During mild moxibustion treatment, uncertainties are involved in the operating parameters, such as the moxa-burning temperature, the moxa stick sizes, the stick-to-skin distance, and the skin moisture content. It results in fluctuations in skin surface temperature during mild moxibustion. Existing mild moxibustion treatments almost ignore the uncertainty of operating parameters. The uncertainties lead to excessive skin surface temperature causing intense pain, or over-low temperature reducing efficacy. Therefore, the interval model was employed to measure the uncertainty of the operation parameters in mild moxibustion, and the uncertainty optimization design was performed for the operation parameters. It aimed to provide the maximum thermal penetration of mild moxibustion to enhance efficacy while meeting the surface temperature requirements. The interval uncertainty optimization can fully consider the operating parameter uncertainties to ensure optimal thermal penetration and avoid patient discomfort caused by excessive skin surface temperature. To reduce the computational burden of the optimization solution, a high-precision surrogate model was established through a radial basis neural network (RBNN), and a nonlinear interval model for mild moxibustion treatment was formulated. By introducing the reliability-based possibility degree of interval (RPDI), the interval uncertainty optimization was transformed into a deterministic optimization problem, solved by the genetic algorithm. The results showed that this method could significantly improve the thermal penetration of mild moxibustion while meeting the skin surface temperature requirements, thereby enhancing efficacy.
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