Engineering structures often exhibit multiple potential vulnerable positions during strong earthquakes, such as porcelain insulators and connection flanges of electrical equipment in substations. This paper proposes two types of machine learning (ML) chain models, where multiple individual models are linked end to end, to predict multiple peak seismic responses of substation equipment at the same time using intensity measures (IMs). One is a simple chain where the next input is the previous output, while in another one, the next input is combined by IMs and the previous output. The training mechanisms of ML chain models are presented by means of bio-inspired multi-objective optimization techniques for the hyperparameters of multiple individual ML models. A case study on a 1100 kV transformer bushing is then conducted. Artificial neural network-gradient boosting regression and artificial neural network-kernel ridge regression chain models are respectively established for predicting the peak stresses at two most vulnerable positions. Both the evaluation indicators and shaking table tests show enough prediction accuracy of the two ML chain models. Such chain models are qualified for identifying the initial damage to equipment, which can be employed for assisting post-earthquake rapid judgement and relief.