## 1 Introduction
[PERSON] [21] proposed a self-organizing feature mapping (SOM) neural network to assess the health state of the gearbox rolling bearing. The neural network model can automatically extract complex features and has strong nonlinear modeling capabilities, but it requires a large amount of high-quality labeled data, which is hard to obtain and has poor model interpretability. Probabilistic models are also commonly used in the health assessment of rolling bearings. [PERSON] [19] used the hidden Markov dynamic pattern recognition theory to evaluate the health of rolling bearings. [PERSON] [20] used the Gaussian mixture model to calculate the likelihood probability as a health factor characterizing component degradation. Based on Bayesian theory, [PERSON] [20] quantified the overlap degree between the features of the state space to be evaluated and the health state space as the health indicator of the bearing degradation state so as to realize the state degradation assessment of rolling bearings. The probabilistic model has strong interpretability and can clearly describe the probabilistic relationship between the bearing state and the monitoring data. However, probabilistic models have relatively poor robustness and are highly sensitive to data quality and distribution assumptions. When the data contains noise or deviates from the assumed distribution, the performance of bearings evaluated by the model may significantly degrade. The multivariate state estimation technique (MSET) is a non-parametric data-driven model [20]. By taking the historical health data of the equipment as input, the model can build the historical memory matrix of MSET, which contains health observation vectors under different working conditions, learning the health law and service characteristics of the equipment. When a new observation vector is input, it will be matched with vectors under all working conditions in the historical memory matrix, and the health vector output under the most similar working conditions will be set as the baseline to achieve the effect of removing the influence of working conditions. When the new observed data deviates from the health space, the performance of the equipment deteriorates [20]. Since MSET can establish a health baseline for mechanical equipment under multiple operating conditions without relying on hard-to-obtain fault data, and due to its strong robustness, it has been widely applied in the field of mechanical equipment health assessment [20]. [PERSON] [20] proposed a wind turbine condition monitoring method based on MSET, which aims to achieve fault early warning of wind turbine components. [PERSON] [20] proposed an improved MSET with a composite operator (CO-MSET) for electro-mechanical actuators' health indicator extraction. [PERSON] [20] established a fault warning model for induced draft fans by using MSET. These studies established a health baseline based on the health data of the mechanical equipment, which is convenient for the subsequent health assessment and maintenance strategy formulation. Owing to the characteristics of MSET, both the input observation vector and the output estimation vector (health baseline) are typically high-dimensional vectors encompassing multiple performance parameters. This allows the algorithm to construct a high-dimensional state-space model, thereby more accurately characterizing the complex nonlinear relationships between bearing operating states and multi-sensor data. However, in current research utilizing MSET for mechanical equipment health assessment, Euclidean distance is commonly integrated with MSET to quantify the deviation between the observation vector and the estimation vectors (the health baseline). However, Euclidean distance fails to effectively eliminate the influence of dimensional differences when processing multidimensional parameters with varying units [20], and errors may be introduced into the deviation measurement, consequently compromising the accuracy and reliability of health assessment.