Sudden change is a widespread phenomenon in the process of engineering. The time system states changes occurs abruptly, the lower accuracy the traditional mathematical modeling methods based on calculus it will be. Theoretically, machine learning algorithms such as artificial neural networks, etc, can approximate any nonlinear function, this type of black box method makes no reasonable explanation for the catastrophe phenomenon. People tend to apply the cusp catastrophe model based on catastrophe theory to explain discontinuous changes in system state, however, the construction of traditional cusp catastrophe models is often based on amounts of prior knowledge to select input variables. On the condition that there is a lacking of prior knowledge and comparatively large dimensions of input variables, the model enjoys high complexity and poor accuracy. In order to solve the above-mentioned problems, the researcher has put forward a two-step method for constructing a cusp catastrophe model based on the selection of variables. The first step is to apply Multi-model Ensemble Important Variable Selection (MEIVS) to quantify the importance of the variables to be selected and extract important variables. The second is to use the extracted important variables to construct a cusp catastrophe model on the framework of Maximum Likelihood Estimation (MLE) and make comparison between linear and logistic models. It proved that the model is simple in form through MEIVS dimensionality reduction and enjoys better outperforms than the unreduced model in terms of evaluation indicators, which showed that the algorithm proposed in this essay had improved the accuracy of the model and reduced the complexity of the model. On a data set with catastrophe flags, cusp catastrophe model enjoys higher accuracy compared with linear model and logistic model. Therefore it can be used to explain the discontinuous changes of the research object, boasting practical engineering significance.