What are the benefits and challenges of using gradient-based sensitivity analysis in aerospace engineering?

1 Gradient-based sensitivity analysis

Gradient-based sensitivity analysis (GBSA) is a class of methods that use the first-order or higher-order derivatives of the system outputs with respect to the inputs to quantify the sensitivity of the outputs to the inputs. The inputs can be design variables, uncertain parameters, or objectives, and the outputs can be performance measures, constraints, or gradients. GBSA can be applied to both deterministic and stochastic optimization problems, and can be used for local or global sensitivity analysis.

2 Benefits of GBSA

GBSA has several advantages over other sensitivity analysis methods, especially for aerospace engineering problems. It can provide accurate and precise sensitivity information, as it captures linear or nonlinear relationships between inputs and outputs. GBSA can be integrated with gradient-based optimization algorithms, such as the adjoint method, to efficiently find optimal solutions for complex systems. Additionally, GBSA can handle high-dimensional problems without needing to sample or interpolate the input space. Furthermore, it can exploit the structure and sparsity of the system by using analytical, semi-analytical, or numerical methods to compute derivatives.

4 How to use GBSA effectively

To use GBSA effectively for aerospace engineering problems, there are some important factors and best practices to consider. For example, the level of derivative information should be chosen depending on the problem complexity, accuracy requirements, and computational resources. Additionally, the suitable method for computing the derivatives should be selected based on the system characteristics, model availability, and software capabilities. Moreover, derivative information should be validated and verified using techniques such as finite difference or complex step to guarantee the correctness and reliability of the sensitivity analysis results. It is also important to compare and contrast the GBSA results with other sensitivity analysis methods such as variance-based or sampling-based methods to determine the robustness and comprehensiveness of the sensitivity information.