Soft sensors are used to calculate the real-time values of process variables which can be measured in the laboratory only or require expensive online measurement tools. A set of mathematical expressions are developed and trained from historical data to exploit the statistical knowledge between online and offline measurements to ensure a reliable prediction performance, for optimization and control purposes. This study focuses on the development of a mixed-integer optimization problem to perform input selection and outlier filtering simultaneously using rigorous algorithms during the training procedure, unlike traditional heuristic and sequential methods. Nonlinearities and nonconvexities in the optimization problem is further tailored for global optimality and computational advancements by reformulations and piecewise linearizations to address the complexity of the task with additional binary variables, representing the selection of a particular input or data. The proposed approach is implemented on actual data from two different industrial plants and compared to traditional approach.

软传感器用于计算过程变量的实时值，这些值只能在实验室中测量或需要昂贵的在线测量工具。根据历史数据开发和训练一组数学表达式，以利用在线和离线测量之间的统计知识，以确保可靠的预测性能，以实现优化和控制目的。本研究的重点是开发混合整数优化问题，以便在训练过程中使用严格的算法同时执行输入选择和异常值过滤，这与传统的启发式和顺序方法不同。通过重构和分段线性化，优化问题中的非线性和非凸性进一步针对全局最优性和计算进步进行定制，以使用额外的二进制变量（表示特定输入或数据的选择）来解决任务的复杂性。所提出的方法是根据来自两个不同工厂的实际数据实施的，并与传统方法进行比较。