## 1 Introduction  
Recently, pipelines have become regarded as important lifeline projects for transporting energy [1, 2]. As the dependence of global energy demand on oil/gas grows steadily, pipelines have become the primary transportation infrastructure [3]. Many methods for monitoring the condition of pipelines and for leak detection/pinpointing through proper sensors have been developed [4, 5, 6, 7]. However, the 21 st century is an era of frequent earthquakes [8, 9]. The Hyogo-Ken Nanbu earthquake of 1995 in Japan was a recent example of an earthquake which caused damage to pipelines; it not only led to gas leakage, but also caused fires [10]. Furthermore, the Chi-Chi earthquake of 1999 in Taiwan caused serious damage to pipelines along with serious economic losses and environmental damage [11].  
In order to analyze the response of pipelines to seismic loads, numerous research methods have been presented. Wave theory is a classic analysis applied to the response of pipelines to earthquakes. However, this method can only be used for simply static analysis, without considering the dynamic behavior of a pipeline in seismic analysis [12, 13]. It is well known that seismic loading is described by a random process. Random seismic response analysis of buried pipelines has been presented, considering the random spatial influence [14, 15]. In some areas, it is impossible to obtain sufficient seismic data samples, and therefore the convex model theory is proposed [16]. A structural dynamic response method based on interval analysis has been put forward, which involves only the boundary of uncertain parameters [17]. Subsequently, many interval analysis techniques were used to calculate the static response and dynamic response of uncertain structures with the loads [18; 19]. Therefore, the establishment of a non-random process model for seismic loads based on small amounts of data is an effective complement to the random vibration method for investigating the response of pipelines with earthquakes. The application of fuzzy comprehensive evaluation model focuses on management science, safety assessment, risk assessment, and other fields [20]. In a fuzzy set, the degree of membership is used to describe the degree of comparison, which is better than the certain evaluation. However, the determination of precise membership is subjective and usually relies on expert experience or statistical methods. Meanwhile, evaluation itself has characteristics of randomness and fuzziness. Therefore, the cloud model is proposed to transform between qualitative knowledge description and qualitative concept, which has quantitative value to reflect the uncertainty of the concept. In the meantime, the cloud inference can interpret not only classical random theory and fuzzy set theory, but also define the randomness and fuzziness of data [21]. Thus, the cloud inference is more applicable and universal in the representation of uncertain conceptions when referring to the evaluation of practical engineering [22; 23].  
In this paper, a model of buried pressure pipelines with seismic excitation of non-random processes is proposed to solve the seismic response with a small sample. After obtaining the interval response results, the fuzziness and randomness of the membership relationship are both considered. A corresponding analysis method of pipeline damage degree based on cloud model is additionally obtained to make the evaluation result more objective and accurate.