The detection of change(s) in machine running state has become an important problem in the field of condition monitoring of industrial machinery. The graph model has been introduced very recently for this problem with an assumption of periodical stationarity of condition signals. In real-world engineering scenarios, however, machines often operate under unsteady environment and external loading conditions, thus resulting in non-stationary condition signals. This paper is a significant upgrade and expansion on the potential of the graph model to machine monitoring under unsteady operating conditions, where the collected signals are considered to be non-stationary. This paper proposes a new algorithm to achieve this end, which basically includes two steps: cycle segmentation and cycle normalization. Cycle segmentation is first performed to temporally divide the original data into individual cycles. The resulting cycles are subsequently normalized with a timing average procedure. With this, the obtained periodically normalized data can be appropriate for the graph model to process. Meanwhile, in order to avoid the over-segmentation problem, a control time-line is also designed, and simultaneously operates to report a potential change when performing cycle segmentation and normalization. The proposed algorithm is validated on both simulation data and real-world engineering signals. Experimental results reveal its great potential in real applications.