发表机构
SyCoIA, IMT Mines Ales; EuroMov Digital Health in Motion, Univ Montpellier, IMT Mines Ales（阿莱斯矿业学院; 蒙彼利埃大学、阿莱斯矿业学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从系统控制理论视角重新审视体能疲劳模型，利用状态表示研究可控性、可观测性与可诊断性，以正式回答训练方案制定、疲劳评估和伤病预防等核心问题。
AI 中文摘要
体能疲劳模型（FFM）最初设计用于从生理学角度更好地理解训练负荷对运动表现的影响。近50年来，模拟结果一直与运动表现对训练负荷的观测响应进行比较。理解训练负荷与表现之间的关系本应为体能教练或运动教练解答一些基本问题：1/如何定义最佳训练方案，在不使运动员精疲力竭的情况下达成表现，或如何在有限时间内达成表现；2/如何可靠地评估运动员的疲劳与体能，以更好地理解其表现；3/如何预防受伤风险。但事实并非如此。专门针对FFM的研究仅限于对Banister初始模型进行某种程度的改进，而未真正退后一步，以利用状态表示（FFM隐含的形式化基础）所提供的数学框架。该研究策略背后的想法是，拥有一个有效且准确的模型，就能通过模拟轻松解决上述问题：可以模拟多种训练场景，直到为给定训练问题找到理想场景。这种方法的主要缺点是问题的组合性质。本文不讨论模型的相关性，而是讨论如何使用它。状态表示使得研究系统（即运动员）的可控性、可观测性和可诊断性成为可能，从而正式回答上述三个实际问题。可以认为，运动科学研究错过了FFM模型的丰富性。人工学习方法越来越被优先于FFM模型，因为它们被认为能更好地捕捉观测。然而，基于状态表示，FFM模型仍可自然扩展，同时保持数学可解释性，提供数学工具来估计运动员的状态，定义最合适的训练方案并预防受伤风险。本文不旨在解决实践中最佳训练的问题，因为这需要由生理学和运动科学专家验证，它只是提议以全新视角看待训练问题，并揭开Banister所采用的数学形式化的神秘面纱。
英文摘要
The Fitness-Fatigue model (FFM) was initially designed to gain a better physiological understanding of the impact of training loads on sports performance. For almost 50 years, simulations have been compared with the observed response of sports performance to training loads. Understanding the relationship between training load and performance should have answered some fundamental questions for the physical trainer or sports coach: 1/ how to define the best training to achieve a performance without exhausting an athlete or how to achieve a performance in a limited time; 2/ how to assess the athlete's fatigue and fitness reliably to better understand his performance; 3/ how to prevent the risk of injury. But this was not the case. Studies dedicated to the FFM have been limited to improving somewhat on Banister's initial model without really taking the necessary step back to take advantage of the mathematical framework offered by the state representation, the implicit formalism underlying the FFM. The idea behind this research strategy is that having a valid and accurate model makes it easy to address previous questions through simulation: multiple training scenarios can be simulated until the ideal scenario for a given training question is identified. The main drawback to this approach is the combinatorial nature of the exercise. This paper is not discussing the relevance of the model, but how to use it. The state representation makes it possible to study the controllability, observability and diagnosability of a system (i.e, the athlete) and thus to formally answer the three previous practical questions. It can be considered that sports science studies have missed the richness of the FFM model. Artificial learning approaches are increasingly preferred to the FFM model because they are supposed to better capture observation. However, in the light of the state representation, the FFM model could still be extended naturally while remaining mathematically interpretable, offering mathematical tools to estimate the state of the athlete, and to define the most adequate training and prevent the risk of injury. This article does not aim to solve the question of optimal training in practice, for that it would need to be validated by specialists in physiology and sports science, it just proposes to take a fresh look at training issues and to demystify the mathematical formalism adopted by Banister.
