各态历经性的案例教学法研究

Study on Case Teaching of Ergodicity

平稳随机过程的各态历经性是工程应用中非常重要的概念。在随机过程理论授课时,需要学生转换思维去理解各态历经性意义的同时,也要求学生能够熟练掌握各态历经性的物理含义。用传统教学方式和公式列举的推导方式教学,对于学生学习难度较大。该文将各态历经性与工程应用案例相结合,通过从掷骰子的实验结果引入对各态历经性概念的理解,介绍各态历经性的判定方法与物理意义,并借由航天微波遥感中噪声抑制这一工程应用案例,进一步引发学生对各态历经性应用的思考,充分理解各态历经性的实际工程作用;最后根据各态历经性的物理意义,引申到科研生活体悟的人生哲理,让学生学习新概念的同时,在自身思想上也能有所提升。

The states of smooth stochastic processes are very important concepts in engineering applications.In the lecture of"Theory of Stochastic Processes",students are required to change their thinking to understand the meaning of each state ephemerality,and at the same time,they are required to master the physical meaning of each state ephemerality,which is difficult to learn by the traditional teaching method and the derivation of formulae.In this paper,we combine the state ephemerality with engineering application cases,introduce the understanding of the concept of state ephemerality from the experimental results of dice rolling,introduce the determination method and physical meaning of state ephemerality,and use the engineering application case of noise suppression in aerospace microwave remote sensing to further provoke students to think about the application of state ephemerides and fully understand the practical engineering role of state ephemerides;finally,according to the physical meaning of state ephemerides,it is extended to scientific research.Finally,according to the physical meaning of each state ephemerality,it can be extended to the philosophy of life in scientific life,so that students can learn new concepts and improve their own thinking at the same time.