# Event-Driven Dynamics Model of Operating State Evolution for Cantilever Roadheader
## 2 Dynamics Model of the State Evolution of Cantilever Roadheader
### Event-Driven Graph Construction of Operating State Evolution
#### 2.2.2 Event State Model  
The automated mapping change relies on event triggering, which requires a predefined anomaly judgment scheme. Monitoring the acceleration variation in key cutting actions is essential to detect operational event changes. During normal operation, key cutting actions maintain uniform speed, and acceleration fluctuations indicate state abnormalities. For example, the platform's rotary speed \(v_{t}\) and acceleration \(a_{t}\) are calculated by the following formula based on current time \(T_{t}\) and the specific rotation angle \(\theta_{H,t}\):  
\[v_{t}=(\theta_{H,t}-\theta_{H,t-1})/(T_{t}-T_{t-1})\] \[a_{t}=(v_{t}-v_{t-1})/(T_{t}-T_{t-1})\]  
where \(v_{t}\), \(a_{t}\), \(\theta_{H,t}\), _and_\(T_{t}\) denote the respective parameters at time step \(t\). By monitoring these parameters, the operating state normality can be determined, enabling timely measures to ensure safety and operational continuity. Abnormal acceleration fluctuations may signal operational anomalies, necessitating corrective actions for inspection. The operational state \(S\) of the equipment is characterized by the following four key parameters: the timestamp, rotation angle, lifting angle, and extension length. Variations in the acceleration of critical movements stem from the following two distinct sources: controlled adjustments following operational commands and kinematic deformations caused by external disturbances. During command-driven movements, the system maintains stable states before and after adjustments with near-zero acceleration, where the magnitude and duration of acceleration changes strictly correspond to control instructions, enabling precise action range determination. In contrast, the disturbance generates irregular acceleration patterns, whose abnormality can be identified through non-zero acceleration residuals combined with deviations from the expected command execution timelines, providing a robust mechanism for operational anomaly detection. When acceleration deviations diverge from control commands or maintain non-zero values beyond the prescribed operation period, this indicates potential disturbance impacts on the operational behavior. Immediate corrective measures are then required to ensure the operational quality and safety. This approach enables the effective monitoring of intelli  
Figure 6: Closed-loop state evolution graph. gent cutting processes, allowing for timely responses to various disturbance events. The definition and characterization of events directly determine the effectiveness of the detection algorithms. Event definitions must encompass both command-triggered behaviors specified in the planned cutting trajectory and unplanned disturbances caused by complex geological conditions. The core of event analysis lies in state monitoring and control. Therefore, event description methods should be derived from the state definition model. The cutting state is defined through temporal nodes and spatial coordinates, with discretization based on operational plans. Each state transition reflects significant changes in equipment parameters, representing the triggering of planned events. Based on state discretization and key state node definitions, events can be characterized through variations in the key kinematic parameters of the cutting arm of the roadheader. As shown in Figure 7, each state node is preceded by a corresponding event node. Events A to H are triggered by the planned operation instructions, which cause the state of the cutting operation to change in an orderly manner according to the planned cutting trajectory. Events \(E\)1, \(E\)4, and \(E\)7 are caused by parameter shifts due to unexpected situations, and the occurrence of such disturbing events leads to the shift of the operation state beyond the planned threshold, thus failing to guarantee the heading section quality. Based on the correspondence between events and states, events can be defined vectorially, \(Event_{1}=\{M_{1},E1,S_{1}\}\).