The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

A Search for Energy Minimized Sequences of Proteins

In this paper, we present numerical evidence that supports the notion of minimization in the sequence space of proteins for a target conformation. We use the conformations of the real proteins in the Protein Data Bank (PDB) and present computationally efficient methods to identify the sequences with minimum energy. We use edge-weighted connectivity graph for ranking the residue sites with reduced amino acid alphabet and then use continuous optimization to obtain the energy-minimizing sequences. Our methods enable the computation of a lower bound as well as a tight upper bound for the energy of a given conformation. We validate our results by using three different inter-residue energy matrices for five proteins from protein data bank (PDB), and by comparing our energy-minimizing sequences with 80 million diverse sequences that are generated based on different considerations in each case. When we submitted some of our chosen energy-minimizing sequences to Basic Local Alignment Search Tool (BLAST), we obtained some sequences from non-redundant protein sequence database that are similar to ours with an E-value of the order of 10(-7). In summary, we conclude that proteins show a trend towards minimizing energy in the sequence space but do not seem to adopt the global energy-minimizing sequence. The reason for this could be either that the existing energy matrices are not able to accurately represent the inter-residue interactions in the context of the protein environment or that Nature does not push the optimization in the sequence space, once it is able to perform the function.

Fuzzy waste load allocation model: a multiobjective approach

Fuzzy Waste Load Allocation Model (FWLAM), developed in an earlier study, derives the optimal fractional levels, for the base flow conditions, considering the goals of the Pollution Control Agency (PCA) and dischargers. The Modified Fuzzy Waste Load Allocation Model (MFWLAM) developed subsequently is a stochastic model and considers the moments (mean, variance and skewness) of water quality indicators, incorporating uncertainty due to randomness of input variables along with uncertainty due to imprecision. The risk of low water quality is reduced significantly by using this modified model, but inclusion of new constraints leads to a low value of acceptability level, A, interpreted as the maximized minimum satisfaction in the system. To improve this value, a new model, which is a combination Of FWLAM and MFWLAM, is presented, allowing for some violations in the constraints of MFWLAM. This combined model is a multiobjective optimization model having the objectives, maximization of acceptability level and minimization of violation of constraints. Fuzzy multiobjective programming, goal programming and fuzzy goal programming are used to find the solutions. For the optimization model, Probabilistic Global Search Lausanne (PGSL) is used as a nonlinear optimization tool. The methodology is applied to a case study of the Tunga-Bhadra river system in south India. The model results in a compromised solution of a higher value of acceptability level as compared to MFWLAM, with a satisfactory value of risk. Thus the goal of risk minimization is achieved with a comparatively better value of acceptability level.

The effect of horizontal resolution on simulation of very extreme US precipitation events in a global atmosphere model

We investigate the ability of a global atmospheric general circulation model (AGCM) to reproduce observed 20 year return values of the annual maximum daily precipitation totals over the continental United States as a function of horizontal resolution. We find that at the high resolutions enabled by contemporary supercomputers, the AGCM can produce values of comparable magnitude to high quality observations. However, at the resolutions typical of the coupled general circulation models used in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, the precipitation return values are severely underestimated.

Conservative Design Optimization of Laminated Composite Structures Using Genetic Algorithms and Multiple Failure Criteria

This article analyzes the effect of devising a new failure envelope by the combination of the most commonly used failure criteria for the composite laminates, on the design of composite structures. The failure criteria considered for the study are maximum stress and Tsai-Wu criteria. In addition to these popular phenomenological-based failure criteria, a micromechanics-based failure criterion called failure mechanism-based failure criterion is also considered. The failure envelopes obtained by these failure criteria are superimposed over one another and a new failure envelope is constructed based on the lowest absolute values of the strengths predicted by these failure criteria. Thus, the new failure envelope so obtained is named as most conservative failure envelope. A minimum weight design of composite laminates is performed using genetic algorithms. In addition to this, the effect of stacking sequence on the minimum weight of the laminate is also studied. Results are compared for the different failure envelopes and the conservative design is evaluated, with respect to the designs obtained by using only one failure criteria. The design approach is recommended for structures where composites are the key load-carrying members such as helicopter rotor blades.

A Combinatorial Optimization Problem for High Order PODs with Few Sensors

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

Performance evaluation of elitist-mutated multi-objective particle swarm optimization for integrated water resources management

Optimal allocation of water resources for various stakeholders often involves considerable complexity with several conflicting goals, which often leads to multi-objective optimization. In aid of effective decision-making to the water managers, apart from developing effective multi-objective mathematical models, there is a greater necessity of providing efficient Pareto optimal solutions to the real world problems. This study proposes a swarm-intelligence-based multi-objective technique, namely the elitist-mutated multi-objective particle swarm optimization technique (EM-MOPSO), for arriving at efficient Pareto optimal solutions to the multi-objective water resource management problems. The EM-MOPSO technique is applied to a case study of the multi-objective reservoir operation problem. The model performance is evaluated by comparing with results of a non-dominated sorting genetic algorithm (NSGA-II) model, and it is found that the EM-MOPSO method results in better performance. The developed method can be used as an effective aid for multi-objective decision-making in integrated water resource management.

Design Optimization of Field Emission From A Stacked Carbon Nanotube Array

Fluctuation of field emission in carbon nanotubes (CNTs) is riot desirable in many applications and the design of biomedical x-ray devices is one of them. In these applications, it is of great importance to have precise control of electron beams over multiple spatio-temporal scales. In this paper, a new design is proposed in order to optimize the field emission performance of CNT arrays. A diode configuration is used for analysis, where arrays of CNTs act as cathode. The results indicate that the linear height distribution of CNTs, as proposed in this study, shows more stable performance than the conventionally used unifrom distribution.

Quasi-periodic, global oscillations in sea level pressure on intraseasonal timescales

The sea level pressure (SLP) variability in 30-60 day intraseasonal timescales is investigated using 25 years of reanalysis data addressing two issues. The first concerns the non-zero zonal mean component of SLP near the equator and its meridional connections, and the second concerns the fast eastward propagation (EP) speed of SLP compared to that of zonal wind. It is shown that the entire globe resonates with high amplitude wave activity during some periods which may last for few to several months, followed by lull periods of varying duration. SLP variations in the tropical belt are highly coherent from 25A degrees S to 25A degrees N, uncorrelated with variations in mid latitudes and again significantly correlated but with opposite phase around 60A degrees S and 65A degrees N. Near the equator (8A degrees S-8A degrees N), the zonal mean contributes significantly to the total variance in SLP, and after its removal, SLP shows a dominant zonal wavenumber one structure having a periodicity of 40 days and EP speeds comparable to that of zonal winds in the Indian Ocean. SLP from many of the atmospheric and coupled general circulation models show similar behaviour in the meridional direction although their propagation characteristics in the tropical belt differ widely.

Compiler-assisted instruction decoder energy optimization for clustered VLIW architectures

Traditionally, an instruction decoder is designed as a monolithic structure that inhibit the leakage energy optimization. In this paper, we consider a split instruction decoder that enable the leakage energy optimization. We also propose a compiler scheduling algorithm that exploits instruction slack to increase the simultaneous active and idle duration in instruction decoder. The proposed compiler-assisted scheme obtains a further 14.5% reduction of energy consumption of instruction decoder over a hardware-only scheme for a VLIW architecture. The benefits are 17.3% and 18.7% in the context of a 2-clustered and a 4-clustered VLIW architecture respectively.

Global lopsided instability in a purely stellar galactic disc

It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A(1), increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction (approximately a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the groundstate lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N-body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global m = 1 instabilities, with almost zero pattern speed.

Reactive Pulsed Laser Deposition of titanium nitride thin film: Optimization of process parameters using Secondary Ion Mass Spectrometry

Reactive Pulsed Laser Deposition is a single step process wherein the ablated elemental metal reacts with a low pressure ambient gas to form a compound. We report here a Secondary Ion Mass Spectrometry based analytical methodology to conduct minimum number of experiments to arrive at optimal process parameters to obtain high quality TiN thin film. Quality of these films was confirmed by electron microscopic analysis. This methodology can be extended for optimization of other process parameters and materials. (C) 2009 Elsevier B.V. All rights reserved.

Predicting spin of compact objects from their QPOs: A global QPO model

We establish a unified model to explain Quasi-Periodic-Oscillation (QPO) observed from black hole and neutron star systems globally. This is based on the accreting systems thought to be damped harmonic oscillators with higher order nonlinearity. The model explains multiple properties parallelly independent of the nature of the compact object. It describes QPOs successfully for several compact sources. Based on it, we predict the spin frequency of the neutron star Sco X-1 and the specific angular momentum of black holes GRO J1655-40, GRS 1915+105.

Real-coded genetic algorithm for machining condition optimization

In this paper, we consider the machining condition optimization models presented in earlier studies. Finding the optimal combination of machining conditions within the constraints is a difficult task. Hence, in earlier studies standard optimization methods are used. The non-linear nature of the objective function, and the constraints that need to be satisfied makes it difficult to use the standard optimization methods for the solution. In this paper, we present a real coded genetic algorithm (RCGA), to find the optimal combination of machining conditions. We present various issues related to real coded genetic algorithm such as solution representation, crossover operators, and repair algorithm in detail. We also present the results obtained for these models using real coded genetic algorithm and discuss the advantages of using real coded genetic algorithm for these problems. From the results obtained, we conclude that real coded genetic algorithm is reliable and accurate for solving the machining condition optimization models.

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.