A complex random spectrum fatigue life fast prediction method based on load spectrum similarity factor and relative miner criterion

Abstract

The application discloses a kind of complex random spectrum fatigue life fast prediction method based on load spectrum similarity factor and relative Miner criterion, comprising: obtaining multiple random load spectrum, including reference spectrum and analysis spectrum;Group fatigue test is carried out to reference spectrum to obtain its fatigue initiation life;According to the equivalent damage rate of each spectrum, the basic calculation life of each analysis spectrum is calculated using the relative Miner criterion;The dynamic time warping distance combined with SWT formula is used to calculate the load spectrum similarity factor of each analysis spectrum relative to reference spectrum;The fatigue initiation life of at least one analysis spectrum is obtained and the error relationship function of the absolute value of calculation error and load spectrum similarity factor is fitted;According to the function, the prediction calculation error of each analysis spectrum is calculated and the basic calculation life is corrected.The application can realize high-precision prediction under the condition of a small amount of test, has less parameter demand, and has strong engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of aircraft structural life monitoring and fatigue life assessment technology, and particularly relates to a rapid prediction method for fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion. Background Technology

[0002] Accurate prediction of fatigue life under random load spectra is a key issue in aircraft structural life design, single-aircraft life monitoring, and service life management. Existing fatigue life analysis methods mainly include nominal stress method, local stress-strain method, critical distance method, field strength method, and crack propagation analysis method. These methods typically require a large number of material parameters, empirical parameters, and model correction parameters. Under complex random spectrum conditions, supplementary experiments are often needed for calibration to obtain high prediction accuracy. Therefore, from an engineering application perspective, how to obtain high-accuracy life prediction results with as few parameters and a small number of experimental supports as possible remains the core technical problem in random spectrum life analysis.

[0003] In existing engineering applications, the relative Miner criterion is widely used for random spectrum lifetime estimation due to its fewer parameter requirements, simpler calculation process, and strong engineering feasibility. The basic idea of ​​this method is to first obtain the calculated lifetime of the target spectrum using a basic fatigue analysis model, and then use the experimental results of a reference spectrum to relatively correct the calculated lifetime. Compared with traditional fatigue analysis methods, the relative Miner criterion has less dependence on material constants and additional correction parameters, exhibiting significant engineering advantages. However, the correction capability of this method usually depends on the comparability between the reference spectrum and the target spectrum. When different random spectra differ significantly in spectral structure, load order, or local peak distribution, relying solely on the relative correction of a single reference spectrum is insufficient to reliably guarantee prediction accuracy.

[0004] To address this issue, existing research often employs parameters such as the load spectrum shape factor (SSF) to characterize differences between spectra and establish correction relationships. These methods essentially still operate from the perspective of damage calculation or spectrum shape conversion, and are suitable for load spectra with relatively fixed mission profiles, well-defined block structures, or relatively controllable spectrum shape differences. However, for complex random spectra formed by different flight missions, maneuver combinations, and service environments, the SSF struggles to fully reflect the differences between random spectra that truly lead to changes in lifetime error due to the more complex time-series characteristics such as load order, high-low load interactions, and local peak clusters. This limits its applicability.

[0005] Dynamic time warping (DTW) methods can nonlinearly align and measure differences between different random spectra from the perspective of load time series, and are theoretically more suitable for similarity analysis between complex random spectra. Especially when the task composition between random spectra is not completely fixed, or when there is time shift or stretching deformation in the local load structure, DTW-type methods can characterize the differences between spectra more effectively than traditional SSF methods.

[0006] The existing technology still has the following shortcomings: First, traditional fatigue analysis methods have many parameters and are highly dependent on experiments; second, although they have fewer parameters than the Miner criterion, their correction accuracy is insufficient when there are large differences between spectra; third, existing correction methods based on SSF are more suitable for spectra with fixed task profiles and are difficult to be universally applied to complex random spectra; fourth, there is still a lack of a method based on the similarity of load time series that can achieve high-precision lifetime correction under a small number of test conditions. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention proposes a rapid prediction method for fatigue life of complex random spectra based on load spectrum similarity factor and relative Miner criterion, thereby resolving the issues existing in the prior art.

[0008] To achieve the above objectives, this invention provides a rapid prediction method for fatigue life of complex stochastic spectra based on load spectrum similarity factor and relative Miner criterion, comprising: Multiple random load spectra are acquired, including a reference spectrum and an analysis spectrum; Group fatigue tests were conducted on the reference spectrum to obtain the fatigue initiation life of the reference spectrum; Based on the equivalent damage rate of each of the random load spectra, the basic computational lifetime of each of the analytical spectra is calculated using the relative Miner criterion. The load spectrum similarity factor of each analytical spectrum relative to the reference spectrum is calculated by using the dynamic time bending distance combined with the SWT formula; Obtain the fatigue initiation lifetime of at least one of the analytical spectra; Based on the fatigue initiation lifetime of the reference spectrum and the fatigue initiation lifetime of at least one analytical spectrum, a function relating the absolute value of the calculation error to the load spectrum similarity factor is fitted. Calculate the prediction error of each of the analytical spectra based on the error relationship function; The basic calculated lifetime of each analytical spectrum is corrected according to the error relationship function to obtain the corrected calculated lifetime of each analytical spectrum, thus completing the rapid prediction of fatigue lifetime of complex random spectrum.

[0009] Optionally, based on the equivalent damage rate of each of the random load spectra, the basic computational lifetime of each of the analytical spectra is calculated using the relative Miner criterion, including: Rainflow counting is performed on each of the random load spectra to obtain the peak and trough values ​​of each stress cycle in each random load spectrum; the SWT formula is used to convert each stress cycle into a symmetrical cycle with equal damage, and the equivalent damage of each stress cycle is obtained; based on the equivalent damage of each stress cycle, the Miner linear cumulative damage theory is used to calculate the total equivalent damage of each of the random load spectra; based on the total equivalent damage of each of the random load spectra and its corresponding basic cycle flight hours, the equivalent damage rate of each of the random load spectra is calculated; the random load spectrum with the largest equivalent damage rate is selected as the reference spectrum, and the remaining random load spectra are selected as the analysis spectra; based on the fatigue initiation life of the reference spectrum, the equivalent damage rate of the reference spectrum, and the equivalent damage rate of each of the analysis spectra, the relative Miner criterion is used to calculate the basic calculated life of each of the analysis spectra.

[0010] Optionally, the load spectrum similarity factor of each analytical spectrum relative to the reference spectrum is calculated using the dynamic time bending distance combined with the SWT formula, including: The load time series of the reference spectrum and the load time series of each of the analytical spectra are dynamically time-bending aligned to obtain a regularized path. An improved distance metric combining the SWT formula is used to calculate the distance between each pair of aligned points on the regularized path. Based on the improved distance metric of each pair of aligned points on the regularized path, the dynamic time-bending distance between the reference spectrum and each of the analytical spectra is calculated as the load spectrum similarity factor of each analytical spectrum relative to the reference spectrum. The ratio of the larger absolute value of the two load points to the test stress level of the reference spectrum is used as a weighting coefficient, and the product of the absolute difference between the two load points and the weighting coefficient is used as the improved distance metric.

[0011] Optionally, the FastDTW algorithm is used to dynamically align the load time series of the reference spectrum with the load time series of each of the analyzed spectra.

[0012] Optionally, obtaining the fatigue initiation lifetime of at least one of the analyzed spectra includes: The analytical spectrum with the largest difference in similarity factor with the load spectrum of the reference spectrum is selected as the first experimental spectrum, and group fatigue tests are performed on the first experimental spectrum to obtain the fatigue initiation life of the first experimental spectrum. The analytical spectrum whose load spectrum similarity factor is closest to that of the reference spectrum among all the analytical spectra is selected as the second experimental spectrum, and a group fatigue test is performed on the second experimental spectrum to obtain the fatigue initiation life of the second experimental spectrum.

[0013] Optionally, based on the fatigue initiation lifetime of the reference spectrum and the fatigue initiation lifetime of at least one of the analytical spectra, an error relationship function between the absolute value of the calculation error and the load spectrum similarity factor is fitted, including: The absolute value of the calculation error of the at least one analytical spectrum is calculated based on the basic calculated lifetime of the at least one analytical spectrum and the fatigue initiation lifetime of the at least one analytical spectrum. Using the load spectrum similarity factor of the at least one analytical spectrum as the independent variable and the absolute value of the calculation error of the at least one analytical spectrum as the dependent variable, an error relationship function is fitted, wherein the error relationship function is in the form of a power function.

[0014] Optionally, before correcting the basic calculation lifetime of each analytical spectrum based on the prediction calculation error of each analytical spectrum, the method further includes determining the sign of the prediction calculation error of each analytical spectrum.

[0015] Optionally, the process of determining the sign of the prediction calculation error for each of the analytical spectra includes: The equivalent damage rate of the reference spectrum is compared with the equivalent damage rate of each analytical spectrum; if the equivalent damage rate of the reference spectrum is greater than the equivalent damage rate of the analytical spectrum, the prediction calculation error is determined to be positive; if the equivalent damage rate of the reference spectrum is less than the equivalent damage rate of the analytical spectrum, the prediction calculation error is determined to be negative.

[0016] Optionally, the basic calculation lifetime of each analytical spectrum is corrected based on the prediction calculation error of each analytical spectrum, including: The corrected calculated lifetime of each analytical spectrum is obtained by dividing the basic calculated lifetime of each analytical spectrum by the difference between the base lifetime and the predicted calculation error.

[0017] Optionally, the load spectrum similarity factor is the FastDTW distance combined with the SWT formula, which characterizes the temporal difference between the load time series of the analyzed spectrum and the load time series of the reference spectrum.

[0018] Compared with the prior art, the present invention has the following advantages and technical effects: (1) Few parameter requirements and strong engineering applicability; This invention uses the relative Miner criterion as the basic life calculation framework. Compared with the nominal stress method, local stress-strain method and other complex fatigue analysis methods, it has less dependence on a large number of material parameters, notch parameters and empirical correction coefficients, making it easier to implement in engineering single-machine life monitoring scenarios.

[0019] (2) High-precision life correction can be achieved under limited testing conditions; This invention establishes an error-DTW distance relationship by selecting one reference spectrum for testing and combining it with the results of a small number of other random spectrum tests. This allows for the correction of lifetime calculations for complex random spectra even with a small number of test samples, significantly reducing the reliance of traditional methods on large-scale fatigue test databases.

[0020] (3) Characterize the differences between spectra from the perspective of time series, breaking through the applicability limitations of SSF; The SSF method, which is essentially based on damage reduction, is more suitable for load spectra with fixed task profiles and relatively stable spectral structures. This invention, on the other hand, takes the load time series perspective and uses FastDTW to perform nonlinear alignment and distance measurement on random spectra, which can characterize the temporal differences between general complex random spectra. Therefore, it has better spectral adaptability and engineering universality.

[0021] (4) Improve the accuracy and stability of lifetime prediction for complex random spectra; After establishing the relationship between "FastDTW distance and life calculation error", this invention can quantitatively correct the basic calculated life, thereby reducing the prediction deviation of the relative Miner criterion under the condition of significant spectral differences and improving the accuracy and stability of random spectrum fatigue life prediction.

[0022] (5) Facilitates integration with subsequent lifetime correction and machine learning prediction methods; The DTW similarity factor and error correction relationship formed by this invention can be further used as the basic input for load spectrum similarity lifetime analysis, random spectrum feature dimensionality reduction and physical information-guided machine learning prediction, providing a unified data interface for subsequent complex random spectrum lifetime modeling. Attached Figure Description

[0023] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the lifetime prediction method based on load spectrum similarity factor according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the dynamic time bending path according to an embodiment of the present invention; Figure 3 This is a schematic diagram comparing DTW calculations under different load cycles according to an embodiment of the present invention; Figure 4 The load spectrum shape factor in this embodiment of the invention and load spectrum similarity factor Comparison with the fitting relationship of calculation error; Figure 5 The load spectrum shape factor in this embodiment of the invention and load spectrum similarity factor Comparison of correction accuracy: (a) is a comparison of calculated lifetime, and (b) is a comparison of calculated error. Detailed Implementation

[0024] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0026] Example 1 like Figure 1 As shown, this embodiment provides a method for rapid prediction of fatigue life of complex random spectra based on load spectrum similarity factor and relative Miner criterion, including: (a) Framework for constructing load spectrum similarity factors; First, based on the existing random load spectra, a reference spectrum and other analytical spectra are determined. For test specimens of the same material and structure, group fatigue tests are conducted under the reference spectrum to obtain the fatigue initiation life. The equivalent damage for each random spectrum is calculated using the relative Miner criterion combined with the SWT formula, and the theoretical calculated life is obtained based on the reference spectrum. Then, the DTW basic algorithm is improved by combining the SWT formula to make the DTW distance calculation more consistent with fatigue characteristics, and the load spectrum similarity factor of each analytical spectrum relative to the reference spectrum is calculated using the FastDTW algorithm. Then, based on the fatigue test lifetime under a small number of random spectra, the relationship curve between lifetime error and the similarity factor SSiF is fitted; finally, this fitting function is used to correct the lifetime under any random spectrum. The process is as follows: Figure 1 .

[0027] (ii) Calculation method for shape factor of load spectrum; (1) DTW distance; The dynamic time warping method, based on dynamic programming, seeks the shortest distance between two time series. The specific steps are as follows: Given time series... and time series Sort them according to their time position and construct m OK n Column distance matrix D ,Right now: (1) In the distance matrix Find a line from the top left corner (11) to the bottom right corner ( m , n The regularized path satisfies the following constraints: (1) Boundary constraints: The path starts at (1, 1) and ends at (...). m , n ); (2) Monotonicity constraint: and Neither decreases; (3) Continuity constraint: Adjacent steps can only be in three directions: (1,0), (0,1) or (1,1) (right, down, down right).

[0028] The DTW distance formula is: (2) In the formula, .

[0029] A schematic diagram of the dynamic time bending path is shown below. Figure 2 As shown.

[0030] (2) DTW distance based on SWT formula; The method described in (ii) (1) only considers the load range and cannot take into account the influence of stress magnitude. Figure 3 The two cycles on the left are 1-A-3 and 1-B-3. Figure 3 The two cycles on the right, 1-C-3 and 1-D-3, have the same valley value and their peak values ​​differ by 0.3. Calculated according to formula (2), the results are as follows: Figure 3 The DTW distance between the two cycles on both the left and right sides is 0.3, indicating that the two cycles are equally different. Clearly, this cannot characterize cycle differences.

[0031] From the perspective of fatigue damage, the average stress between points (A, B) is higher than the average stress between points (C, D). Figure 3 As shown in the load cycle, changing B to A has a greater impact on damage than changing D to C. Therefore, the similarity analysis of fatigue load spectra needs to comprehensively consider the mean and amplitude between load points. In order to make the DTW distance reflect the difference in peak stress and amplitude, based on the point-to-point distance in equation (2), the two load points are... Treating it as a hypothetical load cycle, the magnitude of the load cycle is measured using distance. Instead of traditional Euclidean distance The distance between the components of two sequences is defined as: (3) In the formula, and Representing the load sequence and In the and the The stress value at each sampling point. In this definition, All of these are dimensionless parameters.

[0032] Compared to equation (2), equation (3) can reflect the difference in load magnitude and also the degree of similarity between the two load spectra. When equation (3) is used to calculate the results... Figure 3 The DTW distances for the two cycles on the left and right sides are 0.27 and 0.21 respectively, which reflects the degree of difference between the two cycles. Therefore, this is more consistent with the characteristics of actual fatigue damage.

[0033] The DTW distance sign combined with the SWT formula is defined as... .

[0034] (3) FastDTW algorithm; The number of cycles for load spectrum sequences often exceeds tens of thousands. Traditional DTW algorithms are inefficient for long sequences. To improve computational efficiency, the FastDTW algorithm is used to accelerate DTW. The core of FastDTW consists of three parts: coarse-grained optimization, projection, and fine-grained constraint search.

[0035] (a) Coarse-grained processing; Downsampling is achieved by averaging adjacent points: (4) In the formula, For coarse-grained operators, This is the original payload sequence.

[0036] (b) Projection; The optimal regularized path computed on the coarse-grained sequence is used to construct a restricted search region at the fine-grained scale, thus reducing the dynamic programming of fine-scale DTW from a full matrix search to a search within the region. This is due to the coarse-scale indexing... Corresponding to fine-scale index intervals and Therefore, coarse-scale path points Projection on a fine scale Grid blocks: coarse-scale waypoints Projection on a fine scale Grid blocks: (5) In the formula, This represents the optimal regularized path for DTW calculated at a coarse-grained scale.

[0037] The purpose of this projection is to optimize the distortion path projected from a coarser-grained scale by locally adjusting the distortion path.

[0038] (c) Fine-grained constraint search; At a fine scale, the search is performed only within the neighborhood of the projection path, where the neighborhood is determined by the radius parameter. control. The larger the value, the closer it is to the standard DTW accuracy, but the computational cost increases.

[0039] FastDTW is a recursive multi-scale algorithm. Its core principle is to continuously coarse-graineden the sequence until it is sufficiently short, then use standard DTW to find the optimal path at that scale, and finally project it back to the fine scale layer by layer. Therefore, a termination condition must be set: a minimum length threshold. The larger the threshold, the earlier the recursion stops, resulting in slower computation but less loss of coarse-scale information; the smaller the threshold, the deeper the recursion, but the more likely the coarsening error will affect the accuracy.

[0040] Finally, the load spectrum similarity factor for fatigue life was obtained. .

[0041] (III) Lifespan Calculation Method; (1) Relative Miner criterion; In contrast to Miner's cumulative damage theory, the lifetime of other spectra is calculated based on the test lifetime of one load spectrum. The lifetime calculation formula is as follows: (6) In the formula, The test lifetime is for the reference spectrum. The damage is the reference spectrum calculated according to the damage calculation method and Miner's rule. To analyze spectral lifetime, The damage is calculated using the same method for the analytical spectrum.

[0042] Aircraft structural load spectra are typically compiled in units of a certain life cycle. Introducing the basic life cycle of the load spectrum, equation (6) can be transformed into: (7) In the formula, Represents lifetime under analytical spectrum. The basic period flight hours corresponding to the reference spectrum. The basic period flight hours corresponding to the analysis spectrum.

[0043] even so, There is still an error, and the error formula is: (8) In the formula, E represents the calculation error of the analytical spectrum B. To analyze the experimental lifetime of spectrum B, The calculated lifetime of the analytical spectrum B is obtained by equation (7).

[0044] (2) Equivalent damage calculation method based on SWT formula and Miner criterion; Rainflow counting was performed on the stress spectrum to obtain the first Peak and valley pairs of each load cycle ( , and stress ratio ( i =1,…, n The SWT formula is used to convert single loops into symmetric loops with equal damage: (9) In the formula, The symmetrical cyclic peak obtained from the conversion.

[0045] Material property parameters with R=-1 SN The curve is taken as the Basquin equation: (10) In the formula, m This represents the stress index in the material.

[0046] According to Miner's criterion, the damage from a single stress cycle is: (11) because C The constant is the sum of the effects of a single injury and... Proportional, let the equivalent damage per cycle be: (12) The equivalent damage of the load spectrum is calculated using Miner's linear cumulative damage theory. The calculation formula is as follows: (13) In the formula: D The equivalent damage represents the load spectrum.

[0047] If the fundamental period flight hours corresponding to the payload spectrum are Unit flight low-yield damage rate for: (14) (iv) Specific steps for life prediction; Based on the random load spectrum similarity factor The specific steps for fatigue life correction are as follows: (1) Calculate the damage rate of each spectrum using the method described in (iii); (2) Select the spectrum with the highest damage rate as the reference spectrum.

[0048] (3) Calculate the similarity factor of each spectrum relative to the reference spectrum using the method described in (ii), i.e., the FastDTW distance combined with the SWT formula. ; (4) Select two more single-machine spectra for fatigue testing, and select the load spectrum similarity factor with the reference spectrum. The spectrum with the largest difference is selected as the additional experimental spectrum 1, and the spectrum closest to the one analyzed is chosen. The random spectrum is used as the experimental spectrum 2.

[0049] (5) Obtain the median lifetime under the two additional random spectra, calculate the error and similarity factor, and fit to obtain the absolute value of the calculation error. and load spectrum similarity factor Relationships can usually be taken as .

[0050] (6) From (5) - Relationship, calculating the absolute value of the calculation error for arbitrary analytical spectra. .

[0051] (7) Assign (6) calculation error The sign of the variable determines the prediction calculation error. .

[0052] The Miner linear cumulative damage criterion and life calculation methods based on relative damage use a reference spectrum life as a benchmark, mapping the load spectrum of the unknown life onto the reference spectrum. Because the Miner criterion ignores load sequence effects and stress interactions, it is insensitive to extreme values, often overestimating damage caused by low loads and underestimating damage caused by high loads. Therefore, the statistical results of the calculated life tend to "converge" to the reference spectrum life, resulting in a narrower predicted life distribution range than the actual experimental life range. Based on the assumption of a narrowed calculated life distribution range, in the case of damage ratio... A value of 1 indicates a positive error, and the damage ratio is... A value of 1 indicates a negative error. Therefore, a criterion for determining the sign of the error is proposed, as shown in equation (15).

[0053] (15) In the formula, Damage rate as a reference spectrum To analyze the damage rate of the spectrum.

[0054] (8) Calculation error of each analytical spectrum obtained from (7) Combined with equation (7) and formula (8), the corrected calculated lifetime is... The calculation formula is: (16) (v) Implementation Cases; Based on the usage of the aircraft in the fleet, 10 aircraft were randomly selected, and stress spectra for 10 key components of each aircraft were compiled. These spectra were divided into two categories according to actual usage: the first category consisted of mission profiles of the same type and number, with the same composition order, numbered as spectra 1-5; the second category consisted of mission profiles of different types and numbers, with completely different compositions, numbered as spectra 6-10. Group fatigue tests were conducted on the 10 random spectra, and the fracture morphology was observed using a universal tool microscope. Marker lines were interpreted, crack propagation data were obtained, and the corresponding crack lengths were interpolated to obtain the data. a =0.8mm germination lifetime. The germination lifetimes of spectra 1 to 10 are: 34465, 11542, 16070, 6503, 2866, 13328, 14400, 9848, 34937, 22873.

[0055] According to (iv) the load spectrum similarity factor The lifetime correction step uses the equivalent damage calculation method based on the SWT formula and Miner criterion described in (II) to calculate the total damage of 10 random spectra. D The lifetime was calculated using an analogy method.

[0056] The corrected formula for calculating lifetime and corresponding calculation error is as follows: (17) In the formula, This represents the calculation error before correction. This represents the corrected calculation error.

[0057] Using the random spectrum lifetime calculation method described in (III), the damage ratio, calculated lifetime, calculation error, and positive / negative discrimination results are obtained based on the SWT formula and the relative Miner criterion, as shown in Table 1.

[0058] Table 1 Using the random spectrum similarity factor calculation method described in (II), and following the lifetime correction process based on load spectrum similarity described in (IV), spectrum 5 is selected as the reference spectrum, and spectra 1 and 3 are selected as supplementary experimental spectra. Based on the load spectrum similarity factor... The lifetime correction results are shown in the table below.

[0059] The calculation error is obtained based on the SWT formula and the relative Miner criterion. E Similarity factor with load spectrum The fitting relationship is shown in equation (18).

[0060] (18) Lifetime correction was performed using equation (18), and the results are shown in Table 2.

[0061] Table 2 The similarity calculation method of this invention is compared with the spectrum shape factor (SSF). The SSF is defined as: (19) In the formula, The sum of the cycle numbers of each load level in the program block spectrum. Damage calculation for load cycles at each level in the program block spectrum This is the sum of the number of cycles corresponding to the maximum load.

[0062] Combining equation (13), using the equivalent damage method for damage conversion, and substituting into equation (19), it can be transformed into: (20) In the formula, This represents the equivalent damage value for the maximum number of cycles in the load spectrum. The calculated lifetime after SSF correction is... .

[0063] The similarity factor proposed in (II) and (3) of this invention Equation (20) is used to measure the difference between the analytical spectrum and the reference spectrum, while Equation (20) is used to measure the deviation between the random spectrum and the constant amplitude spectrum. To compare the two similarity factor calculation methods, Equation (20) is modified as follows: (twenty one) In the formula, To analyze the degree of difference between the spectrum and the reference spectrum, The SSF value is the reference spectrum. The SSF values ​​are for the remaining analytical spectra.

[0064] Using the lifetime correction process based on load spectrum similarity described in (iv), spectrum 5 is selected as the reference spectrum, and spectrum 1 and spectrum 8 are selected as supplementary test spectra.

[0065] The calculation error is obtained based on the SWT formula and the relative Miner criterion. E Similarity factor with load spectrum The fitting relationship is shown in equation (22).

[0066] (twenty two) Lifetime correction was performed using equation (22), and the results are shown in Table 3.

[0067] Table 3 Load spectrum similarity factor and load spectrum shape factor For example, the fitting relationship with the calculation error Figure 4 As shown, (a) is (b) is .

[0068] Since spectra 1, 3, 5, and 8 were selected as reference or experimental spectra under both similarity corrections, the correction results for spectra 2, 4, 6, 7, 9, and 10 were compared. Loading spectral shape factor. and load spectrum shape factor The lifetime correction results for, for example Figure 5 As shown.

[0069] In summary, for the 10 random spectra, the computational lifetimes obtained using the SWT-based relative Miner criterion are all within the 2x error band except for spectrum 1, where the computational error is 63.99%. For the corrected spectra 2, 4, 6, 7, 9, and 10, the proposed load spectrum similarity factor method is used. The calculated lifetimes obtained by the lifetime prediction method all fall within the 1.1x error band.

[0070] The calculation errors obtained directly using relative Miner for spectra 2, 4, 6, 7, 9, and 10 are 34.79%, 11.45%, 24.28%, 38.72%, 43.31%, and 39.94%, respectively. Using the loading spectrum shape factor... The corrected calculation errors were 12.86%, 2.47%, 23.16%, 33.94%, 19.50%, and 15.35%, respectively, and the calculation lifetimes corrected using the load spectrum similarity factor were -5.76%, -0.31%, -2.33%, 3.90%, -5.09%, and 3.78%, respectively.

[0071] Compared to directly using the computational lifetime obtained from the relative miner, using The calculation error can be appropriately reduced. This method is only applicable to load spectra with relatively fixed mission profiles and differs from the modified fitting function used in this study. A load spectrum similarity factor is used. The obtained computational lifetime has significantly improved prediction accuracy compared to the uncorrected result, and has a wider range of applications.

[0072] Therefore, the load spectrum similarity factor proposed in this invention The lifetime analysis method, while maintaining high-accuracy prediction, is superior to the load spectrum shape factor. It has strong universality.

[0073] This invention proposes a mechanism for constructing a similarity factor for complex random load spectra based on FastDTW. The similarity factor is directly derived from the differences between load time series, rather than from equivalent damage or spectral statistics.

[0074] This invention proposes a basic lifetime calculation mechanism based on the relative Miner criterion, employing the relative Miner criterion to obtain the basic calculated lifetime of the target random spectrum, and a lifetime calculation form that connects with subsequent DTW error correction. It emphasizes using the relative Miner criterion as a low-parameter, highly engineering-feasible basic lifetime analysis framework.

[0075] This invention proposes a mechanism for constructing the error-DTW distance relationship based on a small number of reference experiments. It selects one reference spectrum and a small number of random spectrum experimental results, defines the lifetime error index E, and utilizes the DTW distance or similarity factor to establish the E-DTW error curve. Essentially, it elevates the traditional "reference spectrum empirical correction" to "correction based on inter-spectral temporal differences."

[0076] This invention selects the spectrum with the highest equivalent damage rate, calculated using the SWT formula, as the reference spectrum for all random spectra requiring analysis. Two individual spectra are then selected for fatigue testing, and the similarity factor of the load spectrum with the reference spectrum is chosen. The spectrum with the largest difference is selected as the additional experimental spectrum 1, and the spectrum closest to the one analyzed is chosen. The random spectrum is used as the experimental spectrum 2.

[0077] The Miner linear cumulative damage criterion and life calculation methods based on relative damage use a reference spectrum life as a benchmark, mapping the load spectrum of the unknown life onto the reference spectrum. Because the Miner criterion ignores load sequence effects and stress interactions, it is insensitive to extreme values, often overestimating damage caused by low loads and underestimating damage caused by high loads. Therefore, the statistical results of the calculated life tend to "converge" to the reference spectrum life, resulting in a narrower predicted life distribution range than the actual experimental life range. Based on the assumption of a narrowed calculated life distribution range, in the case of damage ratio... A value of 1 indicates a positive error, and the damage ratio is... A value of 1 indicates a negative error. Therefore, a criterion for determining the sign of the error is proposed, as shown in equation (15).

[0078] This invention proposes a lifetime correction mechanism based on the E-DTW error curve. It applies the error-DTW distance relationship to the basic lifetime calculation of the target spectrum to obtain the corrected lifetime. Instead of simply using empirical coefficients for correction, it quantitatively adjusts the lifetime based on the degree of time-series difference between the target spectrum and the reference spectrum.

[0079] This invention employs a distinct technical approach from the SSF correction method. The SSF method, starting from damage calculation or spectral shape reduction, is primarily applicable to load spectra with fixed mission profiles or relatively stable spectral structures. This invention, however, focuses on load time series analysis, utilizing FastDTW to calculate temporal differences between random spectra and establishing an error-DTW distance relationship to correct the relative Miner lifetime calculation. Therefore, the two methods differ fundamentally in their theoretical foundation, similarity representation objects, applicable spectral ranges, and lifetime correction mechanisms.

[0080] The method of this invention is applicable to complex random load spectra formed by different mission compositions, different maneuver combinations, and different levels of randomness, and is not limited to spectra with fixed mission profile structures.

[0081] This invention uses the relative Miner criterion as the basic life calculation framework. Compared with the nominal stress method, local stress-strain method and other complex fatigue analysis methods, it has less dependence on a large number of material parameters, notch parameters and empirical correction coefficients, making it easier to implement in engineering single-machine life monitoring scenarios.

[0082] This invention establishes an error-DTW distance relationship by selecting one reference spectrum for testing and combining it with the results of a small number of other random spectrum tests. This allows for the correction of lifetime calculations for complex random spectra even with a small number of test samples, significantly reducing the reliance of traditional methods on large-scale fatigue test databases.

[0083] The SSF method, which is essentially based on damage reduction, is more suitable for load spectra with fixed task profiles and relatively stable spectral structures. This invention, on the other hand, takes the load time series perspective and uses FastDTW to perform nonlinear alignment and distance measurement on random spectra, which can characterize the temporal differences between general complex random spectra. Therefore, it has better spectral adaptability and engineering universality.

[0084] After establishing the relationship between "FastDTW distance and life calculation error", this invention can quantitatively correct the basic calculated life, thereby reducing the prediction deviation of the relative Miner criterion under the condition of significant spectral differences and improving the accuracy and stability of random spectrum fatigue life prediction.

[0085] The DTW similarity factor and error correction relationship formed by this invention can be further used as the basic input for load spectrum similarity lifetime analysis, random spectrum feature dimensionality reduction and physical information-guided machine learning prediction, providing a unified data interface for subsequent complex random spectrum lifetime modeling.

[0086] This invention obtains the basic computational lifetime of complex random spectra with minimal material and model parameters. It establishes a method for characterizing the differences between complex random spectra from the perspective of load time series rather than damage conversion, namely, constructing a load spectrum similarity factor for fatigue lifetime. Using a small amount of experimental data, a quantitative relationship between lifetime calculation error and DTW distance is established to achieve high-precision correction of the lifetime calculated by the relative Miner. Overcoming the limitation that SSF is only applicable to mission profiles with relatively fixed load spectra, a lifetime correction method applicable to complex random spectra is established.

[0087] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included 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 rapid prediction method for fatigue life of complex stochastic spectra based on load spectrum similarity factor and relative Miner criterion, characterized in that, Includes the following steps: Multiple random load spectra are acquired, including a reference spectrum and an analysis spectrum; Group fatigue tests were conducted on the reference spectrum to obtain the fatigue initiation life of the reference spectrum; Based on the equivalent damage rate of each of the random load spectra, the basic computational lifetime of each of the analytical spectra is calculated using the relative Miner criterion. The load spectrum similarity factor of each analytical spectrum relative to the reference spectrum is calculated by using the dynamic time bending distance combined with the SWT formula; Obtain the fatigue initiation lifetime of at least one of the analytical spectra; Based on the fatigue initiation lifetime of the reference spectrum and the fatigue initiation lifetime of at least one analytical spectrum, a function relating the absolute value of the calculation error to the load spectrum similarity factor is fitted. Calculate the prediction error of each of the analytical spectra based on the error relationship function; The basic calculated lifetime of each analytical spectrum is corrected according to the error relationship function to obtain the corrected calculated lifetime of each analytical spectrum, thus completing the rapid prediction of fatigue lifetime of complex random spectrum.

2. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 1, characterized in that, Based on the equivalent damage rate of each of the aforementioned random load spectra, the basic computational lifetime of each of the aforementioned analytical spectra is calculated using the relative Miner criterion, including: Rainflow counting is performed on each of the random load spectra to obtain the peak and trough values ​​of each stress cycle in each random load spectrum; the SWT formula is used to convert each stress cycle into a symmetrical cycle with equal damage, and the equivalent damage of each stress cycle is obtained; based on the equivalent damage of each stress cycle, the Miner linear cumulative damage theory is used to calculate the total equivalent damage of each of the random load spectra; based on the total equivalent damage of each of the random load spectra and its corresponding basic cycle flight hours, the equivalent damage rate of each of the random load spectra is calculated; the random load spectrum with the largest equivalent damage rate is selected as the reference spectrum, and the remaining random load spectra are selected as the analysis spectra; based on the fatigue initiation life of the reference spectrum, the equivalent damage rate of the reference spectrum, and the equivalent damage rate of each of the analysis spectra, the relative Miner criterion is used to calculate the basic calculated life of each of the analysis spectra.

3. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 1, characterized in that, The load spectrum similarity factor of each analytical spectrum relative to the reference spectrum is calculated using the dynamic time bending distance combined with the SWT formula, including: The load time series of the reference spectrum and the load time series of each of the analytical spectra are dynamically time-bending aligned to obtain a regularized path. An improved distance metric combining the SWT formula is used to calculate the distance between each pair of aligned points on the regularized path. Based on the improved distance metric of each pair of aligned points on the regularized path, the dynamic time-bending distance between the reference spectrum and each of the analytical spectra is calculated as the load spectrum similarity factor of each analytical spectrum relative to the reference spectrum. The ratio of the larger absolute value of the two load points to the test stress level of the reference spectrum is used as a weighting coefficient, and the product of the absolute difference between the two load points and the weighting coefficient is used as the improved distance metric.

4. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 3, characterized in that, The FastDTW algorithm is used to dynamically align the load time series of the reference spectrum with the load time series of each of the analyzed spectra.

5. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 1, characterized in that, Obtaining the fatigue initiation lifetime of at least one of the analytical spectra includes: The analytical spectrum with the largest difference in similarity factor with the load spectrum of the reference spectrum is selected as the first experimental spectrum, and group fatigue tests are performed on the first experimental spectrum to obtain the fatigue initiation life of the first experimental spectrum. The analytical spectrum whose load spectrum similarity factor is closest to that of the reference spectrum among all the analytical spectra is selected as the second experimental spectrum, and a group fatigue test is performed on the second experimental spectrum to obtain the fatigue initiation life of the second experimental spectrum.

6. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 1, characterized in that, Based on the fatigue initiation lifetime of the reference spectrum and the fatigue initiation lifetime of at least one of the analyzed spectra, an error relationship function between the absolute value of the calculation error and the load spectrum similarity factor is fitted, including: The absolute value of the calculation error of the at least one analytical spectrum is calculated based on the basic calculated lifetime of the at least one analytical spectrum and the fatigue initiation lifetime of the at least one analytical spectrum. Using the load spectrum similarity factor of the at least one analytical spectrum as the independent variable and the absolute value of the calculation error of the at least one analytical spectrum as the dependent variable, an error relationship function is fitted, wherein the error relationship function is in the form of a power function.

7. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 1, characterized in that, Before correcting the basic calculation lifetime of each analytical spectrum based on the prediction calculation error of each analytical spectrum, the method further includes determining the sign of the prediction calculation error of each analytical spectrum.

8. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 7, characterized in that, The process of determining the sign of the prediction calculation error for each of the analytical spectra includes: The equivalent damage rate of the reference spectrum is compared with the equivalent damage rate of each analytical spectrum; if the equivalent damage rate of the reference spectrum is greater than the equivalent damage rate of the analytical spectrum, the prediction calculation error is determined to be positive; if the equivalent damage rate of the reference spectrum is less than the equivalent damage rate of the analytical spectrum, the prediction calculation error is determined to be negative.

9. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 1, characterized in that, Based on the prediction calculation error of each of the analytical spectra, the basic calculation lifetime of each of the analytical spectra is corrected, including: The corrected calculated lifetime of each analytical spectrum is obtained by dividing the basic calculated lifetime of each analytical spectrum by the difference between the base lifetime and the predicted calculation error.

10. The method for rapid prediction of fatigue life of complex random spectrum based on load spectrum similarity factor and relative Miner criterion according to claim 1, characterized in that, The load spectrum similarity factor is the FastDTW distance combined with the SWT formula, which characterizes the temporal difference between the load time series of the analyzed spectrum and the load time series of the reference spectrum.

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