On modern ships, the quick development in data acquisition technologies is producing data-rich environments where variable measurements are continuously streamed and stored during navigation and thus can be naturally modelled as functional data or profiles. Then, both the CO${}_2$${}_2$ emissions (i.e. the quality characteristic of interest) and the variable profiles that have an impact on them (i.e. the covariates) are called to be explored in the light of the new worldwide and European regulations on the monitoring, reporting and verification of harmful emissions. In this paper, we show an application of the functional regression control chart (FRCC) with the ultimate goal of answering, at the end of each ship voyage, the question: given the value of the covariates, is the observed CO${}_2$${}_2$ emission profile as expected? To this aim, the FRCC focuses on the monitoring of residuals obtained from a multivariate functional linear regression of the CO${}_2$${}_2$ emission profiles on the functional covariates. The applicability of the FRCC is demonstrated through a real-case study of a Ro-Pax ship operating in the Mediterranean Sea. The proposed FRCC is also compared with other alternatives available in the literature and its advantages are discussed over some practical examples.

中文翻译：

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用于监测船舶 CO2$_{2}$ 排放的功能回归控制图

在现代船舶上，数据采集技术的快速发展正在产生数据丰富的环境，在这些环境中，可变测量值在航行期间不断流式传输和存储，因此可以自然地建模为功能数据或配置文件。然后，两个 CO${}_2$${}_2$排放（即感兴趣的质量特征）和对其有影响的变量概况（即协变量）被要求根据全球和欧洲关于有害排放监测、报告和验证的新法规进行探索。在本文中，我们展示了函数回归控制图 (FRCC) 的应用，其最终目标是在每次船舶航行结束时回答以下问题：给定协变量的值，观察到的 CO${}_2$${}_2$ 排放曲线是否符合预期？为此，FRCC 侧重于监测从 CO 的多元函数线性回归中获得的残差${}_2$${}_2$函数协变量的发射曲线。FRCC 的适用性通过对在地中海运营的 Ro-Pax 船舶的真实案例研究得到证明。提议的 FRCC 也与文献中可用的其他替代方案进行了比较，并通过一些实际示例讨论了它的优点。