Leaders in the aerospace and defense industries are typically engaged in large-scale projects that seek to produce next generation capabilities and technologies. These projects include the development of the Digital Twin and a Digital Engineering Ecosystem as discussed in the Department of Defense’s Digital Engineering Strategy. The scale and complexity of these projects means that high-fidelity physics-based simulations can take weeks to run and deliver results even for sub-components of the overall project.
This is too slow to make large volume performance predictions such as for design space exploration, optimization, and Uncertainty Quantification (UQ) or to develop an authoritative truth source. However, without performing these analyses, engineers may fail to account for variability and uncertainty at each step of the design, the manufacturing, and the implementation. Therefore, there exists a need for tools and techniques that balance computational speed and model accuracy.
SmartUQ has developed a cutting-edge statistical and machine learning toolset to build fast and accurate predictive models (a.k.a., emulators). SmartUQ allows users to build emulators of complicated systems based on a limited number of high-fidelity simulation runs or experimental tests. Emulators can be sampled to perform valuable engineering functions including optimization, sensitivity analysis, Verification, Validation and UQ (VVUQ), and rapid evaluation of potential designs. Recognition of the coming necessity of such statistical and data analytics driven approaches can be found in government standards and memoranda.
NASA’s Standard for Models and Simulations (NASA-STD-7009A) requires the documentation of model input uncertainties as well as estimation of output uncertainties. As stated in Section 4.2.7, “No M&S [modeling and simulation] is a perfect replica or imitator of the RWS [real world system] for which the model is used to study. Characterizing the uncertainty in M&S results is, therefore, at least one way to qualify those results.”
The Director, Operational Test and Evaluation (DOT&E), an advisor to the US Secretary of Defense, has stressed the need for statistical approaches to modeling and simulation both in memoranda and in the DOT&E Test and Evaluation Master Plan (TEMP) guidebook.
In a memorandum dated January 17, 2017, the Director makes clear the need for a statistical toolset including “empirical models (a.k.a. emulators or meta-models) should be used to understand M&S outcomes across the operational space and assist in the uncertainty quantification.”
The memorandum goes on to discuss the significance of quantifying uncertainties in M&S through probabilistic methods and the need for a tool that can combine or calibrate M&S with physical data, as “these additional tools can support a variety of important activities including uncertainty analysis and error propagation, sensitivity analysis, and data assimilation.”
In addressing the design concern of flutter of a rocket fin or aircraft wing, it is important to quantify the major vibrational modes and frequencies. The interaction between the fins or the wing and the airflow can be modeled in a CFD package. At its root, this is essentially a stochastic process, owing to the time varying turbulence of the flow during flight. Further, as time proceeds, the modes and frequencies may change due to the fuel consumption or other activities during flight. Thus, it is necessary to predict the probability of certain modes as a function of time. However, performing the necessary high-fidelity simulations to investigate all potential modes over the flight duration is too computationally expensive to be feasible in practice.
Enter SmartUQ’s functional emulation technology and tools for building accurate predictive models. A limited number of simulation runs is selected using SmartUQ’s Design of Experiments (DOE) tools, and an emulator is created from the simulation results. The emulator is a statistical model representing the high-fidelity physics-based simulations which can be rapidly sampled to obtain the data necessary to statistically quantify the uncertainty in the vibrational modes.
For a given launch vehicle dry weight, the amount of solid rocket fuel needed for launch into a desired orbit varies. Carrying too much or too little fuel comes with the risk of unnecessary costs ranging from tens of thousands of dollars per kilogram of excessive mass launched to hundreds of millions of dollars if the payload is lost or rendered inoperable.
The ability to quantify the probability distribution of fuel requirements for a given mission profile is therefore an important consideration. The source of the variability in fuel requirements is due to uncertainty in the propellant’s burning rate. This uncertainty can be traced to every stage of the rocket motor’s production beginning with variability in the chemical properties of the raw materials, to the processing conditions under which the propellent is manufactured, to the process of bonding the grain onto the motor case.
SmartUQ can be used to analyze how the various uncertainties combine and propagate from the selection and procurement of raw materials to the final rocket motor. Doing so helps ensure a successful launch while reducing fuel waste and the potentially large costs associated with launching unnecessary fuel mass.
To learn more about UQ in the aerospace and defense industries, check out SmartUQ's white papers and webinars.
