Modeling and effectiveness evaluation of a stiffness-elasticity synergistic aerospace defense system

Abstract:

To address the challenges of insufficient cross-domain coordination effectiveness, poor robustness, and weak adaptability in modern air-space defense systems, caused by the fragmentation between rigid structural elements and elastic capability elements, thereby enhancing comprehensive effectiveness and survivability/recovery capabilities in complex adversarial environments, this paper innovatively constructs a stiffness-elasticity coupling dynamics based modeling and effectiveness evaluation framework for air-space defense systems. First, breaking through the limitations of traditional linear superposition models, we propose a four-dimensional dynamic stiffness matrix (4D DSM) and its feedback reorganization mechanism to characterize the bidirectional dynamic coupling between operational readiness and system architecture. Second, by establishing a Markov state transition model incorporating asymmetric constraints, the steady-state probability distribution of the system is rigorously derived. Then, based on nonlinear system stability theory, the state transition mechanism of the aerospace defense system from steady-state operation to critical failure is elucidated. A closed-loop management system comprising situational awareness, threshold-based early warning, and parameter optimization is proposed. Finally, rigorous mathematical derivation is employed to prove that the dynamic adjustment mechanism enabled by rigid-elastic coupling ensures an enhancement in the comprehensive effectiveness of the aerospace defense system. Theoretical analysis and scenario-based validation demonstrate that the proposed dynamic stiffness-elasticity adjustment mechanism significantly enhances the systems architectural adaptability. While ensuring a relative stability margin (10%) for the system, it effectively improves comprehensive effectiveness, restores operational readiness, and reduces system failure probability. This research supports early warning and command decision-making for aerospace defense systems, thereby proposing a new theoretical framework for synergistic stiffness-elasticity warfare in intelligent air-space defense systems, achieving stiffness shaping and elasticity modeling of dynamic potential.