## 1 Introduction
[13] employed an independently developed heterogeneous surrounding rock test simulation system to analyze the impact of periodic wind temperature on the evolution of the surrounding rock temperature field. The results indicate that, under periodic ventilation conditions, the relationship between the surrounding rock temperature and time aligns with the cosine function relationship. [PERSON] et al. [14] explored the impact of seasonal wind temperature on the evolution patterns of the temperature field in the surrounding rock of roadways. The results show that the surrounding rock can be adjusted due to the influence of seasonal temperature differences. In their study, [PERSON] et al. [15] formulated a mathematical model for the unsteady temperature field of roadway-surrounding rock grounded in energy conservation principles and Fourier's law. They developed a solution program and utilized the finite volume calculation method to solve the temperature field of the roadway-surrounding rock. [PERSON] et al. [16] examined the correlation between the temperature field of the roadway-surrounding rock and the depth and ventilation time of the surrounding rock. They noted that the farther away from the roadway wall, the more stable the temperature change. The shape and size of the heat-regulating ring visibly change over time. [PERSON] et al. [17] conducted experiments on the thermal characteristics of surrounding rock based on a mathematical model of surrounding rock heat transfer in deep underground spaces. They examined the effects of heat transfer time, air temperature, and radial displacement on temperature distribution. In their study, [PERSON] et al. [18] developed a mathematical model for deep roadway-surrounding rock. They investigated the impact of the insulation layer on the temperature field inside and outside the tunnel. The results indicated that the disturbance range of wall temperature and surrounding rock temperature decreased due to the insulation layer. When dealing with data obtained from experimentsor numerical simulations, many researchers analyze correlations among the data through fitting. For instance, using a Yunnan roadway as a case study, [PERSON] et al. [19] observed that the temperature field of the roadway-surrounding rock with secondary lining exhibited a rapid increase, rapid decrease, stability, and slight decrease over time. In the spatial dimension, the temperature in the roadway follows an 'n' shape along the longitudinal direction, and the temperature profile of the surrounding rock is parabolic. [PERSON] et al. [20,21] examined the spatio-temporal evolution pattern of the dimensionless surrounding rock temperature field using physical modeling tests and performed nonlinear fitting of the data using some mathematical software. They observed that the dimensionless temperature and dimensionless radius of the roadway-surrounding rock exhibited an exponential function relationship, while the dimensionless temperature and dimensionless time approximated the Hill function relationship. [PERSON] et al. [22] formulated a numerical model for the temperature field of roadway-surrounding rock employing the finite difference method. Nonlinear fitting of the numerical simulation results revealed the relationship between the disturbance range of the surrounding rock temperature field and ventilation time. According to the case analysis, when the disturbance range is \(R=13.6\), the temperature disturbance range does not significantly expand after four years of ventilation. As the above shows, the fitting relationship between surrounding rock temperature and time or space is typically nonlinear. In addressing nonlinear fitting problems, many researchers commonly employ the Gauss-Newton method or its enhancements. For instance, [PERSON] et al. [23] introduced an effective curve-fitting technique based on the Gauss-Newton (GN) method with a variable damping coefficient to assess the voltage parameters of the lightning pulse.