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Uncertainty quantification of squeal instability via surrogate modelling

机译：通过替代模型对尖叫不稳定性进行不确定性量化

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摘要

One of the major issues that car manufacturers are facing is the noise and vibration of brake systems. Of the different sorts of noise and vibration, which a brake system may generate, squeal as an irritating high-frequency noise costs the manufacturers significantly. Despite considerable research that has been conducted on brake squeal, the root cause of squeal is still not fully understood. The most common assumption, however, is mode-coupling. Complex eigenvalue analysis is the most widely used approach to the analysis of brake squeal problems. One of the major drawbacks of this technique, nevertheless, is that the effects of variability and uncertainty are not included in the results. Apparently, uncertainty and variability are two inseparable parts of any brake system. Uncertainty is mainly caused by frictioa contact, wear and thermal effects while variability mostly stems from the manufacturing process, material properties and component geometries. Evaluating the effects of uncertainty and variability in the complex eigenvalue analysis improves the predictability of noise propensity and helps produce a more robust design. The biggest hurdle in the uncertainty analysis of brake systems is the computational cost and time. Most uncertainty analysis techniques rely on the results of many deterministic analyses. A full finite element model of a brake system typically consists of millions of degrees-of-freedom and many load cases. Running time of such models is so long that automotive industry is reluctant to do many deterministic analyses. This paper, instead, proposes an efficient method of uncertainty propagation via surrogate modelling. A surrogate model of a brake system is constructed in order to reproduce the outputs of the large-scale finite element model and overcome the issue of computational workloads. The probability distribution of the real part of an unstable mode can then be obtained by using the surrogate model with a massive saving of computational time and cost The established model can be used subsequently for design, reliability analysis and optimisation.
机译：汽车制造商面临的主要问题之一是制动系统的噪音和振动。制动系统可能产生的各种噪声和振动中，尖叫声是令人讨厌的高频噪声，这使制造商付出了巨大的代价。尽管已经对制动尖叫进行了大量研究，但尖叫的根本原因仍未完全理解。但是，最常见的假设是模式耦合。复杂特征值分析是分析制动尖叫问题的最广泛使用的方法。但是，该技术的主要缺点之一是结果中未包括可变性和不确定性的影响。显然，不确定性和可变性是任何制动系统不可分割的两个部分。不确定性主要是由摩擦接触，磨损和热效应引起的，而可变性主要来自制造过程，材料特性和部件几何形状。在复杂特征值分析中评估不确定性和可变性的影响可提高噪声倾向的可预测性，并有助于产生更可靠的设计。制动系统不确定性分析的最大障碍是计算成本和时间。大多数不确定性分析技术都依赖于许多确定性分析的结果。制动系统的完整有限元模型通常包含数百万个自由度和许多载荷工况。这种模型的运行时间很长，以至于汽车行业不愿进行许多确定性分析。相反，本文提出了一种通过替代模型进行不确定性传播的有效方法。为了再现大型有限元模型的输出并克服计算工作量的问题，构造了制动系统的替代模型。然后，可以通过使用替代模型来获得不稳定模式实部的概率分布，从而节省大量的计算时间和成本。所建立的模型可以随后用于设计，可靠性分析和优化。

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