix for the t-th iteration. Let be the variable matrix for the (t+1)th iteration. For the residual vector, For the residual function, This is the residual calculation result for the i-th equivalent stress amplitude.

[0038] This embodiment introduces a conditional correlation order to account for the temporal correlation of the equivalent stress amplitude sequence. The dynamic response signals of actual engineering equipment are often correlated; the equivalent stress amplitude at a certain moment is related to the stress state at several previous moments. The conditional exceedance probability can capture this memory effect. Based on an exponential form function and using an empirical average conditional exceedance rate function, the equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold benchmark are fitted. This is because extremum theory shows that the exceedance rate in the tail region asymptotically follows an exponential distribution, and this exponential form function can accurately describe the attenuation law in the high-threshold region. Taking two logarithmic operations on both sides of the exponential ACER function aims to transform the complex exponential form into a linear form, facilitating the establishment of an optimization function based on the residual sum of squares minimization criterion to solve for the optimal parameters. The Levenberg-Marquardt algorithm combined with weighted least squares is used to optimize the parameter combination; this hybrid strategy balances computational efficiency and fitting accuracy. The final optimal parameter combination ensures that the fitted target average conditional exceedance rate function highly matches the empirical data in the tail region, laying an accurate foundation for subsequent extremum distribution modeling and extrapolation.

[0039] In this embodiment, the extreme value distribution function is obtained in the following way: According to the definition of the extreme value distribution function, we can obtain ; when When it approaches 0, Therefore, we can obtain ; Substituting the target mean conditional exceedance rate function into the above equation, we can obtain... ; That is, the extreme value distribution function is: ; Where N is the total number of equivalent stress amplitudes in the equivalent stress amplitude sequence, and k is the conditional correlation order. For the first The conditional exceedance probability corresponding to each equivalent stress amplitude For the j-th equivalent stress amplitude, For the (j-1)th equivalent stress amplitude, This is the (j-k+1)th equivalent stress amplitude; The first value in the equivalent stress amplitude sequence that is greater than or equal to the initial threshold baseline. One equivalent stress amplitude; For the first The target average conditional exceedance rate corresponding to each equivalent stress amplitude For the first The cumulative distribution probability corresponding to each equivalent stress amplitude; The quantile function is obtained as follows: By solving the inverse function of the extreme value distribution function, the quantile function is obtained. The quantile function is: ; in, c k As the first parameter, b k For the second parameter, a k As the third parameter, q k The fourth parameter, a k , b k , c k and q k All are constants. For the first The cumulative distribution probability corresponding to each equivalent stress amplitude For the first The predicted extreme values ​​corresponding to each equivalent stress amplitude.

[0040] In this embodiment, the extreme value distribution function is a function describing the cumulative distribution probability of the maxima in the equivalent stress amplitude sequence. Solving for the inverse function involves mathematical operations to find the inverse function of a known function; for example, given the mapping relationship between the cumulative distribution probability and the equivalent stress amplitude, the mapping relationship between the equivalent stress amplitude and the cumulative distribution probability can be calculated. The quantile function is the inverse function of the extreme value distribution function, used to deduce the corresponding equivalent stress amplitude from a given cumulative distribution probability.

[0041] In this embodiment, after obtaining the target mean conditional exceedance rate function, it needs to be transformed into a form suitable for engineering applications. The target mean conditional exceedance rate function directly expresses the relationship between the mean conditional exceedance rate and the equivalent stress amplitude, while fatigue damage estimation and Monte Carlo simulation require the correspondence between the cumulative distribution probability and the equivalent stress amplitude. Therefore, the target mean conditional exceedance rate function is first transformed into an exponential distribution function, converting the expression from mean conditional exceedance rate to cumulative distribution probability. The independent variable of the exponential distribution function is the equivalent stress amplitude, and the dependent variable is the cumulative distribution probability. However, in practical applications, it is often necessary to inversely calculate the corresponding equivalent stress amplitude based on the given cumulative distribution probability. To this end, the inverse function of the exponential distribution function is solved to obtain the quantile function, which takes the cumulative distribution probability as input and directly outputs the corresponding equivalent stress amplitude.

[0042] For example, this embodiment substitutes the target average conditional transcendence rate function into the definition of the extreme value distribution function. Specifically, for any given equivalent stress amplitude, firstly, the equivalent stress amplitude is substituted into the target average conditional transcendence rate function to calculate the corresponding average conditional transcendence rate. Then, the negative value of the exponential function with the natural constant as the base of the average conditional transcendence rate is taken, and the result is the cumulative distribution probability corresponding to the equivalent stress amplitude. This cumulative distribution probability represents the probability that the equivalent stress amplitude does not exceed a given value. Next, the inverse function of the extreme value distribution function is solved, i.e., the inverse function of the expression for the cumulative distribution probability with respect to the equivalent stress amplitude is obtained, yielding the quantile function. The solution process uses the cumulative distribution probability as the independent variable and the equivalent stress amplitude as the dependent variable. Finally, the quantile function is used as the basis for subsequent Monte Carlo simulations to generate extrapolated equivalent stress amplitudes.

[0043] This embodiment establishes a direct mapping relationship between the cumulative distribution probability and the equivalent stress amplitude by deriving the extreme value distribution function from the target mean conditional exceedance function and solving the quantile function. This quantile function has a concise form and optimized parameters, enabling efficient conversion of uniform random numbers generated by Monte Carlo simulations into corresponding equivalent stress amplitudes for subsequent extrapolation of the equivalent stress amplitude spectrum.

[0044] S103: Based on the target initial threshold, the equivalent stress amplitude sequence is divided into a first region and a second region. The equivalent stress amplitude in the first region is greater than or equal to the target initial threshold, and the equivalent stress amplitude in the second region is less than the target initial threshold. The extreme value distribution extrapolation of the first region is performed to obtain the extrapolated equivalent stress amplitude spectrum of the first region. The linear extrapolation of the second region is performed to obtain the extrapolated equivalent stress amplitude spectrum of the second region. The extrapolated equivalent stress amplitude spectrum of the first region and the extrapolated equivalent stress amplitude spectrum of the second region are merged to obtain the extrapolated equivalent stress amplitude spectrum.

[0045] In this embodiment, the extreme value distribution function and quantile function corresponding to the target initial threshold are determined; For the first region, the maximum predicted extreme value is obtained based on the quantile function corresponding to the target initial threshold; the maximum predicted extreme value corresponds to a maximum cumulative distribution probability; the maximum cumulative distribution probability is calculated by the extreme value distribution function corresponding to the target initial threshold; The Monte Carlo method is used to generate uniformly distributed random numbers, which are greater than 0 and less than the maximum cumulative distribution probability. Each random number is substituted as the cumulative distribution probability into the quantile function corresponding to the target initial threshold to obtain the corresponding extrapolated equivalent stress amplitude, which is used as the extrapolated equivalent stress amplitude spectrum of the first region; the number of random numbers is equal to the number of equivalent stress amplitudes in the first region.

[0046] In this embodiment, linear extrapolation is performed on the second region to obtain the extrapolated equivalent stress amplitude spectrum of the second region, including: For the second region, the proportion of the equivalent stress amplitude at each level in the second region is determined based on the probability distribution map; The extrapolated equivalent stress amplitude spectrum of the second region is obtained by linear extrapolating the proportion of equivalent stress amplitudes at each level.

[0047] In this embodiment, the maximum predicted extremum is the upper limit of the equivalent stress amplitude obtained based on the quantile function; the maximum cumulative distribution probability is the cumulative probability value corresponding to the maximum predicted extremum. The Monte Carlo method is a statistical calculation method that relies on uniform random sampling to complete numerical simulation. The random numbers are uniformly distributed values ​​generated within a range greater than 0 and less than the maximum cumulative distribution probability, and the number of random numbers is equal to the number of equivalent stress amplitudes in the first region. The proportion of equivalent stress amplitudes at each level is the ratio of the number of equivalent stress amplitudes at each level in the second region to the total number of equivalent stress amplitudes in the second region. Linear extrapolation is a method of proportionally extending the equivalent stress amplitudes at each level in the second region to generate the extrapolated equivalent stress amplitude spectrum for the second region. The extrapolated equivalent stress amplitude spectrum for the first region is the set of equivalent stress amplitudes obtained by extrapolating the extreme value distribution from the first region, and the extrapolated equivalent stress amplitude spectrum for the second region is the set of equivalent stress amplitudes obtained by linear extrapolation from the second region.

[0048] The equivalent stress amplitude in the first region is the high-stress equivalent stress amplitude, which is greater than the target initial threshold. This type of high-stress equivalent stress amplitude accounts for a relatively low proportion in the measured data, and its distribution follows an extreme value variation law. Using linear extrapolation uniformly would severely underestimate the cyclic frequency of the high-stress equivalent stress amplitude. Therefore, an extreme value distribution extrapolation based on quantile functions and Monte Carlo sampling is chosen. The equivalent stress amplitude in the second region is the low-stress equivalent stress amplitude, which is less than or equal to the target initial threshold. This type of low-stress equivalent stress amplitude accounts for a relatively high proportion in the measured data, and its distribution is relatively stable. Linear extrapolation based on the proportion of each level of equivalent stress amplitude can efficiently generate the extrapolated equivalent stress amplitude spectrum for the second region. By using a partitioned adaptive differential extrapolation algorithm, the limitation of a single extrapolation model in not being able to simultaneously consider the high and low stress distribution characteristics is overcome. The extrapolated equivalent stress amplitude spectra of the first and second regions are merged to obtain the final extrapolated equivalent stress amplitude spectrum.

[0049] For example, one measuring point of a mobile bridge erecting machine is selected, with a total of 3972 equivalent stress amplitudes for processing. Using 44 MPa as the target initial threshold, the equivalent stress amplitude sequence is divided into a first region and a second region. Equivalent stress amplitudes higher than 44 MPa are assigned to the first region, and the remaining equivalent stress amplitudes are assigned to the second region. When processing the equivalent stress amplitudes in the first region, the maximum predicted extreme value of 122.38 MPa and the corresponding maximum cumulative distribution probability of 99.99% are obtained through the quantile function. The total number of equivalent stress amplitudes required for extrapolation is determined to be 165,000. An equal number of uniformly distributed random numbers are generated within the interval greater than 0 and less than 99.99%. Each random number is substituted into the quantile function corresponding to the target initial threshold to calculate the corresponding equivalent stress amplitude. All equivalent stress amplitudes are then summarized to form the extrapolated equivalent stress amplitude spectrum for the first region. For the equivalent stress amplitude in the second region, the proportion of each level of equivalent stress amplitude is statistically analyzed according to the probability distribution map. The linear extrapolation is completed by expanding the cycle frequency according to the predetermined proportion, and the extrapolated equivalent stress amplitude spectrum of the second region is generated. Finally, the extrapolated equivalent stress amplitude spectrum of the first region and the extrapolated equivalent stress amplitude spectrum of the second region are merged to obtain the extrapolated equivalent stress amplitude spectrum.

[0050] In this embodiment, the partitioned differential extrapolation can match the data distribution characteristics of different stress ranges. The first region uses the Monte Carlo method and quantile function to accurately simulate the extreme equivalent stress amplitude, avoiding underestimation of the high-stress equivalent stress amplitude. The second region uses linear extrapolation based on the proportion of equivalent stress amplitudes at each level, taking into account the extrapolation efficiency of the conventional equivalent stress amplitude in the second region. After merging the two types of extrapolated equivalent stress amplitude spectra, the full-range equivalent stress amplitude characteristics of the equipment under long-term service conditions are completely restored, improving the accuracy of the extrapolated equivalent stress amplitude spectrum and making the subsequent calculation results of cumulative fatigue damage more consistent with the actual service wear of the equipment.

[0051] S104: Based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, the cumulative fatigue damage of engineering equipment is calculated using Palmgren-Miner linear cumulative damage.

[0052] In this embodiment, based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, the cumulative fatigue damage of the engineering equipment is calculated using Palmgren-Miner linear cumulative damage, including: The extrapolated equivalent stress amplitude spectrum is graded to obtain multi-level extrapolated equivalent stress amplitudes; and the total number of levels of the extrapolated equivalent stress amplitude spectrum and the number of equivalent stress amplitudes in each level of the extrapolated equivalent stress amplitude spectrum are determined. For each level of extrapolated equivalent stress amplitude, the fatigue life corresponding to that level of extrapolated equivalent stress amplitude is determined by the stress-life curve; Based on the total number of levels of the extrapolated equivalent stress amplitude spectrum, the number of equivalent stress amplitudes in the extrapolated equivalent stress amplitude of that level, and the fatigue life corresponding to the extrapolated equivalent stress amplitude of that level, the cumulative fatigue damage of the engineering equipment is obtained by using the Palmgren-Miner linear cumulative damage formula. The Palmgren-Miner linear cumulative damage formula is: ; in, m The total number of series in the extrapolated equivalent stress amplitude spectrum. Indicates the first The number of equivalent stress amplitudes in the extrapolated equivalent stress amplitude. The first stress-life curve Fatigue life corresponding to the extrapolated equivalent stress amplitude. This refers to the cumulative fatigue damage of engineering equipment.

[0053] In this embodiment, the multi-level extrapolated equivalent stress amplitude refers to the equivalent stress amplitude of each level obtained by classifying the extrapolated equivalent stress amplitude spectrum according to a fixed stress interval. The total number of levels is the total number of levels obtained after the extrapolated equivalent stress amplitude spectrum is graded. The number of extrapolated equivalent stress amplitudes at each level is the number of cycles corresponding to each level of equivalent stress amplitude. The stress-life curve is the curve showing the correspondence between the equivalent stress amplitude and fatigue life obtained through material fatigue testing. Fatigue life is the number of cycles required for the structure to undergo fatigue failure under the continuous action of a specified level of equivalent stress amplitude. The Palmgren-Miner linear cumulative damage formula is a calculation formula for solving the overall cumulative fatigue damage by accumulating the fatigue damage at each level.

[0054] Different magnitudes of equivalent stress significantly affect the fatigue damage rate of a structure. A unified calculation of the damage contribution of each equivalent stress amplitude level cannot accurately reflect the damage contribution of each stress level. Therefore, it is necessary to extrapolate the equivalent stress amplitude spectrum and classify it to distinguish the contribution of each equivalent stress amplitude level to structural fatigue damage. The inherent properties of the material determine the unique fatigue life corresponding to a specific equivalent stress amplitude; this parameter needs to be determined through the stress-life curve. Material fatigue damage follows the objective law of linear superposition. By calculating the damage caused by each stress level step by step using the Palmgren-Miner linear cumulative damage formula, and then summing up the damage at each level, we can align with the fatigue accumulation mechanism, avoid data distortion caused by overall calculation, and ensure that the final cumulative fatigue damage calculation result conforms to the actual damage pattern of the structure.

[0055] For example, the extrapolated equivalent stress amplitude spectrum corresponding to a certain measuring point of the mobile bridge erecting machine is selected for calculation. A 5MPa interval is chosen as the grading interval, and grading is completed within the amplitude range of 44MPa to 122.38MPa to obtain multi-level extrapolated equivalent stress amplitudes. The total number of levels of the extrapolated equivalent stress amplitude spectrum is calculated, and the number of extrapolated equivalent stress amplitudes for each level is counted. The stress-life curve of the target material used in the curved beam of the bridge erecting machine, calibrated through standard fatigue tests, is retrieved. The equivalent stress amplitude for each level is checked one by one to determine the fatigue life corresponding to each level of extrapolated equivalent stress amplitude. Three types of parameters are collected: the total number of levels, the number of extrapolated equivalent stress amplitudes for each level, and the corresponding fatigue life. Single-level damage is calculated step-by-step according to the Palmgern-Miner linear cumulative damage formula. After completing the calculation for all levels, the values ​​are summed to obtain the cumulative fatigue damage value of the engineering equipment at that location.

[0056] This embodiment classifies the equivalent stress amplitude spectrum by extrapolation, enabling precise differentiation of fatigue losses corresponding to different stress levels. It accurately matches various life parameters based on the stress-life curve, and then performs step-by-step superposition calculations using the Palmgren-Miner linear cumulative damage formula. This graded calculation mode refines the damage sources for each equivalent stress amplitude level, reduces calculation errors by relying on high-precision extrapolated equivalent stress amplitude spectra, and yields accurate and reliable cumulative fatigue damage results. This allows maintenance personnel to rationally set maintenance nodes based on damage values, mitigating the risk of sudden structural fatigue failure.

[0057] As can be seen from the above, the embodiments of this application determine a reasonable initial target threshold based on the probability distribution map corresponding to the equivalent stress amplitude sequence, avoiding human experience intervention and ensuring that the initial target threshold conforms to the objective distribution law of the equivalent stress amplitude. Since the initial target threshold is objectively determined based on the probability distribution map, it can reasonably divide the first region and the second region, thereby ensuring that a sufficient number of equivalent stress amplitudes in the first region participate in the extreme value distribution extrapolation, and preventing the equivalent stress amplitudes in the second region from being incorrectly included in the object range of the extreme value distribution extrapolation. The embodiments of this application adopt a partitioned differentiated extrapolation mode: for the high-stress first region, extreme value distribution extrapolation is used, utilizing the distribution characteristics of equivalent stress amplitudes greater than or equal to the initial target threshold in the equivalent stress amplitude sequence to accurately capture the distribution of low-frequency, high-risk high stress amplitudes, avoiding the underestimation of extreme values ​​by traditional linear extrapolation; for the low-stress second region, linear extrapolation is used, extending the equivalent stress amplitudes less than the initial target threshold in the equivalent stress amplitude sequence, avoiding the fitting error introduced by complex models. By merging the extrapolated equivalent stress amplitude spectra of the first and second regions, the extreme value distribution characteristics of the first region are accurately depicted while retaining the main statistical features of the second region. This fully restores the full-range equivalent stress amplitude characteristics under long-term service conditions, improving the extrapolation accuracy of the equivalent stress amplitude spectrum. Based on this, the Palmgren-Miner linear cumulative damage calculation is applied to the cumulative fatigue damage of the engineering equipment using the extrapolated equivalent stress amplitude spectrum in conjunction with the stress-life curve, making the fatigue damage assessment results more closely match the actual service wear of the equipment. Therefore, this embodiment can improve the extrapolation accuracy of the equivalent stress amplitude spectrum, thereby improving the accuracy of fatigue damage estimation.

[0058] Specifically, taking the curved beam structure of a mobile bridge erecting machine as an example, the processing procedure in this embodiment of the application can be as follows: The first step is to identify the critical stress areas of the engineering equipment. A rigid-flexible coupled dynamic model of the bridge erecting machine and the road surface is established using multibody dynamics software. The dynamic stress of the structure during beam transport is obtained under different road spectrum excitations. The maximum stress hotspots in the top 200 sections of the structure are statistically analyzed. The main concentration areas of stress hotspots are shown in Table 1, and the specific measurement points are as follows: Figure 2 As shown. Strain sensors were placed at corresponding locations in the stress hotspot distribution area during the dynamic simulation of the bridge erecting machine. Strain time history data of the measurement point ⑦ were collected, and the strain time history data were converted into stress time history data using the fourth strength theory to obtain the measured dynamic response signal.

[0059] Table 1. Stress Hotspot Distribution Areas of Mobile Bridge Erection Machine

[0060] The second step is to determine the probability distribution model of the stress amplitude.

[0061] Power spectral density (PSD) analysis was performed on the dynamic response signal, and the results are as follows: Figure 3 As shown in the figure. The power spectral density curve shows that the excitation energy of the bridge erecting machine is mainly concentrated within 2Hz, because greater than or equal to 90% of the energy is concentrated in this frequency range. Therefore, a low-pass filter with a cutoff frequency of 2Hz is used to filter the dynamic response signal to eliminate the influence of high-frequency noise components. The time history curve of the filtered dynamic response signal is shown in the figure. Figure 4 As shown.

[0062] This embodiment uses the rainflow counting method to process the filtered dynamic response signal, obtaining a two-dimensional stress spectrum containing the mean stress and stress amplitude, such as... Figure 5 As shown in the diagram. The horizontal axis represents the mean stress, the vertical axis represents the stress amplitude, and each data point corresponds to a complete stress cycle. The vertical axis represents the cycle count corresponding to each combination of mean stress and stress amplitude. Figure 5 It can be seen that after the filtered dynamic response signal is processed by the rainflow counting method, multiple sets of stress cycles consisting of stress amplitude and stress mean are obtained.

[0063] This embodiment uses the Goodman equation to... Figure 5 The stress cycles shown are corrected to convert asymmetric cyclic stresses into equivalent stress amplitudes. Specifically, for each set of stress amplitudes and mean stresses, the corresponding equivalent stress amplitude is calculated using the Goodman equation, taking into account the tensile strength of the target material, thus eliminating the influence of the mean stress. The corrected equivalent stress amplitude sequence is shown below. Figure 6 As shown, this equivalent stress amplitude sequence is the basis for subsequent extreme value distribution modeling and extrapolation.

[0064] In this embodiment, a log-normal distribution model is used to fit the modified symmetric cyclic equivalent stress amplitude spectrum. Each value in the equivalent stress amplitude sequence is taken as a random variable x, and its log-normal distribution probability density function is expressed as follows:

[0065] Where x is the equivalent stress amplitude, μ and σ These are the location and shape parameters of the log-normal distribution, respectively.

[0066] In this embodiment, the equivalent stress amplitude sequence is input into data processing software for probability density function parameter estimation. The software automatically iterates to obtain the optimal parameter estimate. In this embodiment, the fitted parameter value is... μ= 0.53, σ =1.64. The probability density function model determined in this way can describe the overall distribution characteristics of the equivalent stress amplitude sequence.

[0067] The third step is to determine the extreme value distribution model of the structural dynamic response.

[0068] This embodiment calculates the equivalent stress amplitude sequence to obtain the empirical average conditional transcendence rate function, and then obtains the relationship between the empirical average conditional transcendence rate and the equivalent stress amplitude under different conditional correlation orders k, such as... Figure 7 As shown. Figure 7 The figure shows the empirical average conditional transcendence rate curves when the conditional correlation order k takes values ​​from 1 to 5. Figure 7 It can be seen that in the range of lower equivalent stress amplitude, there are significant differences between the empirical average conditional exceedance rates of different orders, indicating that there is a significant conditional correlation in the low stress region; however, in the high stress tail region, the empirical average conditional exceedance rates of each order tend to converge and become close to each other, indicating that the prediction results of the empirical average conditional exceedance rate functions of different conditional exceedance orders for the tail extrema tend to be consistent.

[0069] Then, determine the initial threshold range. Plot the probability distribution of the equivalent stress amplitude sequence, as shown below. Figure 8 As shown. The theoretical data is the cumulative distribution probability corresponding to the equivalent stress amplitude calculated based on the aforementioned fitted log-normal distribution model, while the measured data is the cumulative distribution probability of the equivalent stress amplitude sequence generated from the measured dynamic response signal. Figure 8 The red reference line represents the ideal state where the measured data perfectly match the fitted log-normal distribution model. From... Figure 8 It can be observed that the first half of the measured data fits the theoretical data well, but the fitting accuracy drops sharply near the tail of the data, exhibiting a typical heavy-tailed distribution phenomenon. Considering the impact of data volume on fitting accuracy, the equivalent stress amplitude of the measured data that is greater than or equal to the 95% confidence interval is taken as the starting point of the initial threshold interval, and (42, 63) MPa is selected as the initial threshold interval.

[0070] Then, determine the initial threshold range and plot the probability distribution of the equivalent stress amplitude spectrum, such as... Figure 8 As shown, the theoretical data are the equivalent stress amplitudes calculated using the probability density function, while the measured data are the equivalent stress amplitudes generated by the measured dynamic response signals. The red reference line in the figure indicates that the measured data perfectly match the fitted log-normal distribution model. From Figure 8 It can be observed that the measured data in the first half fits the theoretical data well, but the fitting accuracy drops sharply near the tail of the data, exhibiting a typical heavy-tailed distribution phenomenon. Considering the impact of the amount of equivalent stress amplitude data on the fitting accuracy, the points where the measured data exceed the 95% confidence interval are taken as the starting point of the initial threshold, and (42, 63) MPa is selected as the initial threshold interval.

[0071] To further refine the selection of the initial threshold, a step size is set. =0.5MPa, gradually update the threshold. i = 0 As an initial threshold, different starting points ( , Substitute the quantile function corresponding to the target initial threshold. In this method, the extreme values ​​under different average conditional exceedance rates are predicted, and the predicted extreme values ​​are obtained, such as... Figure 9 As shown, Figure 9 The image shows the predicted extreme values ​​corresponding to different average conditional transcendence rates when different initial thresholds are selected. Figure 9 It can be observed that when the initial threshold is greater than or equal to 44 MPa, the prediction results of subsequent extreme values ​​tend to be stable and similar. In order to maximize the amount of data of the equivalent stress amplitude above the threshold, it is more reasonable to set it as the initial threshold.

[0072] Then, a first-order ACER1 was fitted at 95% confidence level. )function The fitting results are as follows Figure 10 As shown, Figure 10 The curves of the first-order average conditional transcendence function and the upper and lower boundaries of its confidence interval are fitted in the figure.

[0073]

[0074] in, k =1, q I = 0.017 a 1 = 0.0019 b 1 = 38.46 c 1 = 1.98 0 = 44 MPa.

[0075] The fourth step is to determine the extrapolated equivalent stress amplitude spectrum.

[0076] In this embodiment, the initial target threshold is obtained as 44 MPa in the third step, based on the equivalent stress amplitude spectrum in the second step ( Figure 6 It can be seen that there are 3972 equivalent stress amplitudes. The equivalent stress amplitude sequence is divided into two regions: a first region where the equivalent stress amplitude is greater than or equal to 44 MPa, and a second region where the equivalent stress amplitude is less than 44 MPa. Figure 11 As shown. This embodiment extrapolates by 10. -7The equivalent stress amplitude spectrum under the mean conditional exceedance rate (MDRR) is obtained. The predicted extreme value under this MRR is 122.38 MPa, with a confidence interval of (99.24, 129.11) MPa. The number of extreme values ​​exceeding the initial target threshold is 165,000, and the corresponding cumulative distribution value is 99.99%. For the extrapolation of the first region, the extreme value distribution extrapolation method is used. Monte Carlo simulation is used to generate 165,000 uniformly distributed random numbers within the interval (0, 0.9999). Then, each random number is used as the cumulative distribution probability and substituted into the quantile function corresponding to the initial target threshold to calculate the corresponding equivalent stress amplitude. The equivalent stress amplitude interval (44, 122.38) MPa is divided into multiple levels with an interval width of 5 MPa. The frequency of the equivalent stress amplitude of each level is counted to obtain the extrapolated equivalent stress amplitude spectrum of the first region. For the extrapolation of the second region, a linear extrapolation method is adopted, that is, based on the portion of the equivalent stress amplitude less than 44 MPa in the equivalent stress amplitude sequence, the proportion of each equivalent stress amplitude level is counted, and linear extrapolation is performed according to the proportion of each level to obtain the extrapolated equivalent stress amplitude spectrum of the second region.

[0077] After extrapolation, the extrapolated equivalent stress amplitude spectrum of the first region is merged with that of the second region to obtain the complete extrapolated equivalent stress amplitude spectrum. The cumulative distribution of the extrapolated equivalent stress amplitude spectrum is as follows: Figure 12 As shown, Figure 12 The cumulative distribution curves of the equivalent stress amplitude spectrum (i.e., the sample amplitude spectrum), the linear extrapolated stress amplitude spectrum (i.e., the extrapolated equivalent stress amplitude spectrum of the second region), and the ACER method extrapolated stress amplitude spectrum (i.e., the extrapolated equivalent stress amplitude spectrum of the first region) are shown. The frequency distribution of the equivalent stress amplitude at each extrapolated level is as follows: Figure 13 As shown. Figure 13 The horizontal axis represents the range of equivalent stress amplitudes, and the vertical axis represents the frequency of equivalent stress amplitudes at each level, showing the distribution of the number of equivalent stress amplitudes at each level under the linear extrapolation method and the extreme value distribution extrapolation method, respectively.

[0078] contrast Figure 12 and Figure 13 It can be seen that the overall equivalent stress amplitude spectrum obtained by direct linear extrapolation of short-term measured data has a significant difference in the distribution statistics of the equivalent stress amplitude spectrum in the high stress extreme value region compared with the equivalent stress amplitude spectrum obtained by the partitioned differential extrapolation method of this embodiment. This indicates that the partitioned differential extrapolation method of this embodiment can more accurately characterize the distribution characteristics of the extreme equivalent stress amplitude.

[0079] Using the Palmgren-Miner linear cumulative damage theory, the 10 -7 Fatigue damage caused by the equivalent stress amplitude at each level under the mean condition exceedance rate, and the changing trend of cumulative fatigue damage, such as Figure 14 As shown. Figure 14 The diagram illustrates the fatigue damage caused by various equivalent stress amplitudes under linear extrapolation and extreme value distribution extrapolation methods, respectively, along with the cumulative fatigue damage curves for both methods. The slope of the cumulative fatigue damage curve reflects the strength of the structural damage caused by the equivalent stress amplitude within that interval. Figure 14 It can be seen that the cumulative fatigue damage curve grows at the highest rate within the equivalent stress amplitude range of 50MPa to 70MPa, indicating that the equivalent stress amplitude in this range causes the fastest damage growth rate to the structure and is the dominant equivalent stress amplitude range for structural fatigue failure. When optimizing structural design, appropriate vibration isolation measures can be implemented specifically for this level of equivalent stress amplitude to reduce the contribution of loads in this range to the fatigue damage of the structure, thereby helping to extend the service life of the structure.

[0080] The cumulative fatigue damage of the curved beam measuring point ⑦ structure of the mobile bridge erecting machine, calculated using the extrapolated equivalent stress amplitude spectrum in this embodiment, is 0.05282. In comparison, the cumulative fatigue damage calculated using the traditional linear extrapolation method is 0.04879. Further analysis shows that for the equivalent stress amplitude range greater than or equal to 60 MPa, when using the extreme value distribution extrapolation method, the damage caused by the equivalent stress amplitude in this range accounts for 53.46% of the cumulative fatigue damage; while when using the linear extrapolation method, the damage caused by the equivalent stress amplitude in this range accounts for only 46.69% of the cumulative fatigue damage. The above comparison results indicate that the linear extrapolation method underestimates the fatigue damage caused by high-stress equivalent stress amplitudes, thus significantly affecting the fatigue damage assessment results under long-term service conditions.

[0081] Corresponding to the fatigue damage estimation method for engineering equipment in the above embodiments, Figure 15 This is a structural block diagram of an engineering equipment fatigue damage estimation device provided according to an embodiment of this application. For ease of explanation, only the parts relevant to the embodiment of this application are shown. References Figure 15 The fatigue damage estimation device 20 for this engineering equipment includes: an equivalent stress amplitude sequence generation module 21, an initial threshold determination module 22, an equivalent stress amplitude extrapolation module 23, and a cumulative fatigue damage estimation module 24.

[0082] The equivalent stress amplitude sequence generation module 21 is used to acquire the dynamic response signal of the dangerous stress area of ​​the engineering equipment, generate the equivalent stress amplitude sequence based on the dynamic response signal, and determine the probability distribution map corresponding to the equivalent stress amplitude sequence. The initial threshold determination module 22 is used to determine the initial threshold interval based on the probability distribution map, divide the initial threshold interval into multiple sub-intervals, use the initial equivalent stress amplitude of each sub-interval as the initial threshold benchmark, and determine the target initial threshold based on each initial threshold benchmark. The equivalent stress amplitude extrapolation module 23 is used to divide the equivalent stress amplitude sequence into a first region and a second region based on a target initial threshold. The equivalent stress amplitude in the first region is greater than or equal to the target initial threshold, and the equivalent stress amplitude in the second region is less than the target initial threshold. The extreme value distribution extrapolation is performed on the first region to obtain the extrapolated equivalent stress amplitude spectrum of the first region. Linear extrapolation is performed on the second region to obtain the extrapolated equivalent stress amplitude spectrum of the second region. The extrapolated equivalent stress amplitude spectrum of the first region and the extrapolated equivalent stress amplitude spectrum of the second region are merged to obtain the extrapolated equivalent stress amplitude spectrum. The cumulative fatigue damage estimation module 24 is used to calculate the cumulative fatigue damage of engineering equipment based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, using Palmgren-Miner linear cumulative damage.

[0083] In one embodiment of this application, the equivalent stress amplitude sequence generation module 21 is specifically used for: Obtain the tensile strength of the target material; the target material is a structural material used to manufacture dangerous stress-bearing parts of engineering equipment. The dynamic response signal is obtained by low-pass filtering. The filtered dynamic response signal is processed by rainflow counting method to obtain multiple sets of stress cycles, which include stress amplitude and stress mean. Based on the tensile strength of the target material, each set of stress cycles is corrected using the Goodman equation to obtain the corresponding equivalent stress amplitude; multiple equivalent stress amplitudes form an equivalent stress amplitude sequence; The Goodman equation is: ; in, This refers to the stress amplitude; This represents the average stress value. The equivalent stress amplitude when the mean is 0; The tensile strength of the target material.

[0084] In one embodiment of this application, the initial threshold determination module 22 is specifically used for: Obtain the initial threshold benchmark for the target sub-interval, and calculate the predicted extreme value corresponding to the initial threshold benchmark; Obtain the predicted extreme value corresponding to the initial threshold benchmark of the previous sub-interval adjacent to the target sub-interval, calculate the absolute value of the difference between the predicted extreme value corresponding to the initial threshold benchmark of the previous sub-interval and the predicted extreme value corresponding to the initial threshold benchmark of the target sub-interval, and obtain the predicted extreme value difference. If the difference between predicted extreme values ​​is greater than or equal to the preset convergence threshold, the process is repeated to obtain the initial threshold benchmark of the next adjacent sub-interval of the target sub-interval, calculate the predicted extreme value corresponding to the initial threshold benchmark, until the preset stopping condition is met, and the initial threshold benchmark that meets the preset stopping condition is taken as the target initial threshold. The preset stopping condition is that the difference between predicted extreme values ​​is less than the preset convergence threshold. The steps for calculating the predicted extreme value corresponding to the initial threshold benchmark include: Determine the target average conditional exceedance function corresponding to this initial threshold benchmark; Based on this initial threshold benchmark, the average conditional exceedance rate corresponding to the initial threshold benchmark is calculated using the corresponding target average conditional exceedance rate function. Based on the average conditional exceedance rate, the cumulative distribution probability corresponding to the initial threshold benchmark is obtained by calculating through the extreme value distribution function. Based on the cumulative distribution probability, the predicted extreme value corresponding to the initial threshold benchmark is obtained by calculating using the quantile function.

[0085] In one embodiment of this application, the initial threshold determination module 22 is specifically used for: The empirical average conditional exceedance rate function is obtained by calculating the equivalent stress amplitude sequence; Based on the exponential form function, and by fitting the equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold benchmark through the empirical average conditional exceedance function, the exponential form average conditional exceedance function is obtained; the values ​​of the parameter combination in the exponential form average conditional exceedance function are unknown, and the parameter combination includes the first parameter, the second parameter, the third parameter, and the fourth parameter; By taking the logarithm of both sides of the exponential form of the average conditional transcendence function, an optimization function is established with the goal of minimizing the sum of squared residuals. The optimal parameter combination is then iteratively fitted based on the Levenberg-Marquardt algorithm and the weighted least squares method. Substituting the optimal parameter combination into the exponential form of the average conditional exceedance function yields the target average conditional exceedance function. The target mean conditional exceedance function is: ; in, The first value in the equivalent stress amplitude sequence that is greater than or equal to the initial threshold baseline. One equivalent stress amplitude, As the initial threshold benchmark, For the first The target average conditional exceedance rate corresponding to each equivalent stress amplitude; , where n is the number of equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold baseline;a k As the first parameter, b k For the second parameter, c k As the third parameter, q k The fourth parameter, a k , b k , c k and q k All are constants.

[0086] In one embodiment of this application, the equivalent stress amplitude extrapolation module 23 is specifically used for: Determine the extreme value distribution function and quantile function corresponding to the initial threshold of the target; For the first region, the maximum predicted extreme value is obtained based on the quantile function corresponding to the target initial threshold; the maximum predicted extreme value corresponds to a maximum cumulative distribution probability; the maximum cumulative distribution probability is calculated by the extreme value distribution function corresponding to the target initial threshold; The Monte Carlo method is used to generate uniformly distributed random numbers, which are greater than 0 and less than the maximum cumulative distribution probability. Each random number is substituted as the cumulative distribution probability into the quantile function corresponding to the target initial threshold to obtain the corresponding extrapolated equivalent stress amplitude, which is used as the extrapolated equivalent stress amplitude spectrum of the first region; the number of random numbers is equal to the number of equivalent stress amplitudes in the first region.

[0087] In one embodiment of this application, the equivalent stress amplitude extrapolation module 23 is specifically used for: For the second region, the proportion of the equivalent stress amplitude at each level in the second region is determined based on the probability distribution map; The extrapolated equivalent stress amplitude spectrum of the second region is obtained by linear extrapolating the proportion of equivalent stress amplitudes at each level.

[0088] In one embodiment of this application, the cumulative fatigue damage estimation module 24 is specifically used for: The extrapolated equivalent stress amplitude spectrum is graded to obtain multi-level extrapolated equivalent stress amplitudes; and the total number of levels of the extrapolated equivalent stress amplitude spectrum and the number of equivalent stress amplitudes in each level of the extrapolated equivalent stress amplitude spectrum are determined. For each level of extrapolated equivalent stress amplitude, the fatigue life corresponding to that level of extrapolated equivalent stress amplitude is determined by the stress-life curve; Based on the total number of levels of the extrapolated equivalent stress amplitude spectrum, the number of equivalent stress amplitudes in the extrapolated equivalent stress amplitude of that level, and the fatigue life corresponding to the extrapolated equivalent stress amplitude of that level, the cumulative fatigue damage of the engineering equipment is obtained by using the Palmgren-Miner linear cumulative damage formula. The Palmgren-Miner linear cumulative damage formula is: ; in, m The total number of series in the extrapolated equivalent stress amplitude spectrum. Indicates the first The number of equivalent stress amplitudes in the extrapolated equivalent stress amplitude. The first stress-life curve Fatigue life corresponding to the extrapolated equivalent stress amplitude. This refers to the cumulative fatigue damage of engineering equipment.

[0089] See Figure 16 , Figure 16 This is a schematic block diagram of an electronic device provided according to an embodiment of this application. Figure 16 The electronic device 300 in this embodiment may include one or more processors 301, one or more input devices 302, one or more output devices 303, and one or more memories 304. The processors 301, input devices 302, output devices 303, and memories 304 communicate with each other via a communication bus 305. The memories 304 store computer programs, including program instructions. The processors 301 execute the program instructions stored in the memories 304. Specifically, the processors 301 are configured to invoke the program instructions to perform the functions of each module / unit in the above-described device embodiments, for example... Figure 15 The functions of the equivalent stress amplitude sequence generation module 21, the initial threshold determination module 22, the equivalent stress amplitude extrapolation module 23, and the cumulative fatigue damage estimation module 24 are shown.

[0090] It should be understood that, in the embodiments of this application, the processor 301 may be a central processing unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0091] Input device 302 may include a touchpad, a fingerprint sensor (for collecting the user's fingerprint information and fingerprint orientation information), a microphone, etc., and output device 303 may include a display (LCD, etc.), a speaker, etc.

[0092] The memory 304 may include read-only memory and random access memory, and provides instructions and data to the processor 301. A portion of the memory 304 may also include non-volatile random access memory.

[0093] In specific implementations, the processor 301, input device 302, and output device 303 described in the embodiments of this application can execute the implementation method described in the engineering equipment fatigue damage estimation method provided in the embodiments of this application, or they can execute the implementation method of the electronic device described in the embodiments of this application, which will not be repeated here.

[0094] In another embodiment of this application, a computer-readable storage medium is provided. This computer-readable storage medium stores a computer program, which includes program instructions. When executed by a processor, the program instructions implement all or part of the processes in the methods described above. Alternatively, the computer program can instruct related hardware to complete the process. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include any entity or device capable of carrying computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0095] The computer-readable storage medium can be an internal storage unit of the electronic device in any of the foregoing embodiments, such as a hard disk or memory of the electronic device. The computer-readable storage medium can also be an external storage device of the electronic device, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the electronic device. Furthermore, the computer-readable storage medium can include both internal and external storage units of the electronic device. The computer-readable storage medium is used to store computer programs and other programs and data required by the electronic device. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0096] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this application.

[0097] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the electronic devices and units described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0098] In the several embodiments provided in this application, it should be understood that the disclosed electronic devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through some interfaces or units, or they may be electrical, mechanical, or other forms of connection.

[0099] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of this application, depending on actual needs.

[0100] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0101] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for estimating fatigue damage of engineering equipment, characterized in that, include: Acquire the dynamic response signal of the dangerous stress area of ​​the engineering equipment, and generate an equivalent stress amplitude sequence based on the dynamic response signal; Determine the probability distribution diagram corresponding to the equivalent stress amplitude sequence; Based on the probability distribution map, an initial threshold interval is determined, and the initial threshold interval is divided into multiple sub-intervals; the initial equivalent stress amplitude of each sub-interval is used as the initial threshold benchmark, and a target initial threshold is determined based on each initial threshold benchmark. Based on the target initial threshold, the equivalent stress amplitude sequence is divided into a first region and a second region, wherein the equivalent stress amplitude in the first region is greater than or equal to the target initial threshold, and the equivalent stress amplitude in the second region is less than the target initial threshold; Extrapolating the extreme value distribution of the first region yields the extrapolated equivalent stress amplitude spectrum of the first region; Linear extrapolation is performed on the second region to obtain the extrapolated equivalent stress amplitude spectrum of the second region. The extrapolated equivalent stress amplitude spectrum of the first region and the extrapolated equivalent stress amplitude spectrum of the second region are then combined to obtain the extrapolated equivalent stress amplitude spectrum. Based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, the cumulative fatigue damage of the engineering equipment is calculated using Palmgren-Miner linear cumulative damage.

2. The fatigue damage estimation method for engineering equipment as described in claim 1, characterized in that, The generation of the equivalent stress amplitude sequence based on the dynamic response signal includes: The tensile strength of the target material is obtained; the target material is a structural material used to manufacture the dangerous stress-bearing parts of the engineering equipment. The dynamic response signal is low-pass filtered to obtain the filtered dynamic response signal; The filtered dynamic response signal is processed by rainflow counting method to obtain multiple sets of stress cycles, wherein the stress cycle includes stress amplitude and stress mean. Based on the tensile strength of the target material, each set of stress cycles is corrected using the Goodman equation to obtain the corresponding equivalent stress amplitude; multiple equivalent stress amplitudes constitute the equivalent stress amplitude sequence. The Goodman equation is: ； in, This refers to the stress amplitude; This represents the average stress value. The equivalent stress amplitude when the mean is 0; The tensile strength of the target material.

3. The fatigue damage estimation method for engineering equipment as described in claim 1, characterized in that, The determination of the target initial threshold based on each of the initial threshold benchmarks includes: Obtain the initial threshold benchmark for the target sub-interval, and calculate the predicted extreme value corresponding to the initial threshold benchmark; Obtain the predicted extreme value corresponding to the initial threshold benchmark of the previous sub-interval adjacent to the target sub-interval, calculate the absolute value of the difference between the predicted extreme value corresponding to the initial threshold benchmark of the previous sub-interval and the predicted extreme value corresponding to the initial threshold benchmark of the target sub-interval, and obtain the predicted extreme value difference. If the difference between predicted extreme values ​​is greater than or equal to a preset convergence threshold, then the process of obtaining the initial threshold benchmark of the next sub-interval adjacent to the target sub-interval is repeated, and the predicted extreme value corresponding to the initial threshold benchmark is calculated until a preset stopping condition is met. The initial threshold benchmark that meets the preset stopping condition is taken as the target initial threshold. The preset stopping condition is that the difference between predicted extreme values ​​is less than a preset convergence threshold. The step of calculating the predicted extreme value corresponding to the initial threshold benchmark includes: Determine the target average conditional exceedance function corresponding to this initial threshold benchmark; Based on this initial threshold benchmark, the average conditional exceedance rate corresponding to the initial threshold benchmark is calculated using the corresponding target average conditional exceedance rate function. Based on the average conditional exceedance rate, the cumulative distribution probability corresponding to the initial threshold benchmark is obtained by calculating through the extreme value distribution function. Based on the cumulative distribution probability, the predicted extreme value corresponding to the initial threshold benchmark is obtained by calculating using the quantile function.

4. The fatigue damage estimation method for engineering equipment as described in claim 3, characterized in that, The determination of the target average conditional exceedance function corresponding to the initial threshold benchmark includes: The empirical average conditional exceedance rate function is obtained by calculating the equivalent stress amplitude sequence. Based on the exponential form function, and through the empirical average conditional exceedance rate function, the equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold benchmark are fitted to obtain the exponential form average conditional exceedance rate function; the value of the parameter combination in the exponential form average conditional exceedance rate function is an unknown value, and the parameter combination includes a first parameter, a second parameter, a third parameter, and a fourth parameter; By taking the logarithm of both sides of the exponential form of the conditional transcendence function, an optimization function is established with the goal of minimizing the sum of squared residuals. The optimal parameter combination is then iteratively fitted based on the Levenberg-Marquardt algorithm and the weighted least squares method. Substituting the optimal parameter combination into the exponential form of the average conditional exceedance function yields the target average conditional exceedance function. The target average conditional exceedance rate function is: ； in, The first value in the equivalent stress amplitude sequence that is greater than or equal to the initial threshold baseline. One equivalent stress amplitude, As the initial threshold benchmark, For the first The target average conditional exceedance rate corresponding to each equivalent stress amplitude; , where n is the number of equivalent stress amplitudes in the equivalent stress amplitude sequence that are greater than or equal to the initial threshold baseline; a k As the first parameter, b k For the second parameter, c k As the third parameter, q k The fourth parameter, a k , b k , c k and q k All are constants.

5. The fatigue damage estimation method for engineering equipment as described in claim 3, characterized in that, The step of extrapolating the extreme value distribution of the first region to obtain the extrapolated equivalent stress amplitude spectrum of the first region includes: Determine the extreme value distribution function and quantile function corresponding to the initial threshold of the target; For the first region, the maximum predicted extreme value is obtained based on the quantile function corresponding to the target initial threshold; the maximum predicted extreme value corresponds to a maximum cumulative distribution probability; the maximum cumulative distribution probability is calculated using the extreme value distribution function corresponding to the target initial threshold; A uniformly distributed random number is generated using the Monte Carlo method, wherein the random number is greater than 0 and less than the maximum cumulative distribution probability; Each random number is substituted as a cumulative distribution probability into the quantile function corresponding to the target initial threshold to obtain the corresponding extrapolated equivalent stress amplitude, which is used as the extrapolated equivalent stress amplitude spectrum of the first region; the number of random numbers is equal to the number of equivalent stress amplitudes in the first region.

6. The fatigue damage estimation method for engineering equipment as described in claim 5, characterized in that, The step of performing linear extrapolation on the second region to obtain the extrapolated equivalent stress amplitude spectrum of the second region includes: For the second region, the proportion of each level of equivalent stress amplitude in the second region is determined based on the probability distribution map; The extrapolated equivalent stress amplitude spectrum of the second region is obtained by linear extrapolating the proportions of the equivalent stress amplitudes at each level.

7. The fatigue damage estimation method for engineering equipment as described in claim 1, characterized in that, The calculation of cumulative fatigue damage of engineering equipment based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, using Palmgren-Miner linear cumulative damage, includes: The extrapolated equivalent stress amplitude spectrum is graded to obtain multi-level extrapolated equivalent stress amplitudes; and the total number of levels of the extrapolated equivalent stress amplitude spectrum and the number of equivalent stress amplitudes in each level of the extrapolated equivalent stress amplitude spectrum are determined. For each level of extrapolated equivalent stress amplitude, the fatigue life corresponding to that level of extrapolated equivalent stress amplitude is determined by the stress-life curve. Based on the total number of levels of the extrapolated equivalent stress amplitude spectrum, the number of equivalent stress amplitudes in the extrapolated equivalent stress amplitude of that level, and the fatigue life corresponding to the extrapolated equivalent stress amplitude of that level, the cumulative fatigue damage of the engineering equipment is obtained by calculating using the Palmgren-Miner linear cumulative damage formula. The Palmgren-Miner linear cumulative damage formula is as follows: ； in, m The total number of series in the extrapolated equivalent stress amplitude spectrum. Indicates the first The number of equivalent stress amplitudes in the extrapolated equivalent stress amplitude. The first stress-life curve Fatigue life corresponding to the extrapolated equivalent stress amplitude. This refers to the cumulative fatigue damage of engineering equipment.

8. A fatigue damage estimation device for engineering equipment, characterized in that, include: An equivalent stress amplitude sequence generation module is used to acquire the dynamic response signal of the dangerous stress area of ​​engineering equipment and generate an equivalent stress amplitude sequence based on the dynamic response signal; Determine the probability distribution diagram corresponding to the equivalent stress amplitude sequence; An initial threshold determination module is used to determine an initial threshold interval based on the probability distribution map, divide the initial threshold interval into multiple sub-intervals, use the initial equivalent stress amplitude of each sub-interval as an initial threshold benchmark, and determine a target initial threshold based on each initial threshold benchmark. An equivalent stress amplitude extrapolation module is used to divide the equivalent stress amplitude sequence into a first region and a second region based on the target initial threshold, wherein the equivalent stress amplitude in the first region is greater than or equal to the target initial threshold, and the equivalent stress amplitude in the second region is less than the target initial threshold. Extrapolating the extreme value distribution of the first region yields the extrapolated equivalent stress amplitude spectrum of the first region; Linear extrapolation is performed on the second region to obtain the extrapolated equivalent stress amplitude spectrum of the second region. The extrapolated equivalent stress amplitude spectrum of the first region and the extrapolated equivalent stress amplitude spectrum of the second region are then combined to obtain the extrapolated equivalent stress amplitude spectrum. The cumulative fatigue damage estimation module is used to calculate the cumulative fatigue damage of engineering equipment based on the extrapolated equivalent stress amplitude spectrum and stress-life curve, using Palmgren-Miner linear cumulative damage.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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