Parameter estimation of fractional uncertain differential equations via Adams method

Parameter estimation of uncertain differential equations becomes popular very recently. This paper suggests a new method based on fractional uncertain differential equations for the first time, which hold more parameter freedom degrees. The Adams numerical method and Adam algorithm are adopted for the optimization problems. The estimation results are compared to show a better forecast. Finally, the predictor–corrector method is adopted to solve the fractional uncertain differential equations. Numerical solutions are demonstrated with varied α-paths

A measurement application to surfaces using nonlinear interpolation and numerical integration methods

In this article, the area of a two-dimensional surface of the exteriors of the Universidad Nacional Mayor de San Marcos was calculated. It was done using the curve equation integration method, which will be obtained from the perimeter of the sector to be worked on by dividing it into sections, for which Google Maps was used to calculate the reference parameters. In general, not all curve equations are integrable; for this, the approximation methods such as Simpson 3/8, 1/3, and trapezoid were used. In addition, we will apply the Lagrange interpolation to find the equation of the curve; with the results obtained, we make a comparison between the methods, and So we see that the methods differ. Of them, the one with the least margin of error will be taken; these methods can be used in future works where the surface is irregular.Campus Lima Centr

A Hierarchical Spatio-Temporal Statistical Model Motivated by Glaciology

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.Comment: Revision accepted for publication by the Journal of Agricultural, Biological, and Environmental Statistic

Company R&D and University R&D - How Are They Related?

At the same time as we can observe strong tendencies of a globalisation of R&D, we also can observe a strong spatial clustering of R&D and related innovative activities. The standard explanation in the literature of the clustering of innovative activities is that such clusters offer external knowledge economies to innovative companies, since they are dependent upon knowledge flows and that knowledge flows are spatially bounded. Obviously, location is crucial in understanding knowledge flows and knowledge production, since knowledge sources have been found to be geographically concentrated. There are two major performers of R&D: industry and universities. It seems rather straight-forward to assume that industrial R&D might be attracted to locate near research universities doing R&D in fields relevant to industry. Already as far back as in the 1960s a number of case studies confirmed the important roles played by Stanford University and MIT for commercial innovation and entrepreneurship. During the years a large number of formal studies have presented evidences of a positive impact of university R&D on firm performance. The question is, does it also work the other way around? Does industrial R&D function as an attractor for university R&D? We may actually think of several reasons why university R&D may grow close to industry R&D. First of all political decision-makers may decide to start or expand university R&D at locations where industry already is doing R&D. Secondly, we can imagine that industry doing R&D in a region might use part of their R&D funds to finance university R&D. Thirdly, universities in regions with industrial R&D might find it easier to attract R&D funds from national and international sources due to co-operation with industry. Obviously, not all types of university R&D attract industrial R&D. There are reasons to believe that, in particular, university R&D in natural, technical and medical sciences attracts industrial R&D but that there are also strong reasons to believe that there are variations between different sectors of industry regarding how dependent their R&D is to be located close to university R&D. The above implies that there are behavioural relationships between industrial R&D and university R&D and vice versa. However, the litrature contains few studies dealing with this problem. Most studies have concentrated on the one-directional effect from university R&D to industrial R&D and the outputs of industrial R&D in most cases measured in terms of the number of patents and neglected the possible mutual interaction. However, if there is a mutual interaction between university and industry R&D, and if there are knowledge externalities involved, then we can develop a dynamic explanation to the clustering of innovative activities based on positive feedback loops. This would imply strong tendencies to path dependency and that policy initiatives to transfer non-innovative regions to innovative regions would have small chances to succeed. The fact that knowledge flows seem to be spatially bounded implies that proximity matters. Most contributions analysing spatial knowledge flows have used very crude measures of proximity. However, there are some authors that have argued that proximity could be measured using accessibility measures. Accessibility measures can be used to model interaction opportunities at different spatial scales: local, intra-regional and inter-regional. The purpose of this paper is to analyse the locational relationship between industry R&D and university R&D in Sweden using a simultaneous equation approach and to analyse existing differences between different science areas and different industry sectors.

Topology Optimization for Multi-Functional Components in Multibody Dynamics Systems.

This research extends topology optimization techniques to consider multibody dynamics systems with a much more open design space, which can include passive, active, and reactive components, with a special application focus on a gunner restraint system (GRS) design problem. General representative models for the multi-functional components are established in a multibody dynamics system. The topology optimization process has been advanced for the optimization of geometrically nonlinear, time-dependent, and timing-dependent multibody dynamics systems undergoing large nonlinear displacements with nonlinear dynamics responses as design objectives. Three efficient sensitivity analysis methods have been proposed, which include the constant dynamic loading method, the time integration incorporated method based on the Generalized-Alpha algorithm and the iterative method. These new methods have made it possible to calculate the sensitivities in complicated multibody dynamic systems and provide users with choices to significantly reduce the computational costs, especially, in the topology optimization process, and to obtain desired accuracy in the sensitivity analysis. In addition to the sensitivity analysis methods, an efficient and reliable Kriging variable screening method based on the REML criterion has been developed to identify significant variables in the systems to determine the worst cases for various system uncertainty studies. A specific application of the multi-functional components system optimization technology is the GRS design problem, in which both the vehicle and the gunner can undergo large relative and absolute motions under various driving or threat conditions. In meanwhile, the restraint components may need to allow amplitude-dependent, time-dependent, timing-dependent nonlinear response behaviors, such as those seeing in restraint belts, airbags, and retractors. The restraint system layout design needs to keep a wide open design space, thus to find the truly optimal design. The developed methodologies have been employed in the GRS design problems to demonstrate usage of the new methodologies.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91444/1/dongg_1.pd