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Crowd stability analysis is one of research hotspots to alleviate the severe situation of stampede accidents worldwide. Different from the conventional analysis models for crowd stability based on pedestrian density, this study analyses the characteristics of external disturbances and internal obstacle disturbance based on Lyapunov's theory. The critical range of crowd acceleration in crowd evacuation is obtained, a crowd merging acceleration-critical density time delay model is established, and a stability criterion of acceleration vector based on Lyapunov is obtained based on Lyapunov stability analysis. This provides new information for ensuring the stability of crowd movement in public places, assessing the stability of the crowd in the area, and taking reasonable protection and guidance measures prior to instability of a crowd flow.

In public places, it is significant to analyze the stability of the crowd which can support the crowd management and control, and protect the evacuees safely and effectively. The numerical analysis method of system stability based on Lyapunov theory suffers problems that it is difficult to avoid random errors in the initialization of pedestrian density and velocity, as well as cumulative errors due to time increasing, limiting its application. This study adopts a complementary model of theoretical numerical analysis and machine vision with a parallel convolutional neural network (CNN) model. It proposes an approach of stability analysis and closed-loop verification for crowd merging systems. Thereby, this research provides theoretical and methodological support for planning of the functional layout of crowd flow in public crowd-gathering places and the control measures for stable crowd flow.

It is significant to detect abnormal postures of pedestrians in the crowd to crowd stability control. This study locates the joint points of pedestrians based on the pose estimation algorithm OpenPose. After the analysis of 18 nodes and six body parts, the sudden value of node acceleration is obtained, which is compared with the acceleration of the pedestrian’s centre of mass. When there is at least one difference in the direction or acceleration value of the two, it means that the pedestrian has abnormal behaviour. Furthermore, this study analyses the result of comparing the change of z-coordinate value in pedestrian movement with 20% of pedestrian height. These two judgment methods together constitute the dynamic criterion of pedestrian abnormal posture, and judge whether the pedestrian has abnormal behaviour. Compared with the previous dynamic analysis of pedestrian abnormal posture, the accuracy of abnormal posture judgment is improved. This provides a theoretical basis for crowd stability analysis.

Crowd merging is a complex process, and any sudden external or internal disturbance will destroy the stability of the crowd. The occurrence of abnormal behavior will affect the crowd flow process and inevitably affect the stability of the crowd flow system. The position information of the joint points is obtained through the OpenPose algorithm, and the kinematics characteristics of each node are studied. It is judged whether the number of pedestrians in the crowd and the scale of the building scene are greater than the empirical setting value based on engineering statistical data and expert experience. When the number of pedestrians is more than 2,000 and the total area of the passage is more than 2,000 square meters, the appropriate macro-dynamic model is selected. The Aw-Rascle (AR) fluid dynamics model is selected in this study. The joint point information obtained through the OpenPose is combined with the macroscopic fluid dynamics model to construct a macroscopic crowd flow dynamics model based on the pedestrian's abnormal posture.

In recent years, with the rapid development of computer vision technology, image-based human body research has become an important task, such as pedestrian target detection, trajectory tracking, posture estimation and behaviour recognition. The centre of mass is one of the important characteristics that can reflect the phenomenon of pedestrian movement. This paper first introduces the biped robot model in robotics, starting from forward and inverse kinematics, to find the mapping relationship between the position of each joint and the pose of the end effector. Then, corresponding to the skeleton model of the human joint points, the characteristics of the bone posture and joint angle are determined. The moment of inertia factor is introduced, and the motion superposition of different joint points is considered to establish a pedestrian motion centroid model. By calculating the equivalent dynamic centroid, the pedestrian kinematics law can be explored and the pedestrian movement mechanism can be more deeply recognized.