Efficient extrapolation for parallel co-simulation of coupled systems (CHOPtrey)
Résumé
Building high-fidelity system-level models of Cyber-Physical Systems (CPS) is a challenging duty. A first problem is the diversity of modeling and simulation environments used by the various involved multidisciplinary teams. Particular environments are preferred for a specific use, due to distinctive strengths (modeling language, libraries, solvers, cost, etc.). The Functional Mock-up Interface (FMI) specification has been proposed to improve this issue. A second problem is the growing complexity of such high-fidelity models and their induced prohibitive CPU execution time. Indeed, major system-level simulation softwares are relying on sequential ODE/DAE solvers. They are currently unable to efficiently exploit the available parallelism provided by multi-core chips. In addition, CPS are commonly modeled as hybrid models where the major challenge resides in their numerous discontinuities. Indeed, discontinuities usually prevent high integration speeds with variable-step solvers. We propose a modular co-simulation of a split model, where each sub-model is integrated with its own solver. Thanks to splitting, high integration speeds can be reached when using LSODAR ,a variable step solver with a root-finding capability. Nevertheless, partitioning a complex model into several lesser complex sub-models also brings some difficulties that need to be managed. First, partitioning may add virtual algebraic loops, therefore involving delayed outputs, even with an efficient execution order. To avoid the latter, we propose in a new co-simulation method based on a refined scheduling approach. This technique, denoted "RCosim" , retains the speed-up advantage of modular co-simulation thanks to the parallel execution of the sub-models. Furthermore, it improves the accuracy of simulation results through an offline scheduling of operations that takes care of model input/output dynamics. Second, partitioning and even co-simulation require synchronization between coupled models to exchange updated data to reduce numerical error propagation in simulation results. Thus, tight synchronization, using small communication steps, is required between blocks. This greatly limits the possibilities to accelerate the simulation. Adaptive communication steps may better handle changes in model dynamics. Meanwhile, stability of multi-rate simulators needs to be carefully assessed. Data extrapolation over steps is expected to enhance the precision over large communication steps. However, complex models usually present non-linearities and discontinuities, entangling forecasts from past observations only. We propose a Computationally Hasty Online Prediction framework (CHOPred) to stretch out synchronization steps with negligible precision changes in the simulation, at low-complexity. It allows to improve the trade-off between speed-ups, needing large communication steps, and precision, needing frequent updates for model inputs. It is based on a Contextual & Hierarchical Ontology of Patterns (CHOPatt) that handles the discontinuities of exchanged signals by selecting appropriate Causal Hopping Oblivious Polynomials (CHOPoly). CHOPtrey uses a time-depending oblivion
faculty for polynomial extrapolation with an independent power weighting on past samples. It
accounts for memory depth changes required to adapt to sudden variations. Computations are per-
formed on frames of samples hopping at synchronization steps.It is implemented on xMOD tool
in combination with model splitting and parallel simulation. It is applied on a hybrid dynamical
engine model where the split parts are exported as FMUs from Dymola.
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