The Effect of Systematic Error in Forced Oscillation Testing

One of the fundamental problems in flight dynamics is the formulation of aerodynamic forces and moments acting on an aircraft in arbitrary motion. Classically, conventional stability derivatives are used for the representation of aerodynamic loads in the aircraft equations of motion. However, for modern aircraft with highly nonlinear and unsteady aerodynamic characteristics undergoing maneuvers at high angle of attack and/or angular rates the conventional stability derivative model is no longer valid. Attempts to formulate aerodynamic model equations with unsteady terms are based on several different wind tunnel techniques: for example, captive, wind tunnel single degree-of-freedom, and wind tunnel free-flying techniques. One of the most common techniques is forced oscillation testing. However, the forced oscillation testing method does not address the systematic and systematic correlation errors from the test apparatus that cause inconsistencies in the measured oscillatory stability derivatives. The primary objective of this study is to identify the possible sources and magnitude of systematic error in representative dynamic test apparatuses. Sensitivities of the longitudinal stability derivatives to systematic errors are computed, using a high fidelity simulation of a forced oscillation test rig, and assessed using both Design of Experiments and Monte Carlo methods

Kriging metamodeling in constrained simulation optimization: an explorative study.

Simulation; Optimization; Studies;

Feedback control of gas metal arc braze-welding using thermal signals

textIn serial manufacturing processes, localized energy sources (e.g. plasma cutters, arc welders or water jets) induce material geometry transformations that yield a desired product. Simple parameter control of these energy sources does not necessarily ensure an optimal or successful part because of disturbances in the manufacturing process (material and temperature variations, etc). Currently, control in manufacturing is based on statistical process control where large databases for the manufacturing of a fixed process are available and have been compiled over several manufacturing runs. In the absence of a statistical database, and with the increased need for improved monitoring and throughput, there is need for active process control in manufacturing. In this work, Gas Metal Arc Braze-Welding (GMABW) will serve as a test-bed for the implementation of model predictive control (MPC) for a serial manufacturing process. This dissertation investigates the integration of real time modeling of the temperature field with control algorithms to control the evolving temperature field in the ix braze-welded base metal. Fundamental problems involving MPC that are addressed are modeling techniques to calculate temperature fields with reduced computational requirements and control algorithms that utilize the thermal models directly to inform the controller. The dissertation first outlines and compares analytical and computational thermal models and comparison with experimental data are obtained. A thermal model based on a metamodeling approach is used as the plant model for a classical control system and control parameters are found. Various techniques for dealing with signal noise encountered during experimentation are investigated. A proportional controller is implemented in the experimental setup that applies feedback control of the braze –welding process using thermal signals. A novel approach to MPC is explored by using a metamodel as the plant model for the braze-welding process and having the temperature trajectory dictated by the metamodel in the steady state region of the weld. Lastly, future work and extensions of this research are outlined.Mechanical Engineerin

The design exploration method for adaptive design systems

The design exploration method for adaptive design systems is developed to facilitate the pursuit of a balance between the efficiency and accuracy in systems engineering design. The proposed method is modified from an existing multiscale material robust design method, the Inductive Design Exploration Method (IDEM). The IDEM is effective in managing uncertainty propagation in the model chain. However, it is not an appropriate method in other systems engineering design outside of original design domain due to its high computational cost. In this thesis, the IDEM is augmented with more efficient solution search methods to improve its capability for efficiently exploring robust design solutions in systems engineering design. The accuracy of the meta-model in engineering design is one uncertainty source. In current engineering design, response surface model is widely used. However, this method is shown as inaccurate in fitting nonlinear models. In this thesis, the local regression method is introduced as an alternative of meta-modeling technique to reduce the computational cost of simulation models. It is proposed as an appropriate method in systems design with nonlinear simulations models. The proposed methods are tested and verified by application to a Multifunctional Energetic Materials design and a Photonic Crystal Coupler and Waveguide design. The methods are demonstrated through the better accuracy of the local regression model in comparison to the response surface model and the better efficiency of the design exploration method for adaptive design systems in comparison to the IDEM. The proposed methods are validated theoretically and empirically through application of the validation square.M.S.Committee Chair: Janet K. Allen; Committee Member: Benjamin Klein; Committee Member: Farrokh Mistree; Committee Member: Seung-Kyum Cho

Augmenting Bottom-Up Metamodels with Predicates

Metamodeling refers to modeling a model. There are two metamodeling approaches for ABMs: (1) top-down and (2) bottom-up. The top down approach enables users to decompose high-level mental models into behaviors and interactions of agents. In contrast, the bottom-up approach constructs a relatively small, simple model that approximates the structure and outcomes of a dataset gathered fromthe runs of an ABM. The bottom-up metamodel makes behavior of the ABM comprehensible and exploratory analyses feasible. Formost users the construction of a bottom-up metamodel entails: (1) creating an experimental design, (2) running the simulation for all cases specified by the design, (3) collecting the inputs and output in a dataset and (4) applying first-order regression analysis to find a model that effectively estimates the output. Unfortunately, the sums of input variables employed by first-order regression analysis give the impression that one can compensate for one component of the system by improving some other component even if such substitution is inadequate or invalid. As a result the metamodel can be misleading. We address these deficiencies with an approach that: (1) automatically generates Boolean conditions that highlight when substitutions and tradeoffs among variables are valid and (2) augments the bottom-up metamodel with the conditions to improve validity and accuracy. We evaluate our approach using several established agent-based simulations

Metamodel-Based Probabilistic Design for Dynamic Systems with Degrading Components

The probabilistic design of dynamic systems with degrading components is difficult. Design of dynamic systems typically involves the optimization of a time-invariant performance measure, such as Energy, that is estimated using a dynamic response, such as angular speed. The mechanistic models developed to approximate this performance measure are too complicated to be used with simple design calculations and lead to lengthy simulations. When degradation of the components is assumed, in order to determine suitable service times, estimation of the failure probability over the product lifetime is required. Again, complex mechanistic models lead to lengthy lifetime simulations when the Monte Carlo method is used to evaluate probability. Based on these problems, an efficient methodology is presented for probabilistic design of dynamic systems and to estimate the cumulative distribution function of the time to failure of a performance measure when degradation of the components is assumed. The four main steps include; 1) transforming the dynamic response into a set of static responses at discrete cycle-time steps and using Singular Value Decomposition to efficiently estimate a time-invariant performance measure that is based upon a dynamic response, 2) replacing the mechanistic model with an approximating function, known as a “metamodel” 3) searching for the best design parameters using fast integration methods such as the First Order Reliability Method and 4) building the cumulative distribution function using the summation of the incremental failure probabilities, that are estimated using the set-theory method, over the planned lifetime. The first step of the methodology uses design of experiments or sampling techniques to select a sample of training sets of the design variables. These training sets are then input to the computer-based simulation of the mechanistic model to produce a matrix of corresponding responses at discrete cycle-times. Although metamodels can be built at each time-specific column of this matrix, this method is slow especially if the number of time steps is large. An efficient alternative uses Singular Value Decomposition to split the response matrix into two matrices containing only design-variable-specific and time-specific information. The second step of the methodology fits metamodels only for the significant columns of the matrix containing the design variable-specific information. Using the time-specific matrix, a metamodel is quickly developed at any cycle-time step or for any time-invariant performance measure such as energy consumed over the cycle-lifetime. In the third step, design variables are treated as random variables and the First Order Reliability Method is used to search for the best design parameters. Finally, the components most likely to degrade are modelled using either a degradation path or a marginal distribution model and, using the First Order Reliability Method or a Monte Carlo Simulation to estimate probability, the cumulative failure probability is plotted. The speed and accuracy of the methodology using three metamodels, the Regression model, Kriging and the Radial Basis Function, is investigated. This thesis shows that the metamodel offers a significantly faster and accurate alternative to using mechanistic models for both probabilistic design optimization and for estimating the cumulative distribution function. For design using the First-Order Reliability Method to estimate probability, the Regression Model is the fastest and the Radial Basis Function is the slowest. Kriging is shown to be accurate and faster than the Radial Basis Function but its computation time is still slower than the Regression Model. When estimating the cumulative distribution function, metamodels are more than 100 times faster than the mechanistic model and the error is less than ten percent when compared with the mechanistic model. Kriging and the Radial Basis Function are more accurate than the Regression Model and computation time is faster using the Monte Carlo Simulation to estimate probability than using the First-Order Reliability Method