## 1 Introduction
### Problem Description
As shown in Figure 1, most of these parameters are environment-dependent variables across operational stages. Sensor limitations in precision and application conditions prevent real-time acquisition of these time-varying physical quantities. Consequently, VML models constructed using initial-stage grease parameters may exhibit deviations between calculated bearing temperatures and actual measurements, rendering them insufficiently accurate for real-time bearing temperature estimation. Furthermore, from the perspective of the solving process, traditional thermal models adopt a forward-solving approach from physical infrastructure to simulation models to temperature rise results. Consequently, the calculation of thermal capacities, TRs, and heat sources inherently depends on dimensional and material parameters of bearing components [27; 28]. However, in most practical applications, only bearing type and basic model data are available. Critical manufacturing parameters such as detailed cage dimensions, raceway diameters of inner/outer rings, material properties, and lubrication conditions are either partially missing or entirely unknown, introducing significant uncertainties and complexities in thermal model construction. Although parameter ambiguity can be mitigated, the model can be used to predict the effect of the model on the material parameters. Figure 1: Comparison of temperature, grease state, and surface morphology of traction motor bearings during long-term durability operation. gated through high-precision metrology or inverse-solving approaches, the multi-objective optimization-based inverse calculation method for convective heat transfer coefficients proposed in [29]--which derives optimized parameters from limited experimental data--is currently restricted to steady-state temperature rise analysis under single constant-speed conditions. Its applicability throughout the entire lifecycle requires further investigation. Parameter identification, as a high-precision method for determining ambiguous numerical values, integrates theoretical models with experimental data for predictive applications. This technique has been widely implemented across multiple domains, such as motor control [30], aerospace systems [31], power transmission lines [32], and chemical engineering [33], addressing the identification of electromagnetic properties, modal parameters, vibration characteristics, and gas concentrations. In thermal parameter identification, [PERSON] et al. [34] developed a model-optimized automatic parameter identification scheme for lithium-ion batteries to mitigate thermal runaway in battery materials. [PERSON] et al. [35] proposed a thermal model and parameter identification method for calculating axial conductor temperatures of overhead lines in laboratory environments. [PERSON] et al. [36] established an advanced inverse thermal tomography strategy based solely on boundary-layer thermographic measurements. [PERSON] et al. [37] designed a modified particle filter algorithm with adaptive prediction time windows to identify time-varying parameters in HVAC spatial thermal models. [PERSON] et al. [38] introduced an online prediction method for electromagnetic-thermal behaviors in permanent magnet motors using improved lumped-parameter thermal networks with global parameter identification. When thermal model parameters exhibit uncertainties or time-dependent characteristics, constructing simplified mathematical frameworks with dedicated data transfer protocols to determine invariant parameters from partial sampled data becomes critically significant for developing reliable virtual layer mathematical models. In summary, while DT technology has garnered significant attention in industrial applications in recent years, its implementation for bearing thermal prediction remains in its nascent stages.