A non-constant amplitude interval random load equivalent compiling system and method

Abstract

The present application relates to the technical field of mechanical structure fatigue test and durability verification, in particular to a non-equal amplitude interval random load equivalent system and method, the system comprises preprocessing, feature extraction, clustering classification, optimal classification number determination, initial equivalent spectrum construction, loading sequence correction and simulation verification module. The method is: first, the original load spectrum is preprocessed and the cycle characteristics are extracted, the optimal classification number is determined by hierarchical clustering and multi-objective weighted comprehensive evaluation index, the initial equivalent spectrum is constructed, and the reference fatigue life and damage of the initial equivalent spectrum are obtained through simulation. Based on the Corten-Dolan model, a correction factor sensitive to the loading sequence is constructed, the simulation result is corrected, the life deviation caused by the loading sequence is compensated, and finally the error is ensured to be less than 15%. The present application retains more than 99% of the pseudo-damage of the original spectrum, shortens the loading time by 80%, balances the efficiency and accuracy, and is suitable for bench verification of complex mechanical structures such as electric drive systems.

Description

Technical Field

[0001] This invention relates to the field of mechanical structure fatigue testing and durability verification technology, specifically to a non-equal amplitude interval random load equivalent compilation system and method. Background Technology

[0002] In the durability verification of automotive assemblies, electric drive systems, and various core mechanical structures, the loads these structures experience during actual service often exhibit complex random amplitude characteristics. The load spectrum formed by these loads is a core factor directly determining the fatigue life of the structure. Therefore, systematically and scientifically compiling the original service load spectra of these structures to generate equivalent load spectra that accurately reflect actual load characteristics and have high loading efficiency has become a core technical requirement in this field for improving durability testing efficiency, ensuring verification accuracy, and reducing testing costs.

[0003] Currently, the mainstream load spectrum compilation methods in this field are mainly divided into the equal amplitude interval method and the non-equal amplitude interval method. The equal amplitude interval method, which divides load amplitudes into levels at equal intervals, is easy to implement, but it struggles to retain the core damage characteristics of the original load spectrum. This results in a significant deviation between the experimental results of the equivalent spectrum and the damage characteristics of the actual service load, failing to meet the high-precision durability verification requirements of complex mechanical structures. In contrast, the non-equal amplitude interval method, which divides load amplitudes into levels based on the difference in contribution of load cycles to fatigue damage, retains more core load information related to the structure's fatigue life and more closely reflects the actual loading conditions of the structure. Therefore, it has become the mainstream research direction for structural load spectrum compilation in this field.

[0004] However, existing non-equal amplitude interval load spectrum compilation techniques still face numerous technical bottlenecks that urgently need to be overcome. These issues directly restrict the improvement of the accuracy and efficiency of durability verification for complex mechanical structures. For example, patent document CN115510564A, entitled "A Multi-Level Load Spectrum Compilation Method, Storage Medium, and Equivalent Bench Durability Test Method for Automobile Stabilizer Bars," proposes a multi-level load spectrum compilation method for automobile stabilizer bar durability verification. This method constructs multi-level spectra by pre-setting the load interval width, rainflow decomposition, and finite element calculation, and uses the maximum damage value ratio as the basis for equivalence judgment. However, the load grading process of this method highly relies on empirical interval division and manual merging operations, lacking unified and quantitative optimization evaluation indicators, and cannot objectively measure the rationality of clustering results, thus limiting the verification accuracy.

[0005] For example, the patent document CN114036654A, entitled "A method for compiling a random multi-parameter fatigue test spectrum based on damage equivalence", focuses on achieving consistency of total fatigue damage under multi-axis random loads. Its load level classification depends on the cumulative frequency curve and the equal interval division method. The load spectrum is synthesized by random splicing, which leads to limited accuracy of life prediction.

[0006] For example, the patent document CN114297782A, entitled "Load Spectrum Processing Method, Apparatus, Equipment and Storage Medium", converts the random load spectrum into an equivalent load block spectrum through four-point cyclic statistics and level-through counting, and performs block spectrum correction based on pseudo-damage. It adopts order-independent damage equivalence logic, which leads to insufficient damage fitting accuracy between the equivalent spectrum and the original service spectrum.

[0007] In summary, existing techniques for compiling equivalent random loads with non-uniform amplitude intervals generally suffer from three major problems, which are analyzed in detail below:

[0008] 1. Existing equivalent spectrum compilation techniques rely heavily on manual experience or simple statistical methods to determine the number of load levels and level boundaries. The classification results are highly subjective and lack universality, making it difficult to achieve a quantitative trade-off between shortening loading time and improving damage fitting accuracy. This results in a trade-off between experimental efficiency and verification reliability.

[0009] 2. Existing equivalent spectrum compilation techniques are mostly based on the order-independent damage equivalence assumption, resulting in large lifetime prediction errors and failing to meet the high-precision durability verification requirements of complex mechanical structures.

[0010] 3. Existing equivalent spectrum compilation techniques are not adaptable to complex structures. For mechanical structures with complex load characteristics and sensitive damage mechanisms, such as electric drive systems, they either lose accuracy due to oversimplification of load information or have excessive loading time due to retaining too much redundant data, making it difficult to meet the rapid verification needs of actual engineering.

[0011] With the increasing demands for structural durability in fields such as new energy vehicles and aerospace, there is an urgent need for a method for compiling and correcting equivalent random loads with non-equal amplitude intervals that combines scientific rigor, high efficiency, and high precision. Summary of the Invention

[0012] The purpose of this invention is to address the shortcomings of existing technologies by providing an equivalent compilation system and method for non-equal amplitude interval random loads. This system can retain more than 99% of the pseudo-damage in the original service load spectrum while reducing the loading time by 80%, balancing efficiency and accuracy. It is suitable for bench verification of complex mechanical structures such as electric drive systems and has high engineering practical value.

[0013] The objective of this invention is achieved through the following approach:

[0014] A non-equal amplitude interval random load equivalent compilation system includes a preprocessing module, a feature extraction module, a clustering and grading module, an optimal grading number determination module, an initial equivalent spectrum construction module, a loading order correction module, and a simulation verification module;

[0015] The preprocessing module is used to receive the original service load spectrum collected during the service of the structure and output a standardized load time history.

[0016] The feature extraction module is used to receive the standardized load time history output by the preprocessing module, obtain the amplitude, mean and number of cycles for each load cycle, and output a set of feature vectors with amplitude, mean and number of cycles as elements;

[0017] The clustering and hierarchical module is used to receive the feature vector set output by the feature extraction module and output a preliminary non-uniform amplitude interval random load spectrum.

[0018] The optimal number of grade determination module is used to receive the non-equal amplitude interval random load spectrum output by the clustering and grading module, filter out the number of load level clusters that maximizes the multi-objective weighted comprehensive evaluation index, and use it as the optimal number of grade, and output each load level cluster corresponding to the optimal number of grade.

[0019] The initial equivalent spectrum construction module is used to receive the load level clusters corresponding to the optimal number of levels output by the optimal number of levels determination module, and output the initial equivalent load spectrum with non-equal amplitude intervals.

[0020] The loading order correction module is used to receive the initial equivalent load spectrum output by the initial equivalent spectrum construction module, and based on the Corten-Dolan model, introduces a fatigue index correction factor and outputs a life correction factor and a damage correction factor.

[0021] The simulation verification module receives the initial equivalent load spectrum output by the initial equivalent spectrum construction module, the correction factor output by the loading order correction module, and the original service load spectrum; it inputs the original service load spectrum and the initial equivalent load spectrum into the finite element fatigue simulation system to calculate the baseline fatigue life and baseline damage; then, it uses the correction factor to correct the baseline results to obtain the corrected fatigue life and corrected damage, and then calculates the fatigue life error and damage error.

[0022] If both fatigue life error and damage error meet the preset error threshold, then it is determined that they meet the preset accuracy requirements, and the final equivalent load spectrum is output.

[0023] If the fatigue life error or damage error does not meet the preset error threshold, it is determined that it does not meet the preset accuracy requirements. It can be returned to the optimal grade number determination module to optimize the error by re-selecting the optimal grade number, or returned to the loading order correction module to optimize the error by optimizing the fatigue index correction factor. The above determination and optimization process is repeated until the fatigue life error and damage error both meet the preset error threshold, and then the final equivalent load spectrum is output.

[0024] A method for equivalent compilation of non-uniform amplitude interval random loads using the above system includes the following steps:

[0025] 1) Input the original service load spectrum collected during the service of the structure into the preprocessing module, and perform noise reduction, filtering and resampling on the original service load spectrum to obtain a standardized load time history;

[0026] 2) Using the rainflow counting method, load cycle extraction is performed on the standardized load time history obtained in step 1) to obtain the amplitude, mean and number of cycles for each load cycle, resulting in a set of feature vectors with amplitude, mean and number of cycles as elements;

[0027] 3) Based on the Ward minimum variance criterion, using amplitude as the main clustering feature, hierarchical clustering is performed on the feature vector set obtained in step 2), and the intra-cluster centroid and sample variance of each load level cluster are dynamically updated until the intra-cluster sum of squares increments meet the convergence threshold, thus obtaining the preliminary non-equal amplitude interval random load spectrum.

[0028] 4) Based on the preliminary non-equal amplitude interval random load spectrum obtained in step 3), traverse all candidate grade numbers within the preset range, calculate the overall profile coefficient and pseudo-damage relative error of each candidate grade number, construct a multi-objective weighted comprehensive evaluation index, and select the load grade cluster number that maximizes the multi-objective weighted comprehensive evaluation index as the optimal grade number, and obtain the load grade clusters corresponding to the optimal grade number.

[0029] 5) Based on the load level clusters corresponding to the optimal number of grades obtained in step 4), the average amplitude within the cluster is used as the equivalent amplitude, and the sum of the number of cycles within the cluster is used as the equivalent cycle number. The clusters are sorted from largest to smallest according to the equivalent amplitude to obtain the initial equivalent load spectrum with non-equal amplitude intervals.

[0030] 6) Based on the Corten–Dolan model, the fatigue index correction factor is introduced into the initial equivalent load spectrum obtained in step 5), and the corrected fatigue life, damage correction factor, and life correction factor are calculated. The life correction factor and damage correction factor are also calculated.

[0031] 7) Input the original service load spectrum and the initial equivalent load spectrum obtained in step 5) into the finite element fatigue simulation system to calculate the reference fatigue life and reference damage at the maximum damage point of the structure; then use the life correction factor and damage correction factor obtained in step 6) to correct the reference fatigue life and reference damage to obtain the corrected fatigue life and corrected damage; then calculate the life error between the corrected fatigue life and the original fatigue life, and the damage error between the corrected damage and the original damage.

[0032] If both fatigue life error and damage error meet the preset error threshold, the corrected equivalent load spectrum will be output as the final equivalent spectrum.

[0033] If the preset error threshold is not met, return to step 4), perform iterative optimization by adjusting the weighting coefficient or optimizing the fatigue index correction factor, and repeat steps 4) to 7) until the error meets the preset error threshold, and output the final equivalent load spectrum.

[0034] Preferably, in step 2), the rainflow counting method includes a two-parameter rainflow counting method.

[0035] Preferably, in step 3), the increment of the sum of squared deviations within a class is calculated according to the following formula:

[0036] ;

[0037] In the formula, For the increment of the sum of squared deviations within the class, The sequence number of a single load cycle in the original load spectrum (with values...) =1, 2, 3, ... ( (This represents the total number of independent load cycle samples extracted from the original load spectrum). For the original load spectrum to be compared with the first The sequence number of another load level cluster merged from one load level cluster ( ≠ ), For the first to be merged The total number of cycles for each load level cluster. For the first to be merged The total number of cycles for each load level cluster. For the first Intraclass centroids of each load level cluster, For the first Intraclass centroids of each load level cluster.

[0038] Preferably, in step 3), after hierarchical clustering is completed, the maximum amplitude value in all load level clusters is automatically identified, load level clusters with amplitude values ​​less than 10% of the maximum amplitude value are deleted, and the cumulative pseudo-damage of the remaining load level clusters is verified and ensured to be no less than 99% of the cumulative pseudo-damage of the original service load spectrum.

[0039] Preferably, in step 4), the multi-objective weighted comprehensive evaluation index is calculated according to the following formula:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] In the formula, The number of load level clusters, For the number of load levels Multi-objective weighted comprehensive evaluation index at time, These are the weighting coefficients for the profile coefficients. For the number of load levels The average profile coefficient at that time, The number of candidate payload levels is Time corresponding The minimum value, The number of candidate payload levels is Time corresponding The maximum value, The weighting coefficients for the relative error of spurious damage. For the number of load levels The relative error of pseudo-damage at that time The number of candidate payload levels is Time corresponding The minimum value, The number of candidate payload levels is Time corresponding The maximum value, This represents the total number of independent load cycle samples extracted from the original load spectrum. This refers to the sequence number of the original load cycle sample. For the first Profile coefficients of a single load cycle sample. For the first The average distance between a load cycle sample and all other load cycle samples in the same cluster For the first The average distance between a cyclic load sample and all cyclic load samples in its nearest neighbor cluster (not its own cluster). For the number of load levels The fatigue pseudo-damage value of the equivalent load spectrum at that time. The fatigue pseudo-damage value is the original load spectrum. The first in the equivalent load spectrum The amplitude of each load cycle, The first in the equivalent load spectrum The total number of cycles for each load cycle. This represents the total number of independent load cycles in the equivalent load spectrum. This is a pseudo-damage index. The first in the original load spectrum The amplitude of each load cycle, The first in the original load spectrum The total number of cycles for each load cycle.

[0048] Preferably, in step 6), the corrected fatigue life is calculated according to the following formula:

[0049] ;

[0050] ;

[0051] ;

[0052] In the formula, The sequence number of the load level cluster ( =1,2,3,... ), This represents the total number of load level clusters (i.e., the optimal number of levels). To take into account the structural fatigue life after loading sequence correction (i.e. the total number of cycles the structure can withstand before fatigue failure under the current equivalent load spectrum). To the maximum load amplitude The number of cycles required for the structure to undergo fatigue failure under individual action. For the first The equivalent amplitude of the load class cluster, The maximum amplitude value among all load level clusters. For the first Cyclic percentage of load class clusters For the first The corrected fatigue index corresponding to the load level cluster. For the first Total number of cycles for each load class cluster When arranged in loading order, the first The equivalent amplitude of the load class cluster, This is the basic fatigue index of the material.

[0053] Preferably, the damage correction factor and lifetime correction factor in step 6) are calculated according to the following formula:

[0054] ;

[0055] ;

[0056] In the formula, It is a damage correction factor (reflecting the degree of influence of loading sequence on fatigue damage). To account for the corrected pseudo-damage in the equivalent load spectrum after loading sequence correction, The baseline pseudo-damage for the equivalent load spectrum without considering the loading order. This is the life correction factor (reflecting the degree of influence of loading sequence on fatigue life). To account for the modified fatigue life of the structure after the loading sequence is adjusted, This represents the baseline fatigue life of the structure without considering the loading sequence.

[0057] Preferably, in step 7), the fatigue life error and damage error are calculated according to the following formula:

[0058] ;

[0059] ;

[0060] In the formula, The final pseudo-damage relative error (reflects the degree of deviation between the corrected pseudo-damage and the baseline pseudo-damage, and is expressed as a percentage). It is the damage correction factor (i.e., the ratio of the corrected spurious damage to the baseline spurious damage). The final fatigue life relative error (reflects the degree of deviation between the corrected life and the reference life, and is expressed as a percentage). This is the life correction factor (i.e., the ratio of the corrected life to the baseline life).

[0061] The beneficial effects of this invention are as follows:

[0062] 1. This invention, through non-equal amplitude interval grading and redundant level elimination (removing levels with amplitudes below 10% of the maximum amplitude), reduces the total loading time to 20% of the original spectrum (i.e., a reduction of 80%) while retaining over 99% of the spurious damage in the original service spectrum, significantly improving the test efficiency of the bench. Simultaneously, this invention constructs structured spectrum blocks by sorting load level clusters according to amplitude from largest to smallest, resulting in clear loading logic that is suitable for engineering test scenarios, especially for structures requiring batch verification, such as the output shaft of an electric drive system motor.

[0063] 2. This invention constructs a multi-objective weighted comprehensive evaluation index of "profile coefficient + pseudo-damage relative error", traverses the load level number in the range of 4 to 64, and selects the optimal solution that maximizes the comprehensive index. This avoids the problems of traditional technology where the number of levels depends on manual experience and the classification logic is inconsistent, and realizes the theorization and automation of the classification.

[0064] 3. This invention employs the Ward minimum variance criterion for hierarchical clustering, dynamically updating intra-cluster centroids and sample variances during the clustering process to minimize the increment of the sum of squared deviations within clusters, ensuring superior intra-cluster compactness and inter-cluster separation. Furthermore, by using load amplitude as the core clustering feature and employing a non-equal amplitude interval partitioning method, this invention better reflects the differences in load contribution to damage compared to the traditional equal amplitude interval method. This preserves more fatigue information from the original service load spectrum. Moreover, by removing low-contribution load levels, it strictly ensures a spurious damage retention rate of ≥99%, balancing "improved loading efficiency" and "damage characteristic preservation," effectively avoiding equivalence deviations caused by indiscriminate deletion.

[0065] 4. This invention breaks through the traditional "sequence-independent" damage equivalence assumption. By constructing a fatigue index correction factor sensitive to loading sequence using the Corten-Dolan model, and then adjusting the fatigue index by the amplitude ratio of adjacent load levels, a loading sequence-sensitive life / damage correction model is established. This effectively compensates for the life prediction error caused by changes in the high and low load sequence, ensuring that the fatigue life error and damage error of the corrected equivalent spectrum can be controlled within 15%. This effectively ensures the good fit between the equivalent spectrum and the original service load spectrum, fully meeting the accuracy requirements of engineering verification. Furthermore, this invention, through its clearly defined life correction factor and damage correction factor, can be directly embedded into finite element and fatigue simulation models. The correction logic is clear and quantifiable, facilitating practical application by engineers.

[0066] 5. This invention is applicable to electric drive systems, vehicle transmission systems and other engineering structures with variable amplitude fatigue loads, especially for non-equal amplitude interval random load scenarios, filling the gap in the existing technology for the targeted compilation of equivalent spectrum of complex mechanical structures.

[0067] 6. This invention forms a closed-loop process of “grading-correction-verification-iteration” by comparing the fatigue life of the maximum damage node and the cumulative damage value of the original service load spectrum and the corrected equivalent spectrum. If the error does not meet the requirements, the weighting coefficient can be adjusted to re-determine the optimal grading number, so as to ensure the reliability and stability of the final equivalent spectrum.

[0068] Glossary

[0069] Original service load spectrum: In this invention, the original service load spectrum refers to the set of load time history signals that reflect the actual stress state of a structure during actual use (service), collected by sensors and other devices. It serves as the foundational raw data for subsequent equivalent load spectrum compilation, fatigue damage analysis, and durability verification. Specifically, the original service load spectrum is a complete record of the random amplitude loads borne by a structure (such as an electric drive system or vehicle transmission system) in a real working scenario. It is presented as a history curve with time on the horizontal axis and load (such as torque or force) on the vertical axis. It includes core features such as load amplitude, mean, and number of cycles. Without equivalent simplification, classification, or correction, only basic preprocessing such as denoising, filtering, and resampling is required to extract load cycle information for fatigue analysis.

[0070] Non-equal amplitude interval random load spectrum: In this invention, the non-equal amplitude interval random load spectrum refers to a random load spectrum formed by dividing load amplitude levels in a non-equal interval manner according to the differences in the contribution of load cycles to structural fatigue damage. This is the core technical form that distinguishes it from the traditional equal amplitude interval load spectrum. Specifically, this load spectrum does not divide levels based on a fixed amplitude interval, but dynamically determines the level boundaries based on the degree of damage contribution. It can retain more key load information directly related to the fatigue life of the structure, and is more in line with the actual loading conditions of complex mechanical structures such as electric drive systems. It is the core carrier for this invention to achieve efficient and high-precision equivalent compilation.

[0071] Equivalent Load Spectrum: In this invention, the equivalent load spectrum refers to a simplified load spectrum generated based on the original service load spectrum after preprocessing, feature extraction, hierarchical clustering, optimal number of levels selection, loading order correction, and simulation verification. It can directly replace the original spectrum for bench fatigue durability testing. Specifically, this equivalent spectrum retains over 99% of the spurious damage from the original service load spectrum while reducing the loading time by 80%, and simultaneously controlling both fatigue life error and damage error within 15%, achieving a balance between testing efficiency and verification accuracy, making it suitable for batch engineering verification scenarios.

[0072] Pseudo-damage: In this invention, pseudo-damage refers to a relative fatigue damage metric calculated based on the material fatigue index and weighted by the load amplitude and the number of cycles. It does not represent actual structural damage and is only used to quantitatively measure the contribution of the load spectrum to fatigue. Specifically, pseudo-damage is defined by the formula... Calculation, where For load amplitude, For the number of loops, The fatigue index is the core evaluation criterion for the present invention in selecting load levels, determining the optimal number of grades, verifying equivalence, and calculating correction factors.

[0073] Rainflow counting method: In this invention, the rainflow counting method refers to a standard fatigue statistical method for extracting discrete load cycle characteristics from the time history of continuous random loads. It is the core means of load spectrum preprocessing and cycle extraction. Specifically, this method can automatically identify and count the amplitude, mean, and corresponding number of cycles for each load cycle, converting the continuous load signal into discrete cycle data that can be used for cluster analysis and damage calculation, providing basic feature input for subsequent non-uniform amplitude interval grading.

[0074] Two-parameter rainflow counting method: In this invention, the two-parameter rainflow counting method refers to a preferred implementation of the rainflow counting method, which can simultaneously extract two key parameters of load cycle: amplitude and mean, unlike the single-parameter rainflow counting method that only extracts amplitude. Specifically, this method can output a feature vector containing amplitude, mean, and cycle number, meeting the requirements of hierarchical clustering for multi-dimensional features, improving the accuracy of load grading and pseudo-damage calculation, and is the core method of the feature extraction stage of this invention.

[0075] Hierarchical Clustering (Ward's Minimum Variance Criterion): In this invention, hierarchical clustering (Ward's minimum variance criterion) refers to a hierarchical clustering algorithm that aims to minimize the increment of the sum of squared deviations within each cluster and uses load amplitude as the main clustering feature. It is used to automatically classify non-uniform amplitude intervals of load cycles. Specifically, this algorithm dynamically updates the intra-cluster centroids and sample variances of each load level cluster during the clustering process, successively merging the optimal cluster pairs until the convergence condition is met. This ensures that the clustering results possess optimal intra-cluster compactness and inter-cluster separation, avoiding the shortcomings of traditional equal-interval classification and empirical classification.

[0076] Increment of Intra-Clan Sum of Squares: In this invention, the increment of the intra-clan sum of squares refers to the change in the sum of squares of intra-clan deviations resulting from merging any two loading level clusters when using the Ward minimum variance criterion for hierarchical clustering. It is a core quantitative indicator for determining the rationality of cluster merging. Specifically, this increment is expressed by the formula... The smaller the value, the more compact the data within the cluster after merging and the better the clustering effect, which directly determines the quality of the non-equal amplitude interval classification.

[0077] Silhouette coefficient: In this invention, the silhouette coefficient is an index used to quantitatively evaluate the intra-cluster compactness and inter-cluster separation of clustering results. Its value ranges from -1 to 1, and it is one of the core criteria for selecting the optimal number of gradations. Specifically, the silhouette coefficient of a single sample is expressed by the formula... The overall silhouette coefficient is calculated as the mean of all samples. The closer the value is to 1, the more concentrated the clusters are and the more separated the clusters are, resulting in a more ideal grading effect.

[0078] Multi-objective weighted comprehensive evaluation index: In this invention, the multi-objective weighted comprehensive evaluation index refers to a comprehensive evaluation function constructed by weighting the contour coefficient and the relative error of pseudo-damage after normalization, used to automatically and quantitatively select the optimal load level. Specifically, this index is expressed by the formula... The calculation balances clustering quality and damage equivalence, using default weighting coefficients. It can be adjusted according to engineering needs to achieve a quantitative trade-off between efficiency and accuracy.

[0079] Optimal number of levels: In this invention, the optimal number of levels refers to the number of levels that, after traversing the candidate number of levels, makes the multi-objective weighted comprehensive evaluation index... The number of load level clusters with the maximum value is the core parameter for achieving automated and quantitative grading in this invention. Specifically, this number of gradations does not require manual experience to set; it is automatically selected through an algorithm. This ensures a pseudo-damage retention rate of ≥99% while minimizing the number of load levels and shortening the test loading time.

[0080] The Corten–Dolan model: In this invention, the Corten–Dolan model refers to a cumulative damage prediction model that considers the impact of loading sequence on fatigue life. It differs from the traditional order-independent Miner cumulative damage model and is the fundamental theoretical model for loading sequence-sensitive correction in this invention. Specifically, this model can reflect the nonlinear influence of high and low load order on fatigue life. By introducing a fatigue index correction mechanism, it compensates for life prediction deviations caused by changes in loading sequence, thereby improving the accuracy of the equivalent spectrum.

[0081] Fatigue index correction factor: In this invention, the fatigue index correction factor refers to a correction coefficient constructed based on the amplitude ratio of adjacent load levels and strongly correlated with the loading sequence, used to adjust the original fatigue index of the Corten-Dolan model. Specifically, this factor is expressed by the formula... The calculation, which can dynamically correct the fatigue index according to the loading order of the load level and accurately compensate for the life deviation caused by the change of high and low load sequence, is the core innovative correction method of this invention.

[0082] Damage Correction Factor: In this invention, the damage correction factor refers to the ratio of the pseudo-damage in the corrected equivalent load spectrum to the pseudo-damage in the original service load spectrum. It is used to quantify the degree of damage fit between the equivalent spectrum and the original spectrum, providing a basis for damage correction in fatigue simulation. Specifically, this factor is expressed by the formula... The calculation directly reflects the degree to which the equivalent spectrum retains the damage characteristics of the original spectrum, and is a key parameter for determining the effectiveness of the equivalent spectrum.

[0083] Lifetime Correction Factor: In this invention, the lifetime correction factor refers to the ratio of the fatigue life of the corrected equivalent load spectrum to the fatigue life of the original service load spectrum. It is used to compensate for lifetime prediction errors caused by the loading sequence and improve the accuracy of equivalent spectrum lifetime calculation. Specifically, this factor is expressed by the formula... The calculation can be directly embedded into the finite element fatigue simulation model to achieve rapid correction of equivalent spectrum life deviation.

[0084] Fatigue life error: In this invention, fatigue life error refers to the relative error between the corrected equivalent load spectrum and the original service load spectrum at the point of maximum structural damage, used to verify the accuracy of the equivalent spectrum life prediction. Specifically, this error is expressed by the formula... According to calculations, this invention requires the error to be less than 15% to meet the engineering accuracy requirements for durability verification of complex mechanical structures.

[0085] Damage Error: In this invention, damage error refers to the relative error between the corrected equivalent load spectrum and the original service load spectrum at the point of maximum structural damage, used to verify the equivalence of the equivalent spectrum damage. Specifically, this error is expressed by the formula... The calculations in this invention require that the error be less than 15% to ensure that the fatigue damage characteristics of the equivalent spectrum are highly consistent with those of the original spectrum. Attached Figure Description

[0086] Figure 1 This is a schematic diagram of the equivalent compilation system for non-equal amplitude interval random loads in this invention;

[0087] Figure 2 This is a flowchart illustrating the method for equivalent compilation of non-equal amplitude interval random loads in an embodiment of the present invention.

[0088] Figure 3 This is a schematic diagram of the installation and arrangement of the sensors and equipment for acquiring the electric drive torque signal in an embodiment of the present invention;

[0089] Figure 4 This is a schematic diagram of the torque load spectrum of the motor output shaft of the electric drive system after load spectrum preprocessing in an embodiment of the present invention.

[0090] Figure 5 This is a graph showing the relationship between the profile coefficient and the relative error of pseudo-damage as a function of the number of load levels in an embodiment of the present invention.

[0091] Figure 6 This is a graph showing the change of the multi-objective weighted comprehensive evaluation index when determining the optimal number of levels in an embodiment of the present invention;

[0092] Figure 7 This is a schematic diagram of the equivalent load spectrum with non-equal amplitude intervals compiled in an embodiment of the present invention. Detailed Implementation

[0093] like Figure 1 As shown, a non-equal amplitude interval random load equivalent compilation system includes a preprocessing module, a feature extraction module, a clustering and grading module, an optimal grading number determination module, an initial equivalent spectrum construction module, a loading order correction module, and a simulation verification module. The modules are connected sequentially according to the data flow direction. The simulation verification module simultaneously receives the original service load spectrum, forming a closed-loop optimization mechanism of "grading-correction-verification-iteration".

[0094] 1. Preprocessing module

[0095] The preprocessing module is used to receive the original service load spectrum collected during the actual service of the structure, perform noise reduction, filtering and resampling on the original random load spectrum, remove interference noise in the signal, smooth signal fluctuations, unify the sampling frequency and data format, and output a standardized load time history.

[0096] 2. Feature Extraction Module

[0097] The feature extraction module receives the standardized load time history output by the preprocessing module, uses the two-parameter rainflow counting method to extract load cycles from the standard load spectrum, obtains the amplitude, mean and corresponding number of cycles for each load cycle, and outputs a set of standardized feature vectors with amplitude, mean and number of cycles as core elements.

[0098] 3. Clustering and Hierarchical Module

[0099] The clustering and hierarchical module receives the feature vector set of each load cycle output by the feature extraction module. It uses the amplitude of the feature vector of each load cycle as the main clustering feature to construct the Euclidean distance matrix. The Ward minimum variance criterion is used to perform hierarchical clustering on the feature vector set of each load cycle. During each iteration of the clustering process, the intra-cluster centroid and sample variance of each load level cluster are dynamically updated. The clustering objective is to minimize the increment of the sum of squared deviations within the cluster. After the clusters are merged, a preliminary non-equal amplitude interval random load spectrum is obtained.

[0100] 4. Optimal number of gradations determination module

[0101] The optimal grade number determination module receives the non-uniform amplitude interval random load spectrum output by the clustering and grading module. By traversing all candidate grade numbers within a preset range, it calculates the overall profile coefficient and pseudo-damage relative error corresponding to each grade number. After normalizing these two indicators, it constructs a multi-objective weighted comprehensive evaluation index, selects the number of load grade clusters that maximizes the comprehensive evaluation index as the optimal grade number, and outputs each load grade cluster corresponding to the optimal grade number. This achieves full automation and quantification of the load grading process, completely eliminating the reliance on human experience in traditional methods.

[0102] 5. Initial Equivalent Spectrum Construction Module

[0103] The initial equivalent spectrum construction module receives the load level clusters corresponding to the optimal number of load levels output by the optimal number of load levels determination module. It uses the mean amplitude within the cluster as the equivalent amplitude of the load level cluster and the sum of the number of load cycles within the cluster as the equivalent cycle number of the equivalent load. It sorts all load level clusters in descending order of equivalent amplitude, constructs structured spectrum blocks, and outputs an initial equivalent load spectrum with non-equal amplitude intervals that can be directly used for bench loading.

[0104] 6. Loading order correction module

[0105] The loading order correction module receives the initial equivalent load spectrum output by the initial equivalent spectrum construction module. Based on the Corten–Dolan fatigue cumulative damage model, it introduces a fatigue index correction factor, dynamically adjusts the material fatigue index according to the amplitude ratio of adjacent load levels, establishes a loading order-sensitive lifetime / damage correction model, calculates and generates damage correction factor and lifetime correction factor, and provides a basis for loading order correction for subsequent simulation verification.

[0106] 7. Simulation Verification Module

[0107] The simulation verification module receives the initial equivalent load spectrum output by the initial equivalent spectrum construction module, the correction factor output by the loading order correction module, and the original service load spectrum collected during the structure's service life. It imports the original service load spectrum and the initial equivalent load spectrum into the finite element fatigue simulation system (a finite element model built on Abaqus and NcodeDesignLife fatigue analysis software), respectively, to calculate the baseline fatigue life and baseline damage of the target structure under the two types of load spectra. Then, it uses the correction factor to correct the baseline fatigue life and baseline damage, obtaining the corrected fatigue life and corrected damage. Finally, it calculates the fatigue life error and damage error of the corrected equivalent spectrum relative to the original service load spectrum.

[0108] If both fatigue life error and damage error meet the preset error threshold, then it is determined that they meet the preset accuracy requirements, and the final equivalent load spectrum is output.

[0109] If the fatigue life error or damage error does not meet the preset error threshold, it is determined that it does not meet the preset accuracy requirements. In this case, a reselection instruction can be sent to the optimal grade number determination module to re-select the optimal grade number, and / or an optimization instruction can be sent to the loading order correction module to adjust the fatigue index correction factor. The simulation calculation, error comparison and optimization iteration process is repeated until both errors meet the preset threshold, ensuring that the final output equivalent spectrum has engineering applicability and reliability.

[0110] like Figure 2As shown, the method for equivalent compilation of non-uniform amplitude interval random loads using the above system includes the following steps:

[0111] 1) Preprocessing of the original load spectrum

[0112] The original load time history collected during the service of the structure is input into the preprocessing module. The original service load spectrum is then processed by denoising, filtering, and resampling to eliminate environmental interference noise, signal spikes, and data sampling inconsistencies. The data format and sampling frequency are unified to obtain a standardized load time history.

[0113] 2) Load Cyclic Feature Extraction

[0114] The standardized load time history obtained in step 1) is extracted using a two-parameter rainflow counting method to obtain the amplitude of each load cycle. mean and the corresponding number of loops Construct a feature vector specific to each load cycle. Ultimately, the amplitude is obtained. mean and number of loops It is the set of eigenvectors of the elements.

[0115] in, This represents the sequence number of a single load cycle in the original load spectrum. =1, 2, ..., ( (This represents the total number of independent load cycle samples extracted from the original load spectrum).

[0116] 3) Hierarchical clustering based on Ward's criterion

[0117] The magnitude of the eigenvector obtained in step 2) Load grading is performed based on the main clustering features, and a Euclidean distance matrix is ​​constructed. Hierarchical clustering is performed using the Ward minimum variance criterion, and successive merging increases the sum of squared deviations within each cluster. The smallest cluster pair dynamically updates the intra-cluster centroid (i.e., the mean amplitude of all load cycles within the cluster) and sample variance in each iteration, while continuously updating the Euclidean distance matrix. Until the increment of the sum of squared deviations within the class. The convergence threshold is met (the threshold can be flexibly adjusted according to engineering accuracy requirements). After hierarchical clustering is completed, the maximum amplitude value in all load level clusters is automatically identified, and load levels with amplitude values ​​less than 10% of the maximum amplitude value are deleted. Simultaneously, it is verified and ensured that the cumulative pseudo-damage of the remaining load level clusters is not less than 99% of the cumulative pseudo-damage of the original service load spectrum, thus obtaining a preliminary non-uniform amplitude interval random load spectrum. This preliminary non-uniform amplitude interval random load spectrum includes... Cluster The mean amplitude in each cluster It can be used for validity screening of load cycles (removing abnormal loads whose average amplitude exceeds the structural service range), and the total number of cycles. Used to determine the frequency of action of each load level.

[0118] 3-1) Euclidean distance matrix Construction

[0119] This invention uses Euclidean distance to measure the amplitude difference between load cycles and performs hierarchical clustering by constructing a distance matrix:

[0120] ;

[0121] In the formula, For the first The load cycle and the first The Euclidean distance between load cycles is used to measure the degree of difference in amplitude characteristics between two load cycles. For the first The amplitude eigenvector of each load cycle, For the first The amplitude eigenvector of each load cycle.

[0122] in, The smaller the value, the closer the amplitudes of the two load cycles are, and the more suitable they are to be classified into the same cluster; The larger the value, the greater the difference in amplitude, and they should be classified into different clusters.

[0123] 3-2) Increment of the sum of squared deviations within a class Calculation

[0124] ;

[0125] ≠ ;

[0126] In the formula, For the increment of the sum of squared deviations within the class, This represents the sequence number of a single load cycle in the original load spectrum. For the original load spectrum to be compared with the first The sequence number of another load level cluster merged from the previous load level cluster. For the first The total number of cycles for each load level cluster. For the first The total number of cycles for each load level cluster. For the first Intraclass centroids of each load level cluster, For the first Intraclass centroids of each load level cluster.

[0127] in, Used to measure the first The load level cluster and the first The increase in intra-class discreteness after merging multiple load level clusters into a new cluster. The smaller the value, the closer the mean amplitudes of the two clusters are, the more balanced the sample size distribution, the less the increase in intra-class dispersion after merging, and the more compact the clustering effect. The larger the amplitude mean, the greater the difference between the two clusters. Merging them will significantly increase the amplitude dispersion of the loads within the new cluster, disrupting the compactness of the clustering. Therefore, these two clusters should not be merged; other clusters should be selected instead. Smaller clusters are merged.

[0128] 4) Automatic determination of the optimal number of levels

[0129] For the non-uniform amplitude interval random load spectrum obtained in step 3), traverse all candidate levels within the preset range, and calculate the overall profile coefficient and pseudo-damage relative error for each candidate level:

[0130] 4-1) The number of load ratings is Average profile coefficient at time The is used to measure the intra-cluster compactness and inter-cluster separation of clustering results, and is calculated using the following formula:

[0131] ;

[0132] ;

[0133] ;

[0134] In the formula, The number of load level clusters, For the number of load levels The average profile coefficient at that time, This represents the total number of independent load cycle samples extracted from the original load spectrum after rainflow counting. This represents the sequence number of a single load cycle in the original load spectrum. For the first Profile coefficients of a single load cycle sample. For the first The average distance between a load cycle sample and all other load cycle samples in the same cluster For the first The average distance between a cyclic load sample and all cyclic load samples in its nearest neighbor cluster (not its own cluster).

[0135] In this invention, Used to evaluate the The clustering results for each load cycle are as follows:

[0136] when When the value is approximately 1, it indicates that the clustering effect is good and the samples are closely associated with the current cluster.

[0137] when When the value is approximately 0, it indicates that the sample is located at the cluster boundary, and the clustering effect is generally poor.

[0138] when When the value is approximately -1, it indicates that the sample is more suitable to be assigned to another cluster, indicating a clustering error.

[0139] Used to measure the number of load levels The average clustering quality across all load cycles during the time period, with values ​​ranging from [-1, 1]. The closer the value is to 1, the better the clustering effect, and the better the intra-cluster compactness and inter-cluster separation.

[0140] 4-2) The number of load ratings is relative error of pseudo-damage at time This is used to measure the damage fitting accuracy between the equivalent load spectrum and the original load spectrum, and is calculated using the following formula:

[0141] 4-2-1) Calculation of fatigue pseudo-damage value corresponding to the original load spectrum

[0142] ;

[0143] In the formula, The fatigue pseudo-damage value is the original load spectrum. The first in the original load spectrum The amplitude of each load cycle, The first in the original load spectrum The total number of cycles for each load cycle. This represents the total number of independent load cycle samples extracted from the original load spectrum. This is a pseudo-damage index.

[0144] 4-2-2) The number of load levels is Calculation of fatigue pseudo-damage value corresponding to equivalent load spectrum at time

[0145] ;

[0146] In the formula, For the number of load levels The fatigue pseudo-damage value corresponding to the equivalent load spectrum at that time. The first in the equivalent load spectrum The amplitude of each load cycle, The first in the equivalent load spectrum The total number of cycles for each load cycle. This represents the total number of independent load cycles in the equivalent load spectrum. This is a pseudo-damage index.

[0147] It is worth noting that the pseudo-damage index in this invention The power exponent, derived from the fatigue curve of SN materials, ranges from 3 to 6. Among them, the pseudo-damage index of high-strength steel... The recommended value is 4.8.

[0148] 4-2-3) Relative error of spurious damage Calculation

[0149] ;

[0150] In the formula, This is the relative error of spurious damage. For the number of load levels The fatigue pseudo-damage value corresponding to the equivalent service load spectrum at that time. This represents the fatigue pseudo-damage value corresponding to the original load spectrum.

[0151] In this invention, the relative error of pseudo-damage Used to verify the damage equivalence between the graded equivalent load spectrum and the original load spectrum, and the relative error of the pseudo-damage. The smaller the value, the higher the damage fitting accuracy between the equivalent load spectrum and the original load spectrum; in other words, the better the equivalent load spectrum preserves the fatigue damage characteristics of the original load spectrum. In practical applications, it is usually required that... <15% to ensure the reliability of the equivalent load spectrum.

[0152] Then, the load level number is Overall profile coefficient at time False damage relative error After normalization, a multi-objective weighted comprehensive evaluation index is constructed based on preset weighting coefficients. :

[0153] 4-3) Calculation of multi-objective weighted comprehensive evaluation index:

[0154] ;

[0155] In the formula, The number of load level clusters, For the number of load levels Multi-objective weighted comprehensive evaluation index at time, These are the weighting coefficients for the profile coefficients. For the number of load levels The overall profile coefficient at that time, The number of candidate payload levels is The minimum value of the profile coefficient at that time. The number of candidate payload levels is The maximum value of the profile coefficient at that time. The weighting coefficients for the relative error of spurious damage. For the number of load levels The relative error of pseudo-damage at that time The number of candidate payload levels is The minimum value of the relative error of pseudo-damage at that time. The number of candidate payload levels is The maximum value of the relative error of pseudo-damage at that time.

[0156] In this invention, Used for comprehensive evaluation of load classification numbers The quality of is determined by the value in the range [0, 1]. Maximum This represents the optimal number of levels.

[0157] in, For the number of load levels When the value is close to 1, the normalized value of the overall profile coefficient ranges from [0, 1]. The closer the value is to 1, the better the intra-cluster compactness and inter-cluster separation of the clustering results.

[0158] For the number of load levels When the normalized correction value of the relative error of the pseudo-damage is in the range of [0, 1], the larger the value, the higher the damage fitting accuracy between the equivalent spectrum and the original spectrum.

[0159] (default = =0.5), and of course, it can be adjusted according to the engineering requirements for clustering quality or damage accuracy.

[0160] By iterating through the comprehensive evaluation indicators corresponding to the number of clusters at different load levels, the indicators that make the comprehensive evaluation indicators... The maximum number of load level clusters is taken as the optimal number of levels.

[0161] 5) Construct the initial equivalent load spectrum

[0162] Based on the optimal number of grades obtained in step 4), the load level clusters corresponding to each cluster are calculated using the average amplitude within the cluster. As the equivalent amplitude for the corresponding level, it is the sum of the number of cycles within the cluster. As the equivalent cycle number for the corresponding level, the equivalent amplitude of all levels is grouped with the equivalent cycle number, and then the entire dataset is sorted from largest to smallest equivalent amplitude to form a structured, non-equal amplitude interval initial equivalent load spectrum that can be directly used for bench loading. .

[0163] Among them, the equivalent cycle number of each load level cluster Calculate using the following formula:

[0164] ;

[0165] In the formula, For the first Each load level cluster For the first load level clusters The total number of loops, The first in the original load spectrum The number of cycles for each independent load cycle.

[0166] The equivalent cycle number of each load level cluster The average amplitude of the cluster Pairing to form the basic units of the equivalent load spectrum It is used to construct equivalent load spectra with non-equal amplitude intervals.

[0167] 6) Loading order sensitive fix

[0168] First, based on the Corten–Dolan fatigue cumulative damage model, a fatigue index correction factor is constructed for the initial equivalent load spectrum obtained in step 5) according to the amplitude ratio of adjacent load levels. The initial fatigue index is then corrected using this correction factor to obtain the corrected fatigue index. Finally, the corrected fatigue life corresponding to the load spectrum is calculated based on the corrected fatigue index. By combining the fatigue life and cumulative damage results before and after the correction, the damage correction factor is further obtained. With lifespan correction factor This is used for subsequent sensitive correction of loading order effects on simulation results.

[0169] The corrected fatigue life is calculated according to the following formula:

[0170] ;

[0171] ;

[0172] ;

[0173] In the formula, The sequence number of the load level cluster ( =1,2,3,... ), This represents the total number of load level clusters (i.e., the optimal number of levels). To take into account the structural fatigue life after loading sequence correction (i.e. the total number of cycles the structure can withstand before fatigue failure under the current equivalent load spectrum). To the maximum load amplitude The number of cycles required for the structure to undergo fatigue failure under individual action. For the first The equivalent amplitude of the load class cluster, The maximum amplitude value among all load level clusters. For the first Cyclic percentage of load class clusters (i.e., the first load class cluster) The proportion of the number of cycles for each load level cluster to the total number of cycles is used to reflect the contribution weight of each load level to the total damage. For the first Corrected fatigue index for load class clusters. For the first Total number of cycles for each load class cluster When arranged in loading order, the first The equivalent amplitude of the load class cluster, This is the basic fatigue index of the material.

[0174] In this invention, the fatigue index is corrected. Based on the ratio of adjacent load amplitudes The decision is made when the load is applied in either a "large to small" or "small to large" order. Changes will occur, thus altering the final fatigue life. This invention solves the problem of the traditional Corten–Dolan model ignoring the loading order. Furthermore, this invention equates multi-level loads to the maximum load. Lifespan under action Through weight and the correction index Weighted summation of the damage contributions from each load level ensures damage equivalence, making... It can accurately reflect the fatigue life of the structure under actual service loads.

[0175] The damage correction factor and lifetime correction factor are calculated according to the following formulas:

[0176] ;

[0177] ;

[0178] In the formula, As a damage correction factor, To correct the spurious damage in the equivalent spectrum, The spurious damage is the result of the original load spectrum. This is a lifetime correction factor. The fatigue life is the equivalent spectrum after correction. This represents the fatigue life of the original load spectrum.

[0179] 7) Simulation verification and iterative optimization

[0180] The original service load spectrum and the initial equivalent load spectrum obtained in step 5) are input into the finite element fatigue simulation system to calculate the reference fatigue life and reference damage of the target structure under the two types of load spectra respectively. Then, the reference fatigue life and reference damage are corrected by the life correction factor and damage correction factor obtained in step 6) to obtain the corrected fatigue life and corrected damage. Then, the fatigue life error and damage error of the corrected results relative to the original service load spectrum are calculated.

[0181] The fatigue life error and damage error are calculated according to the following formulas:

[0182] ;

[0183] ;

[0184] In the formula, The final pseudo-damage relative error (reflecting the degree of deviation between the corrected pseudo-damage and the baseline pseudo-damage). It is the damage correction factor (i.e., the ratio of the corrected spurious damage to the baseline spurious damage). The final life relative error (reflects the degree of deviation between the corrected life and the reference life). This is the life correction factor (i.e., the ratio of the corrected life to the baseline life).

[0185] in, The smaller the value, the closer the corrected damage is to the baseline damage, and the better the model stability / consistency. The larger the value, the more significant the impact of the loading sequence on fatigue damage; The smaller the value, the closer the corrected lifespan is to the baseline lifespan; The larger the value, the more significant the impact of loading sequence on fatigue life.

[0186] In practical applications, fatigue life error and damage error are respectively compared with preset error thresholds (e.g., ...). <15% <15%) will be compared and judged:

[0187] If both fatigue life error and damage error meet the preset error threshold, it is determined that the accuracy requirement is met, and the corrected equivalent load spectrum is output as the final equivalent load spectrum.

[0188] If any error does not meet the preset error threshold, iterative optimization is performed by adjusting the weighting coefficient of the profile coefficient and the relative error of the pseudo-damage, and / or optimizing the fatigue index correction factor, and repeating steps 4) to 7) until both errors meet the preset engineering accuracy requirements, and the final equivalent load spectrum is obtained.

[0189] Specifically, if the error exceeds the standard due to unreasonable clustering classification: return to step 4), adjust the weighting coefficients to re-determine the optimal number of classifications, and then execute steps 5 to 7); if the error exceeds the standard due to insufficient loading order correction: directly return to step 6), optimize the fatigue index correction factor, and then execute step 7).

[0190] The entire text unifies this iterative logic in the method steps and system modules, and supplements the iterative path determination rules (such as "when the relative error of pseudo-damage exceeds the standard, return to step 4; when the fatigue life error exceeds the standard, return to step 6)").

[0191] The following is an example of using the above method:

[0192] Example

[0193] like Figures 3 to 7 As shown, this embodiment uses the motor output shaft of a new energy vehicle electric drive system as the verification object to explain in detail the specific implementation process of the non-equal amplitude interval random load equivalent compilation method of the present invention, which includes the following steps:

[0194] 1. Load data acquisition and preprocessing

[0195] Wheel-end torque signals were collected through real-vehicle road tests. The torque load spectrum of the motor output shaft was calculated by combining this with the transmission ratio of the electric drive system. The sampling frequency of this load spectrum was set to 10Hz, and the actual data acquisition time was approximately 3.25 hours. The raw torque signal was input into a preprocessing module. After noise reduction, filtering, and resampling, a standardized, smooth, and stable time history of the motor output shaft torque load was obtained. The processing results are as follows: Figure 4 As shown.

[0196] 2. Rainflow counting and load cycle feature extraction

[0197] A two-parameter rainflow counting method is used to extract the load cycle from the torque load time history of the preprocessed motor output shaft, accurately identifying the amplitude, mean, and corresponding cycle number of all load cycles, so as to construct a complete set of load cycle feature vectors, providing standardized and complete basic data input for subsequent hierarchical clustering and grading.

[0198] 3. Hierarchical clustering classification based on Ward's criterion

[0199] Using load amplitude as the core clustering feature, hierarchical clustering is performed on the feature vector set using the Ward minimum variance criterion. During the clustering process, the intra-cluster centroids and sample variances of each load level cluster are dynamically updated to complete the non-uniform amplitude interval classification of load cycles. After clustering, the algorithm automatically identifies the maximum equivalent amplitude of all load level clusters, removes low-contribution load levels whose equivalent amplitude is less than 10% of the maximum amplitude, and simultaneously verifies that the cumulative pseudo-damage retention rate of the remaining load level clusters is greater than or equal to 99% of the pseudo-damage of the original load spectrum, finally obtaining a preliminary non-uniform amplitude interval random load spectrum.

[0200] 4. Determine the optimal number of levels

[0201] All candidate grade levels within the range of 4 to 64 are traversed, and the overall profile coefficient and relative error of pseudo-damage corresponding to each candidate grade level are calculated. After normalizing these two indicators, a multi-objective weighted comprehensive evaluation index is constructed. After full-domain traversal calculation and screening, the optimal load grade level in this embodiment is determined to be 12 levels. The changing trends of relevant indicators and the determination results of the optimal value are as follows. Figure 5 , Figure 6 As shown.

[0202] 5. Constructing the initial equivalent load spectrum with non-uniform amplitude intervals

[0203] Based on the 12 optimal load level clusters, the average amplitude of each cluster is used as the equivalent amplitude of the corresponding level, and the sum of the number of cycles of each cluster is used as the equivalent cycle number of the corresponding level. All load level clusters are sorted in descending order of equivalent amplitude to construct a structured initial equivalent load spectrum block with non-equal amplitude intervals.

[0204] 6. Equivalent Spectrum Correction Based on Loading Order Effect

[0205] Based on the Corten-Dolan fatigue cumulative damage model, with the loading frequency set to 1Hz and a fatigue index correction factor introduced, the life correction factor and damage correction factor in this embodiment are calculated to be 1.65 and 0.61, respectively.

[0206] 7. Simulation Verification Results

[0207] Using Abaqus+Ncode DesignLife fatigue simulation software, the original service load spectrum and the initial equivalent load spectrum were substituted into the finite element model of the motor output shaft to obtain the baseline damage and baseline life. Then, the correction factor obtained in step 6) was used to correct the baseline results, yielding the corrected damage and corrected life. The error comparison before and after correction is as follows:

[0208] Before correction (initial equivalent spectrum): relative error of damage 46.25%, relative error of fatigue life 86.04%;

[0209] After correction (adjusted by correction factor): relative error of damage 11.32%, relative error of fatigue life 13.50%.

[0210] Therefore, it can be seen that the corrected relative error of damage and relative error of fatigue life are both controlled within the preset threshold of 15%, which fully meets the engineering accuracy requirements for the durability verification of the motor output shaft of the electric drive system of new energy vehicles.

[0211] The final equivalent load spectrum obtained in this embodiment was applied to the bench fatigue durability test of the output shaft of a new energy vehicle motor. The total loading time of the test was shortened to 20% of the original service load spectrum, which means that the loading efficiency was improved by 80%. In other words, the final equivalent load spectrum obtained in this embodiment can ensure the accuracy and reliability of the verification results of fatigue life and damage characteristics while significantly shortening the test cycle and reducing the test cost. It can be directly used for batch bench verification of electric drive systems for new energy vehicles.

[0212] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications made to the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A non-uniform amplitude interval random load equivalent compilation system, characterized in that, It includes a preprocessing module, a feature extraction module, a clustering and grading module, an optimal grading number determination module, an initial equivalent spectrum construction module, a loading order correction module, and a simulation verification module; The preprocessing module is used to receive the original service load spectrum collected during the service of the structure and output a standardized load time history. The feature extraction module is used to receive the standardized load time history output by the preprocessing module, obtain the amplitude, mean and number of cycles for each load cycle, and output a set of feature vectors with amplitude, mean and number of cycles as elements; The clustering and hierarchical module is used to receive the feature vector set output by the feature extraction module and output a preliminary non-uniform amplitude interval random load spectrum. The optimal number of grade determination module is used to receive the non-equal amplitude interval random load spectrum output by the clustering and grading module, filter out the number of load level clusters that maximizes the multi-objective weighted comprehensive evaluation index, and use it as the optimal number of grade, and output each load level cluster corresponding to the optimal number of grade. The initial equivalent spectrum construction module is used to receive the load level clusters corresponding to the optimal number of levels output by the optimal number of levels determination module, and output the initial equivalent load spectrum with non-equal amplitude intervals. The loading order correction module is used to receive the initial equivalent load spectrum output by the initial equivalent spectrum construction module, and based on the Corten-Dolan model, introduces a fatigue index correction factor and outputs a life correction factor and a damage correction factor. The simulation verification module is used to receive the initial equivalent load spectrum output by the initial equivalent spectrum construction module, the correction factor output by the loading order correction module, and the original service load spectrum collected during the service of the structure; the original service load spectrum and the initial equivalent load spectrum are respectively input into the finite element fatigue simulation system to calculate the reference fatigue life and reference damage. The baseline fatigue life and baseline damage are then corrected using the life correction factor and damage correction factor to obtain the corrected fatigue life and corrected damage. Then, fatigue life error and damage error are calculated, and the corrected equivalent load spectrum is determined to meet the preset error threshold requirements based on the preset error threshold.

2. The equivalent compilation system for non-uniform amplitude interval random loads according to claim 1, characterized in that, The simulation verification module determines whether the corrected equivalent load spectrum meets the preset error threshold requirement based on the preset error threshold in the following specific way: If both fatigue life error and damage error meet the preset error threshold, then it is determined that they meet the preset accuracy requirements, and the final equivalent load spectrum is output. If the fatigue life error or damage error does not meet the preset error threshold, it is determined that it does not meet the preset accuracy requirements. It can be returned to the optimal grade number determination module to optimize the error by re-selecting the optimal grade number, or returned to the loading order correction module to optimize the error by optimizing the fatigue index correction factor. The above determination and optimization process is repeated until the fatigue life error and damage error both meet the preset error threshold, and then the final equivalent load spectrum is output.

3. A method for equivalent compilation of non-uniform amplitude interval random loads using the system described in claim 1, characterized in that, Includes the following steps: 1) Input the original service load spectrum collected during the service of the structure into the preprocessing module, and perform noise reduction, filtering and resampling on the original service load spectrum to obtain a standardized load time history; 2) Using the rainflow counting method, load cycle extraction is performed on the standardized load time history obtained in step 1) to obtain the amplitude, mean and number of cycles for each load cycle, resulting in a set of feature vectors with amplitude, mean and number of cycles as elements; 3) Based on the Ward minimum variance criterion, using amplitude as the main clustering feature, hierarchical clustering is performed on the feature vector set obtained in step 2), and the intra-cluster centroid and sample variance of each load level cluster are dynamically updated until the intra-cluster sum of squares increments meet the convergence threshold, thus obtaining the preliminary non-equal amplitude interval random load spectrum. 4) Based on the preliminary non-equal amplitude interval random load spectrum obtained in step 3), traverse all candidate grade numbers within the preset range, calculate the overall profile coefficient and pseudo-damage relative error of each candidate grade number, construct a multi-objective weighted comprehensive evaluation index, and select the number of load grade clusters that maximizes the multi-objective weighted comprehensive evaluation index as the optimal grade number, and obtain the load grade clusters corresponding to the optimal grade number. 5) Based on the load level clusters corresponding to the optimal number of grades obtained in step 4), the average amplitude within the cluster is used as the equivalent amplitude, and the sum of the number of cycles within the cluster is used as the equivalent cycle number. The clusters are sorted from largest to smallest according to the equivalent amplitude to obtain the initial equivalent load spectrum with non-equal amplitude intervals. 6) Based on the Corten–Dolan model, the fatigue index correction factor is introduced into the initial equivalent load spectrum obtained in step 5), and the life correction factor and damage correction factor are calculated. 7) Input the original service load spectrum and the initial equivalent load spectrum obtained in step 5) into the finite element fatigue simulation system to calculate the reference fatigue life and reference damage at the maximum damage point of the structure. Then, the life correction factor and damage correction factor obtained in step 6) are used to correct the reference fatigue life and reference damage to obtain the corrected fatigue life and corrected damage; then the life error between the corrected fatigue life and the original fatigue life, and the damage error between the corrected damage and the original damage are calculated. If both fatigue life error and damage error meet the preset error threshold, the corrected equivalent load spectrum will be output as the final equivalent spectrum. If the preset error threshold is not met, return to step 4), perform iterative optimization by adjusting the weighting coefficient or optimizing the fatigue index correction factor, and repeat steps 4) to 7) until the error meets the preset error threshold, and output the final equivalent load spectrum.

4. The method for equivalent compilation of non-uniform amplitude interval random loads according to claim 3, characterized in that, In step 2), the rainflow counting method includes the two-parameter rainflow counting method.

5. The method for equivalent compilation of non-uniform amplitude interval random loads according to claim 3, characterized in that, In step 3), the increment of the sum of squared deviations within a class is calculated according to the following formula: ； In the formula, For the increment of the sum of squared deviations within the class, This represents the sequence number of a single load cycle in the original load spectrum. For the original load spectrum to be compared with the first The sequence number of another load level cluster merged from the previous load level cluster. For the first to be merged The total number of cycles for each load level cluster. For the first to be merged The total number of cycles for each load level cluster. For the first Intraclass centroids of each load level cluster, For the first Intraclass centroids of each load level cluster.

6. The method for equivalent compilation of non-uniform amplitude interval random loads according to claim 3, characterized in that, In step 3), after hierarchical clustering is completed, the maximum amplitude value in all load level clusters is automatically identified, load level clusters with amplitude values ​​less than 10% of the maximum amplitude value are deleted, and the cumulative pseudo-damage of the remaining load level clusters is verified and ensured to be no less than 99% of the cumulative pseudo-damage of the original service load spectrum.

7. The method for equivalent compilation of non-uniform amplitude interval random loads according to claim 3, characterized in that, In step 4), the multi-objective weighted comprehensive evaluation index is calculated according to the following formula: ； ； ； ； ； ； ； In the formula, The number of load level clusters, For the number of load levels Multi-objective weighted comprehensive evaluation index at time, These are the weighting coefficients for the profile coefficients. For the number of load levels The average profile coefficient at that time, The number of candidate payload levels is Time corresponding The minimum value, The number of candidate payload levels is Time corresponding The maximum value, The weighting coefficients for the relative error of spurious damage. For the number of load levels The relative error of pseudo-damage at that time The number of candidate payload levels is Time corresponding The minimum value, The number of candidate payload levels is Time corresponding The maximum value, This represents the total number of independent load cycle samples extracted from the original load spectrum. This refers to the sequence number of the original load cycle sample. For the first Profile coefficients of a single load cycle sample. For the first The average distance between a load cycle sample and all other load cycle samples in the same cluster For the first The average distance between a load cycle sample and all load cycle samples in its nearest neighbor cluster. For the number of load levels The fatigue pseudo-damage value of the equivalent load spectrum at that time. The fatigue pseudo-damage value is the original load spectrum. The first in the equivalent load spectrum The amplitude of each load cycle, The first in the equivalent load spectrum The total number of cycles for each load cycle. This represents the total number of independent load cycles in the equivalent load spectrum. This is a pseudo-damage index. The first in the original load spectrum The amplitude of each load cycle, The first in the original load spectrum The total number of cycles for each load cycle.

8. In the method for equivalent compilation of non-equal amplitude interval random loads according to claim 3, in step 6), the corrected fatigue life is calculated according to the following formula: ； ； ； In the formula, This is the sequence number of the load level cluster. The total number of load level clusters, To account for the structural fatigue life after the loading sequence is corrected, To the maximum load amplitude The number of cycles required for the structure to undergo fatigue failure under individual action. For the first The equivalent amplitude of the load class cluster, The maximum amplitude value among all load level clusters. For the first Cyclic percentage of load class clusters For the first The corrected fatigue index corresponding to the load level cluster. For the first Total number of cycles for each load class cluster When arranged in loading order, the first The equivalent amplitude of the load class cluster, This is the basic fatigue index of the material.

9. The method for equivalent compilation of non-equal amplitude interval random loads according to claim 3, wherein the damage correction factor and lifetime correction factor in step 6) are calculated according to the following formulas: ； ； In the formula, As a damage correction factor, To account for the corrected pseudo-damage in the equivalent load spectrum after loading sequence correction, The baseline pseudo-damage for the equivalent load spectrum without considering the loading order. This is a lifetime correction factor. To account for the modified fatigue life of the structure after the loading sequence is adjusted, This represents the baseline fatigue life of the structure without considering the loading sequence.

10. In the method for equivalent compilation of non-equal amplitude interval random loads according to claim 3, in step 7), the fatigue life error and damage error are calculated according to the following formulas: ； ； In the formula, The final pseudo-damage relative error, As a damage correction factor, This represents the relative error in the final fatigue life. This is the lifetime correction factor.

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