## 6 Conclusions  
In this paper, a new in situ GAD is proposed for rotational speed estimation, and it is applied in the order tracking scene for fault diagnosis of a gearbox under non-stationary working conditions. The core contribution of the paper is to discover and utilize the  
Figure 24: MPR values of the three methods in different working conditions.  
time-varying gravity acceleration relative to the phase change in the rotation obtained by the tangential in situ accelerometer. A corresponding GAD method for the gravity acceleration component is first proposed based on linear-phase FIR filter, CEEMDAN and Hilbert transformation methods. The correctness and effectiveness of the proposed method are verified by a motor-shaft-disc experimental setup. Furthermore, the proposed method is successfully applied in order tracking for fault diagnosis of a gearbox. Based on the analyzation of the results, conclusions can be drawn as follows:  
1. The principle of estimating rotational speed based on decoupling the gravity acceleration component from the tangential in situ accelerometer measurements is indeed feasible. By employing techniques such as filtering or signal processing algorithms, the gravity component can be separated from the tangential acceleration component, enabling the calculation of rotational speed.
2. The utilization of the CEEMDAN, ICEEMDAN and EWT methods for decomposition and reconstruction reveals minimal differences among the three approaches. As a result, these minor variations are likely to have a negligible impact on the estimation errors of the rotational speed. This suggests that the choice of decomposition technique, within the range of these three methods, may not significantly affect the overall accuracy of rotational speed estimation.
3. The proposed method demonstrates satisfactory estimation performance for both average and instantaneous rotational speeds. Specifically, the majority of the relative estimation errors for the average rotational speeds are confined to within \(\pm\)0.5%, indicating a high level of accuracy. Similarly, for the instantaneous rotational speeds, most of the relative estimation errors are within \(\pm\)5%, demonstrating a reasonable degree of precision compared to encoder-based measurement methods.
4. The proposed method exhibits superior performance in rotational speed estimation and order tracking within gearboxes, achieving an average gain of 5.36 dB over Method 2, 4.06 dB over Method 3 and a substantial 7.27 dB over Method 4. Above all, the average and instantaneous rotational speeds can be well estimated based on the proposed GAD method, which offers good insights for enhancing fault detection and diagnostic capabilities in non-stationary applications.  
Conceptualization, L.W.; methodology, L.W.; validation, Y.L.; formal analysis, Y.L.; investigation, Z.C.; writing--original draft preparation, Y.L. and L.W.; writing--review and editing, Z.C.; supervision, L.W.; funding acquisition, L.W. All authors have read and agreed to the published version of the manuscript.  
This study was funded by the Chongqing Natural Science Foundation (Grant No. CSTB2022 NSQC-MSX1243, cstc2022 ycjh-bgzxm0009) and the National Natural Science Foundation of China (Grant No. 52035002).  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.