Thermal Modeling and Optimization of Mobile Device using modified LPV ROM

As computing power increases rapidly, thermal limit becomes the bottleneck of device performance. Therefore, performance estimation and design optimization through fast transient thermal simulation are crucial in the early design stage of System on Chip (SOC). The conventional linear time-invariant (LTI) reduced order model (ROM) has errors to predict the temperature of the mobile set because the mobile set has natural convection and radiative heat transfer condition which is a nonlinear factor. We introduce modified LPV (Linear Parameter Varying) ROM that can consider nonlinear terms. LPV ROM uses flow velocity as a scheduling parameter, but in the proposed modified LPV ROM approach we used heat transfer coefficient (HTC) as a scheduling parameter. This HTC is a function of the surface temperature and will include the non-linearity presented by natural convection and radiation. LPV ROM builds instant LTI ROM continuously for each time step by interpolating LTI ROM for various surface temperatures. A smartphone model with application processor (AP) was used for proof of concept. First, we generated the step responses of the smartphone for multiple heat transfer coefficient levels through “conduction only” transient thermal simulation. Second, LTI ROM was created for different heat transfer coefficients. Also, the relation between surface temperature and heat transfer coefficient was correlated through “computational fluid dynamics (CFD)” transient thermal simulation. Third, quick thermal simulation with modified LPV ROM was conducted by updating instant LTI ROM for each time step based on surface temperature. To verify the accuracy of modified LPV ROM, the transient temperature response of modified LPV ROM, LTI ROM, and detailed CFD simulation were compared. Using the modified LPV ROM, the acceptable temperature error was achieved at a speed more than 88,000 times faster than the existing CFD simulation for solving time. Finally, as an example of applying the modified LPV ROM, hundreds of transient simulations were performed through the EA algorithm to optimize Dynamic Thermal Management (DTM) parameters. Optimal DTM starting temperature and Proportional-Integral (PI) parameters were obtained successfully within 2 hours. Based on 500 EA solving, even including ROM creation time, LPV-ROM is about 30 times faster than CFD.