How do you incorporate uncertainty in rocket mission planning?

1 Uncertainty sources

Uncertainty can have a significant impact on different aspects of a rocket mission, from the initial conditions to the objectives. Common sources of uncertainty include weather, measurement errors, system failures, and environmental disturbances. For instance, changes in wind, temperature, pressure, humidity, and precipitation can affect the rocket's aerodynamics and propulsion. Sensor and instrument inaccuracies or noise can disrupt the navigation and guidance systems. Additionally, components or subsystems such as engines, valves, pumps, batteries, computers, or communication devices may fail or degrade which can lead to performance issues. Finally, external forces or torques like gravity, drag, lift, solar radiation, magnetic fields, or collisions with debris or other spacecraft can cause changes to the rocket's trajectory or attitude.

2 Uncertainty quantification

Uncertainty quantification (UQ) is a process used to characterize and estimate the uncertainty in a rocket mission. It involves mathematical models, statistical methods, and computational tools to provide information on the probability, range, and distribution of uncertain parameters and variables. Aerospace engineers may use Monte Carlo simulation, sensitivity analysis, or surrogate modeling for UQ. Monte Carlo simulation involves generating a large number of random samples from the uncertainty distributions and evaluating the rocket mission performance for each sample. Sensitivity analysis varies one or more uncertain parameters or variables to measure their impact on the rocket mission performance. Surrogate modeling creates a simplified model of the rocket mission that can capture its main features and behaviors. UQ can reduce computational cost and complexity for analysis and optimization.

3 Uncertainty propagation

Uncertainty propagation (UP) is a process used to evaluate how the uncertainty in the input parameters or variables affects the uncertainty in the output parameters or variables of a rocket mission. UP seeks to provide information on the correlation, covariance, and dependency of the uncertain parameters or variables that determine the rocket mission outcomes. Aerospace engineers have several methods and tools for UP, such as linear propagation, nonlinear propagation, and Bayesian inference. Linear propagation assumes that the output parameters or variables are linear functions of the input parameters or variables and uses analytical formulas or matrix operations to calculate the uncertainty in the output parameters or variables. Nonlinear propagation does not assume any linearity or functional form of the output parameters or variables and uses numerical methods or simulation techniques to calculate the uncertainty in the output parameters or variables. Bayesian inference utilizes prior knowledge and observed data to update the uncertainty in the input parameters or variables and then propagate it to the output parameters or variables. Each of these techniques can provide fast, accurate, realistic, reliable, informative, and adaptive results depending on the uncertainty level and model type.

4 Uncertainty management

Uncertainty management (UM) is the process of reducing, mitigating, or exploiting uncertainty in a rocket mission to improve its performance, reliability, and robustness. Aerospace engineers use a variety of methods and tools for UM, such as robust design, adaptive control, and flexible operation. Robust design involves designing components and subsystems to be insensitive or tolerant to uncertainty in their parameters. Adaptive control involves adjusting control inputs or parameters to counteract the uncertainty in the dynamics. Lastly, flexible operation involves changing mission objectives or constraints to exploit uncertainty in the environment or opportunities. All of these techniques can help improve the rocket's quality, durability, efficiency, stability, accuracy, agility, flexibility, resilience, and profitability under uncertainty.