The stochastic aeroelastic response analysis of helicopter rotors using deep and shallow machine learning

This paper addresses the influence of manufacturing variability of a helicopter rotor blade on its aeroelastic responses. An aeroelastic analysis using finite elements in spatial and temporal domains is used to compute the helicopter rotor frequencies, vibratory hub loads, power required and stability in forward flight. The novelty of the work lies in the application of advanced data-driven machine learning (ML) techniques, such as convolution neural networks (CNN), multi-layer perceptron (MLP), random forests, support vector machines and adaptive Gaussian process (GP) for capturing the nonlinear responses of these complex spatio-temporal models to develop an efficient physics-informed ML framework for stochastic rotor analysis. Thus, the work is of practical significance as (i) it accounts for manufacturing uncertainties, (ii) accurately quantifies their effects on nonlinear response of rotor blade and (iii) makes the computationally expensive simulations viable by the use of ML. A rigorous performance assessment of the aforementioned approaches is presented by demonstrating validation on the training dataset and prediction on the test dataset. The contribution of the study lies in the following findings: (i) The uncertainty in composite material and geometric properties can lead to significant variations in the rotor aeroelastic responses and thereby highlighting that the consideration of manufacturing variability in analyzing helicopter rotors is crucial for assessing their behaviour in real-life scenarios. (ii) Precisely, the substantial effect of uncertainty has been observed on the six vibratory hub loads and the damping with the highest impact on the yawing hub moment. Therefore, sufficient factor of safety should be considered in the design to alleviate the effects of perturbation in the simulation results. (iii) Although advanced ML techniques are harder to train, the optimal model configuration is capable of approximating the nonlinear response trends accurately. GP and CNN followed by MLP achieved satisfactory performance. Excellent accuracy achieved by the above ML techniques demonstrates their potential for application in the optimization of rotors under uncertainty

Percentile Queries in Multi-Dimensional Markov Decision Processes

Markov decision processes (MDPs) with multi-dimensional weights are useful to analyze systems with multiple objectives that may be conflicting and require the analysis of trade-offs. We study the complexity of percentile queries in such MDPs and give algorithms to synthesize strategies that enforce such constraints. Given a multi-dimensional weighted MDP and a quantitative payoff function $f$, thresholds $v_i$ (one per dimension), and probability thresholds $\alpha_i$, we show how to compute a single strategy to enforce that for all dimensions $i$, the probability of outcomes $\rho$ satisfying $f_i(\rho) \geq v_i$ is at least $\alpha_i$. We consider classical quantitative payoffs from the literature (sup, inf, lim sup, lim inf, mean-payoff, truncated sum, discounted sum). Our work extends to the quantitative case the multi-objective model checking problem studied by Etessami et al. in unweighted MDPs.Comment: Extended version of CAV 2015 pape

Value Iteration for Long-run Average Reward in Markov Decision Processes

Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks

MonoPerfCap: Human Performance Capture from Monocular Video

We present the first marker-less approach for temporally coherent 3D performance capture of a human with general clothing from monocular video. Our approach reconstructs articulated human skeleton motion as well as medium-scale non-rigid surface deformations in general scenes. Human performance capture is a challenging problem due to the large range of articulation, potentially fast motion, and considerable non-rigid deformations, even from multi-view data. Reconstruction from monocular video alone is drastically more challenging, since strong occlusions and the inherent depth ambiguity lead to a highly ill-posed reconstruction problem. We tackle these challenges by a novel approach that employs sparse 2D and 3D human pose detections from a convolutional neural network using a batch-based pose estimation strategy. Joint recovery of per-batch motion allows to resolve the ambiguities of the monocular reconstruction problem based on a low dimensional trajectory subspace. In addition, we propose refinement of the surface geometry based on fully automatically extracted silhouettes to enable medium-scale non-rigid alignment. We demonstrate state-of-the-art performance capture results that enable exciting applications such as video editing and free viewpoint video, previously infeasible from monocular video. Our qualitative and quantitative evaluation demonstrates that our approach significantly outperforms previous monocular methods in terms of accuracy, robustness and scene complexity that can be handled.Comment: Accepted to ACM TOG 2018, to be presented on SIGGRAPH 201

Robust topological designs for extreme metamaterial micro-structures

We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson’s ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson’s ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design

Systematic and Stochastic Variations in Pulsar Dispersion Measures

We analyze deterministic and random temporal variations in dispersion measure (DM) from the full three-dimensional velocities of pulsars with respect to the solar system, combined with electron-density variations on a wide range of length scales. Previous treatments have largely ignored the pulsar's changing distance while favoring interpretations involving the change in sky position from transverse motion. Linear trends in pulsar DMs seen over 5-10~year timescales may signify sizable DM gradients in the interstellar medium (ISM) sampled by the changing direction of the line of sight to the pulsar. We show that motions parallel to the line of sight can also account for linear trends, for the apparent excess of DM variance over that extrapolated from scintillation measurements, and for the apparent non-Kolmogorov scalings of DM structure functions inferred in some cases. Pulsar motions through atomic gas may produce bow-shock ionized gas that also contributes to DM variations. We discuss possible causes of periodic or quasi-periodic changes in DM, including seasonal changes in the ionosphere, annual variation of the solar elongation angle, structure in the heliosphere-ISM boundary, and substructure in the ISM. We assess the solar cycle's role on the amplitude of ionospheric and solar-wind variations. Interstellar refraction can produce cyclic timing variations from the error in transforming arrival times to the solar system barycenter. We apply our methods to DM time series and DM gradient measurements in the literature and assess consistency with a Kolmogorov medium. Finally, we discuss the implications of DM modeling in precision pulsar timing experiments.Comment: 24 pages, 17 figures, published in Ap

Mining Novel Multivariate Relationships in Time Series Data Using Correlation Networks

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.Comment: This is the accepted version of article submitted to IEEE Transactions on Knowledge and Data Engineering 201