# Reliability Analysis of Hybrid Laser INS Under Multi-Mode Failure Conditions
## 1 Introduction
For instance, [PERSON] et al. [14] applied finite element analysis to assess and optimize the static and vibrational modes of an INS frame to enhance rigidity and anti-vibration performance. Similarly, [PERSON] et al. [15] performed mechanical tests on aluminum-lithium alloy 8090, using the results to simulate and iteratively optimize the finite element analysis of an aluminum-lithium alloy platform in a strapdown INS. In addition to structural optimization, material selection significantly impacts structural performance [16]. Traditional materials such as aluminum alloys are commonly used for structural components, such as the base, platform, and frames, in hybrid INSs. However, with advancements in new composite materials, inertial measurement systems have entered a phase characterized by \"high precision\", \"miniaturization\", and \"extended service life\". In this phase, the inherent limitations of traditional materials, such as low rigidity and dimensional instability, have become prominent obstacles to achieving high-precision INSs. Therefore, the use of new materials is essential for the progress of inertial technology and military equipment. Aluminum matrix composites, which offer the benefits of being lightweight and possessing high elastic modulus and high dimensional stability, have become crucial in aerospace applications and are widely used in antennae, skins, and support structures for aircraft [17; 18; 19; 20; 21]. Traditional inertial measurement device analysis and optimization generally rely on deterministic system parameters and optimization models, using classical deterministic methods for model solutions [22; 23]. However, in engineering practice, uncertainty factors are inevitably present in the parameters of the base, platform, and inner and outer frames of inertial measurement devices, such as geometric parameters, measurement errors, and material properties. Although these uncertainties are typically minor, the nonlinear nature and multi-system coupling of the inertial measurement system can cause significant fluctuations in structure or system performance, potentially preventing it from fulfilling its intended function and even leading to serious consequences. There are two main approaches to addressing these uncertainties: (1) minimizing or controlling their range by enhancing component precision and reducing tolerance bands during manufacturing, although uncontrollable factors may limit the effectiveness of this approach; (2) mitigating the impact of uncertainties on structural performance, aiming to make performance less sensitive to these variations and to ensure high reliability [24]. Conventional reliability analysis methods include approximate analytical methods, numerical simulation, and surrogate models, all applicable to hybrid inertial measurement system reliability analysis [25]. The approximate analytical method mainly refers to the first-order reliability method (FORM) [26] and the second-order reliability method (SORM) [27], which estimate failure probability by linearizing the failure boundary at the design point. However, these methods require explicit mathematical models of the inertial measurement system and perform poorly in highly nonlinear problems. The numerical simulation approach, primarily the Monte Carlo method [28], uses a set number of samples to obtain response values and calculates failure probability based on these samples. Although the accuracy of this method improves with sample size, the computational and time costs are substantial, especially for complex precision systems such as inertial measurement systems, where obtaining failure samples is costly and impractical for large datasets. Therefore, surrogate models are commonly employed in engineering to improve computational efficiency. Surrogate models use limited sample points to predict outputs in real time, reducing the need for computationally intensive finite element simulationsor physical model calculations.