Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): II. Paradigm Application to a Bernoulli Model Comprising Uncertain Parameters

This work presents the application of the recently developed “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N)” to a simplified Bernoulli model. The 5th-CASAM-N builds upon and incorporates all of the lower-order (i.e., the first-, second-, third-, and fourth-order) adjoint sensitivities analysis methodologies. The Bernoulli model comprises a nonlinear model response, uncertain model parameters, uncertain model domain boundaries and uncertain model boundary conditions, admitting closed-form explicit expressions for the response sensitivities of all orders. Illustrating the specific mechanisms and advantages of applying the 5th-CASAM-N for the computation of the response sensitivities with respect to the uncertain parameters and boundaries reveals that the 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Uncoupled PID Control of Coupled Multi-Agent Nonlinear Uncertain Systems

In this paper, PID（proportional-integral-derivative） controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimensional nonlinear uncertain dynamical system, which only has access to its own tracking error information and does not need to communicate with others. This paper will show that a 3-dimensional manifold can be constructed based on the information about the Lipschitz constants of the system nonlinear dynamics, such that whenever the three parameters of each PID controller are chosen from the manifold, the whole multi-agent system can be stabilized globally and the tracking error of each agent approaches to zero asymptotically. For a class of coupled first-order multi-agent nonlinear uncertain systems, a PI controller will be designed to stabilize the whole system.

Adaptive-surrogate-based robust optimization of transonic natural laminar flow nacelle

Natural Laminar Flow(NLF)technology is very effective for reducing the skin friction drag of aircraft engine nacelle,but the aerodynamic performance of NLF nacelle is highly sensitive to uncertain working conditions.Therefore,it’s imperative to incorporate uncertainties into the design of NLF nacelle.In this study,for a robust optimization of NLF nacelle and for improving its efficiency,an adaptive-surrogate-based robust optimization strategy is established,which is an iterative optimization process where the surrogate model is updated to obtain the real Pareto front of multi-objective optimization problem.A case study is carried out to validate its feasibility and effectiveness.The results show that the optimization increases the favorable pressure gradient region and the volume ratio of the nacelle by increasing its lip radius and reducing its maximum diameter.And the aerodynamic robustness of the NLF nacelle is mainly determined by the lip radius,maximum diameter of nacelle and location of the maximum diameter.Compared to the initial nacelle,the optimized nacelle maintains a wide range of low drag and high laminar flow ratio in the disturbance space,which extends the average laminar flow region to 21.6%and facilitates a decrease of 1.98 counts in the average drag coefficient.