Supporting multi-point fan design with dimension reduction

Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades—under the same parametrisation—largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection—a non-linear least-squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.

A nonlinear dynamics approach to data-enabled science: Reconstructing soil-moisture dynamics from big data collected by wireless sensor networks

<p>The complex soil biome is a center piece in providing essential ecosystem services that humans rely on (carbon sequestration, food security, one-health interactions).  Agricultural engineers and soil scientists are developing wireless sensor networks (WSN) that collect large/big data on the soil key state variables (water content, temperature, chemistry) to better understand the soil biome primary environmental drivers. The profession extracts information from WSN records with methods including soil-process modeling and artificial-intelligence (AI) algorithms.  However, these approaches carry their own limitations.  A recent review article faulted current soil-process modeling for inadequately detecting and resolving model structural (abstraction) errors.  AI experts themselves caution against indiscriminant use of AI methods because of: a) problems including replication of past results due to inconsistent experimental methods; b) difficulty in explaining how a particular method arrives at its conclusions (the black box problem) and thus in correcting algorithms that learn ‘bad lessons’; and c) lack of rigorous criteria for selecting AI architectures.  An alternative approach to address these limitations is to investigate new strategies for reducing large/big data problems into smaller, more interpretable causal abstractions of the soil system.  </p><p>We develop an innovative data diagnostics framework—based on empirical nonlinear dynamics techniques from physics—that addresses the above concerns over soil-process modeling and AI algorithms.  We diagnose whether WSN and other similar environmental large/big data are likely generated by dimension-reducing (i.e., dissipative) nonlinear dynamics.  An n-dimensional nonlinear dynamic system is dissipative if long-term dynamics are bounded within m<<n dimensions, so that the problem of modeling long-term dynamics shrinks by the n-m inactive degrees of freedom.  If so, long-term system dynamics can be investigated with relatively few degrees of freedom that capture the complexity of the overall system generating observed data.  To make this diagnosis, we first apply signal processing to isolate structured variation (signal) from unstructured variation (noise) in large/big data time series records, and test signals for nonlinear stationarity.  We resolve the structure of isolated signals by distinguishing between stochastic-forcing and deterministic nonlinear dynamics; reconstruct phase space dynamics most likely generating signals, and test the statistical significance of reconstructed dynamics with surrogate data.  If the reconstructed phase space is dimension-reducing, we can formulate low-dimensional (phenomenological) ODE models to investigate nonlinear causal interactions between key soil environmental driving factors.  When we do not diagnose dimension-reducing nonlinear real-world dynamics, then underlying dynamics are most likely high dimensional and the information-extraction problem cannot be shrunk without losing essential dynamic information. In this case, other high-dimensional analysis techniques like AI offer a better modeling alternative for mapping out interactions.  Our framework supplies a decision-support tool for data practitioners toward the most informative and parsimonious information-extraction method—a win-win result.       </p><p>We will share preliminary results applying this empirical framework to three soil moisture sensor time series records analyzed with machine learning methods in Bean, Huffaker, and Migliaccio (2018).</p>

A modal impedance-based statistical energy analysis for vibro-acoustic analysis of complex systems having structural uncertainty

A modal impedance-based statistical energy analysis for point, line, and area connected complex structural-acoustic systems is introduced. The proposed methodology is applied to perform mid- and high-frequency vibro-acoustic analysis of a cabinet model. The cabinet is composed of several composite plates with local mass variability simulating structural uncertainty, isotropic beams, and an acoustic enclosure. The method uses point mobilities, which are determined using modal parameters obtained by finite element method, to define line and area mobilities via dimension reducing principle. The methodology presented here is successfully verified by several numerical and experimental Monte Carlo computations. With this study, conventional statistical energy analysis is improved for mid-frequency vibro-acoustic analysis of complex systems.

Political conflict in Bismarck’s Germany: An analysis of parliamentary voting, 1867–1890

Imperial Germany is a prominent historical case in the study of Western Europe’s political development. This article investigates the number and content of political conflict dimensions from the foundation of the modern German state in 1867 to the end of Bismarck’s reign as Chancellor in 1890. Methodologically, it applies dimension-reducing statistical methods to a novel data set of content-coded parliamentary roll call votes. The analysis suggests that the emergence of the Catholic Centre Party in 1871 permanently transformed the conflict space from a single liberal-conservative divide to a two-dimensional space that distinguished positions on socio-economic issues and regime matters, respectively. The fact that positions on redistributive and regime issues were not aligned implies that theories stressing economic inequality as a driver for regime change are of limited applicability. Instead, the case of Imperial Germany highlights the importance of cross-cutting non-economic societal cleavages and the role of societal and political organizations in drawing attention to and perpetuating these divisions.

Role of Principal Component Analysis (PCA) in the Evaluation of Competitiveness of Small Firms

Principal Component Analysis (PCA) is a method of multivariate statistical analysis and has been widely used in statistical and mathematical analysis. We use this method in the evaluation of competitiveness of small firms. Using the data of 30 small firms, we build the index system to evaluate competitiveness. Our results show that Principal Component Analysis (PCA) is useful in dimension reducing and we find that profitability, growth,size and human resource are important influencing factors in the competitiveness of small firms.