## 4 Conclusions  
In this paper, two novel algorithms are proposed to estimate each bearings' coefficients of a multi-disc and multi-span rotor using unbalance responses. Numerical simulations are conducted to study the proposed algorithms and the results are summarized as follows. 1. The proposed algorithms provide a technique by which the stiffness and damping coefficients of each bearing can be monitored online under operation conditions. To identify the coefficients of all bearings in a rotor with n bearings and m discs, there should be m + n + 1 measured unbalance responses in both x and y directions. Moreover, the unbalance responses of each bearing should be measured. Algorithm I is suitable for rolling bearing coefficient identification, while Algorithm II can be applied to estimating both rolling-bearing coefficients and oil-journal bearing coefficients. External excitations and test runs are not required for the two algorithms. However, it is necessary to change the rotating speed slightly when using Algorithm II. 2. Adjustment points play a critical role in improving the identification accuracy of the two algorithms. Numerical simulations indicate that the coefficients of the bearing, which the adjustment point is near, are accurately identified. While the identification errors of the bearing, from which the adjustment point is far away, are often very big. Hence, in order to identify all bearings' coefficients accurately, there should be an adjustment point near each bearing. 3. Accuracy of the unbalance response measurement system is very important to the two algorithms. Numerical simulations indicate that if the measuring errors of all the required unbalance responses are zero or the same, the identification errors are almost equal to zero. It is indicated that the repeatability precision of each measuring channel of the unbalance response measurement system plays a key role when using the two algorithms. Moreover, the two algorithms require high sensor resolution. The sensor resolution is higher, and the estimation accuracy is higher. Sensors with a resolution of 1 um should be avoided and sensors with a resolution of 0.1 nm are recommended for practical application. For further study, experimental investigations should be organized to prove the proposed methods. The continuous model of the rotor can be developed based on Timoshenko theory because gyroscopic moments are considered. The limitation of the proposed algorithms is that high accuracy of the measurement of unbalance responses is strongly demanded. The research method of this paper can be regarded as a tool for future study. Conceptualization, A.W. ; methodology, A.W. ; software, A.W., Y.B., Y.X. and Y.F. ; formal analysis, A.W. ; investigation, Y.X., X.C. and J.Y. ; writing--original draft preparation, A.W. and Y.B. ; writing--review and editing, A.W. and Y.B. ; supervision, G.M. ; funding acquisition, G.M. All authors have read and agreed to the published version of the manuscript. This research was funded by the Fundamental Research Funds for the Central Universities, grant number 8000150A084 and the Yue Qi Scholar Project, China University of Mining & Technology, Beijing, grant number 800015Z1145. Not applicable. The study did not report any data. The authors declare no conflict of interest. Figure 16: Identified bearing coefficients changing with frequency of g1.4 based on algorithm 1. Considering adjustment point and sensor resolution 1 um: (**a**) obtained main stiffness coefficients in x and y directions; (**b**) obtained main damping coefficients in x and y directions. Figure 6: Identified bearing coefficients changing with frequency of g1.1 based on algorithm I considering adjustment point and sensor resolution 1 am: (**a**) obtained main stiffness coefficients in x and y directions.