System-level Co-simulation of Mechatronic Systems for Design Space Exploration

Cost-driven design optimization helps companies to increase their net profits by reducing their production and planning costs from the design to mass production phases. Involving an accurate performance model as well as a cost estimation model at the design stage is essential to manufacture cost-optimal products that meet design specifications. Therefore, the developments in the accuracy and efficiency of the modeling, simulation and optimization of the products reckoning performance and cost-related aspects of the design have a profound effect on the end product.

Numerical modeling and simulation of mechatronic systems aim to reduce cost by replacing or minimizing the expensive test procedures at the design stage. However, they require a multi-domain approach as the physical domains that interact with each other are getting more multi-disciplinary in such systems. Besides the difference in inherent physical behavior over the subsystems of system-level models, the modeling formalism can also differ depending on the purpose of the simulation and the required level of detail. Some parts of the system require a distributed parameter description if an accurate geometrical representation is of paramount importance whereas for others an approximate lumped parameter description suffices. Due to this heterogeneity, each subsystem respectively can benefit from a dedicated modeling and time integration strategy. As the engineer or the simulation algorithm is up to some extent aware of the time scale of the physics of each subsystem, this information can be exploited by adopting a multi-rate integration approach.

Co-simulation is a special technique that enables each subsystem to be solved by a dedicated integrator and couples the input-output data between subsystems at run-time by a master orchestrator. Apart from using a dedicated time integration strategy intersystems, co-simulation allows adaptive stepping methods for communication and time integration based on the rate of change in system dynamics. The state-of-the-art adaptive co-simulation algorithms assume each co-simulation unit as black-box, and do not capitalize on existing dynamics or past simulation data sufficiently. This thesis proposes an adaptive algorithm to predefine time steps before running a co-simulation using the directional derivatives of subsystems and past co-simulations with similar dynamics. This offline adaptation methodology accelerates the solution and ensures a certain accuracy if sufficient iterations are provided. Moreover, an adaptive scheduling algorithm is developed to reduce the co-simulation error caused by the ad-hoc selection of the solution sequence of subsystems in serial co-simulations. 

The proposed offline adaptive co-simulation is especially beneficial for design space exploration applications where the system is repeatedly analyzed with gradually changing dynamics. The value proposition of this method is based on the assumption that the variables between consecutive design iterates do not change drastically. If such an assumption fails, the proposed benefits of the offline adaptation of time steps fall behind the state-of-the-art adaptation methodologies that adapt the time steps at run-time. An algorithm that guides the decision to select either run-time or offline adaptive co-simulation is proposed to ensure stable simulations in design optimization. The algorithm is validated in design optimization cases that it reduces the time-to-solution significantly providing that appropriate error tolerance is chosen.

Design optimization considering standardization of components leads to significant cost reduction of a product in mass production. To achieve cost reduction without sacrificing the diversity of customer needs, companies form families of similar products with distinguishable features. In this book, a product family optimization methodology is proposed. The methodology aims to minimize the production cost of an existing product family through the benefits of economies of scale while satisfying individual performance criteria. The methodology uses a nested approach to optimize the commonalities of components across products and component variants simultaneously. Optimization of commonalities is a computationally expensive combinatorial process. The methodology accelerates optimization by searching only the vicinity of the current design point in the commonality design space.

As a result, the research proposes a performant cost-driven optimization framework for product families. The framework uses the cost model as an objective function and performance models as constraint functions.
A simplified generic cost model that includes fundamental cost drivers, as well as standardization benefits, is developed.  A C-based co-simulation library that performs the proposed co-simulation techniques is implemented to evaluate the performance models of the products. An automated model update tool is developed to update multibody FE models from parametric CAD models if 3D models are present in performance models. Through the compilation of the tools and methodologies presented in this book, accurate and efficient simulations can be carried out to optimize industry-level mechatronic products.