To better handle problems with non-preferential multi-outputs (NPMO), a new approach is proposed in this study by employing the belief rule base (BRB) to provide a superior nonlinearity modeling ability as well as good explainability. The new approach is thus called NPMO–BRB. First, a new optimization model is constructed where the optimization objective is the integration of multi-outputs and respective constraints are designed. Then, a new optimization algorithm with a new customized gene makeup is designed where the NPMO–BRB inferencing process is embedded in the fitness calculation procedure. A practical case study on Changsha Metro Line 4 is studied to use multiple geological parameters to infer multiple operational parameters. Case study results show that NPMO–BRB has shown superior performance in comparison with the random forest (RF), the backpropagation neural network (BPNN), the Gradient Gaussian Process (GPR), as well as multiple separate BRBs. Owing to the explainability provided by the NPMO–BRB approach, further investigations into the belief distribution comparison reveal more information that can be used as practical work guidelines.

为了更好地处理非优先多输出（NPMO）问题，本研究提出了一种新方法，该方法采用置信规则库（BRB）来提供卓越的非线性建模能力和良好的可解释性。因此，新方法被称为 NPMO-BRB。首先，构建了一个新的优化模型，其中优化目标是多输出的集成，并设计了各自的约束。然后，设计了一种具有新的定制基因组成的新优化算法，其中 NPMO-BRB 推理过程嵌入在适应度计算过程中。以长沙地铁 4 号线的实际案例为研究对象，利用多个地质参数推断多个运行参数。案例研究结果表明，与随机森林 (RF) 相比，NPMO-BRB 表现出优越的性能，反向传播神经网络 (BPNN)、梯度高斯过程 (GPR) 以及多个独立的 BRB。由于 NPMO-BRB 方法提供的可解释性，对信念分布比较的进一步调查揭示了更多可用作实际工作指南的信息。