Abstract Recently, dual-phase high-strength steel has attracted increasing attention in the automotive industry due to its prominent physical and mechanical properties. Microstructures of dual-phase high-strength steel have a significant effect on the properties of steel, such as wear resistance and strength, so they have an important role in the quality of steel. Therefore, statistical modeling of the microstructures of steel is of great interest. However, most existing methods require many model parameters due to the complex topological forms of microstructures, which make these models suffer from overfitting and high computational time for parameter estimation. To overcome these challenges, a novel statistical model is proposed to characterize microstructures and select the most effective parameters. Furthermore, an efficient parameter estimation method is developed to estimate the model parameters given a microstructure sample. The developed method is based on a penalized pseudo log-likelihood and the accelerated proximal gradient. A simulation study is conducted to verify the developed methods. The proposed methodology is validated by a real-world example of the microstructures of high-strength steel, and the case study shows the superior performance of the developed model compared with existing methods.

中文翻译：

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双相高强度钢微观结构建模的惩罚性自逻辑回归

摘要 近年来，双相高强钢因其突出的物理机械性能而在汽车工业中越来越受到关注。双相高强钢的显微组织对钢的耐磨性和强度等性能有显着影响，因此对钢的质量具有重要作用。因此，对钢的微观结构进行统计建模具有重要意义。然而，由于微观结构的复杂拓扑形式，大多数现有方法需要许多模型参数，这使得这些模型遭受过拟合和参数估计的高计算时间。为了克服这些挑战，提出了一种新的统计模型来表征微观结构并选择最有效的参数。此外，开发了一种有效的参数估计方法来估计给定微观结构样品的模型参数。开发的方法基于惩罚伪对数似然和加速的近端梯度。进行模拟研究以验证所开发的方法。所提出的方法通过高强度钢微观结构的真实示例进行了验证，案例研究表明，与现有方法相比，所开发的模型具有优越的性能。