Application of the finite element method to problems in fracture mechanics

Numerical techniques have been finding increasing use in all aspects of fracture mechanics, and often provide the only means for analyzing fracture problems. The work presented here, is concerned with the application of the finite element method to cracked structures. The present work was directed towards the establishment of a comprehensive two-dimensional finite element, linear elastic, fracture analysis package. Significant progress has been made to this end, and features which can now be studied include multi-crack tip mixed-mode problems, involving partial crack closure. The crack tip core element was refined and special local crack tip elements were employed to reduce the element density in the neighbourhood of the core region. The work builds upon experience gained by previous research workers and, as part of the general development, the program was modified to incorporate the eight-node isoparametric quadrilateral element. Also. a more flexible solving routine was developed, and provided a very compact method of solving large sets of simultaneous equations, stored in a segmented form. To complement the finite element analysis programs, an automatic mesh generation program has been developed, which enables complex problems. involving fine element detail, to be investigated with a minimum of input data. The scheme has proven to be versati Ie and reasonably easy to implement. Numerous examples are given to demonstrate the accuracy and flexibility of the finite element technique.

Optimal input/output reduction in production processes

While conventional Data Envelopment Analysis (DEA) models set targets for each operational unit, this paper considers the problem of input/output reduction in a centralized decision making environment. The purpose of this paper is to develop an approach to input/output reduction problem that typically occurs in organizations with a centralized decision-making environment. This paper shows that DEA can make an important contribution to this problem and discusses how DEA-based model can be used to determine an optimal input/output reduction plan. An application in banking sector with limitation in IT investment shows the usefulness of the proposed method.

Input/output deterioration in production processes

In many real applications of Data Envelopment Analysis (DEA), the decision makers have to deteriorate some inputs and some outputs. This could be because of limitation of funds available. This paper proposes a new DEA-based approach to determine highest possible reduction in the concern input variables and lowest possible deterioration in the concern output variables without reducing the efficiency in any DMU. A numerical example is used to illustrate the problem. An application in banking sector with limitation of IT investment shows the usefulness of the proposed method. © 2010 Elsevier Ltd. All rights reserved.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

Application of calorimetric method for loss measurement of a SynRM drive system

Synchronous reluctance motors (SynRMs) are gaining in popularity in industrial drives due to their permanent magnet-free, competitive performance, and robust features. This paper studies the power losses in a 90-kW converter-fed SynRM drive by a calorimetric method in comparison of the traditional input-output method. After the converter and the motor were measured simultaneously in separate chambers, the converter was installed inside the large-size chamber next to the motor and the total drive system losses were obtained using one chamber. The uncertainty of both measurement methods is analyzed and discussed.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

Constrained nonparametric estimation of input distance function

This paper proposes a constrained nonparametric method of estimating an input distance function. A regression function is estimated via kernel methods without functional form assumptions. To guarantee that the estimated input distance function satisfies its properties, monotonicity constraints are imposed on the regression surface via the constraint weighted bootstrapping method borrowed from statistics literature. The first, second, and cross partial analytical derivatives of the estimated input distance function are derived, and thus the elasticities measuring input substitutability can be computed from them. The method is then applied to a cross-section of 3,249 Norwegian timber producers.

Laser-induced breakdown spectroscopy quantitative analysis method via adaptive analytical line selection and relevance vector machine regression model

Abstract A new LIBS quantitative analysis method based on analytical line adaptive selection and Relevance Vector Machine (RVM) regression model is proposed. First, a scheme of adaptively selecting analytical line is put forward in order to overcome the drawback of high dependency on a priori knowledge. The candidate analytical lines are automatically selected based on the built-in characteristics of spectral lines, such as spectral intensity, wavelength and width at half height. The analytical lines which will be used as input variables of regression model are determined adaptively according to the samples for both training and testing. Second, an LIBS quantitative analysis method based on RVM is presented. The intensities of analytical lines and the elemental concentrations of certified standard samples are used to train the RVM regression model. The predicted elemental concentration analysis results will be given with a form of confidence interval of probabilistic distribution, which is helpful for evaluating the uncertainness contained in the measured spectra. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples have been carried out. The multiple correlation coefficient of the prediction was up to 98.85%, and the average relative error of the prediction was 4.01%. The experiment results showed that the proposed LIBS quantitative analysis method achieved better prediction accuracy and better modeling robustness compared with the methods based on partial least squares regression, artificial neural network and standard support vector machine.

An efficient screening method for computer experiments

Computer simulators of real-world processes are often computationally expensive and require many inputs. The problem of the computational expense can be handled using emulation technology; however, highly multidimensional input spaces may require more simulator runs to train and validate the emulator. We aim to reduce the dimensionality of the problem by screening the simulators inputs for nonlinear effects on the output rather than distinguishing between negligible and active effects. Our proposed method is built upon the elementary effects (EE) method for screening and uses a threshold value to separate the inputs with linear and nonlinear effects. The technique is simple to implement and acts in a sequential way to keep the number of simulator runs down to a minimum, while identifying the inputs that have nonlinear effects. The algorithm is applied on a set of simulated examples and a rabies disease simulator where we observe run savings ranging between 28% and 63% compared with the batch EE method. Supplementary materials for this article are available online.

Novel communication method between power converters for DC micro-grid applications

Communication between power converters is vital for high performance DC micro-grids controls. However, for residential DC micro-grid applications, using external communication link would increase the system cost, and reduce the system flexibility and reliability. This paper presents a novel method to enable the conventional DC/DC converters to transmit data via the common DC Bus. With this technology, cost-effective low bandwidth communication links between power converters can be established within a DC micro-grid, and advanced distributed control algorithms can be developed. A reliable communication with 2 kbps transmission rate has been implemented between the Boost converters through the common input DC bus.

Pulse width modulation (PWM) method for power components estimation in power meters

The scope of this paper is to present the Pulse Width Modulation (PWM) based method for Active Power (AP) and Reactive Power (RP) measurements as can be applied in Power Meters. Necessarily, the main aim of the material presented is a twofold, first to present a realization methodology of the proposed algorithm, and second to verify the algorithm’s robustness and validity. The method takes advantage of the fact that frequencies present in a power line are of a specific fundamental frequency range (a range centred on the 50 Hz or 60 Hz) and that in case of the presence of harmonics the frequencies of those dominating in the power line spectrum can be specified on the basis of the fundamental. In contrast to a number of existing methods a time delay or shifting of the input signal is not required by the method presented and the time delay by n/2 of the Current signal with respect to the Voltage signal required by many of the existing measurement techniques, does not apply in the case of the PWM method as well.

Method for computing the optimal signal distribution and channel capacity

An iterative method for computing the channel capacity of both discrete and continuous input, continuous output channels is proposed. The efficiency of new method is demonstrated in comparison with the classical Blahut - Arimoto algorithm for several known channels. Moreover, we also present a hybrid method combining advantages of both the Blahut - Arimoto algorithm and our iterative approach. The new method is especially efficient for the channels with a priory unknown discrete input alphabet.

The calculation of dynamic ecological footprint on the basis of the dynamic input-output model

The Leontief input-output model is widely used to determine the ecological footprint of consumption in a region or a country. It is able to capture spillover environmental effects along the supply change, thus its popularity is increasing in ecology related economic research. These studies are static and the dynamic investigations are neglected. The dynamic Leontief model makes it possible to involve the capital and inventory investment in the footprint calculation that projects future growth of GDP and environmental impacts. We show a new calculation method to determine the effect of capital accumulation on ecological footprint. Keywords: Dynamic Leontief model, Dynamic ecological footprint, Environmental management, Allocation method

Bomb-tritium input function calculated from the details of the nuclear atmospheric bomb tests released by the UNSCEAR [2000]

Improving the representation of the hydrological cycle in Atmospheric General Circulation Models (AGCMs) is one of the main challenges in modeling the Earth's climate system. One way to evaluate model performance is to simulate the transport of water isotopes. Among those available, tritium (HTO) is an extremely valuable tracer, because its content in the different reservoirs involved in the water cycle (stratosphere, troposphere, ocean) varies by order of magnitude. Previous work incorporated natural tritium into LMDZ-iso, a version of the LMDZ general circulation model enhanced by water isotope diagnostics. Here for the first time, the anthropogenic tritium injected by each of the atmospheric nuclear-bomb tests between 1945 and 1980 has been first estimated and further implemented in the model; it creates an opportunity to evaluate certain aspects of LDMZ over several decades by following the bomb-tritium transient signal through the hydrological cycle. Simulations of tritium in water vapor and precipitation for the period 1950-2008, with both natural and anthropogenic components, are presented in this study. LMDZ-iso satisfactorily reproduces the general shape of the temporal evolution of tritium. However, LMDZ-iso simulates too high a bomb-tritium peak followed by too strong a decrease of tritium in precipitation. The too diffusive vertical advection in AGCMs crucially affects the residence time of tritium in the stratosphere. This insight into model performance demonstrates that the implementation of tritium in an AGCM provides a new and valuable test of the modeled atmospheric transport, complementing water stable isotope modeling.