Recognizing the stability of the traffic evolution process of urban traffic networks has been an important consideration in traffic evolution research. However, little work has been conducted on identifying and associating temporal Traffic State Pattern (TSP) with the traffic evolution process. By clustering multi-dimensional traffic time series, we attempted to map the traffic evolution process into massive transitions of consecutive TSPs. Through the statistics of the time distribution of the transitions, we then defined the stability coefficient to conduct a quantitative analysis of the traffic evolution process. An empirical study using 30 days of traffic flow rate data of multiple road sections from the network of Nanshan District (Shenzhen, China) was carried out. Numerical results indicated that the traffic evolution process experienced obvious nonlinear changes at different periods of the day, but presented a regular cycle characteristic from morning till night. Further, with consideration of different travel purposes and traffic features on weekday and weekend, more traffic dynamics was extracted, which would be conducive to understand the complex behaviour of traffic evolution process.