28 Applying Uncertainty Quantification to Structural Systems: Parameter Reduction for Evaluating Model Complexity 255 for Simulation Analysis (GPM/SA) developed at Los Alamos National Laboratories. Both of these statistical frameworks will predict the probability distribution of how well the N number of model inputs from each 2DOF case will reproduce the experimental response features, such as relative displacement. Before these frameworks are employed, results from the sensitivity analysis study in Fig. 28.10 will eliminate low sensitivity variables contributing less than 2% to all output response features and set them to their mean value using Tables 28.2, 28.3, 28.6, and 28.7. The first DA-SCAM algorithm is based on a two-stage Metropolis-Hastings (MH) algorithm proposed by Christen and Fox [13] that predicts variables during statistical inversion. Calculating the 2DOF MAFDS forward model every iteration can be computationally expensive. The research from [13] by Fox and Christen proposed using an inexpensive approximation to the forward operator, like the 2DOF MAFDS model, based on an algorithm from [14]. Instead of randomly walking through the model space, a single component adaptive Metropolis algorithm (SCAM) from [15] was introduced to improve sampling in high dimensions for all of the variables in cases 1–6. The initial phase of this algorithm runs a single component adaptive Metropolis algorithm to account for the burn-in time of the Markov chain for each 2DOF case. For the preliminary acceptance decision stage, the delayed acceptance portion of the DA-SCAM algorithm begins with computing an inexpensive likelihood estimate to the 2DOF MAFDS model via ordinary kriging or linear interpolation with de-clustering. The DASCAM algorithm is one approach for solving the 2DOF MAFDS model for stiffness and damping cases 1–6. The Bayesian model calibration approach from [16–18] that implements a multivariate simulator with the goal of reducing the computational expense and time during statistical inversion similarly to the DA-SCAM algorithm. The regression model, η(X,θ), X = {hf,mn}, where Xis the set of control variables for drop height and added mass, and θ is the calibration parameters or the input variables at an optimal setting. will capture the random spatial effects from the physics of the data. It is assumed to behave as a multivariate Gaussian distribution with a mean and variance that must be trained to represent the observed training and testing data, which essentially allows the GP model to capture the underlying physical processes of the MAFDS. Since the pdf of the multivariate Gaussian distribution is continuously differentiable, this property of the GP model provides a smoothly varying and continuous simulator η(X,θ) to represent the physics of the MAFDS. By applying the GP model for η(X,θ) in a Markov chain Monte Carlo (MCMC) based algorithm, this algorithm develops a statistical representation of the physically informed system that can be used with any observed data set. This approach will be compared to the results from DA-SCAM algorithm for the six 2ODF cases. In short, two Bayesian frameworks have been introduced as the first paper in a series. The main purpose of this paper is to introduce the MAFDS 2DOF forward model, address model-form uncertainty through six 2DOF cases, and perform suspension stiffness and damping analysis. In the next study, the GPM/SA and DA-SCAM algorithms will solve the 2DOF MAFDS inverse problem presented in this paper to evaluate model-form uncertainty. Acknowledgements The authors gratefully acknowledge the support of the National Science Foundation under grant #1633608, and the German Research Foundation (DFG) SFB 805 project grant for funding this research. 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