目的 为确保防腐领域的熔结环氧粉末涂层(FBE涂层)长期安全运行，采用灰色系统理论构建数学模型，预测涂层在不同环境条件下的失效速度和服役寿命。方法 采用电化学技术，测定了FBE涂层涂覆的碳钢在25、60、70、80和90 ℃ 5种温度下，在3.5%(质量分数)NaCl溶液中的低频交流阻抗值，利用FTIR测试分析FBE涂层在浸泡过程中官能团的变化，利用SEM/EDS对浸泡末期的FBE涂层截面和Q345E的形貌变化进行观察。基于灰色系统理论的GM(1,1)模型，探究了FBE涂层的低频阻抗模值与其在模拟液中浸泡时间的相关性，并据此构建了用于预测涂层腐蚀寿命的数学模型。此外，模型还成功定义了一个定量常数a，用以描述涂层失效的速度。结果 涂层在90 ℃浸泡100 d后，|Z|0.01 Hz下降了4个数量级，为10⁷ Ω.cm²，附着力从1级降为3级，将10⁷ Ω.cm²作为FBE涂层的失效标准。通过对比不同温度浸泡下FBE涂层的失效常数a，发现相较于25 ℃，60 ℃的FBE涂层失效速度提高了1.9倍，60~90 ℃每提高10 ℃，FBE涂层失效速度分别增加了2.1、2.2和1.3倍。200 μm的FBE涂层在25 ℃的常温环境中，服役寿命达2 240 d;环境温度升高至60 ℃，涂层的服役寿命减半至1 120 d。随着温度继续上升，涂层的耐久性急剧下降，70、80和90 ℃的服役寿命分别为400、215和100 d。结论 经过数学统计验证和试验结果对比验证，该模型精度良好，可靠性高，能够对FBE涂层的服役寿命进行准确预测。90 ℃浸泡下，FBE涂层的失效过程虽然大幅缩短，但是涂层失效机理基本没有发生变化，温度升高只是加快了涂层内部分子的运动，没有产生新的老化反应。

In the present day, coatings serve as a vital method for shielding metals from the detrimental effects of corrosion. Most researchers focus on how to improve the performance of the coating, but ignore how to predict the life of the coating. While a few scholars have studied the service life of thin-film, solvent-borne organic coatings, there is a relative lack of research on heavy-duty anti-corrosion coatings under extreme environmental conditions. Therefore, there is an imperative for studies that aim to predict the service life of heavy-duty anti-corrosion coatings. Grey prediction can effectively predict the future trend of an uncertain system with limited data samples and insufficient information. In order to ensure the long-term safe operation of FBE coatings in the field of corrosion protection, the Grey System Theory was adopted to construct a mathematical model for quantifying and predicting the failure rate and service life of coatings under different environmental conditions. With electrochemical techniques, the low-frequency alternating current impedance values of carbon steel coated with FBE were measured at five distinct temperatures of 25, 60, 70, 80 and 90 ℃, all within a simulated seawater solution. Based on the Grey System Theory‘s GM(1,1) model, the correlation between the low-frequency impedance modulus of the FBE coating and the soaking time in the simulated liquid was investigated. Therefore, a mathematical model for predicting the corrosion life of coatings was established. Additionally, the mathematical model successfully defined a quantitative constant α to describe the rate of coating failure. It was found that |Z|0.01 Hz was 107 Ω.cm2 after immersion at 90 ℃ for 100 d, which decreased by four orders of magnitude, and the adhesion also decreased from grade 1 to grade 3, allowing 107 Ω.cm2 to be used as a failure criterion for FBE coatings. FBE coating samples were soaked at five temperatures of 25, 60, 70, 80 and 90 ℃. The low-frequency impedance values in the end period were around 2.69×1010 Ω.cm2, 8.65×109 Ω.cm2, 7.15×108 Ω.cm2, 3.49×107 Ω.cm2, and 1.10×107 Ω.cm2, respectively. A mathematical model was used to successfully predict the service life of 200 μm FBE coatings in 3.5% NaCl solution at five temperatures of 25, 60, 70, 80 and 90 ℃. Compared with 25 ℃, the failure constants of the FBE coatings increased by 1.9, 4.0, 9.0 and 11.5 times at 60, 70, 80 and 90 ℃. It is also concluded that a 200 μm FBE coating has a service life of up to 2 240 days in a room temperature environment of 25 ℃. When the ambient temperature rises to 60 ℃, the service life of the coating is halved to 1 120 days. As the temperature continues to rise, the durability of the coating drops sharply, with the life reduced to 400 days at 70 ℃ and further to 225 days at 80 ℃. Under the extreme high temperature of 90 ℃, the service life of the FBE coating is only 100 days. The model is verified to have good accuracy and high reliability.