# Research on the Scope of Spectral Width Parameter of Frequency Domain Methods in Random Fatigue
## 1 Introduction  
Fatigue failure is one of the most important failure modes in engineering structures, and more than 85% of the structural failures are fatigue failures. Generally, the fatigue load can be divided into three types: constant amplitude fatigue, variable amplitude fatigue, and random fatigue [1]. Among them, constant amplitude fatigue and variable amplitude fatigue have been studied in most fields, and the theory and design are relatively perfect [2]. However, there is little research in the field of random fatigue. Most civil structures inevitably bear random loads, such as wind loads, pedestrian-vehicle loads, etc., so the study of random fatigue in the field of civil engineering is also very necessary. Fatigue life estimation is mainly obtained through the cumulative damage criterion and the S-N curve of the material. For random fatigue, life estimation methods are divided into the time-domain method and frequency-domain method [3]. The time-domain method is to analyze the time history of the response stress of the structure, and obtain the amplitude, mean value and cycle times of the response stress by a certain cycle counting method, and then calculate the fatigue damage and life of the structure by combining with the appropriate cumulative damage theory [4] and S-N curve of the material [5]. In this method, many scholars have proposed different cycle counting methods for the response stress time history, and the rain flow counting method proposed by [PERSON] [5] is considered to be the most accurate cycle counting method in fatigue damage and fatigue life estimation [6; 7; 8]. The rain flow solution is also usually used as an accurate solution or a standard solution in random fatigue life analysis. However, the time-domain method has a large amount of calculation, the time-history curve is difficult to obtain, and the operability is not good in engineering applications [9]. Therefore, in order to avoid various shortcomings of the time-domain method, the frequency-domain method has been developed to simplify the calculation of random fatigue damage and life. The frequency domain refers to another coordinate system used to describe the frequency characteristic of random processes [10]. By performing a fast Fourier transform on the time domain signal, the various frequency components of the random process are separated to obtain the power spectral density and describe the characteristic with its corresponding spectral parameters. This is the basic idea of the frequency domain method [11]. The power spectral density is the \"power\" in a unit frequency band. Mathematically, the area enclosed by the power spectral density curve and the coordinate axis is equal to the mean square value of the signal [12; 13]. The power spectral density can be divided into a broadband random process and a narrow-band random process according to their different spectral types [14; 15]. Many scholars have conducted a lot of research on different frequency domain methods. [PERSON], [PERSON] [16], and others compared the above common methods through the measured data, and found that [PERSON], [PERSON], and [PERSON] methods have high accuracy, applicability, and can be used as the recommended method for fatigue life estimation. [PERSON] [17] proposed a new original index to evaluate the reliability of the frequency domain method for the stochastic process of double peak stress. [PERSON] and [PERSON] [18] performed fatigue testing on tensile shear spot welding specimens, and established a life prediction model for spot welding under random load through damage mechanics. [PERSON] [19] studied the influence of frequency on the fatigue life curve of metal materials, and proposed a fatigue S-N curve model of metal materials. [PERSON] and [PERSON] [20] proposed the fatigue life estimation method for the three-peak stochastic process based on the theory of the two-peak approximation method, and extended it to the generalized broadband stochastic process.