SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method
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Engineering topics
Publications and source records attributed to Joel Sills.
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The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.
Engineers need to effectively communicate the justification and value of their modal testing and model correlation in terminology familiar to decision makers as it relates to the program’s risk tolerance. This communication must relate to the program’s risk tolerance and the metrics used to judge the performance of both the program and individual decision makers. The challenge is the terminologies familiar to engineers and decision makers are quite different and seemingly unrelated. The engineering profession has developed a specific terminology to solve highly technical issues, which are many times themselves unique to very specific engineering problems. It is all too easy for engineers to believe that everyone in their organization, including the decision makers, has an intrinsic understanding of what they do and the value it brings to the program’s success. This is especially true for young engineers who have recently spent the last four plus years in an academic engineering learning environment, which has a highly technical research oriented atmosphere. Effective communication with decision makers is increasingly important as the technical breadth and practical program and project experience level for up and coming decision makers diminishes. It is not unusual for the decision makers to have technical knowledge in a domain different from structural dynamics (e.g., electronics or systems). Competition among satellite manufactures has increased the focus on programmatic cost and ability to deliver on schedule. NASA programs are also seeing more restrictive programmatic cost and schedule constraints, which impact both analysis and testing. It should also be noted that a comprehensive suite of tests are required to verify a satellite’s design capability with some margin. These tests include static strength verification tests, shock, acoustic, and vibration tests (sine and random) of systems, subsystems, and components. Each of these verification tests provide opportunities for model correlation and risk reduction. It is important to recognize dynamic loads/modal test models may not include all of the flight hardware (i.e., harness, coax, waveguides, connectors, etc.) and the previously mentioned tests are still required for qualification/verification of the design. This paper provides tips to young engineers on how to bridge this communications gap, have a better understanding of the environment in which decision makers operate, and assist them to better support successful missions. While this paper primarily focuses on modal testing and model correlation as related to spacecraft missions, the concepts and recommendations presented here are equally applicable to other fields such as aeronautics, automotive, power generation, etc.
As test articles become dimensionally larger, more complex, and massive in weight, combined with the need to excite them to higher than traditional levels in order to identify their nonlinear characteristics, modal shakers that can generate significantly higher force levels, have longer stroke lengths, and possess higher velocity limits are required. While large scale modal tests may be performed with electrodynamic modal shakers, hydraulic modal shakers become attractive since they can generate higher force levels at lower unit cost with a smaller spatial footprint. While test engineers familiar with electrodynamic modal shakers are familiar with the challenges of displacement and velocity limits and the relatively mild shaker nonlinear distortion due to amplifier gains and shaker flexure structural geometric nonlinearities, they probably are not as familiar with the unique set of challenges hydraulic modal shakers present. These unique challenges include significant nonlinear distortion in the shaker force, issues with the setup of the hydraulic power supply and the associated hydraulic hosing, velocity limits as they relate to potentially damaging the hydraulic actuator piston, and safety issues with operating high-pressure hydraulic systems. This paper addresses these unique challenges to help the test engineer to better utilize hydraulic modal shakers on large-scale modal tests.
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ICPSU clearances to the lifting SLS vehicle were computed utilizing a coupled system nonlinear simulation approach in order to accurately capture the impact of system flexibilities, SLS forcing functions, pad separation (twang), ML dynamics and timings • i.e., integrate ICPSU model into a SLS nonlinear Coupled Loads Analysis (CLA) This required utilizing a flexible multibody framework for the CLA and the integration of large displacements/rotations capabilities into that CLA • Gantry rotation • Disconnect and retraction of flexible hoses
Main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (i.e., post pad separation). Given the size of most LVs, free-free testing is a challenge and often not feasible. A test stand, typically the launch pad itself, is utilized as the means to support the LV an Integrated Modal Test (IMT). This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the IMT. Preferably fully test driven (method’s that operate based on measured data only). The Accelerance Decoupling (AD) approach, developed and verified by NASA and ASD, is a method with the capability to “subtract out” the influence of the test stand from the IMT using measured data only
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In this short presentation format, we will provide a set of useful equations, relationships, and physical interpretations direct from the damped two-mode interaction problem. We will demonstrate that the results from the two-mode interaction problem are in direct agreement with observed test data. Practical methods for estimating the parameters driving the relations direct from modal test data are provided. We finalize with two examples demonstrating weak and strong interactions.