Multi-variate soft sensor seeks accurate estimation of multiple quality variables using measurable process variables, which have emerged as a key factor in improving the quality of industrial manufacturing. The current progress stays in some direct applications of multitask network architectures; however, there are two fundamental issues remain yet to be investigated with these approaches: (1) negative transfer, where sharing representations despite the difference of discriminate representations for different objectives degrades performance; (2) seesaw phenomenon, where the optimizer focuses on one dominant yet simple objective at the expense of others. In this study, we reformulate the multi-variate soft sensor to a multi-objective problem, to address both issues and advance state-of-the-art performance. To handle the negative transfer issue, we first propose an Objective-aware Mixture-of-Experts (OMoE) module, utilizing objective-specific and objective-shared experts for parameter sharing while maintaining the distinction between objectives. To address the seesaw phenomenon, we then propose a Pareto Objective Routing (POR) module, adjusting the weights of learning objectives dynamically to achieve the Pareto optimum, with solid theoretical supports. We further present a Task-aware Mixture-of-Experts framework for achieving the Pareto optimum (TMoE-P) in multi-variate soft sensor, which consists of a stacked OMoE module and a POR module. We illustrate the efficacy of TMoE-P with an open soft sensor benchmark, where TMoE-P effectively alleviates the negative transfer and seesaw issues and outperforms the baseline models.

翻译：多变量软传感器旨在利用可测量的过程变量精确估计多个质量变量，已成为提升工业制造质量的关键因素。当前进展主要集中于多任务网络架构的直接应用，但这类方法仍存在两个亟需探究的根本性问题：（1）负迁移——尽管不同目标具有差异性的判别表示，但共享表示会导致性能下降；（2）跷跷板现象——优化器倾向于优先优化主导性且简单的目标，而牺牲其他目标。本研究将多变量软传感器重新定义为多目标问题，以同时解决上述两个问题并推动性能达到前沿水平。针对负迁移问题，我们首先提出目标感知混合专家模块（OMoE），通过目标专属与目标共享专家实现参数共享，同时保持各目标间的区分性；为解决跷跷板现象，我们进一步提出帕累托目标路由模块（POR），基于坚实的理论支撑动态调整学习目标权重以逼近帕累托最优。基于此，我们提出任务感知混合专家框架（TMoE-P），该框架由堆叠的OMoE模块与POR模块构成，旨在实现多变量软传感器的帕累托最优。通过公开软传感器基准实验验证，TMoE-P有效缓解了负迁移与跷跷板问题，并在性能上超越基线模型。