Virtual Sensors Based on Finite Element Method: Balancing Accuracy, Runtime and Offline Effort

Access to internal fields such as stress, temperature, and fatigue indicators is essential for condition monitoring, yet direct sensing is often impractical. Finite element method (FEM)-based virtual sensors address this gap by combining sparse measurements with physics-based models. This work compares two virtual sensor workflows. The live FEM approach executes a model on demand and provides high-fidelity estimates at the cost of multi-second runtimes. The lookup database approach shifts computation offline by precomputing responses and answering online queries by fast interpolation. We introduce a quantitative cost model that links measured runtime scaling, offline construction effort, and online latency to deployment choices. The cost model is evaluated through timing studies, accuracy assessments, and an empirical break-even analysis relating offline effort to the expected number of online queries. Two case studies illustrate the method, a nonlinear tension-bar benchmark and a steady-state thermal model of a CPU die. Live FEM runtime follows a power law with α≈1.2 for the tensile case and an effective α≈0.66 for the CPU case due to dominant overheads. The resulting rules translate accuracy targets and latency budgets into workflow-selection criteria that support integration into digital-twin and monitoring pipelines.