## 1 Introduction  
Cyber-physical systems (CPSs) are an indispensable part of intelligent manufacturing (IM) and Industry 4.0, which is gradually transforming the landscape of the global manufacturing industry. CPSs are multidisciplinary systems that combine computation, communication, and control technologies to conduct real-time measurements, data transmission, monitoring, decision making, feedback control, and other functions on widely distributed embedded computing systems [1, 2]. CPSs are considered to be a major feature of the new industrial revolution [3]. The deployment of a CPS system in Industry 4.0 has attracted the interest of scholars and researchers [4]. [PERSON] et al. [5] believe that the use of CPSs will move the manufacturing industry towards Industry 4.0; they proposed a unified 5C architecture as a guideline for deploying CPS. This guideline shows how to use the feedback from the initial data collection through to analytics in the final decision-making stage. [PERSON] et al. [6] presented a four-level unified architecture for a cyber-physical production system based on a digital twin. [PERSON] et al. [7] presented a three-level CPS framework for workshops and introduced a guideline for the connection of physical components; obtaining and preprocessing data; visualizing results; and the final knowledge acquisition. The various kinds of divisions of the CPS layer framework can be divided into five levels [2; 3; 5; 8; 9; 10; 11; 12; 13], four levels [6; 14], and three levels [7; 15], as shown in Table 1. These layers are divided into simple CPS workflows and basic concepts, the key CPS technologies and modeling methods used in the manufacturing field are not considered, and deep learning-based algorithms are not integrated in the framework. Sophisticated machine learning (ML) based on industrial big data is a key component of CPSs that will enable us to reach a new phase of IM [22]. ML can extract the features of data collected by various sensors in a physical system and ultimately contribute to the integration of the physical system and cyber space. ML has been applied in practical industry and achieved impressive performance [23]. [PERSON] et al. [8] proposed deploying a shop-floor CPS framework where a support vector machine was used as an ML technology for predicting the occurrence of anomalies. They designed and simulated this CPS framework based on ML for Industry 4.0. [PERSON] et al. [3] proposed a real-time data-driven CPS with classification and regression ML algorithms implemented in the system. [PERSON] et al. [21] proposed a novel ML algorithm for imbalanced data in a Prognostics and Health Management (PHM) CPS. Table 2 shows the application area and algorithm implementation of CPS. It can be seen from Tables 1 and 2 that the methods implemented by deep learning (DL) do not have a clear CPS architecture but simply involve the CPS field. Meanwhile, these methods only realize CPS applications based on data modeling, without considering the influence of physical modeling, and lack a framework to monitor the condition of critical transmission components (CTCs) in smart production lines (SPLs) from the perspective of CPS hybrid modeling. With the development of IM and network collaborative manufacturing, data-driven SPL now plays an important role in ensuring the stable production of workshops, enterprises, and industrial chains [24; 25; 26; 27]. The CTCs of SPL, such as motor spindles, bearings, and gears, operate under variable conditions for a long time. The breakdown of mechanical equipment in production lines is caused by motors, bearings, and gears, which account