# Research on the Scope of Spectral Width Parameter of Frequency Domain Methods in Random Fatigue
## 6 Conclusions  
The basic knowledge and methods of the fatigue life analysis including the time domain and frequency domain has been presented in this paper. Combining with the simulated spectra and the theory about random vibration and random fatigue strength, the analysis and comparison between different exiting frequency domain methods have been done. The application scope of the spectrum width parameters of 10 commonly used frequency domain methods are emphatically studied, and an engineering example is introduced for verification and analysis. The detailed results are summarized as follows:  
1. Based on the frequency domain method of random fatigue life estimation theory, the basic principle, advantages and disadvantages of 10 common frequency domain methods are discussed. Then, 44 groups of single-peak spectrum, double-peak spectrum, multi-peak spectrum and band-limited white noise spectrum are simulated to compare the methods in different frequency domains by using steel, aluminum alloy, and spring steel, which are commonly used in engineering. 2. Time-domain simulation of 44 groups of spectrum is carried out. The histogram of the rain flow amplitude and cumulative probability density curve of the rain flow amplitude for each curve are obtained by the rain flow counting method and compared with four approximate amplitude probability distribution methods. It can be concluded that four different life prediction models have the same applicability and variation rule under different spectral width parameters, and are independent of the form of simulation spectrum. The results show that the Reyleigh distribution is suitable for fitting narrowband stochastic processes. The Dirlik method has obvious advantages when the spectrum width parameter is larger than 0.7. The Zhao-Baker method fits the broadband stochastic processes well but underestimates the fatigue life of structures. The Nakagami method can better fit the transition region between narrowband and broadband. 3. By analyzing and comparing the results of random fatigue life and relative error, it can be found that each frequency domain method has different applicability for different spectral width parameters and different materials, but similar applicability for different spectral shapes. Relative error values of different frequency domain methods increase with increasing slope values of material S-N curves. When analyzing the variation rule of each frequency domain method for a specific material, the applicable ranges of spectrum width parameters of 10 common frequency domain methods are obtained, which can provide reference for choosing the appropriate life prediction model. 4. Based on random vibration theory and fatigue life theory, simulation analysis of a stadium grandstand canopy under random vibration conditions was carried out. By changing the spectrum width parameters of the power spectrum, the fatigue life results of the structure are calculated by different frequency domain methods and compared with the rain flow counting method. The results show that when the parameter of spectrum width is 0.1-0.4, the error of the WL method is small, and when the parameter of spectrum width is 0.7-1, the TB2 method and DI method are better than other methods, thus validating the previous conclusions effectively. Conceptualization, investigation, and writing: J.X., Y.Z. ; investigation: J.L. ; review and editing: J.X., Q.H., G.L. ; funding acquisition: Q.H. All authors have read and agreed to the published version of the manuscript. The authors would like to thank the support from National Natural Science Foundation of China (no. 51525803), the Joint Funds of the National Natural Science Foundation of China (U1939208), and the 111 Project (B20039). The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.