## 1 Introduction  
Generally, the vibration and strain signals of a machine are mostly applied to provide dynamic information of the machine's working condition [1; 2], even though they have some common disadvantages, such as contact measurement, limited detecting positions and difficult to maintain detectors in some severe situations. Therefore, vibration and strain measuring is inappropriate or sometimes even impossible in these cases. On the other hand, the sound signal of a machine can be a significant criterion for state recognition or fault diagnosis because it is convenient to collectand does not affect the machine [3]. Thus, acoustic-based diagnosis (ABS) has received much attention in recent years [4]. One of the most important preconditions for ABS is eliminating noise from the initial sound signal, and the performance of denoising directly influences the effect of subsequent processing [5; 6].  
Preliminary analysis of machinery sound shows that significant details distribute in both time and frequency domains, which implies that noise elimination methods considering both scales would perform better than those only focusing one. Throughout the development of signal processing, the most influential time-frequency joint analysis approaches are Fast Fourier Transform (FFT) and Wavelet Transform (WT) [7]. WT was firstly proposed by [PERSON] in 1989 [8]. As the window function of FFT is fixed, WT is obviously superior to FFT for non-stationary signal as the property of characterizing local features in both domains. Six years later, [PERSON] proposed hard-threshold and soft-threshold denoising solutions based on WT. The corresponding threshold value was selected by combining WT and [PERSON]'s unbiased risk estimate (SURE) [9]. However, since the derivative of standard threshold function is not continuous and lacks adaptability, many improved wavelet noise reduction methods have been proposed [10; 11; 12]. With the extensive application of artificial intelligence in recent years, adaptive threshold selecting approaches based on intelligent optimization algorithms, such as the particle swarm optimization (PSO), genetic algorithm (GA) and ant colony optimization (ACO) have been adopted gradually [13; 14; 15].  
Fruit fly optimization algorithm (FOA) was proposed by [PERSON] in 2012 [16; 17; 18]. As a meta-heuristic method, FOA simulates the intelligent foraging behavior of fruit fly group in food finding process [19]. The fruit fly is superior to other species with regard to its senses of osphresis and vision, it can even a smell food source from 40 km away and locate other flocks by its sensitive vision [20]. The FOA has many advantages compared with the above optimization algorithms, such as simple structure, immediately accessible for practical applications, ease of implementation and rapid convergence rate. Since the FOA was proposed, it has been widely applied in financial parameter optimization [21], forecasting [22], scheduling [23], etc. However, like other optimization algorithms, the basic FOA also has the possibility of falling into local extremes due to its fixed fly distance range [24].  
Bearing the above observations in mind, an adaptive wavelet threshold denoising method for machinery sound based on an improved FOA (WTD-IFOA) is proposed. The rest of this paper is organized as follows. In Section 2, some related works are outlined based on the literature. In Section 3, the basic wavelet noise elimination method and optimization process of FOA are presented. In Section 4, an improved fly distance range, obeying normal distribution, is performed, and the denoising solution based on WTD-IFOA is elaborated. In Section 5, Gauss white noise is added into the motor sound signal to verify the effectiveness and superiority of the proposed method, and an industrial application is performed. Some conclusions and outlooks are summarized in Section 6.