Multi-type mixed response Gaussian process with parameter estimation embedded in latent variable approximation

Equipment performance experiments often collect multiple response metrics concurrently, comprising both qualitative and quantitative measures with potential complex interdependencies. However, conventional surrogate models typically fail to capture such intricate data structures. Therefore, joint modelling of multi-type mixed response data remains a critical challenge in the field of experimental design and evaluation. To address this issue, a multi-type mixed response Gaussian process model (MMRGP) is proposed in this paper, inspired by multi-output Gaussian process frameworks. The model unifies disparate data types by introducing latent variables for categorical responses and constructs a mixed-response covariance matrix to characterize inter-response correlations. However, incorporating latent variables makes parameter estimation dependent on them, while their approximate optimization is concurrently affected by model parameters. To resolve this coupled problem of parameter estimation and latent variable approximation, a bi-level optimization method is proposed that embeds latent variable approximation within parameter estimation, enabling simultaneous solving and refinement. The proposed method is validated through numerical examples and real-world datasets involving mixed responses. Comparative analyses show superior prediction accuracy and stability, with prediction errors reduced by approximately 10%–50% compared to independent modelling approaches. Finally, the MMRGP model is applied to radar anti-jamming performance experiment. The results confirm the practical efficacy and reference value for engineering applications.