It is necessary to conduct a safety assessment for pipelines which are regarded as important lifeline projects after an earthquake. Since the random process of loading in earthquake engineering requires a large amount of samples, this paper establishes a non-random vibration method based on convex model theory and applies it to small sample engineering. Moreover, a space–time analytical model of buried pipeline and a finite element model are established to solve the dynamic response of

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... with non-random process seismic excitation. Furthermore, the randomness of the stress values of the pipeline subjected to earthquake and the fuzziness of the degree of damage to pipelines are considered. Therefore, a novel method for assessing damage to pipelines is proposed based on cloud model. The results indicate that an analysis of non-random vibration combined with the cloud inference method can solve the fuzziness and randomness of the quantitative description and qualitative concept conversion for damage evaluation of pipelines. The method is also an adaptive and effective assessment method for pipelines exposed to earthquake and is able to promote safety management of pipeline engineering.