Functions Of Many Parameters Research Articles

Computation of High-Order Sensitivities of Model Responses to Model Parameters—II: Introducing the Second-Order Adjoint Sensitivity Analysis Methodology for Computing Response Sensitivities to Functions/Features of Parameters

This work introduces a new methodology, which generalizes the extant second-order adjoint sensitivity analysis methodology for computing sensitivities of model responses to primary model parameters. This new methodology enables the computation, with unparalleled efficiency, of second-order sensitivities of responses to functions of uncertain model parameters, including uncertain boundaries and internal interfaces, for linear and/or nonlinear models. Such functions of primary model parameters customarily describe characteristic “features” of the system under consideration, including correlations modeling material properties, flow regimes, etc. The number of such “feature” functions is considerably smaller than the total number of primary model parameters. By enabling the computations of exact expressions of second-order sensitivities of model responses to model “features”, the number of required large-scale adjoint computations is greatly reduced. As shown in this work, obtaining the first- and second-order sensitivities to the primary model parameters from the corresponding response sensitivities to the feature functions can be performed analytically, thereby involving just the respective function/feature of parameters rather than the entire model. By replacing large-scale computations involving the model with relatively trivial computations involving just the feature functions, this new second-order adjoint sensitivity analysis methodology reaches unsurpassed efficiency. The applicability and unparalleled efficiency of this “2nd-Order Function/Feature Adjoint Sensitivity Analysis Methodology” (2nd-FASAM) is illustrated using a paradigm particle transport model that involves feature functions of many parameters, while admitting closed-form analytic solutions. Ongoing work will generalize the mathematical framework of the 2nd-FASAM to enable the computation of arbitrarily high-order sensitivities of model responses to functions/features of model parameters.

Effect of thermal response on physical properties during drilling operations-A case study

The temperature induced or generated during deep hole drilling operations is due to the heat generated between the interface of work piece surface and the tool surface. Several research study have been conducted to predict the temperature involved while drilling process as a predominant functions of many parameters like feed rate, torque, depth of cut etc. Similarly many experimental procedures have been conducted by several researchers to measure temperature directly by using thermocouples, infrared measurement, pyrometer, and thermisters etc. There is no precise experimental method is available to measure analytical value of energy, power, heat flux etc, while drilling process. The temperature rigma depends on material compositions and physical properties. This paper presents the influence of temperature on physical properties of some study samples during drilling operations.

Estimation of Performance Airspeeds for High-Bypass Turbofans Equipped Transport-Category Airplanes

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model were used in combination with an airplane polynomial drag model to estimate important performance speeds. Except for the airframe-only dependent control airspeeds, all performance speeds are airframepowerplant dependent. In all analytical considerations one ends up with polynomials of the 4 order that have no closed-form solutions. A real positive-root seeking numerical procedure based on the family of Newton-Raphson methods was used to extract performance airspeeds for variable in-flight weights and altitudes in the ISA troposphere. Extensive testing of the accuracy and convergence of the Newton-Raphson nonlinear equation solvers was conducted before performance speed calculations. A fictitious long-range wide-body transport-category airplane was modeled in combination with a pair of high-bypass and ultra-high bypass ratio flat-rated turbofans. Procedure employed here can be easily extended to cases when fitted, measured drag and thrust data is given in arbitrary polynomial forms. Sensitivity analysis is performed on minimum-drag airspeed and maximum aerodynamic efficiency. Transonic wave drag considerations are introduced.

Fitting Birth-Death Processes to Panel Data with Applications to Bacterial DNA Fingerprinting.

Continuous-time linear birth-death-immigration (BDI) processes are frequently used in ecology and epidemiology to model stochastic dynamics of the population of interest. In clinical settings, multiple birth-death processes can describe disease trajectories of individual patients, allowing for estimation of the effects of individual covariates on the birth and death rates of the process. Such estimation is usually accomplished by analyzing patient data collected at unevenly spaced time points, referred to as panel data in the biostatistics literature. Fitting linear BDI processes to panel data is a nontrivial optimization problem because birth and death rates can be functions of many parameters related to the covariates of interest. We propose a novel expectation-maximization (EM) algorithm for fitting linear BDI models with covariates to panel data. We derive a closed-form expression for the joint generating function of some of the BDI process statistics and use this generating function to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one-dimensional integration. This analytical technique yields a computationally efficient and robust optimization algorithm that we implemented in an open-source R package. We apply our method to DNA fingerprinting of Mycobacterium tuberculosis, the causative agent of tuberculosis, to study intrapatient time evolution of IS6110 copy number, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. Our analysis reveals previously undocumented differences in IS6110 birth-death rates among three major lineages of Mycobacterium tuberculosis, which has important implications for epidemiologists that use IS6110 for DNA fingerprinting of Mycobacterium tuberculosis.

Interaction between an Inclined Shock and Boundary and High-Entropy Layers on a Flat Plate

The flow structure and heat exchange in the zone of interference between an inclined shock and the surface of a flat plate are investigated experimentally and theoretically as functions of many parameters, the interference being studied in both the presence and the absence of bluntness of the leading edge. The experiments were carried out at Mach numbers M = 6, 8, and 10 and the Reynolds numbers Re L , calculated using the plate length L = 120 mm and the free-stream parameters, varied over the range from 0.24 ⋅ 106 to 1.31 ⋅ 106. The bluntness radius of the leading edge of the plate, the intensity of the impinging shock, and its location with respect to the leading edge were varied. The numerical simulation was carried out by solving the complete two-dimensional Navier-Stokes equations and averaged Reynolds equations using the q-ω turbulence model. The laminar boundary layer became turbulent inside the separation zone induced by the shock. It is shown that the plate bluntness significantly reduces the heat exchange intensity in the interference zone, this effect intensifying with increase in the Mach number.

A Priori Constraint Elimination

AbstractThe problem of steel frames optimal design, when it is written in mathematical programming form, gives a moderate number of unknowns and a huge number of constraints. A typical frame has about 50 unknowns and 20000 constraints. The large number of constraints, which are complex functions of many parameters, represents a problem for most non‐linear programming solvers. In order to reduce the number of constraints, we developed a method, which eliminates a large portion of constraints without their costly evaluation. The method is based on the problem specific constraints organization, where the constraints are organized into sets. It turns out that we can remove individual constraints from a set by simply comparing constraint parameters.

Computer-assisted photometry using simulated annealing

The computational technique known as simulated annealing, which traditionally has been used to solve problems in combinatorial optimization, can be quite effectively used to fit functions of many parameters to a set of data. This paper discusses the application of simulated annealing to the fitting of Moffat functions to crowded field star images. Overlapping star profiles can be fit simultaneously and missed stars can be located on the χ2 value of the fit, and the resulting functional model yields excellent photometric results. This method has been integrated into a photometry system that allows the user to select the accuracy of the results at the expense of time needed to perform the calculations.

Likelihood-Based Confidence Intervals for Functions of Many Parameters

Likelihood-Based Confidence Intervals for Functions of Many Parameters

Likelihood-based confidence intervals for functions of many parameters

SUMMARY Methods described first by Madansky (1965) and revived more recently by Cox & Oakes (1984, pp. 51-2) are extended to incorporate the calculation of likelihood-based confidence intervals for functions of many parameters. Examples involving failure time data are used to illustrate the techniques. This paper concerns the derivation of confidence intervals for complicated functions of many binomial parameters. Examples include the probability-of-being-in-response function introduced by Temkin (1978), and the cumulative incidence functions that arise in the context of multivariate failure time data with competing risks. Although point estimates of these 'summary functions' are available, their standard errors, given by the multivariate 8-method, may be algebraically complicated, so that confidence intervals may not always be easily obtained. In ? 2 of this paper we describe a likelihood-based solution to the problem of deriving 1 - a confidence intervals for complicated functions of many parameters. Because the intervals are based directly on the likelihood function, they are invariant under 1-1 transformations of the parameters. The description of the solution is set in the context of k independent binomial samples since the two examples presented in ? 3 arise in this context. However, the method does not appear to be intrinsically limited by the binomial framework, and could yield useful results in many other parametric and nonparametric settings.

Some remarks on the determination of unknown parameters in large nonlinear systems- a problem in spacecraft thermal test evaluation

As a special case of large nonlinear systems with many imprecisely known parameters, this paper considers the thermal behaviour of a spacecraft. It is simu lated in the steady state by a mathematical model consisting of a system of nonlinear equations and in the transient state by a system of nonlinear differ ential equations. The system contains a large number of parameters, many of which cannot be calculated or measured directly with satisfactory precision. The estimated parameters of the initial mathematical model can be improved by analysing the results of thermal tests performed on the spacecraft itself. The objective is to minimize the differences between measured and calculated temperatures. Since the temperatures are nonlinear functions of many para meters, the minimization is a difficult task. Methods which transform the nonlinear functions into linear ones may not result in the minimization of the temperature deviations. The major disadvantage of linearizing methods is the restriction of the validity of the first-order terms to the vicinity of the point about which the linearization was made. Therefore there cannot be a universal, straightfor ward procedure to evaluate a great number of unknown parameters in complex nonlinear systems. Engineering methods for special solutions need to be developed and made as general as ingenuity can make them.