A method and related apparatus for assessing fatigue damage of an offshore structure

Abstract

The application discloses a kind of offshore structure fatigue damage evaluation method and related equipment, first obtain target structure stress power spectral density function and calculate each order spectrum moment, output target high order moment sequence by characteristic moment mapping model, then obtain legal moment sequence by semi-positive definite projection correction and reconstruct stress range probability density function, finally, combined with material S-N curve parameter, determine total fatigue damage using frequency domain closed integral. Narrow-band reference difference is taken to generate low-variance high-order moment true value training model by the moment method, which can accurately reflect the amplitude statistical characteristics of wideband, multi-peak stress process, and improve the evaluation accuracy from the source. In the evaluation stage, stress time history simulation and rainflow counting are not required, and efficient moment estimation can be realized in pure frequency domain, taking into account accuracy and efficiency. Semi-positive definite projection correction ensures that the probability density is non-negative and legal, eliminating the risk of numerical anomalies. Frequency domain closed integral significantly reduces the calculation time, and can meet the fatigue evaluation requirements under complex load scenarios at sea.

Description

Technical Field

[0001] This application relates to the field of fatigue damage assessment technology, and more specifically, to a method and related equipment for assessing fatigue damage to marine structures. Background Technology

[0002] Offshore wind power foundations, offshore platforms and other structures are subjected to random cyclic loads such as waves and wind for a long time. Fatigue damage is the core cause of structural failure, and efficient and accurate fatigue damage assessment is crucial to ensuring the safe service of the structure.

[0003] Existing frequency domain fatigue assessment methods are mostly based on empirical formulas for low-order spectral moments to estimate the stress range distribution. These methods are computationally efficient but only suitable for specific spectral shapes such as narrowband. Some distribution reconstruction schemes based on high-order moments generally suffer from large variance and insufficient accuracy in estimating high-order moments. Furthermore, they do not apply probabilistic nonnegativity constraints to the moment sequence, which can easily lead to abnormal results that violate probability axioms. Ultimately, this results in large fatigue damage assessment errors and makes it difficult to meet the high-precision assessment requirements under complex marine loads.

[0004] Therefore, there is an urgent need for a new method for assessing fatigue damage to marine structures to address the shortcomings of existing technologies and meet the engineering requirements for high-precision fatigue assessment under complex marine load scenarios. Summary of the Invention

[0005] This application provides a method and related equipment for assessing fatigue damage of marine structures. It directly predicts higher-order moments from the stress power spectrum through a characteristic moment mapping model, generates low-variance true values ​​for training using a narrow-band benchmark difference method to ensure moment accuracy, and obtains a valid moment sequence through semi-definite projection correction to reconstruct the probability density of the stress range. Finally, it calculates fatigue damage by combining SN curves and frequency domain integrals of spectral moments, which meets the comprehensive requirements of high accuracy, high efficiency and high robustness for fatigue damage assessment under complex loading scenarios at sea.

[0006] A method for assessing fatigue damage to marine structures, comprising:

[0007] Obtain the stress power spectral density function of the target marine structure under random loads, and calculate the spectral moments of each order of the stress power spectral density function;

[0008] A pre-established characteristic moment mapping model is obtained, and the power spectral features of the stress power spectral density function are input into the characteristic moment mapping model to obtain the target higher-order moment sequence. The characteristic moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequence. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation.

[0009] The target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed based on the legal moment sequence.

[0010] Based on the stress range probability density function, the pre-acquired material SN curve parameters, and the spectral moments of each order, the total fatigue damage is determined by frequency domain closed-loop integration.

[0011] Optionally, the stress power spectral density function of the target marine structure under random loads is obtained, and the spectral moments of each order of the stress power spectral density function are calculated, including:

[0012] Collect stress time history data of the target marine structure under random loads, and determine the duration corresponding to the stress time history data;

[0013] The stress time history data is subjected to Fourier transform to obtain the stress power spectral density function;

[0014] The stress power spectral density function is weighted according to the angular frequency weighting method corresponding to different order moments, and the weighted result is integrated within the frequency range to obtain spectral moments of various orders, including the zero-order spectral moment, the second-order spectral moment, and the fourth-order spectral moment.

[0015] Optionally, the process of establishing the feature moment mapping model includes:

[0016] Construct a sample spectrum library, which includes marine engineering single-peak spectra, double-peak spectra, and various predetermined ideal spectra generated by parameterizing the number of spectral peaks, peak-frequency ratio, energy ratio, and spectral width parameters;

[0017] For each sample spectrum in the sample spectrum library, multiple Gaussian random stress time histories are generated, and the dimensionless stress range sample of each time history is extracted by rainflow counting method;

[0018] The narrowband benchmark difference moment method is adopted. For each sample spectrum, the narrowband Rayleigh distribution analytical moments are used as the benchmark. Based on the mean of the rainflow counting moments of multiple time histories, the difference between the mean of the narrowband estimated moments of the multiple time histories and the narrowband Rayleigh distribution analytical moments, and a correction coefficient, the true higher-order moment sequence after variance reduction is obtained.

[0019] Extract the power spectrum features of each sample spectrum, and combine the power spectrum features with the corresponding ground truth higher-order moment sequence to form training samples, thereby training the feature moment mapping model.

[0020] Optionally, the process of determining the correction coefficient includes:

[0021] The rainflow counting moments and narrowband estimation moments calculated from each of the multiple time histories are statistically analyzed to obtain the covariance estimate of the two and the variance estimate of the narrowband estimation moment. The ratio of the covariance estimate to the variance estimate is used as the correction coefficient.

[0022] The narrowband estimated moments are the corresponding order moments calculated for each time history based on the analytical moment expression of the narrowband Rayleigh distribution.

[0023] Optionally, the estimation formula for obtaining the variance-reduced higher-order moment sequence using the narrowband benchmark difference moment method is as follows:

[0024] ;

[0025] in, Here, N represents the reduced variance estimate of the k-th order true moments, and N is the number of time histories. Let j be the rainfall count moment for the j-th time history. For the narrowband estimation moment of the j-th time history, For narrowband Rayleigh distribution analytical moments, This is a correction factor.

[0026] Optionally, the step of performing semi-positive definite projection correction on the target higher-order moment sequence to obtain a legal moment sequence that satisfies the non-negativity probability density constraint includes:

[0027] The target higher-order moment sequence is normalized using narrowband Rayleigh distribution analytical moments to obtain a normalized moment sequence.

[0028] Based on the normalized moment sequence, a first Hankel matrix is ​​formed according to a preset first construction rule, and a second Hankel matrix is ​​formed according to a preset second construction rule;

[0029] Determine whether both the first Hankel matrix and the second Hankel matrix satisfy the positive semidefinite condition;

[0030] If either condition is not met, then under the constraint of keeping the values ​​of the lower-order normalized moments unchanged, the modified normalized moment sequence with the smallest difference from the current normalized moment sequence is obtained by convex optimization, and the first Hankel matrix and the second Hankel matrix are both positive semi-definite matrices.

[0031] The legal moment sequence is obtained by inverse calculation from the corrected normalized moment sequence.

[0032] Optionally, the step of reconstructing the stress range probability density function based on the legal moment sequence includes:

[0033] A multi-component probability density model is defined, which is composed of a weighted sum of multiple components. Each component consists of a positive coefficient, a stress range variable, and an exponential decay term with the natural constant as the base. The exponential part of the exponential decay term is negatively correlated with the square of the stress range variable.

[0034] The sequence of legal moments is represented as normalized moments, and the Hankel matrix bundle is constructed using the normalized moments;

[0035] The Hankel matrix bundle is subjected to generalized eigenvalue decomposition, and all the obtained generalized eigenvalues ​​are used as nodes corresponding to each component.

[0036] Construct a coefficient matrix using the powers of the nodes, build a corresponding system of linear equations, and solve the system of linear equations to obtain the weights of each component.

[0037] Based on the definitions of nodes and weights, the exponential decay parameter and positive coefficient of each component are calculated in reverse to obtain the closed-form expression of the probability density function of the stress range.

[0038] Optionally, determining the total fatigue damage using frequency domain closed-loop integration includes:

[0039] When the material SN curve has a single slope, the total fatigue damage is obtained by frequency domain closed-form calculation using the evaluation duration, the spectral moments of each order, and the stress range specified moment determined by the stress range probability density function.

[0040] When the SN curve of a material has multiple slope segments, the total fatigue damage is obtained by calculating the segmented damage for each slope segment according to the linear fatigue accumulation criterion and then summing the results.

[0041] The segmented damage of each slope segment is obtained by integrating the stress range probability density function within that stress range segment, using the power of the inverse slope of the stress range as the weight. The integration is achieved by substituting the exponential decay parameter, positive coefficient, and inverse slope of the current slope segment of each component of the stress range probability density function into a predetermined integral relationship, calculating the difference between the integral values ​​determined by the upper and lower limits of the stress range, and summing the differences of all components to achieve a closed-form solution.

[0042] Optionally, when the material's SN curve has a single slope, the expression for the total fatigue damage obtained through closed-form calculation in the frequency domain is:

[0043] ;

[0044] When the material's SN curve has multiple slope segments, the expression for summing the segmented damage calculated for each slope segment according to the linear fatigue accumulation criterion is as follows:

[0045] ;

[0046] Where D represents total fatigue damage, T represents the evaluation duration, m0, m2, and m4 represent the spectral moments of each order, k represents the inverse slope of the SN curve, and C represents the material constant. Let be the k-th moment of the stress range determined by the stress range probability density function, s be the total number of slope segments, ki and Ci be the inverse slope and material constant of the i-th slope segment, respectively, and Li and Hi be the lower and upper limits of the stress range of the i-th slope segment, respectively. Let z be the probability density function of the stress range, where z is the dimensionless stress range.

[0047] Optionally, after determining the total fatigue damage, the following may also be included:

[0048] When the total fatigue damage reaches the preset failure threshold, it is determined that the marine structure has suffered fatigue failure.

[0049] The remaining fatigue life of the marine structure is determined and output based on the ratio of the duration of the assessment to the total fatigue damage.

[0050] Optionally, after training the feature moment mapping model, the method further includes:

[0051] Obtain the validation sample spectrum set, input the power spectrum features of the validation sample spectrum into the feature moment mapping model, and obtain the predicted higher-order moment sequence;

[0052] The true higher-order moment sequence corresponding to the verification sample spectrum is obtained by using the narrow-band benchmark difference moment method. The predicted higher-order moment sequence is compared with the true higher-order moment sequence to confirm that the mapping error is within the preset accuracy range.

[0053] A fatigue damage assessment device for marine structures, comprising:

[0054] The spectral moment analysis module is used to obtain the stress power spectral density function of the target marine structure under random loads and to calculate the spectral moments of the stress power spectral density function.

[0055] The mapping sequence module is used to obtain a pre-established feature moment mapping model. The power spectral features of the stress power spectral density function are input into the feature moment mapping model to obtain the target higher-order moment sequence. The feature moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequences. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation.

[0056] The projection correction module is used to perform semi-positive definite projection correction on the target higher-order moment sequence to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and to reconstruct the stress range probability density function based on the legal moment sequence.

[0057] A damage determination module is used to determine the total fatigue damage using frequency domain closed-loop integration based on the stress range probability density function, pre-acquired material SN curve parameters, and the spectral moments of each order. A fatigue damage assessment device for marine structures includes a memory and a processor.

[0058] The memory is used to store programs;

[0059] The processor is configured to execute the program to implement the various steps of the marine structural fatigue damage assessment method as described in any of the preceding claims.

[0060] A readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the marine structure fatigue damage assessment method as described in any of the preceding claims.

[0061] A computer program product includes a computer program that, when run by a processor, performs the steps of the fatigue damage assessment method for marine structures as described in any of the preceding claims.

[0062] As can be seen from the above technical solution, the fatigue damage assessment method and related equipment for marine structures provided in this application first obtain the stress power spectral density function of the target marine structure under random load and calculate the spectral moments of each order; then, the power spectral features are input into a pre-established characteristic moment mapping model to obtain the target higher-order moment sequence. This model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectral library and the corresponding true higher-order moment sequences. The true higher-order moment sequence is estimated from the stress time history data generated by the narrow-band benchmark difference moment method, using the narrow-band Rayleigh distribution analytical moments as a benchmark and reducing the estimation variance through difference; then, the target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed accordingly; finally, the total fatigue damage is determined by frequency domain closed integral, combining the probability density function, material SN curve parameters, and the spectral moments of each order. This method trains a feature moment mapping model by obtaining low-variance high-order moment ground values ​​using a narrow-band benchmark difference moment method. This allows the high-order moments predicted directly from power spectrum features to accurately reflect the true statistical characteristics of rainfall amplitude in broadband, multi-peak, and non-Gaussian processes, without relying on any fixed empirical distribution shape. Consequently, the reconstructed stress range probability density function closely approximates the actual distribution, fundamentally improving the accuracy of fatigue damage assessment. After model training, only spectral features need to be input during the evaluation phase to instantly output high-fidelity high-order moments, completely avoiding stress time history simulation and rainfall counting. This successfully resolves the contradiction between accurate high-order moment estimation and computational efficiency, achieving fast and accurate moment estimation within a pure frequency domain framework. The introduced positive semi-definite projection correction step forcibly corrects the predicted moment sequence to a legal moment space that satisfies the positive semi-definite condition of the Hankel matrix. Mathematically, this ensures that the reconstructed stress range probability density is everywhere non-negative and meets normalization requirements. This completely eliminates the risk of negative values ​​or oscillations in the probability density caused by moment estimation disturbances or numerical errors, making the fatigue damage calculation results have reliable physical meaning and greatly enhancing the robustness of the method. Finally, based on the legal probability density, SN curve parameters, and spectral moments, the total fatigue damage can be quickly given through frequency domain closed-loop integration. This significantly reduces the computation time for fatigue assessment in multiple sea states and long periods, meeting the comprehensive requirements of high accuracy, high efficiency, and high robustness for fatigue damage assessment under complex marine load scenarios. Attached Figure Description

[0063] 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.

[0064] Figure 1 This is a flowchart of a method for assessing fatigue damage to marine structures disclosed in an embodiment of this application;

[0065] Figure 2 This is a schematic diagram of a marine structural fatigue damage assessment device disclosed in an embodiment of this application;

[0066] Figure 3 This is a hardware structure block diagram of a marine structural fatigue damage assessment device disclosed in an embodiment of this application. Detailed Implementation

[0067] 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 of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0068] 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.

[0069] The following section introduces the solution proposed in this application. The technical solution is as follows, and details are provided below.

[0070] Figure 1 This is a flowchart of a method for assessing fatigue damage to marine structures disclosed in an embodiment of this application.

[0071] like Figure 1 As shown, the method may include:

[0072] Step S1: Obtain the stress power spectral density function of the target marine structure under random loads, and calculate the spectral moments of each order of the stress power spectral density function.

[0073] Specifically, for target structures operating in marine environments, stress response time-domain signals in hotspot areas are collected through on-site monitoring systems, or dynamic analysis models of the structure under the combined effects of random loads such as waves, wind, and currents are constructed using hydrodynamic numerical simulation methods. This allows for the acquisition of the stress power spectral density function, which characterizes the frequency-domain statistical properties of the stress stochastic process. After obtaining the stress power spectral density function, integration operations with different weighting orders are performed along the frequency axis to obtain the zero-order, first-order, second-order, and higher-order spectral moments. Each order of spectral moment characterizes the energy distribution, average spanning frequency, and bandwidth characteristics of the stress stochastic process from different perspectives, providing fundamental frequency-domain statistical parameters for subsequent fatigue damage assessment.

[0074] While extracting the spectral moments, the material SN curve parameters of the corresponding hot spots in the target structure are simultaneously acquired, including the inverse slope of each slope segment, material constants, and segmented stress range boundaries. Different structural parts require different SN curve selections due to differences in welding methods, material grades, and corrosion environments. These curves must be matched one-to-one with the calculation location of the stress power spectral density to ensure consistency of operating conditions in subsequent damage calculations.

[0075] Step S2: Obtain the pre-established characteristic moment mapping model. Input the power spectrum features of the stress power spectral density function into the characteristic moment mapping model to obtain the target higher-order moment sequence. The characteristic moment mapping model is trained based on the mapping relationship between the power spectrum features of sample spectra with various power spectrum shapes in the sample spectrum library and the corresponding true higher-order moment sequences. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation.

[0076] Specifically, the characteristic moment mapping model is a pre-built regression mapping structure that implicitly represents the complex nonlinear correlation between the power spectrum shape characteristics and the higher-order moment sequence of the stress range. The characteristic moment mapping model construction process in this step is a fully offline execution phase. Once trained and solidified, the model can be repeatedly invoked, eliminating the need for repeated time-domain simulations and moment estimations in the online evaluation phase. This offline-online separation architecture moves the most computationally intensive higher-order moment statistical calculations to the offline stage, while the online stage only requires lightweight model inference and matrix operations, thus ensuring the efficiency of real-time evaluation and large-scale batch analysis of operating conditions.

[0077] In the model building phase, a sample spectrum library containing various standardized power spectrum shapes is first established. These sample spectrum shapes cover typical spectral types that actual marine structures may encounter, such as narrowband, broadband, and bimodal. For each sample spectrum, representative stress time history samples are generated through inverse Fourier transform or harmonic superposition. The true values ​​of the higher-order moment sequences are then extracted using the narrowband benchmark difference moment extraction method. This method uses the theoretical higher-order moments corresponding to the narrowband Rayleigh distribution as the initial benchmark, and then introduces the difference sequence of stress time histories to construct correction terms. This effectively reduces the variance of higher-order moment estimation caused by the limited length of the time-domain simulation and random fluctuations, obtaining a true higher-order moment sequence with good convergence and satisfactory accuracy. Essentially, this method is a control variable variance reduction technique. It utilizes the strong positive correlation between rainflow counting moments and narrowband estimated moments, compressing the estimation variance by subtracting the covariance fluctuation component with the narrowband benchmark. Compared to the naive Monte Carlo method, this approach can reduce the estimated variance of higher-order moments by more than an order of magnitude under the same simulation duration, significantly shortening the sample size required to obtain stable higher-order true moments and significantly reducing the computational cost of offline modeling.

[0078] Simultaneously, power spectrum feature vectors, composed of spectral width parameters, irregularity factors, spectral centroid frequencies, spectral peak parameters, and shape descriptors, are extracted from each sample spectrum. These power spectrum feature vectors are used as input, and the true higher-order moment sequence is used as the output label to train a selected machine learning model, resulting in the feature moment mapping model. In the subsequent online evaluation phase, only the corresponding power spectrum features of the stress power spectral density function of the target marine structure need to be input into this model to quickly infer and output the target higher-order moment sequence that conforms to the spectral shape characteristics, eliminating the need for repeated time-domain simulations and cumbersome calculations of higher-order moments.

[0079] Step S3: Perform semi-positive definite projection correction on the target higher-order moment sequence to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and reconstruct the stress range probability density function based on the legal moment sequence.

[0080] Specifically, the target higher-order moment sequence predicted by the eigenmotogram model may violate the positive semi-definite condition of the sequence required for legitimate probability distribution moments due to model errors and unavoidable information compression during power spectrum feature extraction. Directly using this sequence for probability density reconstruction may result in negative density domains or no solution. Therefore, a positive semi-definite projection correction is implemented: the Hankel matrix associated with the target higher-order moment sequence, or other appropriately constructed matrices, is projected onto the nearest point on a positive semi-definite cone. This obtains a legitimate moment sequence that strictly satisfies the positive definiteness constraint of the moment problem while minimizing the correction bias. The projection process can be implemented using numerical strategies such as alternating projection or symmetric eigenvalue adjustment, without changing the main statistical trend of the stress range, only fine-tuning the higher-order moments, thus ensuring the feasibility and physical consistency of subsequent density reconstruction. Based on the corrected legitimate moment sequence, the probability density function of the stress range is reconstructed using the maximum entropy principle or moment matching method. Under the given moment constraints, the reconstruction process selects the probability density with the largest information entropy as the estimation result, or directly expresses the corresponding stress range probability density function with a valid moment sequence through analytical expansion, ensuring that the obtained probability density function is non-negative and normalized everywhere, and accurately reflects the cyclic distribution characteristics of the stress range.

[0081] Step S4: Based on the stress range probability density function, the pre-acquired material SN curve parameters, and the spectral moments of each order, the total fatigue damage is determined by frequency domain closed-loop integration.

[0082] Specifically, the stress range-life curve parameters of the materials used in the target marine structure are obtained in advance. This SN curve characterizes the logarithmic linear relationship between the number of cycles leading to fatigue failure of the material under constant amplitude stress and the stress range. The number of cycles per unit time in fatigue damage calculation is calculated using the peak rate derived from the ratio of the fourth-order spectral moment to the second-order spectral moment. This index is closer to the stress cycle frequency identified by the rainflow counting method and has higher damage calculation accuracy than the traditional average zero-crossing rate, with stronger consistency with the true rainflow damage. Combining the stress range probability density function obtained in step S3 and the stress cycle statistical characteristics derived from the spectral moments in step S1, such as the average zero-crossing rate determined by the ratio of spectral moments, the occurrence frequency of different amplitude stress ranges generated by the random stress process per unit time is weighted and accumulated with the allowable number of cycles given by the SN curve. Using the Miner linear cumulative damage criterion, the damage contribution of the stress range variable is integrated in the frequency domain over all possible values, that is, the integral form of the quotient of the probability density function and the inverse function of the SN curve is calculated to obtain the total expected value of fatigue damage per unit time or design life cycle in one go. This frequency-domain closed-loop integral utilizes the analytical properties of spectral moments and reconstructed probability density functions, avoiding the long-term simulation and iterative extraction processes required by traditional time-domain rainflow counting methods. While ensuring the accuracy of damage assessment, it significantly improves computational efficiency, providing a closed-loop frequency-domain solution for rapid fatigue life assessment of marine engineering structures under random load environments.

[0083] As can be seen from the above technical solution, the fatigue damage assessment method and related equipment for marine structures provided in this application first obtain the stress power spectral density function of the target marine structure under random load and calculate the spectral moments of each order; then, the power spectral features are input into a pre-established characteristic moment mapping model to obtain the target higher-order moment sequence. This model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectral library and the corresponding true higher-order moment sequences. The true higher-order moment sequence is estimated from the stress time history data generated by the narrow-band benchmark difference moment method, using the narrow-band Rayleigh distribution analytical moments as a benchmark and reducing the estimation variance through difference; then, the target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed accordingly; finally, the total fatigue damage is determined by frequency domain closed integral, combining the probability density function, material SN curve parameters, and the spectral moments of each order. This method trains a feature moment mapping model by obtaining low-variance high-order moment ground values ​​using a narrow-band benchmark difference moment method. This allows the high-order moments predicted directly from power spectrum features to accurately reflect the true statistical characteristics of rainfall amplitude in broadband, multi-peak, and non-Gaussian processes, without relying on any fixed empirical distribution shape. Consequently, the reconstructed stress range probability density function closely approximates the actual distribution, fundamentally improving the accuracy of fatigue damage assessment. After model training, only spectral features need to be input during the evaluation phase to instantly output high-fidelity high-order moments, completely avoiding stress time history simulation and rainfall counting. This successfully resolves the contradiction between accurate high-order moment estimation and computational efficiency, achieving fast and accurate moment estimation within a pure frequency domain framework. The introduced positive semi-definite projection correction step forcibly corrects the predicted moment sequence to a legal moment space that satisfies the positive semi-definite condition of the Hankel matrix. Mathematically, this ensures that the reconstructed stress range probability density is everywhere non-negative and meets normalization requirements. This completely eliminates the risk of negative values ​​or oscillations in the probability density caused by moment estimation disturbances or numerical errors, making the fatigue damage calculation results have reliable physical meaning and greatly enhancing the robustness of the method. Finally, based on the legal probability density, SN curve parameters, and spectral moments, the total fatigue damage can be quickly given through frequency domain closed-loop integration. This significantly reduces the computation time for fatigue assessment in multiple sea states and long periods, meeting the comprehensive requirements of high accuracy, high efficiency, and high robustness for fatigue damage assessment under complex marine load scenarios.

[0084] In some embodiments of this application, the process of step S1, obtaining the stress power spectral density function of the target marine structure under random loads, and calculating the spectral moment steps of the stress power spectral density function, is described, and may specifically include:

[0085] Step S11: Collect stress time history data of the target marine structure under random loads, and determine the duration corresponding to the stress time history data.

[0086] Strain or stress sensors are deployed at critical fatigue-sensitive locations on the target marine structure. A data acquisition system continuously records the stress response over time under the combined effects of environmental loads such as waves, currents, and wind at a preset sampling rate, obtaining stress time history data containing real dynamic behavior information of structural hotspot areas. Simultaneously, based on the ergodicity assumption of the stochastic process and the required frequency resolution, the duration of the extracted stress time history samples is determined to ensure that the sample duration is sufficient to cover various sea state cycles and suppress random fluctuations in statistical estimation, providing representative input data for subsequent frequency domain transformation and spectral moment calculations.

[0087] Step S12: Perform a Fourier transform on the stress time history data to obtain the stress power spectral density function.

[0088] The collected stress time history data undergoes preprocessing operations such as mean removal and trend removal to eliminate slow drift components. Then, a windowed Fourier transform is used to convert the time-domain signal to the frequency domain. By appropriately averaging and normalizing the square of the transformed amplitude spectrum, a one-sided stress power spectral density function reflecting the energy distribution of the stress stochastic process at different frequency components is obtained. This function characterizes the mean square value of stress fluctuations within a unit frequency interval; its shape and bandwidth are directly related to the incident load spectrum characteristics and the structural dynamic transmission characteristics, serving as the core input for frequency-domain fatigue analysis.

[0089] Step S13: The stress power spectral density function is weighted according to the angular frequency weighting method corresponding to different order moments, and the weighting result is integrated within the frequency range to obtain the spectral moments of each order, including the zero-order spectral moment, the second-order spectral moment, and the fourth-order spectral moment.

[0090] After obtaining the stress power spectral density function, according to the definition of spectral moments in random vibration theory, the power spectral density function is weighted in the frequency domain using the zero, second, and fourth powers of the angular frequency as weighting functions. For the zeroth-order spectral moment, it directly corresponds to the integral of the power spectral density function over the effective frequency range, and its physical meaning is the mean square value of the stress random process. For the second-order spectral moment, the weighted integral is performed using the square of the angular frequency as the weight, reflecting the mean square value characteristics of the stress change rate process. For the fourth-order spectral moment, the weighted integral is performed using the fourth power of the angular frequency as the weight, capturing energy information in higher frequency bands of the stress process. The above integration operations are performed within the frequency range defined by the structural response bandwidth. The resulting zero-order, second-order, and fourth-order spectral moments constitute the basic parameter set describing the statistical characteristics of stress cycles, and can be further used to derive key fatigue assessment parameters such as the average zero-crossing rate and bandwidth coefficient.

[0091] In some embodiments of this application, the process of performing semi-positive definite projection correction on the target higher-order moment sequence in step S3 to obtain a legal moment sequence that satisfies the non-negativity probability density constraint is described, which may specifically include:

[0092] Step S31: Normalize the target higher-order moment sequence using narrowband Rayleigh distribution analytical moments to obtain a normalized moment sequence.

[0093] Using the Rayleigh distribution derived from a narrowband Gaussian random process as a benchmark, and employing the theoretical moments corresponding to this distribution in the stress range description as normalization factors, the target higher-order moment sequence is dimensionlessly processed step by step. This normalization step can isolate the influence of the absolute energy level and characteristic scale of the stress process, ensuring that the obtained normalized moment sequence remains sensitive only to non-narrowband information directly related to the shape of the stress range distribution, such as spectral width deviation and multi-peak characteristics. This creates standardized conditions for subsequent unified correction and comparison within a positive semidefinite constraint framework.

[0094] Step S32: Based on the normalized moment sequence, form a first Hankel matrix according to a preset first construction rule, and form a second Hankel matrix according to a preset second construction rule.

[0095] Based on the classical positive semi-definite constraint theory that the probability density exists and is non-negative in the moment problem, the normalized moment sequence is mapped to two symmetric Hankel matrices according to a preset matrix arrangement rule. The first preset construction rule typically uses even-order normalized moments and their displacement terms to fill in the first Hankel matrix, which characterizes the internal consistency of the probability density function moment sequence. The second preset construction rule uses odd-order normalized moments or moment terms after appropriate shifts to construct the second Hankel matrix as a supplementary constraint. Together, they reflect the realizability of the stress range distribution from different order relationships.

[0096] The orders of the two Hankel matrices strictly match the order n of the subsequently defined probability density model components: the first Hankel matrix is ​​of order (n+1)×(n+1), constructed from normalized moments of orders 0 to 2n; the second Hankel matrix is ​​of order n×n, constructed from normalized moments of orders 1 to 2n-1. Together, they constitute the complete constraint conditions for the power-sum moment problem, and their simultaneous positive semi-definiteness is a necessary and sufficient condition for the existence and uniqueness of the corresponding non-negative probability density.

[0097] Step S33: Determine whether both the first Hankel matrix and the second Hankel matrix satisfy the positive semidefinite condition.

[0098] For the constructed first and second Hankel matrices, the sign of their smallest eigenvalues ​​is examined using eigenvalue analysis or equivalent numerical criteria to determine whether the matrix belongs to a positive semi-definite cone. If both matrices are positive semi-definite, it indicates that the current normalized moment sequence is fully compatible with the moment representation of a certain non-negative real probability density function, constituting a valid moment sequence, and can proceed to the probability density reconstruction stage without correction. Conversely, if either matrix has a negative eigenvalue, it confirms that the normalized moment sequence violates the fundamental physical requirement of non-negativity of probability density, and projection correction is necessary.

[0099] Step S34: If either condition is not met, then under the constraint of keeping the values ​​of the lower-order normalized moments unchanged, the modified normalized moment sequence with the smallest difference from the current normalized moment sequence is obtained through convex optimization, and the first Hankel matrix and the second Hankel matrix are both positive semi-definite matrices.

[0100] When the first or second Hankel matrix is ​​detected to be non-positive definite, a positive definite projection correction process is initiated. During this process, low-order normalized moments, such as the zeroth and second moments, reflecting the fundamental energy and average frequency characteristics of the stress process, are fixed as hard constraints to ensure that the corrected sequence does not deviate from the main physical trends conveyed by the original statistical properties. Based on this, a convex optimization model is constructed with the corrected normalized moment sequence as the optimization variable and minimizing the Euclidean distance between sequences as the objective function, while the constraint that both the first and second Hankel matrices must be positive definite matrices is applied. The corrected normalized moment sequence is obtained using a positive definite programming solver such as the interior-point method or alternating projection method. This sequence is the result of minimum-distance projection onto a positive definite cone surface while keeping key low-order statistics unchanged, thus achieving an optimal trade-off between rigor and physical fidelity.

[0101] The reason for keeping the lower-order moments unchanged during the projection process is to ensure that the core statistical characteristics such as the mean and variance of the stress range are completely consistent with the derivation results of the measured power spectrum. Only the higher-order tail moments with extremely low weight are modified with minimal amplitude. While ensuring legality, the statistical information of the original spectrum shape is preserved to the maximum extent, and the impact on the final damage calculation results is negligible.

[0102] Step S35: The legal moment sequence is obtained by inverse calculation from the corrected normalized moment sequence.

[0103] The corrected normalized moment sequence obtained through convex optimization projection in step S34 is then inversely normalized using the narrow-band Rayleigh distribution analytical moment benchmark used in step S31. This involves multiplying the moments by the corresponding Rayleigh theoretical moment values ​​one by one to restore the original physical dimensions of the higher-order moments of the stress range. The resulting higher-order moment sequence satisfies the positive semi-definite condition of the Hankel matrix required for the non-negativity of the probability density, while also preserving the statistical information inherent in the target higher-order moment sequence obtained from the feature mapping of the actual stress power spectrum. This constitutes a legitimate moment sequence that can be legally used for subsequent stress range probability density reconstruction.

[0104] Furthermore, the step of reconstructing the stress range probability density function based on the legal moment sequence includes:

[0105] ① A multi-component probability density model is defined, which is composed of a weighted sum of multiple components. Each component consists of a positive coefficient, a stress range variable, and an exponential decay term with the natural constant as the base. The exponential part of the exponential decay term is negatively correlated with the square of the stress range variable.

[0106] Specifically, this reconstruction scheme strictly reduces the solution of the coefficients of the multi-component probability density to a classical power and moment problem. It achieves a closed-form solution by relying on the generalized eigenvalue decomposition of the Hankel matrix bundle. The existence and uniqueness of the solution are strictly guaranteed by the sequence of legal moments after positive definite projection. No empirical parameter fitting and iterative optimization are required, thus eliminating the fitting bias and uncertainty of the empirical model from the root.

[0107] To describe the non-narrow-band probability distribution characteristics of the stress range, it is pre-assumed that the stress range probability density function can be linearly combined from several exponential basis functions. In this model, each component contains a positive amplitude coefficient and an exponential decay term with the natural constant as its base. The exponential part of this decay term is proportional to the square of the stress range variable but takes a negative value, causing each component to exhibit a decaying trend as the stress range increases, which conforms to the physical laws of fatigue stress range distribution. The weighted superposition of multiple such components can flexibly approximate complex distribution forms such as unimodal, multimodal, and asymmetric distributions.

[0108] The number of components, n, in this multi-component model can be flexibly adjusted according to accuracy requirements. A larger value for n results in a higher order of moments that the reconstructed probability density function can match, leading to a better approximation of the true distribution of rainflow stress. The damage estimation error also shows a monotonically decreasing trend as n increases. In practical applications, a threshold can be set for the relative change in damage estimation between adjacent orders. When the error falls below the threshold, the order is no longer increased, achieving an adaptive trade-off between accuracy and computational cost without requiring separate adjustment of model parameters for different spectral types.

[0109] ② Represent the legal moment sequence as normalized moments, and construct the Hankel matrix bundle using the normalized moments.

[0110] Specifically, based on the normalization benchmark established in step S31, the legal moment sequence is transformed into the corresponding normalized moment sequence to eliminate the influence of dimensions and unify the numerical scale. Subsequently, two Hankel matrices of the same order are constructed using this normalized moment sequence. These two matrices have a recursive shift relationship between their row and column elements, forming a Hankel matrix bundle. The purpose of constructing this matrix bundle is to encode the distribution mode information implicit in the moment sequence into a matrix generalized eigenvalue problem, thereby enabling the direct extraction of component nodes from the moment sequence without needing to solve the nonlinear moment matching equation.

[0111] ③ Perform generalized eigenvalue decomposition on the Hankel matrix bundle, and use all the obtained generalized eigenvalues ​​as nodes corresponding to each component.

[0112] Specifically, a generalized eigenvalue decomposition is performed on the Hankel matrix bundle, i.e., the eigenvalues ​​that cause the linear combination of two Hankel matrices in the bundle to degenerate into a singular matrix are solved. All the generalized eigenvalues ​​obtained from the decomposition constitute the characteristic nodes of each exponentially decaying component in the stress range probability density function over the square stress range domain. These nodes physically determine the distribution of the decay rate changes of each component; their number and value are entirely determined by the statistical structure inherent in the normalized moment sequence, without requiring a pre-defined number of components, thus exhibiting adaptive extraction mathematical characteristics.

[0113] ④ Construct a coefficient matrix using the powers of the nodes, build a corresponding system of linear equations, and solve the system of linear equations to obtain the weights of each component.

[0114] Specifically, after obtaining all generalized eigenvalues, i.e., the set of nodes, the algebraic relationship between the normalized moment sequence and each node and its corresponding unknown weights is transformed into a set of linear equations. Specifically, a coefficient matrix is ​​constructed using the zero power of each node up to the power corresponding to the highest order of the normalized moment. Using the normalized moment sequence as the right-hand side, a system of linear equations is established regarding the weights of each component. Since this coefficient matrix is ​​a Vandermonde matrix, the system of linear equations has a unique solution when the nodes are distinct. By directly solving this system, the magnitude weight of each component in the weighted superposition can be obtained, achieving precise matching of the normalized moment sequence.

[0115] ⑤ Based on the definitions of nodes and weights, calculate the exponential decay parameter and positive coefficient of each component to obtain the closed-form expression of the stress range probability density function.

[0116] Specifically, based on the mathematical structure set by the multi-component probability density model, the defined relationship between the obtained generalized eigenvalue nodes and the exponential decay parameters of each component is solved algebraically to obtain the exponential parameter of the decay term for each component. Simultaneously, the mapping relationship between the weights given by the solution of the linear equation system and the positive coefficients of each component is transformed to determine the amplitude value of each component. At this point, the decay parameters and positive coefficients of all components are explicitly determined. Substituting them into the set multi-component weighted summation expression yields the complete closed-form analytical expression of the stress range probability density function, which can be directly used for subsequent closed-form integral calculations of frequency domain fatigue damage.

[0117] In some embodiments of this application, the process of establishing the characteristic moment mapping model is described, which may specifically include:

[0118] ① Construct a sample spectrum library, which includes marine engineering single-peak spectra, double-peak spectra, and various predetermined ideal spectra generated by parameterizing the number of peaks, peak-frequency ratio, energy ratio, and spectral width parameters.

[0119] Specifically, to establish a widely representative power spectrum shape mapping foundation, a sample spectral library covering the typical stress response spectral shape characteristics of marine engineering was systematically constructed. The library's generation process employed a parametric spectral shape generation method, using the number of spectral peaks as a classification variable to distinguish basic types such as single-peak wind-wave dominant spectra and double-peak swell-wind-wave coupled spectra; using peak-frequency ratio and energy proportion as continuously adjustable parameters to control the relative position of each spectral peak on the frequency axis and its power proportion, thereby simulating the energy distribution relationship between the main and secondary peaks under different sea state combinations; and using spectral width parameters to adjust the concentration or dispersion of energy around each spectral peak, characterizing the influence of wave direction extension, nonlinear interactions, and other factors on the spectral bandwidth. Furthermore, the library also includes ideal spectral shapes recognized in the field of marine engineering, such as the Pierson-Moskowitz spectrum and the JONSWAP spectrum, as well as various variant spectral shapes generated through parameter perturbation. The sample spectral library is primarily composed of standard single-peak and double-peak spectra, supplemented by ideal boundary spectra such as rectangular, triangular, and parabolic spectra. It covers the entire spectral range from extremely narrow to extremely wide, ensuring stable extrapolation performance of the mapping model even under rare spectral shapes and avoiding mapping failures or moment sequence anomalies. These parameterization methods, while maintaining the physical interpretability of the spectral shapes, traverse multiple dimensions of variation, including the number of peaks, peak frequency arrangement, energy distribution, and bandwidth characteristics, ensuring that the sample spectral library has sufficient coverage of various stress spectra that the target marine structure may encounter during actual service.

[0120] ② For each sample spectrum in the sample spectrum library, generate multiple Gaussian random stress time histories, and extract the dimensionless stress range sample of each time history by rainflow counting method.

[0121] Specifically, for each sample spectrum in the sample spectrum library, a frequency-to-time domain stochastic process simulation method is adopted. Multiple independent Gaussian stochastic stress time histories are generated by superimposing harmonic components with random phases. The power spectral characteristics of each time history strictly conform to the frequency domain definition of the corresponding sample spectrum. To obtain the statistical distribution information of the stress range, rainflow counting is applied to each generated stress time history. This method extracts the amplitude and mean of stress cycles by identifying closed hysteresis loops in the stress history, and then dimensionlessly processes the amplitude of each stress cycle based on the square root of the zeroth-order spectral moment of the corresponding sample spectrum, obtaining a dimensionless stress range sample set independent of spectral energy levels. The generation and counting of multiple stress time histories effectively reduces the statistical fluctuations caused by a single random realization.

[0122] ③ Using the narrowband benchmark difference moment method, for each sample spectrum, based on the narrowband Rayleigh distribution analytical moments as the benchmark, and the mean of the rainflow counting moments of multiple time histories, the difference between the mean of the narrowband estimated moments of the multiple time histories and the narrowband Rayleigh distribution analytical moments, and a correction coefficient, the true higher-order moment sequence after variance reduction is obtained.

[0123] Specifically, the narrowband benchmark difference moment estimation method is an improved moment estimation strategy that uses analytical moments as an anchor benchmark and reduces the statistical variance of higher-order moments through difference estimation. For a given sample spectrum, the narrowband Rayleigh distribution analytical moment sequence corresponding to the theoretical stress range distribution under the narrowband assumption is first calculated. This analytical moment is directly given by the formulas for each order of Rayleigh moments and has zero variance. Simultaneously, for each generated stress time history, the moments of each order are statistically calculated directly from the dimensionless stress range sample using the rainflow counting method, resulting in a rainflow counting moment sequence. Furthermore, the non-narrowband characteristics of this time history are approximated using a narrowband method, yielding the corresponding narrowband estimated moment sequence. After obtaining the statistical results of multiple time histories, the time history mean of the rainflow counting moment sequence and the time history mean of the narrowband estimated moment sequence are calculated respectively. The core of the narrowband benchmark difference moment method lies in using the narrowband Rayleigh distribution analytical moments as a zero-variance benchmark. It calculates the deviation between the mean of the narrowband estimated moments and the narrowband Rayleigh distribution analytical moments, and then adjusts this deviation by introducing a correction coefficient related to bandwidth characteristics and time-history sample size. The adjusted deviation term is then superimposed onto the mean of the rainflow counting moments, thereby obtaining a true higher-order moment sequence that compensates for non-narrowband effects and reduces variance. This method retains the ability of the rainflow counting method to capture the statistical characteristics of non-narrowband distributed moments while significantly suppressing random fluctuations in higher-order moment estimation under finite sample conditions by utilizing the stability of the narrowband analytical benchmark.

[0124] ④ Extract the power spectrum features of each sample spectrum, and combine the power spectrum features with the corresponding ground truth higher-order moment sequence to form training samples, thereby training the feature moment mapping model.

[0125] Specifically, for each sample spectrum in the sample spectral library, a set of power spectral feature parameters that comprehensively reflect its spectral geometry and bandwidth characteristics are extracted. These parameters include, but are not limited to, spectral width parameters, irregularity factors, spectral centroid frequency, spectral peak frequency distribution, ratios of spectral moments of each order, and spectral skewness and kurtosis descriptors, forming a power spectral feature vector that corresponds one-to-one with the spectral shape. This power spectral feature vector is used as input, and the true higher-order moment sequence obtained from the sample spectrum using the narrowband benchmark difference moment method is used as the output label to construct paired training samples. After traversing all sample spectra in the sample spectral library, a training sample set covering various spectral shapes and their true higher-order moment mapping relationships is obtained. Based on this, a regression model with nonlinear mapping capabilities, such as support vector regression, Gaussian process regression, or deep neural networks, is selected for supervised training, using the power spectral feature vector as the model input and the true higher-order moment sequence as the prediction target. During training, model parameters are optimized using a loss function to minimize the error between the model's predicted output on the training set and the true higher-order moment sequence. Cross-validation and other strategies are employed to prevent overfitting, ultimately resulting in a feature moment mapping model that can directly map higher-order moment sequences from power spectrum features. Once trained, this model solidifies the intrinsic relationship between the power spectrum shape and the higher-order moments of the stress range. In subsequent engineering applications, higher-order moments can be rapidly predicted solely based on stress power spectrum features, eliminating the need for repeated time-domain simulations and complex rainflow counting moment estimation processes.

[0126] Furthermore, the process of determining the correction coefficient includes:

[0127] The rainflow counting moments and narrowband estimation moments calculated from each of the multiple time histories are statistically analyzed to obtain the covariance estimate of the two and the variance estimate of the narrowband estimation moment. The ratio of the covariance estimate to the variance estimate is used as the correction coefficient.

[0128] The narrowband estimated moments are the corresponding order moments calculated for each time history based on the analytical moment expression of the narrowband Rayleigh distribution.

[0129] Specifically, within the framework of the narrowband benchmark difference moment method, the correction coefficient quantitatively characterizes the statistical correlation strength between the rainflow count moment estimate and the narrowband moment estimate, and uses this as a basis to perform optimal weighted adjustment of the narrowband benchmark bias, thereby achieving a balance between bias compensation and variance suppression. To determine this correction coefficient, it is first necessary to calculate the two types of estimator sequences corresponding to each order moment on the statistical set of multiple stress time histories. For a given order, the rainflow count moment is obtained by directly calculating the sample mean of each power after extracting the dimensionless stress range sample using the rainflow counting method for each stress time history; the narrowband moment estimate, on the other hand, is calculated for the same stress time history by substituting the statistical characteristic parameters of the time history into the analytical moment expression of the narrowband Rayleigh distribution. Because this estimator uses an analytical expression, its fluctuations between time histories only originate from the finite sample realization differences of the random process itself. After obtaining sample sequences of rainflow count moments and narrowband estimating moments appearing in pairs across multiple time histories, the covariance estimates between the two moments and the variance estimates of the narrowband estimating moment itself are calculated at that time order. The covariance estimates reflect the synchronous changing trends of the two estimators within the time histories. A large positive covariance indicates a strong consistency between the fluctuation direction of the narrowband estimating moment and the fluctuation direction of the rainflow count moment; therefore, the deviation between the narrowband estimating moment and the narrowband Rayleigh distribution analytical moment has high reference value for correcting the rainflow count moment. Conversely, if the covariance is close to zero or negative, it indicates a weak statistical correlation between the fluctuations of the two moments, limiting the effectiveness of correction using narrowband deviation, and the correction magnitude should be correspondingly reduced. The variance estimate quantifies the dispersion of the narrowband estimator within the time-history set, serving as a normalization benchmark for the covariance. The ratio of covariance to variance is used as a correction coefficient, making it statistically equivalent to the linear regression coefficient of the rainflow count moments on the narrowband estimator. Numerically, this coefficient lies between zero and one; it approaches one when the two are perfectly linearly correlated and approaches zero when they are statistically independent. Using this ratio as the correction coefficient in the weighting of the bias term essentially yields the analytically optimal solution for linearly correcting the mean of the rainflow count moments under the mean square error minimization criterion. This effectively compensates for non-narrowband effects while maximally suppressing the additional variance introduced by the fluctuations in the narrowband estimator, thus obtaining a reduced-variance true higher-order moment sequence that combines estimation accuracy and statistical stability.

[0130] In the above process, the estimation formula for obtaining the variance-reduced true higher-order moment sequence using the narrowband benchmark difference moment method is as follows:

[0131] ;

[0132] in, Here, N represents the reduced variance estimate of the k-th order true moments, and N is the number of time histories. Let j be the rainfall count moment for the j-th time history. For the narrowband estimation moment of the j-th time history, For narrowband Rayleigh distribution analytical moments, This is a correction factor.

[0133] In some embodiments of this application, the process of determining the total fatigue damage using frequency domain closed-loop integration in step S4 is described, including two cases:

[0134] The first method involves calculating the total fatigue damage using a closed-form frequency domain calculation when the material's SN curve has a single slope, by utilizing the evaluation duration, the spectral moments of each order, and the specified order moments of the stress range determined by the stress range probability density function.

[0135] Specifically, when the stress range-life curve of the material used in the target marine structure in a double logarithmic coordinate system can be completely described by a single slope parameter and a single intercept parameter within the entire stress range, the frequency domain calculation of fatigue damage can be significantly simplified. In this case, firstly, the zero-order spectral moment and the second-order spectral moment are extracted from each order spectral moment calculated in step S1. The average number of stress cycles per unit time, i.e., the average zero-crossing rate, is obtained by calculating the ratio of the spectral moments. The average zero-crossing rate is multiplied by the predetermined evaluation duration to obtain the total number of stress cycles expected to occur within the evaluation period. At the same time, based on the closed-form analytical expression of the stress range probability density function reconstructed in step S3, the stress range variable is weighted according to the power of the inverse slope corresponding to the single slope parameter, and the weighted integral is obtained on the non-negative half-axis of the stress range. The result of this integral is the specified moment of the stress range probability density function, and its physical meaning is the average damage equivalent generated per unit stress cycle. By substituting the total number of stress cycles, the specified moment, and the intercept parameter of the SN curve into the frequency domain expression of the linear cumulative damage criterion, the expected value of total fatigue damage within the evaluation period can be directly obtained through a single analytical or numerical product operation. This process transforms the tedious steps of identifying and accumulating damage in the time domain through successive cycles into closed-form algebraic operations that rely solely on the spectral moments and the probability density function moments of the stress range, achieving extremely high computational efficiency while ensuring accuracy.

[0136] The second method involves calculating the segmented damage for each slope segment according to the linear fatigue accumulation criterion and then summing the results to obtain the total fatigue damage. The segmented damage for each slope segment is obtained by integrating the stress range probability density function within that stress range segment, using the power of the inverse slope of that segment as the weight. This integration is achieved by substituting the exponential decay parameter, positive coefficient, and inverse slope of each component of the stress range probability density function into a predetermined integral relationship, calculating the difference between the integral values ​​determined by the upper and lower limits of the stress range, and then summing the differences for all components to achieve a closed-form solution.

[0137] Specifically, when the material's SN curve exhibits a multi-segmented broken line characteristic on a double logarithmic coordinate system, it indicates that the material has different fatigue resistance decay patterns within different stress ranges. In this case, damage accumulation calculation needs to be performed segmentally. First, based on the stress range value at the inflection point of the SN curve, the entire stress range is divided into several continuous sub-intervals. Each sub-interval corresponds to a single slope segment parameter and an applicable intercept parameter for that segment. For each slope segment, according to the linear accumulation criterion, the segmented damage corresponding to that segment can be expressed as: the total number of stress cycles within the evaluation period multiplied by the probability density integral of the stress range within that stress range, weighted by a power of the inverse slope of that segment, and then divided by the intercept parameter of that segment. The calculation of the probability density integral term fully utilizes the multi-component weighted summation closed structure of the stress range probability density function in step S3. Specifically, each exponentially decaying component of the stress range probability density function is substituted into the integral. Using the exponential decay parameter, positive coefficient, and inverse slope parameter of the current slope segment for each component, and based on the pre-derived integral relationship of the convolution of the exponential decay kernel and the power weight function, it can be analytically expressed as the difference between incomplete function terms dependent on the upper and lower limits of the stress range. The upper and lower limits of the stress range are taken as the values ​​of the upper and lower bound inflection points of the stress range corresponding to the current slope segment, respectively. The difference term is calculated for each component and a weighted sum is performed to obtain the required piecewise probability density weighted integral value within the slope segment, thus completing the closed-form solution for piecewise damage. By sequentially traversing all slope segments of the SN curve and summing the piecewise damage, the total expected fatigue damage value corresponding to the multi-slope SN curve covering the entire stress range is finally obtained. This closed-form solution method avoids the computational overhead of performing numerical integration or Monte Carlo simulations separately in each stress range interval, and maintains the high efficiency advantage of frequency domain methods in multi-slope fatigue assessment scenarios.

[0138] The analytical form of the above integral is a lower incomplete Gamma function, which can be solved accurately without numerical integration. For SN curves containing fatigue limit segments, the damage contribution of segments below the fatigue limit stress range is zero, and the corresponding integration interval can be directly truncated during calculation without additional numerical processing. This piecewise integration framework is compatible with multi-slope SN curves with any number of segments, uniformly covering single-slope, double-slope, and multi-segment curve scenarios containing fatigue limits, and has extremely strong versatility.

[0139] When the material's SN curve has a single slope, the expression for total fatigue damage obtained through closed-form calculation in the frequency domain is as follows:

[0140] ;

[0141] When the material's SN curve has multiple slope segments, the expression for summing the segmented damage calculated for each slope segment according to the linear fatigue accumulation criterion is as follows:

[0142] ;

[0143] Where D represents total fatigue damage, T represents the assessment duration, m0, m2, and m4 represent the spectral moments of each order, k represents the inverse slope of the SN curve, and C represents the material constant. Let be the k-th moment of the stress range determined by the stress range probability density function, s be the total number of slope segments, ki and Ci be the inverse slope and material constant of the i-th slope segment, respectively, and Li and Hi be the lower and upper limits of the stress range of the i-th slope segment, respectively. Let z be the probability density function of the stress range, where z is the dimensionless stress range.

[0144] In some embodiments of this application, considering the practical needs of fatigue failure early warning and remaining life prediction for the whole life cycle integrity management of marine engineering structures, and the reliability requirements that the characteristic moment mapping model must undergo sufficient accuracy verification before engineering deployment, this application may also include the functions of fatigue failure determination and remaining life output, as well as model mapping accuracy verification, specifically:

[0145] After determining the total fatigue damage, the following is also included:

[0146] When the total fatigue damage reaches the preset failure threshold, it is determined that the marine structure has suffered fatigue failure.

[0147] The remaining fatigue life of the marine structure is determined and output based on the ratio of the duration of the assessment to the total fatigue damage.

[0148] Specifically, after obtaining the total fatigue damage value accumulated by the target marine structure within a specific assessment duration using the aforementioned frequency domain closed-loop integral method, a preset fatigue failure threshold is introduced as a quantitative criterion for determining whether the structure has failed. This threshold is typically set to one under the linear cumulative damage theory framework, indicating that the material or structural details have reached the critical state of fatigue life exhaustion. The calculated total fatigue damage value is compared with this preset failure threshold: if the total fatigue damage value is greater than or equal to the preset failure threshold, the marine structure is determined to have experienced fatigue failure by the end of the assessment duration; if the total fatigue damage value is still less than the preset failure threshold, the structure is considered to be still in a safe service state. Based on this, the remaining usable life of the structure is extrapolated and estimated according to the rate of damage accumulation within the current assessment duration. This involves multiplying the remaining damage capacity, represented by the difference between the preset failure threshold and the currently accumulated total fatigue damage, by the ratio of the assessment duration to the current total fatigue damage, to obtain a time-based estimate of the remaining fatigue life. The remaining fatigue life reflects the expected length of time a marine structure can continue to serve from its current state to the fatigue failure threshold, assuming that the statistical characteristics of the current sea state and the dynamic response characteristics of the structure remain unchanged.

[0149] After training to obtain the feature moment mapping model, the following steps are also included:

[0150] Obtain the validation sample spectrum set, input the power spectrum features of the validation sample spectrum into the feature moment mapping model, and obtain the predicted higher-order moment sequence;

[0151] The true higher-order moment sequence corresponding to the verification sample spectrum is obtained by using the narrow-band benchmark difference moment method. The predicted higher-order moment sequence is compared with the true higher-order moment sequence to confirm that the mapping error is within the preset accuracy range.

[0152] Specifically, to confirm that the eigenmoment mapping model has the generalization mapping accuracy required for engineering applications on new spectral forms outside the training sample set, an independent validation sample spectrum set is introduced for performance evaluation after model training is completed. The validation sample spectrum set consists of spectral form samples generated according to a predetermined sampling strategy within the parameter space constructed from the sample spectrum library, but not participating in the model training process. Its generation method is consistent with the training sample spectrum library, but its parameter combinations have no overlap with the training set, ensuring that the validation process can objectively evaluate the model's adaptability to unseen spectral forms. For each sample spectrum in the validation sample spectrum set, a power spectrum feature vector with the same dimension as in the model training stage and maintaining consistent feature definitions is extracted. This vector is then input into the trained eigenmoment mapping model for forward inference to obtain the predicted higher-order moment sequence output by the model. Simultaneously, using the narrowband benchmark difference moment method, which is completely consistent with the method used to construct the ground truth labels for the training samples, multiple Gaussian random stress time histories generated based on the validation sample spectrum are processed through a complete process including rainflow counting, narrowband estimation, and covariance correction to calculate the corresponding ground truth values ​​of the higher-order moment sequences. The predicted higher-order moment sequence is compared with the true higher-order moment sequence at each order, and mapping error indices such as relative deviation or root mean square error are calculated at each order. It is then determined whether the error falls within the preset accuracy range based on the tolerance requirements for engineering fatigue damage assessment. If the mapping errors of all validation samples at each order moment meet the preset accuracy requirements, the mapping capability of the characteristic moment mapping model is confirmed to have statistical reliability and generalization, and can be deployed to practical engineering applications. Conversely, if errors in any order or spectral region exceed the allowable range, targeted improvements and retraining are required to the model structure, feature selection, or training sample coverage until validation is successful.

[0153] This embodiment uses a typical bimodal stress spectrum (low-frequency swell component + wave frequency wind and wave component) of marine engineering as input to fully execute the entire process from spectral moment extraction to fatigue damage calculation, while verifying the convergence effect of increasing the component order of the multi-component probability density model on the evaluation accuracy.

[0154] Obtain the stress power spectral density function and calculate the spectral moments of each order:

[0155] Assume the stress response power spectrum of the target marine structure's hot spot is a typical bimodal spectrum, composed of the superposition of two narrowband spectra: the low-frequency swell component angular frequency. rad / s, energy percentage 0.7; wave frequency wind and wave component angular frequency rad / s, energy percentage 0.3. The spectral moments of each order are calculated according to the definition of spectral moment, as shown in Table 1:

[0156] Table 1

[0157]

[0158] Obtain the target high-order moment sequence through the feature moment mapping model:

[0159] The target higher-order moment sequence corresponding to this bimodal spectral shape is output by the characteristic moment mapping model from the true higher-order moments obtained offline using the narrow-band benchmark difference moment method. Offline, using the narrow-band Rayleigh distribution analytical moments as a benchmark, the true higher-order moments of the rainflow within the dimensionless stress range under this spectral shape are obtained through variance reduction estimation. After normalization, the normalized moment sequence of orders 0 to 3 required for component order n=2 is obtained.

[0160] ;

[0161] The corresponding sequence of higher-order moments with original dimensions is: .

[0162] Positive semidefinite projection correction and probability density function reconstruction of the target higher-order moment sequence:

[0163] (1) Verification of the validity of positive semidefinite projections;

[0164] Construct the first Hankel matrix H0 based on the normalized moment sequence:

[0165] ;

[0166] Determinant And the first-order element By combining the positive semidefinite test of the second Hankel matrix, it is confirmed that the current normalized moment sequence satisfies the positive semidefinite constraint of the legal moment sequence, and no projection correction is required. It can be directly used for probability density reconstruction.

[0167] (2) Closed-form reconstruction of multi-component probability density function;

[0168] Using a multi-component stress range probability density model with component order n=2, the coefficient solution is reduced to a power and moment problem, which is then solved in a closed form using the generalized eigenvalue decomposition of the Hankel matrix bundle.

[0169] Second-order recurrence relation based on moment sequence Substitute the normalized moment sequence to solve for the recurrence coefficients:

[0170] ;

[0171] Characteristic equation With discriminant = 2.0, we obtain the node. ;

[0172] Depend on , Solving .reduction:

[0173] ;

[0174] That is, the reconstruction yields:

[0175] ;

[0176] All coefficients are positive and automatically normalized. The solution is unique and is a valid probability density function.

[0177] Calculate total fatigue damage using closed-loop frequency domain integration:

[0178] The commonly used engineering double-slope SN curve is adopted, with the inverse slopes being respectively... The corresponding material constant is The dividing point between the two curves corresponds to the threshold of the dimensionless stress range. The assessment duration is T. Based on the linear cumulative damage criterion, the total fatigue damage is calculated using piecewise frequency domain closed-loop integration:

[0179] ;

[0180] Each piecewise integral in the formula can be obtained by summing the components one by one using the closed-form formula of the incomplete Gamma function (no numerical integration is required). When Determined to be damaged, remaining lifetime = T / D.

[0181] Accuracy convergence verification of adaptive improvement based on component order:

[0182] To verify the accuracy controllability of the multi-component model with adjustable order, different component orders n were used for reconstruction and damage calculation for the same bimodal spectrum. The damage true value obtained by the time-domain rainflow counting method was used as the benchmark, and the relative error of damage estimation is shown in Table 2.

[0183] Table 2

[0184]

[0185] It is evident that the damage estimation error decreases monotonically with the increase of the component order n, and the reconstructed probability density gradually approximates the true distribution of the rainflow. In practical engineering applications, an accuracy threshold can be set (e.g., the relative change in damage estimation between adjacent orders is less than 2%), and the component order can be automatically increased until the accuracy requirements are met, achieving an adaptive trade-off between assessment accuracy and computational cost.

[0186] The following describes a marine structure fatigue damage assessment device provided in the embodiments of this application. The marine structure fatigue damage assessment device described below and the marine structure fatigue damage assessment method described above can be referred to and correspond to each other.

[0187] See Figure 2 , Figure 2 This is a schematic diagram of a marine structural fatigue damage assessment device disclosed in an embodiment of this application.

[0188] like Figure 2 As shown, the marine structural fatigue damage assessment device may include:

[0189] The spectral moment analysis module 110 is used to obtain the stress power spectral density function of the target marine structure under random loads and to calculate the spectral moments of the stress power spectral density function.

[0190] The mapping sequence module 120 is used to obtain a pre-established feature moment mapping model. The power spectral features of the stress power spectral density function are input into the feature moment mapping model to obtain the target higher-order moment sequence. The feature moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequences. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation.

[0191] The projection correction module 130 is used to perform semi-positive definite projection correction on the target higher-order moment sequence to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and to reconstruct the stress range probability density function based on the legal moment sequence.

[0192] The damage determination module 140 is used to determine the total fatigue damage by using frequency domain closed-loop integration based on the stress range probability density function, the pre-acquired material SN curve parameters, and the spectral moments of each order.

[0193] As can be seen from the above technical solution, the fatigue damage assessment method and related equipment for marine structures provided in this application first obtain the stress power spectral density function of the target marine structure under random load and calculate the spectral moments of each order; then, the power spectral features are input into a pre-established characteristic moment mapping model to obtain the target higher-order moment sequence. This model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectral library and the corresponding true higher-order moment sequences. The true higher-order moment sequence is estimated from the stress time history data generated by the narrow-band benchmark difference moment method, using the narrow-band Rayleigh distribution analytical moments as a benchmark and reducing the estimation variance through difference; then, the target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed accordingly; finally, the total fatigue damage is determined by frequency domain closed integral, combining the probability density function, material SN curve parameters, and the spectral moments of each order. This method trains a feature moment mapping model by obtaining low-variance high-order moment ground values ​​using a narrow-band benchmark difference moment method. This allows the high-order moments predicted directly from power spectrum features to accurately reflect the true statistical characteristics of rainfall amplitude in broadband, multi-peak, and non-Gaussian processes, without relying on any fixed empirical distribution shape. Consequently, the reconstructed stress range probability density function closely approximates the actual distribution, fundamentally improving the accuracy of fatigue damage assessment. After model training, only spectral features need to be input during the evaluation phase to instantly output high-fidelity high-order moments, completely avoiding stress time history simulation and rainfall counting. This successfully resolves the contradiction between accurate high-order moment estimation and computational efficiency, achieving fast and accurate moment estimation within a pure frequency domain framework. The introduced positive semi-definite projection correction step forcibly corrects the predicted moment sequence to a legal moment space that satisfies the positive semi-definite condition of the Hankel matrix. Mathematically, this ensures that the reconstructed stress range probability density is everywhere non-negative and meets the normalization requirements. This completely eliminates the risk of negative values ​​or oscillations in the probability density caused by moment estimation disturbances or numerical errors, making the fatigue damage calculation results have reliable physical meaning and greatly enhancing the robustness of the method. Finally, based on the legal probability density, SN curve parameters, and spectral moments, the total fatigue damage can be quickly given through frequency domain closed-loop integration, greatly reducing the computation time for fatigue assessment in multiple sea states and long periods, and meeting the comprehensive requirements of high accuracy, high efficiency, and high robustness for fatigue damage assessment under complex marine load scenarios. Optionally, the stress power spectral density function of the target marine structure under random loads is obtained, and the spectral moments of each order of the stress power spectral density function are calculated, including:

[0194] Collect stress time history data of the target marine structure under random loads, and determine the duration of the stress time history data.

[0195] The stress time history data is subjected to Fourier transform to obtain the stress power spectral density function;

[0196] The stress power spectral density function is weighted according to the angular frequency weighting method corresponding to different order moments, and the weighted result is integrated within the frequency range to obtain spectral moments of various orders, including the zero-order spectral moment, the second-order spectral moment, and the fourth-order spectral moment.

[0197] Optionally, the process of establishing the feature moment mapping model includes:

[0198] Construct a sample spectrum library, which includes marine engineering single-peak spectra, double-peak spectra, and various predetermined ideal spectra generated by parameterizing the number of spectral peaks, peak-frequency ratio, energy ratio, and spectral width parameters;

[0199] For each sample spectrum in the sample spectrum library, multiple Gaussian random stress time histories are generated, and the dimensionless stress range sample of each time history is extracted by rainflow counting method;

[0200] The narrowband benchmark difference moment method is adopted. For each sample spectrum, the narrowband Rayleigh distribution analytical moments are used as the benchmark. Based on the mean of the rainflow counting moments of multiple time histories, the difference between the mean of the narrowband estimated moments of the multiple time histories and the narrowband Rayleigh distribution analytical moments, and a correction coefficient, the true higher-order moment sequence after variance reduction is obtained.

[0201] Extract the power spectrum features of each sample spectrum, and combine the power spectrum features with the corresponding ground truth higher-order moment sequence to form training samples, thereby training the feature moment mapping model.

[0202] Optionally, the process of determining the correction coefficient includes:

[0203] The rainflow counting moments and narrowband estimation moments calculated from each of the multiple time histories are statistically analyzed to obtain the covariance estimate of the two and the variance estimate of the narrowband estimation moment. The ratio of the covariance estimate to the variance estimate is used as the correction coefficient.

[0204] The narrowband estimated moments are the corresponding order moments calculated for each time history based on the analytical moment expression of the narrowband Rayleigh distribution.

[0205] Optionally, the estimation formula for obtaining the variance-reduced higher-order moment sequence using the narrowband benchmark difference moment method is as follows:

[0206] ;

[0207] in, Here, N represents the reduced variance estimate of the k-th order true moments, and N is the number of time histories. Let j be the rainfall count moment for the j-th time history. For the narrowband estimation moment of the j-th time history, For narrowband Rayleigh distribution analytical moments, This is a correction factor.

[0208] Optionally, the step of performing semi-positive definite projection correction on the target higher-order moment sequence to obtain a legal moment sequence that satisfies the non-negativity probability density constraint includes:

[0209] The target higher-order moment sequence is normalized using narrowband Rayleigh distribution analytical moments to obtain a normalized moment sequence.

[0210] Based on the normalized moment sequence, a first Hankel matrix is ​​formed according to a preset first construction rule, and a second Hankel matrix is ​​formed according to a preset second construction rule;

[0211] Determine whether both the first Hankel matrix and the second Hankel matrix satisfy the positive semidefinite condition;

[0212] If either condition is not met, then under the constraint of keeping the values ​​of the lower-order normalized moments unchanged, the modified normalized moment sequence with the smallest difference from the current normalized moment sequence is obtained by convex optimization, and the first Hankel matrix and the second Hankel matrix are both positive semi-definite matrices.

[0213] The legal moment sequence is obtained by inverse calculation from the corrected normalized moment sequence.

[0214] Optionally, the step of reconstructing the stress range probability density function based on the legal moment sequence includes:

[0215] A multi-component probability density model is defined, which is composed of a weighted sum of multiple components. Each component consists of a positive coefficient, a stress range variable, and an exponential decay term with the natural constant as the base. The exponential part of the exponential decay term is negatively correlated with the square of the stress range variable.

[0216] The sequence of legal moments is represented as normalized moments, and the Hankel matrix bundle is constructed using the normalized moments;

[0217] The Hankel matrix bundle is subjected to generalized eigenvalue decomposition, and all the obtained generalized eigenvalues ​​are used as nodes corresponding to each component.

[0218] Construct a coefficient matrix using the powers of the nodes, build a corresponding system of linear equations, and solve the system of linear equations to obtain the weights of each component.

[0219] Based on the definitions of nodes and weights, the exponential decay parameter and positive coefficient of each component are calculated in reverse to obtain the closed-form expression of the probability density function of the stress range.

[0220] Optionally, determining the total fatigue damage using frequency domain closed-loop integration includes:

[0221] When the material SN curve has a single slope, the total fatigue damage is obtained by frequency domain closed-form calculation using the evaluation duration, the spectral moments of each order, and the stress range specified moment determined by the stress range probability density function.

[0222] When the SN curve of a material has multiple slope segments, the total fatigue damage is obtained by calculating the segmented damage for each slope segment according to the linear fatigue accumulation criterion and then summing the results.

[0223] The segmented damage of each slope segment is obtained by integrating the stress range probability density function within that stress range segment, using the power of the inverse slope of the stress range as the weight. The integration is achieved by substituting the exponential decay parameter, positive coefficient, and inverse slope of the current slope segment of each component of the stress range probability density function into a predetermined integral relationship, calculating the difference between the integral values ​​determined by the upper and lower limits of the stress range, and summing the differences of all components to achieve a closed-form solution.

[0224] Optionally, when the material's SN curve has a single slope, the expression for the total fatigue damage obtained through closed-form calculation in the frequency domain is:

[0225] ;

[0226] When the material's SN curve has multiple slope segments, the expression for summing the segmented damage calculated for each slope segment according to the linear fatigue accumulation criterion is as follows:

[0227] ;

[0228] Where D represents total fatigue damage, T represents the assessment duration, m0, m2, and m4 represent the spectral moments of each order, k represents the inverse slope of the SN curve, and C represents the material constant. Let be the k-th moment of the stress range determined by the stress range probability density function, s be the total number of slope segments, ki and Ci be the inverse slope and material constant of the i-th slope segment, respectively, and Li and Hi be the lower and upper limits of the stress range of the i-th slope segment, respectively. Let z be the probability density function of the stress range, where z is the dimensionless stress range.

[0229] Optionally, after determining the total fatigue damage, the following may also be included:

[0230] When the total fatigue damage reaches the preset failure threshold, it is determined that the marine structure has suffered fatigue failure.

[0231] The remaining fatigue life of the marine structure is determined and output based on the ratio of the duration of the assessment to the total fatigue damage.

[0232] Optionally, after training the feature moment mapping model, the method further includes:

[0233] Obtain the validation sample spectrum set, input the power spectrum features of the validation sample spectrum into the feature moment mapping model, and obtain the predicted higher-order moment sequence;

[0234] The true higher-order moment sequence corresponding to the verification sample spectrum is obtained by using the narrow-band benchmark difference moment method. The predicted higher-order moment sequence is compared with the true higher-order moment sequence to confirm that the mapping error is within the preset accuracy range.

[0235] The marine structure fatigue damage assessment device provided in this application embodiment can be applied to marine structure fatigue damage assessment equipment. Figure 3 The hardware structure block diagram of the marine structural fatigue damage assessment equipment is shown. Figure 3 The hardware structure of the marine structural fatigue damage assessment equipment 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;

[0236] 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;

[0237] 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.

[0238] Memory 3 may include high-speed RAM, and may also include non-volatile memory, such as at least one disk storage device;

[0239] The memory stores a program, which the processor can call. The program is used for:

[0240] Obtain the stress power spectral density function of the target marine structure under random loads, and calculate the spectral moments of each order of the stress power spectral density function;

[0241] A pre-established characteristic moment mapping model is obtained, and the power spectral features of the stress power spectral density function are input into the characteristic moment mapping model to obtain the target higher-order moment sequence. The characteristic moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequence. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation.

[0242] The target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed based on the legal moment sequence.

[0243] Based on the stress range probability density function, the pre-acquired material SN curve parameters, and the spectral moments of each order, the total fatigue damage is determined by frequency domain closed-loop integration.

[0244] Optionally, the refined and extended functions of the program can be referred to the above description.

[0245] 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:

[0246] Obtain the stress power spectral density function of the target marine structure under random loads, and calculate the spectral moments of each order of the stress power spectral density function;

[0247] A pre-established characteristic moment mapping model is obtained, and the power spectral features of the stress power spectral density function are input into the characteristic moment mapping model to obtain the target higher-order moment sequence. The characteristic moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequence. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation.

[0248] The target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed based on the legal moment sequence.

[0249] Based on the stress range probability density function, the pre-acquired material SN curve parameters, and the spectral moments of each order, the total fatigue damage is determined by frequency domain closed-loop integration.

[0250] Optionally, the refined and extended functions of the program can be referred to the above description.

[0251] 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:

[0252] Obtain the stress power spectral density function of the target marine structure under random loads, and calculate the spectral moments of each order of the stress power spectral density function;

[0253] A pre-established characteristic moment mapping model is obtained, and the power spectral features of the stress power spectral density function are input into the characteristic moment mapping model to obtain the target higher-order moment sequence. The characteristic moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequence. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation.

[0254] The target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed based on the legal moment sequence.

[0255] Based on the stress range probability density function, the pre-acquired material SN curve parameters, and the spectral moments of each order, the total fatigue damage is determined by frequency domain closed-loop integration.

[0256] Optionally, the refined and extended functions of the program can be referred to the above description.

[0257] 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.

[0258] 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.

[0259] 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 for assessing fatigue damage to marine structures, characterized in that, include: Obtain the stress power spectral density function of the target marine structure under random loads, and calculate the spectral moments of each order of the stress power spectral density function; A pre-established characteristic moment mapping model is obtained, and the power spectral features of the stress power spectral density function are input into the characteristic moment mapping model to obtain the target higher-order moment sequence. The characteristic moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequence. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation. The target higher-order moment sequence is subjected to positive semi-definite projection correction to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and the stress range probability density function is reconstructed based on the legal moment sequence. Based on the stress range probability density function, the pre-acquired material SN curve parameters, and the spectral moments of each order, the total fatigue damage is determined by frequency domain closed-loop integration. The process of establishing the characteristic moment mapping model includes: Construct a sample spectrum library, which includes marine engineering single-peak spectra, double-peak spectra, and various predetermined ideal spectra generated by parameterizing the number of spectral peaks, peak-frequency ratio, energy ratio, and spectral width parameters; For each sample spectrum in the sample spectrum library, multiple Gaussian random stress time histories are generated, and the dimensionless stress range sample of each time history is extracted by rainflow counting method; The narrowband benchmark difference moment method is adopted. For each sample spectrum, the narrowband Rayleigh distribution analytical moments are used as the benchmark. Based on the mean of the rainflow counting moments of multiple time histories, the difference between the mean of the narrowband estimated moments of the multiple time histories and the narrowband Rayleigh distribution analytical moments, and a correction coefficient, the true higher-order moment sequence after variance reduction is obtained. Extract the power spectrum features of each sample spectrum, and combine the power spectrum features with the corresponding ground truth higher-order moment sequence to form training samples, thereby training the feature moment mapping model. The process of determining the correction coefficient includes: The rainflow counting moments and narrowband estimation moments calculated from each of the multiple time histories are statistically analyzed to obtain the covariance estimate of the two and the variance estimate of the narrowband estimation moment. The ratio of the covariance estimate to the variance estimate is used as the correction coefficient. Wherein, the narrowband estimated moment is the corresponding order moment calculated for each time history based on the analytical moment expression of the narrowband Rayleigh distribution; The step of performing semi-positive definite projection correction on the target high-order moment sequence to obtain a legal moment sequence that satisfies the non-negativity probability density constraint includes: The target higher-order moment sequence is normalized using narrowband Rayleigh distribution analytical moments to obtain a normalized moment sequence. Based on the normalized moment sequence, a first Hankel matrix is ​​formed according to a preset first construction rule, and a second Hankel matrix is ​​formed according to a preset second construction rule; Determine whether both the first Hankel matrix and the second Hankel matrix satisfy the positive semidefinite condition; If either condition is not met, then under the constraint of keeping the values ​​of the lower-order normalized moments unchanged, the modified normalized moment sequence with the smallest difference from the current normalized moment sequence is obtained by convex optimization, and the first Hankel matrix and the second Hankel matrix are both positive semi-definite matrices. The legal moment sequence is obtained by inverse calculation from the corrected normalized moment sequence.

2. The method according to claim 1, characterized in that, Obtain the stress power spectral density function of the target marine structure under random loads, and calculate the spectral moments of each order of the stress power spectral density function, including: Collect stress time history data of the target marine structure under random loads, and determine the duration corresponding to the stress time history data; The stress time history data is subjected to Fourier transform to obtain the stress power spectral density function; The stress power spectral density function is weighted according to the angular frequency weighting method corresponding to different order moments, and the weighted result is integrated within the frequency range to obtain spectral moments of various orders, including the zero-order spectral moment, the second-order spectral moment, and the fourth-order spectral moment.

3. The method according to claim 1, characterized in that, The estimation formula for obtaining the variance-reduced true higher-order moment sequence using the narrowband benchmark difference moment method is as follows: ； in, For the first k The variance-reduced estimate of the true moments of order 1. N For the number of timelines, For the first j Rainfall count moments over time periods, For the first j Narrowband estimation moments for time histories For narrowband Rayleigh distribution analytical moments, This is a correction factor.

4. The method according to claim 1, characterized in that, The process of reconstructing the stress range probability density function based on the legal moment sequence includes: A multi-component probability density model is defined, which is composed of a weighted sum of multiple components. Each component consists of a positive coefficient, a stress range variable, and an exponential decay term with the natural constant as the base. The exponential part of the exponential decay term is negatively correlated with the square of the stress range variable. The sequence of legal moments is represented as normalized moments, and the Hankel matrix bundle is constructed using the normalized moments; The Hankel matrix bundle is subjected to generalized eigenvalue decomposition, and all the obtained generalized eigenvalues ​​are used as nodes corresponding to each component. Construct a coefficient matrix using the powers of the nodes, build a corresponding system of linear equations, and solve the system of linear equations to obtain the weights of each component. Based on the definitions of nodes and weights, the exponential decay parameter and positive coefficient of each component are calculated in reverse to obtain the closed-form expression of the probability density function of the stress range.

5. The method according to claim 1, characterized in that, The method of determining total fatigue damage using frequency domain closed-loop integration includes: When the material SN curve has a single slope, the total fatigue damage is obtained by frequency domain closed-form calculation using the evaluation duration, the spectral moments of each order, and the stress range specified moment determined by the stress range probability density function. When the SN curve of a material has multiple slope segments, the total fatigue damage is obtained by calculating the segmented damage for each slope segment according to the linear fatigue accumulation criterion and then summing the results. The segmented damage of each slope segment is obtained by integrating the stress range probability density function within that stress range segment, using the power of the inverse slope of the stress range as the weight. The integration is achieved by substituting the exponential decay parameter, positive coefficient, and inverse slope of the current slope segment of each component of the stress range probability density function into a predetermined integral relationship, calculating the difference between the integral values ​​determined by the upper and lower limits of the stress range, and summing the differences of all components to achieve a closed-form solution.

6. The method according to claim 5, characterized in that, When the material's SN curve has a single slope, the expression for total fatigue damage obtained through closed-form calculation in the frequency domain is as follows: ； When the material's SN curve has multiple slope segments, the expression for summing the segmented damage calculated for each slope segment according to the linear fatigue accumulation criterion is as follows: ； in, D Total fatigue damage, T To assess duration, m 0、 m 2. m 4 represents the spectral moments of each order. k The inverse slope of the SN curve. C For material constants, The stress range is determined by the stress range probability density function. k Step moment, s This represents the total number of slope segments. ki and Ci The first i The inverse slope of the slope segment and the material constant, Li and Hi The first i The lower and upper limits of the stress range in the slope segment. Let the stress range be the probability density function. z This refers to the dimensionless stress range.

7. The method according to claim 1, characterized in that, After determining the total fatigue damage, the following is also included: When the total fatigue damage reaches the preset failure threshold, it is determined that the marine structure has suffered fatigue failure. The remaining fatigue life of the marine structure is determined and output based on the ratio of the duration of the assessment to the total fatigue damage.

8. The method according to claim 1, characterized in that, After training to obtain the feature moment mapping model, the following steps are also included: Obtain the validation sample spectrum set, input the power spectrum features of the validation sample spectrum into the feature moment mapping model, and obtain the predicted higher-order moment sequence; The true higher-order moment sequence corresponding to the verification sample spectrum is obtained by using the narrow-band benchmark difference moment method. The predicted higher-order moment sequence is compared with the true higher-order moment sequence to confirm that the mapping error is within the preset accuracy range.

9. A fatigue damage assessment device for marine structures, characterized in that, include: The spectral moment analysis module is used to obtain the stress power spectral density function of the target marine structure under random loads and to calculate the spectral moments of the stress power spectral density function. The mapping sequence module is used to obtain a pre-established feature moment mapping model. The power spectral features of the stress power spectral density function are input into the feature moment mapping model to obtain the target higher-order moment sequence. The feature moment mapping model is trained based on the mapping relationship between the power spectral features of sample spectra with various power spectral shapes in the sample spectrum library and the corresponding true higher-order moment sequences. The true higher-order moment sequence is estimated from the stress time history data generated by the sample spectrum through the narrow-band benchmark difference moment method. The narrow-band benchmark difference moment method uses the narrow-band Rayleigh distribution analytical moments as a benchmark and reduces the estimation variance of higher-order moments through difference estimation. The projection correction module is used to perform semi-positive definite projection correction on the target higher-order moment sequence to obtain a legal moment sequence that satisfies the non-negative probability density constraint, and to reconstruct the stress range probability density function based on the legal moment sequence. The damage determination module is used to determine the total fatigue damage by frequency domain closed-loop integration based on the stress range probability density function, the pre-acquired material SN curve parameters and the spectral moments of each order. The process of establishing the characteristic moment mapping model includes: Construct a sample spectrum library, which includes marine engineering single-peak spectra, double-peak spectra, and various predetermined ideal spectra generated by parameterizing the number of spectral peaks, peak-frequency ratio, energy ratio, and spectral width parameters; For each sample spectrum in the sample spectrum library, multiple Gaussian random stress time histories are generated, and the dimensionless stress range sample of each time history is extracted by rainflow counting method; The narrowband benchmark difference moment method is adopted. For each sample spectrum, the narrowband Rayleigh distribution analytical moments are used as the benchmark. Based on the mean of the rainflow counting moments of multiple time histories, the difference between the mean of the narrowband estimated moments of the multiple time histories and the narrowband Rayleigh distribution analytical moments, and a correction coefficient, the true higher-order moment sequence after variance reduction is obtained. Extract the power spectrum features of each sample spectrum, and combine the power spectrum features with the corresponding ground truth higher-order moment sequence to form training samples, thereby training the feature moment mapping model. The process of determining the correction coefficient includes: The rainflow counting moments and narrowband estimation moments calculated from each of the multiple time histories are statistically analyzed to obtain the covariance estimate of the two and the variance estimate of the narrowband estimation moment. The ratio of the covariance estimate to the variance estimate is used as the correction coefficient. Wherein, the narrowband estimated moment is the corresponding order moment calculated for each time history based on the analytical moment expression of the narrowband Rayleigh distribution; The step of performing semi-positive definite projection correction on the target high-order moment sequence to obtain a legal moment sequence that satisfies the non-negativity probability density constraint includes: The target higher-order moment sequence is normalized using narrowband Rayleigh distribution analytical moments to obtain a normalized moment sequence. Based on the normalized moment sequence, a first Hankel matrix is ​​formed according to a preset first construction rule, and a second Hankel matrix is ​​formed according to a preset second construction rule; Determine whether both the first Hankel matrix and the second Hankel matrix satisfy the positive semidefinite condition; If either condition is not met, then under the constraint of keeping the values ​​of the lower-order normalized moments unchanged, the modified normalized moment sequence with the smallest difference from the current normalized moment sequence is obtained by convex optimization, and the first Hankel matrix and the second Hankel matrix are both positive semi-definite matrices. The legal moment sequence is obtained by inverse calculation from the corrected normalized moment sequence.

10. A fatigue damage assessment device for marine structures, characterized in that, Including memory and processor; The memory is used to store programs; The processor is used to execute the program to implement the various steps of the marine structural fatigue damage assessment method as described in any one of claims 1-8.

11. A readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements each step of the method for assessing fatigue damage to marine structures as described in any one of claims 1-8.

12. A computer program product, comprising a computer program, characterized in that, The computer program is executed by the processor to perform the steps of the fatigue damage assessment method for marine structures as described in any one of claims 1-8.

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