刚柔协同空天防御体系建模与效能评估

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

摘要:

为解决现代空天防御体系中刚性结构要素与弹性能力要素割裂所导致的跨域协同效能不足、体系鲁棒性与适应性差的问题,提升复杂对抗环境下的综合效能和生存恢复能力,文中创新性地构建了基于刚柔耦合动力学的空天防御体系建模与效能评估框架。首先,突破传统线性叠加模型局限,提出四维动态刚度矩阵及其反馈重组机制,刻画战备状态与体系结构的双向动态耦合。其次,通过建立含非对称约束的马尔可夫状态转移模型,严格推导出体系稳态概率分布。然后,基于非线性系统稳定性理论,阐明空天防御体系从稳态运行到临界失效的状态相变机制,提出包含态势感知、阈值预警与参数优化的闭环管理体系。最后,通过严格数学推导证明刚弹耦合的动态调整机制能够确保空天防御体系综合效能提升。理论研究与想定验证表明,上述刚柔协同机制可显著增强体系结构自适应性,在确保体系稳定性相对裕度（10%）的前提下,有效提升综合效能、恢复战备水平、降低体系失效概率,辅助空天防御体系预警指挥决策,为智能化空天防御体系刚度塑形、弹性塑势的刚柔协同作战提供了新的理论框架。

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.