## 1 Introduction  
With the rapid growth in the field of microelectronics production and testing, industrial manufacturing is increasingly developing in the direction of high precision and ultra-high precision, and the demand for high-precision electronic industrial workshops (microelectronics, optical instruments, lasers, nanomaterials, etc.) is on the rise with each passing day [1]. Precision equipment in electronic industry workshops such as microelectronics, semiconductors and precision instruments have extremely demanding requirements for micro-vibration [2]. As stipulated in the national standard document GB51076-2015, the allowable vibration velocity value of the photoetching equipment and etching equipment in the 5 nm production line in the frequency band of 1-100 Hz is only 1.60 \(\upmu\)m/s [3]. Micro-vibration measurement and evaluation have strict requirements for measuring equipment. For example, [PERSON] used the TROMINO microseismograph of Micromed Company to realize the evaluation of micro-vibration characteristics of the workshop [4,5]. [PERSON] measured external background noise vibrations using an eight-channel vibration analyzer LMS Scadas Mobile-I, and highly sensitive ICP accelerometers AP2006 and BC-130 [6]. [PERSON] et al. built a single-degree-of-freedom vibration isolation system (SDOF) to assess the vibration isolation performance of a specially designed structure [7]. [PERSON] et al. at Tufts University used MEGGITT's piezoelectric accelerometer 731A-P31 to measure environmental micro-vibration of building foundations caused by ground trains and subways [8]. Vibration displacement and velocity are among the key indicators in environmental micro-vibration evaluation of electronic industrial workshop [3]. For example, VC vibration standard, which is widely used in the field of microelectronics production, uses the root mean square (RMS) value of vibration velocity as an evaluation indicator [9; 10]. In the micro-vibration test, due to transportation, maintenance, installation, parameter limitation and other factors, the vibration sensor which directly measures the vibration velocity cannot be applied to the actual measurement of environmental micro-vibration signals. Acceleration sensors are used to measure environmental micro-vibration signals. The micro-vibration velocity and displacement signals are obtained by means of analogue circuits or digital signal processing. However, the raw acceleration signals are often mixed with multiple types of noise. As a result, the velocity and displacement signals obtained through integration contain serious drift and trend term errors [11; 12; 13]. The micro-vibration measurement system established in this paper is used to obtain the observed acceleration signal. Figure 1 shows the velocity spectrum of micro-vibration with low-frequency noise obtained by direct integration. How to overcome the signal drift problem after integration while extracting and suppressing the trend term error is an important research direction of integration algorithms [14]. The integration methods of the micro-vibration signal denoising algorithm can be divided into two categories: a time-domain integration method and a frequency-domain integration method [15]. Eliminating trend term error is an important technique to suppress noise interference in time-domain integration method. The main methods for eliminating trend term error in vibration signals mainly include the difference method, the low-pass filtering method, the least square method, the wavelet transform method and empirical mode decomposition method [16; 17; 18]. Using the difference method, low-pass filtering method and least square method to eliminate trend term errors usually requires a prior assumption about the type of trend term in the signal, such as linear trend terms, polynomial and exponential trends, etc. We need to understand the characteristics of the trend term contained in the mic-vibration signal in advance.