Sensitivity Analysis

The chapter “Sensitivity Analysis” reviews why sensitivity analysis is a critical component of mathematical modeling, and the different ways of approaching it. A sensitivity analysis is an attempt to identify the parts of the model (i.e. structure, parameter values) that are most important for governing the output. It is an important part of modeling because it is used to quantify the degree of uncertainty in the model prediction and, in many cases, is the main goal of the model (i.e. the model was developed to identify the most important ecological processes). The chapter covers the idea of “local” versus “global” sensitivity analysis via individual parameter perturbation, and how interactive effects of parameters can be revealed via Monte Carlo analysis. Structural versus parameter uncertainty is also explained and explored.

The Attempt of the Low-Cycle Fatigue Life Description of Chosen Creep-Resistant Steels Under Mechanical and Thermal Interactions

The study focuses on the problem of determination of low-cycle fatigue properties for the chosen group of creep-resistant steels used in the power and chemical industries. It tries to find the parameter which would describe well the fatigue life and take into account mechanical loads and temperature. The results of LCF tests have been presented in the paper. New parameter P has been introduced. This parameter joins a plastic strain range, a stress range and temperature. The fatigue life has been predicted versus parameter P. The comparison of the predicted and observed values of fatigue life shows the agreement between these values. The method of fatigue life prediction formulated in this way is expected to describe the behavior of materials under thermo-mechanical fatigue.

A bifurcation study to guide the design of a landing gear with a combined uplock/downlock mechanism

This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this approach, crucial features in the response surface, such as bifurcation points, can be identified. By numerically continuing these points in the appropriate parameter space, the resulting bifurcation diagram can be used to guide parameter selection and optimization. In this paper, we demonstrate the potential of this technique by considering an aircraft nose landing gear, with a novel locking strategy that uses a combined uplock/downlock mechanism. The landing gear is locked when in the retracted or deployed states. Transitions between these locked states and the unlocked state (where the landing gear is a mechanism) are shown to depend upon the positions of two fold point bifurcations. By performing a two-parameter continuation, the critical points are traced to identify operational boundaries. Following the variation of the fold points through parameter space, a minimum spring stiffness is identified that enables the landing gear to be locked in the retracted state. The bifurcation analysis also shows that the unlocking of a retracted landing gear should use an unlock force measure, rather than a position indicator, to de-couple the effects of the retraction and locking actuators. Overall, the study demonstrates that bifurcation analysis can enhance the understanding of the influence of design choices over a wide operating range where nonlinearity is significant.

HR XRD and Emission of InxGa1-xAs/GaAs quantum wells with embedded InAs quantum dots at the variation of InxGa1-xAs composition

ABSTRACTThe high resolution X ray diffraction (HR-XRD) diagrams have been studied in the GaAs /InxGa1-xAs /In0.15Ga0.85As/GaAs quantum wells with embedded InAs quantum dots (QDs) in dependence on the composition of the capping InxGa1-xAs layers. The parameter x in capping InxGa1-xAs layers varied from the range 0.10-0.25. These technological changes have been accompanied by the variation non-monotonously of InAs QD emission. Numerical simulation of HR-XRD results has shown that the level of elastic strains and the composition of quantum layers vary none monotonously in studied QD structures. Simultaneously it was revealed that the process of Ga/In inter diffusion at the InxGa1-xAs/InAs QD interface are characterized by the dependence non monotonous versus parameter x in capping InxGa1-xAs layers. The physical reasons of the mentioned optical and structural effects in studied structures have been discussed.