随机过程在工科领域的典型应用案例及教学 实践

Typical Application Cases and Teaching Practice of Stochastic Processes in Engineering Fields

摘要: 随机过程是高校工科专业的核心基础课程，理论抽象、学用脱节是当前课程教学的突出痛点。为贴合新工科人才培养要求，强化学生随机建模、数据处理与工程问题分析能力，本文选取通信网络流量建模(泊松过程)、智能制造设备故障预测(马尔可夫链)两个典型工程场景，采用带噪声的真实模拟工程数据集，完整展示数据采集、清洗、预处理、特征提取、建模求解全流程；在模型求解中引入现实工况约束与随机噪声，分析非理想条件对模型输出结果的影响。结合PBL项目式学习、CDIO工程教育理念设计分层案例教学实施方案，打通理论知识、数据实践与工程应用的壁垒。研究成果可为工科随机过程课程案例教学改革提供理论支撑与可落地的实践范式，助力学生完成从数学理论到工程实践能力的转化。

Abstract: Stochastic Processes is a core fundamental course for engineering majors in colleges and universities. Its highly abstract theories and the disconnection between theoretical learning and practical application have become prominent pain points in current teaching. To meet the talent training requirements of Emerging Engineering Education and strengthen students’ capabilities in stochastic modeling, data processing and engineering problem analysis, this paper selects two typical engineering scenarios: communication network traffic modeling based on the Poisson process and equipment fault prediction for intelligent manufacturing based on the Markov chain. Using real-world simulated datasets with noise, this paper elaborates the whole procedures including data collection, cleaning, preprocessing and feature extraction as well as modeling and solution. Real working condition constraints and random noise are introduced in model solving to analyze their impacts on model outputs. Combined with Problem-Based Learning (PBL) and the Conceive-Design-Implement-Operate (CDIO) engineering education philosophy, a hierarchical implementation scheme for case teaching is formulated to bridge theoretical knowledge, data practice and engineering application. The research findings can provide theoretical support and practical paradigms for the teaching reform of Stochastic Processes in engineering programs, and help students realize the transformation from mathematical theories to engineering competencies.