A method and related equipment for determining the stress range distribution of a structure.

Abstract

This application discloses a method and related equipment for determining the stress range distribution of a structure. By optimizing the frequency domain discretization and time domain reconstruction methods, combined with multi-round statistical optimization and fusion strategies, a stable and reliable structural stress range distribution is output. The method includes: acquiring the stress power spectrum of the target structure, randomly dividing frequency intervals within a preset frequency band and assigning phases to obtain a discrete spectrum; reconstructing the time domain stress history and counting rainflow to generate multiple sets of dimensionless rainflow stress range probability density distributions; after average smoothing and moment preservation correction, using a multi-smoothing strategy to generate candidate sub-distributions, and combining them with evaluation indicators for weighted fusion to obtain the final distribution. This application improves the realism of the time history through random discretization, achieves distribution convergence through multiple statistical fusions, and balances smoothness and statistical characteristics through moment preservation and multi-strategy fusion. Only the stress power spectrum is required as input, making it suitable for complex scenarios such as broadband and multi-peak spectra. It can be embedded into existing systems for automated operation, reducing analysis costs and improving fatigue assessment accuracy.

Description

Technical Field

[0001] This application relates to the field of structural analysis technology, and more specifically, to a method and related equipment for determining the distribution range of structural stress. Background Technology

[0002] In aerospace, engineering machinery, and other fields, structures are subjected to complex dynamic loads for extended periods, and fatigue failure has become the leading cause of equipment malfunctions and safety accidents. The distribution of structural stress range is a core basis for describing load characteristics, calculating fatigue damage, and assessing fatigue life; its accuracy directly determines the level of structural reliability design. Therefore, developing efficient and accurate determination methods is of paramount engineering necessity and practical significance.

[0003] Current mainstream techniques for determining the distribution range of structural stress fall into two main categories, both of which suffer from significant drawbacks. The first is the inverse Fourier reconstruction method based on equally spaced frequency discretization. This method uniformly divides the target stress spectrum into several frequency points in the frequency domain and generates a time-domain signal through random phase superposition. However, equally spaced division cannot accurately capture the local energy characteristics of broadband or multi-peak spectra, resulting in a lack of randomness and authenticity in the reconstructed time-history. Furthermore, the energy distribution of the reconstructed signal is highly sensitive to the number of frequency divisions, leading to drastic fluctuations and extremely poor repeatability in rainflow counting results. Simultaneously, the randomness of random phase allocation causes the stress distribution range of a single rainflow to exhibit obvious non-smooth characteristics, with drastic fluctuations in the probability density curve, lacking statistical representativeness. The second method is the stress distribution construction method based on single-time-history statistics. Some studies achieve smoothing by standardizing, normalizing, or fitting parameters to the single reconstructed time-history, but the sample size for a single statistical analysis is severely insufficient, and the results are significantly affected by random phase and sampling interval. Distribution smoothing relies on manual operation or empirical fitting, lacking a systematic multiple averaging and fusion process, and the physical consistency of the smoothing results is insufficient.

[0004] In summary, existing technologies, while constructing stable, smooth, and statistically representative distributions from stress spectra, suffer from limitations such as discrete and singular frequency domain distributions and high randomness in reconstruction. There is an urgent need for a new method to determine the distribution range of structural stress in order to overcome the shortcomings of existing technologies. Summary of the Invention

[0005] This application provides a method and related equipment for determining the distribution range of structural stress. By optimizing the frequency domain discretization and time domain reconstruction methods, and combining multiple rounds of statistical optimization and fusion strategies, it overcomes the defects of time history distortion and result fluctuation in existing methods, and outputs a stable and reliable distribution range of structural stress.

[0006] A method for determining the stress range distribution of a structure, comprising:

[0007] Obtain the stress power spectrum of the target structure;

[0008] The stress power spectrum is subjected to multiple randomization discretization processes within a preset frequency band. Each randomization discretization process includes randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals of random width. Based on each frequency interval, a representative frequency and the corresponding power spectral density value are determined, and a random phase is assigned to each frequency interval.

[0009] Based on the discrete spectrum obtained from each randomization discretization process, the time-domain stress time history is reconstructed, and rainflow is counted on the time-domain stress time history to obtain the probability density distribution of the dimensionless rainflow stress range for a single event.

[0010] The probability density distribution of all dimensionless rainflow stress ranges is averaged and basically smoothed to obtain a preliminary smoothed distribution.

[0011] The initial smooth distribution is corrected by moment preservation to obtain the corrected distribution;

[0012] Based on the correction distribution, multiple candidate sub-distributions are generated using various smoothing strategies and parameter configurations, and then weighted and fused according to the preset evaluation index of each candidate sub-distribution to generate the structural stress range distribution.

[0013] Optionally, determining the representative frequency and corresponding power spectral density value based on each of the frequency intervals includes:

[0014] For the first type where the stress power spectrum exhibits a gradual change within the frequency range, the geometric midpoint of the frequency range is selected as the candidate representative frequency.

[0015] For the second type where the stress power spectrum exhibits drastic changes within the frequency range, the spectral centroid of the frequency range is selected as the candidate representative frequency.

[0016] At the candidate representative frequency, the corresponding power spectral density value is calculated by performing linear interpolation or smooth interpolation on the stress power spectrum.

[0017] Optionally, the step of averaging and basic smoothing the probability density distribution of all dimensionless rainflow stress ranges to obtain a preliminary smoothed distribution includes:

[0018] The probability density distribution of all dimensionless rainflow stress ranges is interpolated and mapped to a unified discrete stress range coordinate axis that covers all dimensionless stress range values.

[0019] The arithmetic mean of all distribution values ​​corresponding to each discrete point on the coordinate axis of the unified discrete stress range is calculated to generate an average distribution sequence.

[0020] The average distribution sequence is processed by applying a basic smoothing operator, which includes any one of moving average, low-order spline fitting, or kernel smoothing methods, to suppress discrete oscillations and obtain a preliminary smoothed distribution.

[0021] Optionally, the process of performing moment-preserving correction on the initial smooth distribution includes:

[0022] Calculate the low-order origin moments of the preliminary smooth distribution, wherein the low-order origin moments include at least the zeroth to second-order origin moments used to characterize the total probability of the distribution, the average stress range, and the dispersion of the stress range, respectively.

[0023] Construct a preset orthogonal basis function with an expected value of zero under the initial smooth distribution, and generate a moment-preserving correction operator, wherein the moment-preserving correction operator is in the form of a linear combination of the initial smooth distribution and the preset basis function;

[0024] Using the constraint that the low-order origin moments of the preliminary corrected distribution are equal to the low-order origin moments of the preliminary smoothed distribution, the linear combination coefficients in the moment-preserving correction operator are solved to obtain the corrected distribution.

[0025] Optionally, the expression for the moment-preserving correction operator is:

[0026]

[0027] Where r is the dimensionless stress range; P is the order of the lower-order origin moment; This represents the upper limit of the dimensionless stress range; The distribution is initially smooth; For the p-th pre-defined orthogonal basis function, in The condition of zero mean is satisfied. =0; denoted as the linear combination coefficients corresponding to the p-th pre-defined orthogonal basis function.

[0028] Optionally, based on the corrected distribution, multiple candidate sub-distributions are generated using various smoothing strategies and parameter configurations, and weighted and fused according to preset evaluation indicators of each candidate sub-distribution to generate a structural stress range distribution, including:

[0029] Using the corrected distribution as input, at least two different smoothing strategies are applied respectively, and each smoothing strategy is processed with at least two different sets of parameter configurations to generate multiple candidate sub-distributions;

[0030] Calculate the low-order moment deviation index of each candidate sub-distribution relative to the correction distribution, and the smoothness index of the candidate sub-distribution itself.

[0031] Based on the low-order moment deviation index and the smoothness index, calculate the comprehensive evaluation score of each candidate sub-distribution, and assign a fusion weight that matches the comprehensive evaluation score;

[0032] The structural stress range distribution is obtained by weighting and summing all the candidate sub-distributions according to the fusion weights.

[0033] Optionally, the formula for calculating the low-order moment deviation index is:

[0034]

[0035] The formula for calculating the smoothness index is as follows:

[0036]

[0037] in, is the deviation index of the p-th moment of the q-th candidate sub-distribution relative to the corrected distribution; r is the dimensionless stress range; P is the order of the lower-order origin moment; Let q be the candidate sub-distribution; To correct the p-th order raw moment of the distribution; Let be the smoothness index of the q-th candidate sub-distribution; This represents the upper limit of the dimensionless stress range.

[0038] Optionally, the smoothing strategy includes kernel density estimation, spline smoothing, and local regression smoothing;

[0039] The parameter configuration includes the bandwidth for kernel density estimation, the number of nodes for spline smoothing, and the window length for local regression smoothing.

[0040] Optional, also includes:

[0041] A maximum width threshold is set for each frequency range, and the maximum width threshold is determined based on the total width of the preset frequency band and a preset empirical range of discrete segments.

[0042] Optionally, after generating the structural stress range distribution, the method further includes:

[0043] The stress range distribution of the structure is dimensionally restored based on the variance or zero-order moment of the stress power spectrum.

[0044] A device for determining the distribution range of structural stress, comprising:

[0045] The structural power spectrum module is used to obtain the stress power spectrum of the target structure.

[0046] The random discretization processing module is used to perform multiple random discretization processes on the stress power spectrum within a preset frequency band. Each random discretization process includes randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals of random width. Based on each frequency interval, a representative frequency and the corresponding power spectral density value are determined, and a random phase is assigned to each frequency interval.

[0047] The probability density distribution module is used to reconstruct the time-domain stress time history based on the discrete spectrum obtained by each randomization discrete processing, and to count the rainflow in the time-domain stress time history to obtain the probability density distribution of the dimensionless rainflow stress range for a single occurrence.

[0048] The preliminary smoothing distribution module is used to average and perform basic smoothing on the probability density distribution of all the dimensionless rainflow stress ranges to obtain a preliminary smoothing distribution.

[0049] A moment preservation correction module is used to perform moment preservation correction on the preliminary smooth distribution to obtain a corrected distribution;

[0050] The stress range distribution module is used to generate multiple candidate sub-distributions based on the correction distribution using various smoothing strategies and parameter configurations, and to perform weighted fusion according to the preset evaluation index of each candidate sub-distribution to generate the structural stress range distribution.

[0051] A device for determining the distribution range of structural stress, comprising a memory and a processor;

[0052] The memory is used to store programs;

[0053] The processor is configured to execute the program to implement the steps of the method for determining the distribution of structural stress range as described in any of the preceding claims.

[0054] A readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for determining the distribution of structural stress range as described in any of the preceding claims.

[0055] A computer program product includes a computer program that, when executed by a processor, performs the steps of the method for determining the distribution of structural stress range as described in any of the preceding claims.

[0056] As can be seen from the above technical solutions, the method and related equipment for determining the distribution range of structural stress provided in this application introduce a random interval division and random phase superposition mechanism within a preset frequency band, and set an upper limit constraint on the segment width. This makes the energy and phase distribution of the discrete spectrum within the frequency band closer to the random characteristics of the continuous spectrum, overcoming the time-domain roughness caused by equal-interval discretization and significantly improving the realism of the time-domain reconstruction. The time-domain signal generated in this way exhibits higher diversity and physical rationality in frequency domain energy distribution, instantaneous amplitude changes, and peak-valley sequences. It can more accurately reflect the actual time-domain characteristics of the broadband random process, providing a more reliable basic input for subsequent rainflow statistics, and avoiding problems such as energy concentration, waveform repetition, and unnatural time-domain envelope caused by traditional equal-interval division.

[0057] This application employs a strategy of multiple random discretizations and time-history reconstructions, rainflow counting, and sample averaging to achieve a convergence of the rainflow stress range distribution from a single occurrence to a statistically representative distribution in a probabilistic sense. Simultaneously, combined with basic smoothing processing, it effectively suppresses high-frequency oscillations between samples, realizing a statistical convergence process from a single random result to a stable distribution characteristic. This ensures that the obtained dimensionless rainflow stress range probability density function exhibits stable and consistent morphological characteristics across multiple calculations, improving the reliability of the rainflow distribution and solving the problems of traditional single-time-history distributions being greatly affected by random factors and having poor repeatability.

[0058] In terms of distribution optimization, this application introduces a low-order moment preservation constraint correction step on the basis of the basic smoothing results, so that the smoothed distribution basically maintains the original level in key statistical indicators such as mean range and variance. Furthermore, by constructing a candidate sub-distribution set containing multiple smoothing algorithms and multiple sets of parameter settings, a unified evaluation function is constructed based on moment deviation and smoothness index and weighted fusion is performed to form an optimization mechanism that combines moment preservation and multi-strategy multi-parameter fusion. This takes into account both smoothness and statistical characteristic preservation, effectively avoiding the problem of insufficient or excessive smoothing caused by a single smoothing method, so that the final distribution is both continuous and smooth, and can maintain the statistical characteristics of the original random process.

[0059] Furthermore, this application relies solely on the target stress power spectrum as input, eliminating the need for long-period measured stress history. It is applicable to various complex spectral types, including broadband, narrowband, and multi-peak spectra, and exhibits good versatility across various service structures such as marine engineering structures and wind turbines. Embedding it into existing fatigue strength calculation programs or digital twin operation and maintenance systems enables automated construction of stress distribution ranges from the spectral domain to the time domain and then to rainflow, reducing the need for extensive repetitive time-history simulations and large-scale physical experiments, lowering the time and computational costs of engineering analysis, and simultaneously improving the accuracy and stability of fatigue damage assessment. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, 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 embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0061] Figure 1 This is a flowchart of a method for determining the distribution range of structural stress according to an embodiment of this application;

[0062] Figure 2 This is a schematic diagram of a random discretization process for the target stress spectrum disclosed in an embodiment of this application;

[0063] Figure 3 This is a curve comparison diagram of a smooth dimensionless rainflow stress range distribution function disclosed in an embodiment of this application;

[0064] Figure 4 This is a schematic diagram of a device for determining the distribution range of structural stress disclosed in an embodiment of this application;

[0065] Figure 5 This is a hardware structure block diagram of a device for determining the range distribution of structural stress disclosed in an embodiment of this application. Detailed Implementation

[0066] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0067] This application can be used in a wide variety of general-purpose or special-purpose computing device environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor devices, distributed computing environments including any of the above devices, etc.

[0068] The following section introduces the solution proposed in this application. The technical solution is as follows, and details are provided below.

[0069] Figure 1 This is a flowchart of a method for determining the distribution range of structural stress disclosed in an embodiment of this application.

[0070] like Figure 1 As shown, the method may include:

[0071] Step S1: Obtain the stress power spectrum of the target structure.

[0072] Specifically, the stress power spectrum is a core parameter reflecting the stress energy distribution characteristics of a target structure in the frequency domain, and its accuracy directly determines the reliability of subsequent analysis results. The acquisition method can be selected based on actual engineering needs. It can be obtained by conducting on-site measurements of the target structure, collecting stress time history data under typical operating conditions, and then converting the data using signal processing methods such as Fourier transform; alternatively, based on the design parameters and service environment of the target structure, a refined mechanical model can be established using finite element simulation software, and the stress power spectrum can be obtained through dynamic analysis. During the acquisition process, it is necessary to ensure coverage of the frequency range under which the structure bears the main loads to guarantee that the power spectrum data can fully characterize the stress response characteristics of the structure.

[0073] Step S2: Perform multiple randomization discretization processes on the stress power spectrum within a preset frequency band. Each randomization discretization process includes randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals of random width. Based on each frequency interval, determine the representative frequency and the corresponding power spectral density value, and assign a random phase to each frequency interval.

[0074] Specifically, the preset frequency band needs to be determined based on the dynamic characteristics and load excitation features of the target structure, typically selecting a frequency range where stress energy is concentrated and has a significant impact on structural fatigue. The core of each randomized discretization process is to dynamically divide the frequency range by randomly generating non-repeating division points, making the width of each range random and more closely approximating the frequency domain distribution of the actual load. When determining the representative frequency and corresponding power spectral density value, the energy distribution characteristics within the range must be comprehensively considered to ensure that the representative parameters accurately reflect the stress energy properties of that range. Random phase allocation is used to simulate the phase randomness of the actual load; each frequency range corresponds to an independent random phase, avoiding time-domain signal distortion caused by fixed phases. By repeatedly performing the above discretization process, multiple sets of discrete spectral data with statistical differences can be obtained.

[0075] The process of determining the representative frequency and the corresponding power spectral density value based on each of the frequency intervals may further include:

[0076] ① For the first type where the stress power spectrum exhibits a gradual change within the frequency range, the geometric midpoint of the frequency range is selected as the candidate representative frequency;

[0077] ② For the second type where the stress power spectrum exhibits drastic changes within the frequency range, the spectral centroid of the frequency range is selected as a candidate representative frequency;

[0078] ③ At the candidate representative frequency, the corresponding power spectral density value is calculated by performing linear interpolation or smooth interpolation on the stress power spectrum.

[0079] Specifically, when randomizing and discretizing the stress power spectrum, differential adaptation is performed based on the variation characteristics of the stress power spectrum in each frequency range to ensure that the selected parameters can truly reflect the stress energy distribution law in the range.

[0080] First, the stress power spectrum morphology within each randomly divided frequency interval needs to be determined: For the first type of frequency interval, characterized by a stable spectral trend and uniform energy distribution (i.e., a gradual change), the geometric midpoint of this interval is selected as the candidate representative frequency. The geometric midpoint can intuitively and efficiently characterize the center frequency position of the interval. In scenarios with a gradual change in spectral lines, it can minimize the impact of frequency selection deviation on energy characterization and ensure the consistency between the representative frequency and the overall frequency characteristics of the interval.

[0081] For the second type of frequency range, characterized by significant spectral fluctuations and energy concentration in local frequency bands (i.e., exhibiting drastic changes), the spectral centroid is used as a candidate representative frequency. The selection of the spectral centroid is based on the energy distribution of the stress power spectrum within the range, accurately capturing the key frequency positions where energy is concentrated. This avoids energy characterization distortion caused by selecting a fixed midpoint, and is particularly suitable for complex spectral scenarios with multi-peak spectra or local energy abrupt changes.

[0082] After determining the candidate representative frequencies, the power spectral density value corresponding to those frequencies needs to be calculated. For different spectral characteristics, appropriate interpolation methods can be selected: when the spectral variation pattern within the frequency range is clear and there is no significant noise interference, a linear interpolation method is used. This method calculates the power spectral density value at the candidate representative frequency through the linear correlation of known spectral data within the range, balancing computational efficiency and basic accuracy. When there are minor fluctuations or noise interference in the spectral lines, a smoothing interpolation method is used. During the interpolation process, the fluctuating data is appropriately smoothed to ensure the consistency of the power spectral density value with surrounding spectral lines while effectively suppressing the influence of noise on the results, ensuring the stability and reliability of the parameters.

[0083] Furthermore, after determining the representative frequency and power spectral density values, to simulate the random characteristics of phase in actual engineering loads, a random phase needs to be independently assigned to each frequency interval. This design avoids the regular repetition of the time-domain reconstructed signal caused by fixed phase settings, making the discrete spectrum closer to the random nature of the real load, and providing a fundamental guarantee for the accurate reconstruction of the subsequent time-domain stress time history.

[0084] like Figure 2 As shown, to overcome the roughness of time history reconstruction caused by single-time equally spaced discretization, a random interval partitioning method is used to reconstruct the target stress spectrum. In frequency band The random discretization process is then performed. The random discretization method includes the following sub-steps:

[0085] (1) Determine the number of discrete segments The setting is preferably based on the spectral energy distribution characteristics of the target spectrum, for example, an empirical range of 50 to 500, and sensitivity analysis and adaptive adjustment can be performed in subsequent steps.

[0086] (2) In the open interval Endogenous generation Non-repeating independent random cut points The set of random cut points and endpoints Merge the results and arrange them in ascending order to obtain the frequency division boundaries:

[0087]

[0088] (3) Calculate the width of the k-th frequency interval from the adjacent boundaries. With representative frequency :

[0089]

[0090] To avoid numerical instability caused by frequency segmentation, a maximum segment width can be set. Below a certain threshold, for example .

[0091] (4) At each representative frequency Interpolation calculation of power spectral density value Linear interpolation or piecewise smooth interpolation is preferred:

[0092]

[0093] (5) Generate random phase for each frequency sub-band Phase can be in the range Perform continuous uniform sampling within:

[0094]

[0095] Step S3: Based on the discrete spectrum obtained from each randomization discretization process, reconstruct the time-domain stress time history, and count the rainflows in the time-domain stress time history to obtain the probability density distribution of the dimensionless rainflow stress range for a single event.

[0096] Specifically, the time-domain stress time history reconstruction is based on the discrete spectrum obtained from a single randomization discretization. Through time-domain reconstruction algorithms such as inverse Fourier transform, the spectral information in the frequency domain is converted into a time-domain signal that directly reflects the structural stress change over time. During the reconstruction process, it is necessary to ensure that the time length and sampling frequency of the time-domain signal meet the requirements of subsequent rainflow counting, guaranteeing that the signal contains sufficient stress cycle characteristics. The rainflow counting operation uses flow counting to cyclically extract and statistically analyze the reconstructed time-domain stress time history, identifying each stress cycle and its corresponding stress range. To eliminate the magnitude differences in stress amplitude under different structures or operating conditions, the counting results need to be dimensionless, ultimately obtaining the dimensionless rainflow stress range probability density distribution corresponding to the single discretization process. This distribution can intuitively reflect the probability characteristics of each stress range occurring during a single stress process.

[0097] Step S4: Average and smooth the probability density distribution of all dimensionless rainflow stress ranges to obtain a preliminary smooth distribution.

[0098] Specifically, due to the influence of random factors in a single discrete processing step, the corresponding probability density distribution may exhibit local fluctuations or abnormal peaks, lacking statistical representativeness. Therefore, it is necessary to perform an arithmetic mean on all dimensionless distributions obtained from multiple discrete processing steps. This statistical averaging offsets the random errors in the single result, making the distribution trend closer to the statistical characteristics of the actual stress range. The basic smoothing process uses a smoothing algorithm to initially correct the averaged distribution curve. The main purpose is to eliminate high-frequency oscillations and local sawtooth fluctuations in the curve, making the distribution curve present a continuous and smooth shape. During the smoothing process, the degree of smoothing needs to be controlled to avoid excessive smoothing that could lead to the loss of core distribution features while eliminating noise. Ultimately, a preliminary smoothed distribution that combines statistical stability and basic smoothness is obtained.

[0099] Step S5: Perform moment-preserving correction on the preliminary smooth distribution to obtain the corrected distribution.

[0100] Specifically, basic smoothing may cause shifts in the statistical moments of the distribution, such as the mean and variance, disrupting the statistical consistency between the distribution and the original stress process. Statistical moments are key indicators reflecting the core characteristics of the stress distribution and directly affect the accuracy of subsequent fatigue assessments. The core of moment-preserving correction is to maintain the smoothness of the initial smoothed distribution while using numerical adjustments to ensure that the corrected distribution maintains consistency with the statistical moments of the original multi-group dimensionless distribution at lower-order statistical moments. During the correction process, a quantitative evaluation mechanism for statistical moment deviations needs to be established, and targeted adjustments should be made to moment parameters with large deviations to ensure that the corrected distribution possesses both good smoothness and accurately inherits the statistical essence of the original stress data.

[0101] Step S6: Based on the correction distribution, multiple candidate sub-distributions are generated using various smoothing strategies and parameter configurations, and weighted fusion is performed according to the preset evaluation index of each candidate sub-distribution to generate the structural stress range distribution.

[0102] Specifically, to avoid the limitations of a single smoothing strategy, multiple smoothing algorithms and different parameter configurations are used to generate multiple candidate sub-distributions based on the corrected distribution. Common smoothing strategies include multinomial smoothing and spline smoothing. By adjusting the core parameters of each strategy, sub-distributions with different characteristics can be obtained. Some sub-distributions emphasize smoothing effects, while others emphasize preserving distribution details. The preset evaluation index needs to comprehensively consider dimensions such as distribution smoothness, statistical moment deviation, and physical rationality. The comprehensive performance of each candidate sub-distribution is reflected through quantitative scoring. In the weighted fusion process, corresponding weights are assigned according to the evaluation index scores of each candidate sub-distribution. The sub-distribution with better performance receives higher weights. By integrating the advantages of each sub-distribution through weighted calculation, a structural stress range distribution with high smoothness, statistical accuracy, and physical rationality is finally generated, providing a direct basis for structural fatigue life assessment.

[0103] Furthermore, considering that the previously generated dimensionless rainflow stress range distribution eliminates the magnitude difference in stress amplitude, although facilitating statistical analysis, it may not be directly applicable to fatigue life calculations of specific structures and requires reliance on stress data with actual dimensions. Therefore, after generating the structural stress range distribution, a dimensionality reduction step is needed to make it directly applicable in engineering. Following the generation of the structural stress range distribution, the following may also be included:

[0104] The stress range distribution of the structure is dimensionally restored based on the variance or zero-order moment of the stress power spectrum.

[0105] Specifically, the core basis for dimensional reduction is the variance or zero-order moment of the stress power spectrum of the target structure. Both are key parameters reflecting the energy level of the stress signal and can directly correlate the dimensionless distribution with the actual stress level. If variance is chosen as the basis for reduction, the variance value of the original stress power spectrum must first be calculated, which reflects the fluctuation energy of the stress signal. Then, the previously obtained structural stress range distribution (dimensionalless form) is multiplied by the square root of the variance (corresponding to the characteristic magnitude of the stress amplitude) to achieve the conversion from dimensionless to actual dimensions. If the zero-order moment is used, its correspondence with the mean square value of stress is utilized to complete the reduction through similar magnitude correlation calculations. After dimensional reduction, the abscissa (stress range) of the structural stress range distribution will be converted into a value consistent with actual engineering units, which can be directly input into the fatigue damage calculation model, providing directly usable quantitative data for structural fatigue life assessment.

[0106] Furthermore, to avoid energy characterization distortion caused by excessively wide individual frequency ranges during randomization discretization, this application sets a maximum width threshold for each frequency range before random partitioning. This application may also include:

[0107] A maximum width threshold is set for each frequency range, and the maximum width threshold is determined based on the total width of the preset frequency band and a preset empirical range of discrete segments.

[0108] Specifically, the maximum width threshold is determined based on the total width of the preset frequency band as a fundamental constraint, combined with the industry's empirical range of discrete segment counts for stress analysis of similar structures. The total width of the preset frequency band is determined by the dynamic characteristics of the target structure and must cover the main load excitation frequencies and the structural resonance frequency range. The empirical range of discrete segment counts is derived from extensive engineering practice. For example, for broadband spectra, the number of segments is usually sufficient to distinguish each energy concentration region, while for narrowband spectra, the number of segments can be appropriately reduced to improve efficiency. During calculation, an initial threshold reference is first obtained based on the lower limit of the total width and the empirical segment count. Then, it is fine-tuned based on the overall complexity of the spectral lines within the preset frequency band. The more complex the spectral lines and the more dispersed the energy distribution, the lower the threshold needs to be appropriately reduced to increase the discretization accuracy; the relatively simple spectral lines can have the threshold appropriately relaxed, optimizing computational costs while ensuring accuracy. This threshold will serve as a constraint for the generation of random division points, ensuring that the width of all randomly formed frequency intervals does not exceed this value, thus avoiding the problem of spectral feature loss caused by excessively wide intervals from the source.

[0109] As can be seen from the above technical solutions, the method and related equipment for determining the distribution range of structural stress provided in this application introduce a random interval division and random phase superposition mechanism within a preset frequency band, and set an upper limit constraint on the segment width. This makes the energy and phase distribution of the discrete spectrum within the frequency band closer to the random characteristics of the continuous spectrum, overcoming the time-domain roughness caused by equal-interval discretization and significantly improving the realism of the time-domain reconstruction. The time-domain signal generated in this way exhibits higher diversity and physical rationality in frequency domain energy distribution, instantaneous amplitude changes, and peak-valley sequences. It can more accurately reflect the actual time-domain characteristics of the broadband random process, providing a more reliable basic input for subsequent rainflow statistics, and avoiding problems such as energy concentration, waveform repetition, and unnatural time-domain envelope caused by traditional equal-interval division.

[0110] This application employs a strategy of multiple random discretizations and time-history reconstructions, rainflow counting, and sample averaging to achieve a convergence of the rainflow stress range distribution from a single occurrence to a statistically representative distribution in a probabilistic sense. Simultaneously, combined with basic smoothing processing, it effectively suppresses high-frequency oscillations between samples, realizing a statistical convergence process from a single random result to a stable distribution characteristic. This ensures that the obtained dimensionless rainflow stress range probability density function exhibits stable and consistent morphological characteristics across multiple calculations, improving the reliability of the rainflow distribution and solving the problems of traditional single-time-history distributions being greatly affected by random factors and having poor repeatability.

[0111] In terms of distribution optimization, this application introduces a low-order moment preservation constraint correction step on the basis of the basic smoothing results, so that the smoothed distribution basically maintains the original level in key statistical indicators such as mean range and variance. Furthermore, by constructing a candidate sub-distribution set containing multiple smoothing algorithms and multiple sets of parameter settings, a unified evaluation function is constructed based on moment deviation and smoothness index and weighted fusion is performed to form an optimization mechanism that combines moment preservation and multi-strategy multi-parameter fusion. This takes into account both smoothness and statistical characteristic preservation, effectively avoiding the problem of insufficient or excessive smoothing caused by a single smoothing method, so that the final distribution is both continuous and smooth, and can maintain the statistical characteristics of the original random process.

[0112] Furthermore, this application relies solely on the target stress power spectrum as input, eliminating the need for long-period measured stress history. It is applicable to various complex spectral types, including broadband, narrowband, and multi-peak spectra, and exhibits good versatility across various service structures such as marine engineering structures and wind turbines. Embedding it into existing fatigue strength calculation programs or digital twin operation and maintenance systems enables automated construction of stress distribution ranges from the spectral domain to the time domain and then to rainflow, reducing the need for extensive repetitive time-history simulations and large-scale physical experiments, lowering the time and computational costs of engineering analysis, and simultaneously improving the accuracy and stability of fatigue damage assessment.

[0113] In some embodiments of this application, the process of averaging and smoothing the probability density distribution of all dimensionless rainflow stress ranges to obtain a preliminary smoothed distribution is described, which may specifically include:

[0114] Step S41: Interpolate and map all the dimensionless rainflow stress range probability density distributions to a unified discrete stress range coordinate axis that covers all dimensionless stress range values.

[0115] Step S42: Perform an arithmetic mean on all distribution values ​​corresponding to each discrete point on the coordinate axis of the unified discrete stress range to generate an average distribution sequence;

[0116] Step S43: Apply a basic smoothing operator to the average distribution sequence. The basic smoothing operator includes any one of moving average, low-order spline fitting, or kernel smoothing methods to suppress discrete oscillations and obtain a preliminary smoothed distribution.

[0117] Specifically, as a crucial step in integrating multiple sets of discrete statistical results and initially eliminating random errors, the core objective is to transform the probability density distributions of multiple sets of dimensionless rainflow stress ranges with random fluctuations into a preliminary smooth distribution that combines statistical stability and basic smoothness through unified data benchmarking, statistical averaging, and smoothing. This lays the foundation for subsequent correction and fusion. The specific implementation process is as follows:

[0118] To address the inconsistency of distribution coordinate axes caused by randomization, a unified data benchmark is established for multiple distributions. Due to the randomness of each randomization discretization, time-history reconstruction, and rainflow counting, the dimensionless stress range coordinate axes corresponding to multiple dimensionless rainflow stress range probability density distributions may have inconsistencies in the number of discrete points, value intervals, or coverage. Direct averaging would lead to distorted results due to data misalignment. Therefore, a unified discrete stress range coordinate axis covering the dimensionless stress range values ​​of all distributions needs to be constructed first. The boundary of this coordinate axis is based on the extreme values ​​of the dimensionless stress range of all distributions, ensuring complete coverage of all valid statistical data. Simultaneously, the setting of discrete points must balance data resolution and computational efficiency, ensuring that the coordinate axis accurately reflects the detailed characteristics of each distribution without increasing redundant calculations due to an excessive number of points. Subsequently, through interpolation mapping techniques, the probability density values ​​of each dimensionless rainflow stress range probability density distribution are mapped one by one to discrete points on the unified coordinate axis, achieving alignment of multiple distributions under the same data dimension and providing a consistent computational basis for subsequent statistical averaging.

[0119] Arithmetic averaging reduces the random fluctuations of single results and extracts common statistical characteristics from multiple distributions. After mapping multiple distributions to a unified discrete stress range coordinate axis, probability density values ​​corresponding to all distributions at each discrete point on the coordinate axis are collected. Arithmetic averaging of these values ​​utilizes statistical regularities to offset the random errors introduced by single randomization. For example, the probability density values ​​of some distributions at a certain discrete point might be higher due to random factors, while the corresponding values ​​of other distributions might be lower. Averaging allows these deviations to cancel each other out, resulting in a mean value that more closely reflects the statistical characteristics of the true stress range. Ultimately, the means of all discrete points constitute a continuous sequence of average distributions. Compared to a single distribution, this sequence exhibits significantly reduced random fluctuations and a more stable overall trend, providing a preliminary reflection of the true probability distribution of the dimensionless rainflow stress range.

[0120] By applying basic smoothing operators, the discrete oscillations of the average distribution sequence are further suppressed, improving the smoothness of the distribution. Although the distribution sequence after arithmetic averaging has reduced most of the random error, it may still exhibit sawtooth fluctuations or local micro-oscillations due to residual outliers at individual discrete points or the discrete characteristics of data sampling. These oscillations are not characteristics of the true stress distribution, and if not handled, they will affect the accuracy of subsequent analysis. Therefore, it is necessary to apply basic smoothing operators to the average distribution sequence for correction. The appropriate smoothing method can be selected according to the fluctuation characteristics of the sequence: the moving average method replaces the value of a discrete point with the mean of its neighborhood points, which is simple to operate and can effectively suppress high-frequency small-amplitude oscillations; low-order spline fitting approximates the average distribution sequence by constructing a low-order polynomial curve, which can smooth fluctuations while better preserving the overall trend and key inflection points of the sequence; the kernel smoothing method uses kernel functions to perform weighted smoothing of the data, which is suitable for scenarios with more complex fluctuations and can suppress oscillations while taking into account the local details of the distribution. Regardless of the smoothing method used, the smoothing intensity must be controlled to avoid excessive smoothing that could lead to the loss of core distribution features (such as peak positions and tail trends), ultimately resulting in a continuous, smooth, and initially smoothed distribution without obvious non-physical oscillations.

[0121] In some embodiments of this application, the process of performing moment-preserving correction on the preliminary smooth distribution in step S5 is described, which may specifically include:

[0122] Step S51: Calculate the low-order origin moments of the preliminary smooth distribution. The low-order origin moments include at least the zeroth to second-order origin moments used to characterize the total probability of the distribution, the average stress range, and the dispersion of the stress range, respectively.

[0123] Step S52: Construct a preset orthogonal basis function with an expected value of zero under the initial smooth distribution, and generate a moment-preserving correction operator, wherein the moment-preserving correction operator is in the form of a linear combination of the initial smooth distribution and the preset basis function;

[0124] Step S53: Using the constraint that the low-order origin moments of the preliminary corrected distribution are equal to the low-order origin moments of the preliminary smoothed distribution, solve for the linear combination coefficients in the moment-preserving correction operator to obtain the corrected distribution.

[0125] Specifically, moment preservation correction is a crucial step in ensuring the statistical accuracy of the distribution. It addresses the statistical moment shift that may occur during basic smoothing, where excessive elimination of fluctuations during smoothing causes the core statistical characteristics of the distribution to become disconnected from the original multiple sets of data. This process is achieved through three steps: establishing a moment benchmark, constructing correction operators, and solving constraints. It preserves the smoothness of the initial smoothed distribution while maintaining its statistical consistency with the original data, as detailed below:

[0126] Establish the statistical benchmarks to be retained, namely, calculate the lower-order raw moments of the preliminary smooth distribution. Lower-order raw moments are key indicators reflecting the essential characteristics of the distribution. The zeroth-order raw moment corresponds to the total probability of the distribution and is the basis for verifying the distribution's normality; the first-order raw moment characterizes the average stress range and is directly related to the core load level of structural fatigue damage; the second-order raw moment reflects the dispersion of the stress range and affects the risk boundary of fatigue assessment. Calculations must be based on the complete data sequence of the preliminary smooth distribution, ensuring that the calculation of each moment covers all dimensionless stress ranges, providing an accurate target benchmark for subsequent corrections, and avoiding distortion of the correction direction due to moment calculation errors.

[0127] This study focuses on constructing a correction operator that combines correction capabilities with moment preservation properties. First, pre-defined orthogonal basis functions are constructed, with an expected value of zero within the domain of the initially smoothed distribution. This ensures that the introduction of basis functions does not additionally alter the low-order origin moments of the distribution; that is, the basis functions themselves do not contribute to core indicators such as total probability and mean stress range, but only correct the local morphology of the distribution. Based on this, the moment-preserving correction operator is constructed using a linear combination of the initially smoothed distribution and the pre-defined basis functions. The linear combination consists of multiple orthogonal basis functions multiplied by corresponding coefficients. By adjusting these coefficients, fine-grained correction of the local morphology of the distribution can be achieved, while also leveraging the zero-mean property of the orthogonal basis functions.

[0128] The core parameters of the correction operator are determined by solving for constraints, ultimately yielding the corrected distribution. The constraint condition is that the lower-order raw moments of the corrected distribution are exactly equal to those of the initial smoothed distribution. This constraint ensures that the correction process only eliminates non-physical fluctuations in the distribution without altering its core statistical characteristics. Based on this constraint, and combined with the mathematical properties of the pre-defined orthogonal basis functions, a system of equations concerning the linear combination coefficients can be established. Solving this system yields the coefficient values ​​corresponding to each orthogonal basis function. Substituting these coefficients into the moment-preserving correction operator yields the corrected distribution, which maintains the smoothness of the initial smoothed distribution while ensuring consistency with the statistical characteristics of the original data through moment constraints.

[0129] The expression for the moment-preserving correction operator is:

[0130]

[0131] Where r is the dimensionless stress range; P is the order of the lower-order origin moment; This represents the upper limit of the dimensionless stress range; The distribution is initially smooth; For the p-th pre-defined orthogonal basis function, in The condition of zero mean is satisfied. =0; denoted as the linear combination coefficients corresponding to the p-th pre-defined orthogonal basis function.

[0132] In some embodiments of this application, the process of step S6, which involves generating multiple candidate sub-distributions based on the corrected distribution using various smoothing strategies and parameter configurations, and then weighting and fusing these candidate sub-distributions according to preset evaluation indicators to generate a structural stress range distribution, is described. Specifically, it may include:

[0133] Step S61: Using the corrected distribution as input, apply at least two different smoothing strategies, and process each smoothing strategy with at least two different sets of parameter configurations to generate multiple candidate sub-distributions.

[0134] Specifically, based on the moment-preserving correction distribution, a candidate pool is constructed through multiple strategies and parameters. By combining dual-dimensional evaluation and weighted fusion, the limitations of a single smoothing method are overcome, and finally, a structural stress range distribution that can be directly used for fatigue assessment is generated.

[0135] A set of candidate sub-distributions covering different dimensions of characteristics is constructed to provide a rich feature foundation for subsequent fusion. The operation uses the corrected distribution as a unified input and selects three smoothing strategies with complementary characteristics: kernel density estimation, spline smoothing, and local regression smoothing. Kernel density estimation fits the probability density of the data using a kernel function, excelling at handling smooth transitions in continuous distributions; spline smoothing achieves global smoothing through piecewise multinomial fitting, accurately capturing trend inflection points in the distribution; and local regression smoothing performs locally weighted fitting based on neighborhood data, flexibly balancing local details with overall smoothness.

[0136] To enhance the diversity of candidate sub-distributions, each strategy is configured with at least two sets of core parameters: kernel density estimation focuses on adjusting the bandwidth parameter; a smaller bandwidth highlights distribution details but is prone to fluctuations, while a larger bandwidth provides stronger smoothness but blurs details. Spline smoothing uses the number of nodes as a key parameter; increasing the number of nodes improves the fitting accuracy of local distribution features, while too few nodes may lead to trend distortion. Local regression smoothing focuses on the window length parameter; a longer window provides a more significant smoothing effect, while a short window may retain minor oscillations in the original data. By applying at least two different smoothing strategies, and each smoothing strategy employing at least two different parameter configurations, multiple candidate sub-distributions with varying characteristics are generated, ensuring that the candidate pool covers different performance ranges such as high smoothness with low detail and low smoothness with high detail.

[0137] Step S62: Calculate the low-order moment deviation index of each candidate sub-distribution relative to the correction distribution, and the smoothness index of the candidate sub-distribution itself.

[0138] Specifically, a two-dimensional evaluation system encompassing statistical consistency and morphological applicability is constructed to achieve precise quantification of the performance of candidate sub-distributions. The first dimension is the low-order moment deviation index, which uses the zeroth to second-order origin moments of the corrected distribution as a benchmark to calculate the absolute or relative deviation of the corresponding moments of each candidate sub-distribution. This index ensures that candidate sub-distributions inherit the core statistical characteristics of the corrected distribution, namely, total probability conservation, accurate average stress range, and stable stress dispersion, avoiding statistical distortion caused by smoothing processing.

[0139] The second dimension is the smoothness index, which is evaluated by quantifying the morphological characteristics of the candidate sub-distribution curves. Specifically, it can be calculated by measuring parameters such as the rate of change of amplitude between adjacent discrete points of the curve, the number of inflection points of the curve, and the root mean square fluctuation value of the curve, to comprehensively reflect the smoothness of the curve. The smoothness index is directly related to the engineering application value, avoiding abnormal fluctuations in fatigue damage calculations caused by sawtooth undulations or local peaks in the distribution curve. The two types of indices complement each other, preventing the loss of physical meaning due to emphasizing smoothness over statistics, and avoiding insufficient engineering practicality due to emphasizing statistics over smoothness.

[0140] Specifically, the formula for calculating the lower-order moment deviation index is as follows:

[0141]

[0142] The formula for calculating the smoothness index is:

[0143]

[0144] in, is the deviation index of the p-th moment of the q-th candidate sub-distribution relative to the corrected distribution; r is the dimensionless stress range; P is the order of the lower-order origin moment; Let q be the candidate sub-distribution; To correct the p-th order raw moment of the distribution; Let be the smoothness index of the q-th candidate sub-distribution; This represents the upper limit of the dimensionless stress range.

[0145] Step S63: Based on the low-order moment deviation index and the smoothness index, calculate the comprehensive evaluation score of each candidate sub-distribution, and assign a fusion weight that matches the comprehensive evaluation score.

[0146] Specifically, the low-order moment deviation and smoothness indices are first normalized, converting the original index values ​​into standardized scores. Smaller low-order moment deviations and higher smoothness correspond to higher standardized scores. Then, the weighting of the two indices is set according to engineering requirements. For example, in fatigue life sensitivity analysis, the weight of the low-order moment deviation index can be increased to prioritize statistical accuracy; in conventional engineering evaluation scenarios, the weights of the two indices can be balanced. A weighted summation is used to calculate the comprehensive evaluation score for each candidate sub-distribution; a higher score indicates better overall performance. Fusion weights are assigned based on the comprehensive evaluation scores, using a positive correlation rule: the candidate sub-distribution with the highest comprehensive score receives the maximum weight, and the remaining weights are allocated proportionally to the scores of the other sub-distributions. This design ensures that the best-performing sub-distribution dominates the final fusion while also considering the advantages of other sub-distributions, avoiding the inherent limitations of a single sub-distribution.

[0147] Step S64: Weight all the candidate sub-distributions according to the fusion weights to obtain the structural stress range distribution.

[0148] Specifically, using a unified dimensionless stress range discrete coordinate axis as a reference, for each discrete point on the coordinate axis, the probability density values ​​of all candidate sub-distributions corresponding to that point are extracted. Each value is multiplied by the fusion weight of the corresponding candidate sub-distribution and then summed to obtain the final probability density value of that discrete point. The final values ​​of all discrete points constitute the complete structural stress range distribution.

[0149] Sub-distributions with high weights contribute the main distribution pattern, ensuring overall statistical accuracy and smoothness; sub-distributions with lower weights supplement detailed features and suppress extreme fluctuations. The final generated structural stress range distribution not only fully retains the core statistical features of the correction distribution but also possesses a continuous and smooth engineering form, which can be directly input into fatigue damage calculation models, providing accurate and reliable core data support for structural fatigue life assessment.

[0150] like Figure 3 As shown in the figure, this graph presents a comparison of the curves of the smooth dimensionless rainflow stress range distribution function. The figure clearly shows the differences in the curve shapes of the corrected distribution, each candidate sub-distribution, and the final generated structural stress range distribution: although the corrected distribution retains statistical characteristics, it has local minor fluctuations; the candidate sub-distributions generated by a single strategy may exhibit problems such as smooth transitions or insufficient details due to different parameters; while the final distribution curve after weighted fusion in this application, while avoiding sawtooth fluctuations, accurately matches the core trend of the corrected distribution, intuitively demonstrating the technical effect of balancing statistical accuracy and engineering smoothness.

[0151] The following describes a device for determining the distribution range of structural stress provided in an embodiment of this application. The device for determining the distribution range of structural stress described below and the method for determining the distribution range of structural stress described above can be referred to in correspondence.

[0152] See Figure 4 , Figure 4 This is a schematic diagram of a device for determining the distribution range of structural stress disclosed in an embodiment of this application.

[0153] like Figure 4 As shown, the device for determining the distribution range of structural stress may include:

[0154] The structural power spectrum module 110 is used to acquire the stress power spectrum of the target structure.

[0155] The random discretization processing module 120 is used to perform multiple random discretization processes on the stress power spectrum within a preset frequency band. Each random discretization process includes randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals of random width. Based on each frequency interval, a representative frequency and the corresponding power spectral density value are determined, and a random phase is assigned to each frequency interval.

[0156] The probability density distribution module 130 is used to reconstruct the time-domain stress time history based on the discrete spectrum obtained by each randomization discrete processing, and to count the rainflow in the time-domain stress time history to obtain the probability density distribution of the dimensionless rainflow stress range for a single occurrence.

[0157] The preliminary smoothing distribution module 140 is used to average and perform basic smoothing on the probability density distribution of the entire dimensionless rainflow stress range to obtain a preliminary smoothing distribution.

[0158] The moment preservation correction module 150 is used to perform moment preservation correction on the preliminary smooth distribution to obtain the corrected distribution;

[0159] The stress range distribution module 160 is used to generate multiple candidate sub-distributions based on the correction distribution using various smoothing strategies and parameter configurations, and to perform weighted fusion according to the preset evaluation index of each candidate sub-distribution to generate the structural stress range distribution.

[0160] As can be seen from the above technical solutions, the method and related equipment for determining the distribution range of structural stress provided in this application introduce a random interval division and random phase superposition mechanism within a preset frequency band, and set an upper limit constraint on the segment width. This makes the energy and phase distribution of the discrete spectrum within the frequency band closer to the random characteristics of the continuous spectrum, overcoming the time-domain roughness caused by equal-interval discretization and significantly improving the realism of the time-domain reconstruction. The time-domain signal generated in this way exhibits higher diversity and physical rationality in frequency domain energy distribution, instantaneous amplitude changes, and peak-valley sequences. It can more accurately reflect the actual time-domain characteristics of the broadband random process, providing a more reliable basic input for subsequent rainflow statistics, and avoiding problems such as energy concentration, waveform repetition, and unnatural time-domain envelope caused by traditional equal-interval division.

[0161] This application employs a strategy of multiple random discretizations and time-history reconstructions, rainflow counting, and sample averaging to achieve a convergence of the rainflow stress range distribution from a single occurrence to a statistically representative distribution in a probabilistic sense. Simultaneously, combined with basic smoothing processing, it effectively suppresses high-frequency oscillations between samples, realizing a statistical convergence process from a single random result to a stable distribution characteristic. This ensures that the obtained dimensionless rainflow stress range probability density function exhibits stable and consistent morphological characteristics across multiple calculations, improving the reliability of the rainflow distribution and solving the problems of traditional single-time-history distributions being greatly affected by random factors and having poor repeatability.

[0162] In terms of distribution optimization, this application introduces a low-order moment preservation constraint correction step on the basis of the basic smoothing results, so that the smoothed distribution basically maintains the original level in key statistical indicators such as mean range and variance. Furthermore, by constructing a candidate sub-distribution set containing multiple smoothing algorithms and multiple sets of parameter settings, a unified evaluation function is constructed based on moment deviation and smoothness index and weighted fusion is performed to form an optimization mechanism that combines moment preservation and multi-strategy multi-parameter fusion. This takes into account both smoothness and statistical characteristic preservation, effectively avoiding the problem of insufficient or excessive smoothing caused by a single smoothing method, so that the final distribution is both continuous and smooth, and can maintain the statistical characteristics of the original random process.

[0163] Furthermore, this application relies solely on the target stress power spectrum as input, eliminating the need for long-period measured stress history. It is applicable to various complex spectral types, including broadband, narrowband, and multi-peak spectra, and exhibits good versatility across various service structures such as marine engineering structures and wind turbines. Embedding it into existing fatigue strength calculation programs or digital twin operation and maintenance systems enables automated construction of stress distribution ranges from the spectral domain to the time domain and then to rainflow, reducing the need for extensive repetitive time-history simulations and large-scale physical experiments, lowering the time and computational costs of engineering analysis, and simultaneously improving the accuracy and stability of fatigue damage assessment.

[0164] The device for determining the range distribution of structural stress provided in this application embodiment can be applied to equipment for determining the range distribution of structural stress. Figure 5 The hardware structure block diagram of the device for determining the distribution range of structural stress is shown, with reference to... Figure 5 The hardware structure of the device for determining the distribution range of structural stress may include: at least one processor 1, at least one communication interface 2, at least one memory 3, and at least one communication bus 4.

[0165] In this embodiment of the application, the number of processor 1, communication interface 2, memory 3, and communication bus 4 is at least one, and processor 1, communication interface 2, and memory 3 communicate with each other through communication bus 4;

[0166] Processor 1 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention.

[0167] Memory 3 may include high-speed RAM, and may also include non-volatile memory, such as at least one disk storage device;

[0168] The memory stores a program, which the processor can call. The program is used for:

[0169] Obtain the stress power spectrum of the target structure;

[0170] The stress power spectrum is subjected to multiple randomization discretization processes within a preset frequency band. Each randomization discretization process includes randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals of random width. Based on each frequency interval, a representative frequency and the corresponding power spectral density value are determined, and a random phase is assigned to each frequency interval.

[0171] Based on the discrete spectrum obtained from each randomization discretization process, the time-domain stress time history is reconstructed, and rainflow is counted on the time-domain stress time history to obtain the probability density distribution of the dimensionless rainflow stress range for a single event.

[0172] The probability density distribution of all dimensionless rainflow stress ranges is averaged and basically smoothed to obtain a preliminary smoothed distribution.

[0173] The initial smooth distribution is corrected by moment preservation to obtain the corrected distribution;

[0174] Based on the correction distribution, multiple candidate sub-distributions are generated using various smoothing strategies and parameter configurations, and then weighted and fused according to the preset evaluation index of each candidate sub-distribution to generate the structural stress range distribution.

[0175] Optionally, the refined and extended functions of the program can be referred to the above description.

[0176] This application embodiment also provides a readable storage medium that can store a program suitable for execution by a processor, the program being used for:

[0177] Obtain the stress power spectrum of the target structure;

[0178] The stress power spectrum is subjected to multiple randomization discretization processes within a preset frequency band. Each randomization discretization process includes randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals of random width. Based on each frequency interval, a representative frequency and the corresponding power spectral density value are determined, and a random phase is assigned to each frequency interval.

[0179] Based on the discrete spectrum obtained from each randomization discretization process, the time-domain stress time history is reconstructed, and rainflow is counted on the time-domain stress time history to obtain the probability density distribution of the dimensionless rainflow stress range for a single event.

[0180] The probability density distribution of all dimensionless rainflow stress ranges is averaged and basically smoothed to obtain a preliminary smoothed distribution.

[0181] The initial smooth distribution is corrected by moment preservation to obtain the corrected distribution;

[0182] Based on the correction distribution, multiple candidate sub-distributions are generated using various smoothing strategies and parameter configurations, and then weighted and fused according to the preset evaluation index of each candidate sub-distribution to generate the structural stress range distribution.

[0183] Optionally, the refined and extended functions of the program can be referred to the above description.

[0184] This application also provides a computer program product, including a computer program, wherein the computer program is executed by a processor using the following method:

[0185] Obtain the stress power spectrum of the target structure;

[0186] The stress power spectrum is subjected to multiple randomization discretization processes within a preset frequency band. Each randomization discretization process includes randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals of random width. Based on each frequency interval, a representative frequency and the corresponding power spectral density value are determined, and a random phase is assigned to each frequency interval.

[0187] Based on the discrete spectrum obtained from each randomization discretization process, the time-domain stress time history is reconstructed, and rainflow is counted on the time-domain stress time history to obtain the probability density distribution of the dimensionless rainflow stress range for a single event.

[0188] The probability density distribution of all dimensionless rainflow stress ranges is averaged and basically smoothed to obtain a preliminary smoothed distribution.

[0189] The initial smooth distribution is corrected by moment preservation to obtain the corrected distribution;

[0190] Based on the correction distribution, multiple candidate sub-distributions are generated using various smoothing strategies and parameter configurations, and then weighted and fused according to the preset evaluation index of each candidate sub-distribution to generate the structural stress range distribution.

[0191] Optionally, the refined and extended functions of the program can be referred to the above description.

[0192] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0193] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0194] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of determining a distribution of structural stress ranges, characterized by, The method comprises the following steps: obtaining a stress power spectrum of a target structure; performing multiple randomization and discretization processes on the stress power spectrum within a preset frequency band, wherein each randomization and discretization process comprises randomly generating multiple non-repeating division points within the preset frequency band to form multiple frequency intervals with random widths, determining a representative frequency and a corresponding power spectral density value based on each frequency interval, and assigning a random phase to each frequency interval; reconstructing a time-domain stress time history based on the discrete frequency spectrum obtained from each randomization and discretization process, and performing rainflow counting on the time-domain stress time history to obtain a single non-dimensional rainflow stress range probability density distribution; averaging and performing basic smoothing on all the non-dimensional rainflow stress range probability density distributions to obtain a preliminary smoothed distribution; performing moment-preserving correction on the preliminary smoothed distribution to obtain a corrected distribution; generating multiple candidate sub-distributions using multiple different smoothing strategies and parameter configurations based on the corrected distribution, and performing weighted fusion of the candidate sub-distributions according to preset evaluation indicators to generate a structure stress range distribution; the method comprises the following steps: for a first type of stress power spectrum that changes gently within the frequency interval, selecting the geometric midpoint of the frequency interval as a candidate representative frequency; for a second type of stress power spectrum that changes sharply within the frequency interval, selecting the spectral barycenter of the frequency interval as a candidate representative frequency; at the candidate representative frequency, the corresponding power spectral density value is calculated by performing linear interpolation or smooth interpolation on the stress power spectrum; the method comprises the following steps: interpolating and mapping all the non-dimensional rainflow stress range probability density distributions to a unified discrete stress range coordinate axis that covers all non-dimensional stress range values; performing arithmetic averaging on all distribution values corresponding to each discrete point on the unified discrete stress range coordinate axis to generate an average distribution sequence; applying a basic smoothing operator to the average distribution sequence to suppress discrete oscillations and obtain a preliminary smoothed distribution.

2. The method of claim 1, wherein, the process of performing moment-preserving correction on the preliminary smoothed distribution comprises the following steps: calculating low-order origin moments of the preliminary smoothed distribution, wherein the low-order origin moments at least include zeroth-order to second-order origin moments for representing the total probability, average stress range, and dispersion degree of stress range of the distribution, respectively; constructing a preset orthogonal basis function with an expected value of zero under the preliminary smoothed distribution, and generating a moment-preserving correction operator, wherein the moment-preserving correction operator is in the form of a sum of linear combinations of the preliminary smoothed distribution and the preset orthogonal basis function; solving the linear combination coefficients in the moment-preserving correction operator to obtain a corrected distribution, with the constraint that the low-order origin moments of the preliminary corrected distribution are equal to the low-order origin moments of the preliminary smoothed distribution.

3. The method of claim 2, wherein, the expression of the moment-preserving correction operator is: wherein, r is a non-dimensional stress range; P is an order of the low-order origin moment; is an upper limit of the non-dimensional stress range; is a preliminary smoothing distribution; is a preset orthogonal basis function of the p th, which satisfies a zero mean condition = 0; = 0; is a linear combination coefficient corresponding to the p th preset orthogonal basis function.

4. The method of claim 1, wherein, Based on the correction distribution, a plurality of candidate sub-distributions are generated by using a plurality of different smoothing strategies and parameter configurations, and a structural stress range distribution is generated by weighted fusion according to a preset evaluation index of each candidate sub-distribution, comprising: Taking the correction distribution as input, at least two different smoothing strategies are applied respectively, and at least two different parameter configurations are used for processing for each smoothing strategy, to generate a plurality of candidate sub-distributions; The low-order moment deviation index of each candidate sub-distribution relative to the correction distribution and the smoothness index of the candidate sub-distribution itself are calculated respectively; Based on the low-order moment deviation index and the smoothness index, the comprehensive evaluation score of each candidate sub-distribution is calculated, and a fusion weight matching the comprehensive evaluation score is assigned; The structural stress range distribution is obtained by weighted summation of all candidate sub-distributions according to the fusion weight.

5. The method of claim 4, wherein, The calculation formula of the low-order moment deviation index is: The calculation formula of the smoothness index is: wherein, is a first q moment deviation index of a candidate sub-distribution relative to a first p moment of a correction distribution; r is a non-dimensional stress range; P is an order of a low-order origin moment; is a candidate sub-distribution; q is a first origin moment of a correction distribution; p is a smoothing index of a candidate sub-distribution; is a non-dimensional stress range; q is a non-dimensional stress range; and is an upper limit of a non-dimensional stress range.

6. The method according to claim 4 or 5, characterized in that, The smoothing strategy includes kernel density estimation, spline smoothing, and local regression smoothing; The parameter configuration includes the bandwidth of kernel density estimation, the number of nodes of spline smoothing, and the window length of local regression smoothing.

7. The method of claim 1, wherein, Further comprising: A maximum width threshold is set for each frequency interval, which is determined based on the total width of the preset frequency band and a preset discrete segment number experience range.

8. The method of claim 1, wherein, After generating the structural stress range distribution, further comprising: Based on the variance or zero-order moment of the stress power spectrum, the structural stress range distribution is dimensionally reduced.

9. An apparatus for determining a distribution of structural stress ranges, characterized by Comprising: A structural power spectrum module for obtaining a stress power spectrum of a target structure; A random discrete processing module for performing multiple randomization and discrete processing on the stress power spectrum within a preset frequency band, wherein each randomization and discrete processing includes randomly generating a plurality of non-repeating division points within the preset frequency band to form a plurality of frequency intervals with random widths, determining a representative frequency and a corresponding power spectrum density value based on each frequency interval, and assigning a random phase to each frequency interval; A probability density distribution module for reconstructing a time-domain stress time history based on the discrete frequency spectrum obtained by each randomization and discrete processing, and performing rainflow counting on the time-domain stress time history to obtain a single non-dimensional rainflow stress range probability density distribution; A preliminary smoothing distribution module for averaging and basic smoothing of all non-dimensional rainflow stress range probability density distributions to obtain a preliminary smoothing distribution; A moment-preserving correction module for moment-preserving correction of the preliminary smoothing distribution to obtain a correction distribution; A stress range distribution module for generating a structural stress range distribution by using a plurality of different smoothing strategies and parameter configurations based on the correction distribution, and performing weighted fusion according to a preset evaluation index of each candidate sub-distribution; The determination of the representative frequency and the corresponding power spectrum density value based on each frequency interval comprises: For the first type of stress power spectrum that changes gently within the frequency interval, the geometric midpoint of the frequency interval is selected as the candidate representative frequency; For the second type that the stress power spectrum presents sharp change in the frequency interval, the spectral centroid of the frequency interval is selected as a candidate representative frequency; At the candidate representative frequency, a corresponding power spectral density value is calculated by linear interpolation or smooth interpolation on the stress power spectrum; The preliminary smoothed distribution is obtained by averaging and basic smoothing of all the non-dimensional rain flow stress range probability density distributions, including: All the non-dimensional rain flow stress range probability density distributions are interpolated and mapped to a uniform discrete stress range coordinate axis covering all non-dimensional stress range values; An average distribution sequence is generated by arithmetically averaging all the distribution values corresponding to each discrete point on the uniform discrete stress range coordinate axis; A basic smoothing operator is applied to the average distribution sequence, and the basic smoothing operator includes any one of moving average, low-order spline fitting or kernel smoothing method to suppress discrete oscillation to obtain the preliminary smoothed distribution.

10. An apparatus for determining a distribution of structural stress ranges, characterized by comprising a memory and a processor; The memory is configured to store a program; The processor is configured to execute the program to implement each step of the structural stress range distribution determination method according to any one of claims 1-8.

11. A readable storage medium, having stored thereon a computer program, characterized in that, The computer program, when executed by the processor, implements each step of the structural stress range distribution determination method according to any one of claims 1-8.

12. A computer program product comprising a computer program, characterized in that, The computer program, when executed by the processor, implements each step of the structural stress range distribution determination method according to any one of claims 1-8.

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