## 1 Introduction  
Researchers found in the 1950s that the surface heat trails formed by the discharge of cooling water from surface and underwater vehicles had thermal infrared properties that are notably different from those of ordinary seawater and may be used as a key detection method. Therefore, the study of thermal trails left by submerged cars has steadily attracted the interest of scientists. Orthogonal experimental design (OED) is a design approach for studying various components and levels [1]; it is an efficient, quick, and advantageous experimental design method that selects representative points based on orthogonality. In this study, the orthogonal technique was utilized to analyze the experimental data further in order to determine the elements impacting the sea surface infrared features of an underwater vehicle's wake and their interaction laws. Researchers have conducted several theoretical evaluations, numerical simulations, and practical investigations of underwater vehicles' wakes since 1960. Conclusions have been reached about the generating processes, disturbance causes, floating features, and other relevant parameters [2, 3, 4, 5, 6, 7, 8, 9, 10]. According to [PERSON] et al., the key variable determining the detection distance is the temperature differential between the surrounding ocean and the underwater vehicle's wake [11]. In order to detect vehicle wakes, [PERSON] et al. developed a water-based infrared (WDPUV-IR) probability software and established models of detector detection probability and noise equivalent temperature difference, wake and sea surface temperature difference, and evaluation of the detection probability at various resolution levels [12]. A self-propulsion model was used by [PERSON] and [PERSON] [13] to investigate wakes in settings with different densities. [PERSON] and [PERSON] examined the spectrum features of the surface disturbance while researching the influence of an undersea submerged body on a free surface. The submersible's almost free surface navigation track may be acquired using this technique. According to the investigation, the navigation speed has the most impact on the free surface among the three influencing parameters of diving depth, body length, and navigation speed. The distinctive waveform of the submersible at a certain sailing speed may be seen at various depths. It is extremely doable to discover the characteristics of an unknown submersible by detecting the spectral features, which also make it possible to estimate the trip depth and the sailing speed of the submersible [14]. The evolution of a wake from towed and self-propelled submersibles was compared by [PERSON] et al., who found that the self-propelled submersible's wake will fade more quickly on average. Additionally, buoyancy lengthens the duration of the disturbance's wake. The wake width in the vertical direction is wider for self-propelled submersibles [15]. Previous wake trail thermal models were created under a variety of ideal conditions, such as calm water. The underwater vehicle's hot wake's heat exchange process will vary depending on the level of sea conditions, in contrast to the realistic marine environment where sea conditions of three or more levels are typical and where complex sea conditions produce swells that affect the underwater buoyancy pattern and surface distribution characteristics of the underwater vehicle's wake. The examination of the affecting elements, such as speed, diving depth, hot wake spray speed, and hot wake temperature, also uses single-factor analysis. This work used the orthogonal method to preliminarily analyze the influencing factors of the surface infrared characteristics of the wake of underwater vehicles under surge conditions and their interaction; it increases the likelihood of detecting and precisely identifying the wake of large underwater vehicles by accurately modeling the radiation characteristics of the hot wake under surge conditions.