Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three- dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.

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.

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.

Discrete parameter simulation optimization algorithms with applications to admission control with dependent service times

We propose certain discrete parameter variants of well known simulation optimization algorithms. Two of these algorithms are based on the smoothed functional (SF) technique while two others are based on the simultaneous perturbation stochastic approximation (SPSA) method. They differ from each other in the way perturbations are obtained and also the manner in which projections and parameter updates are performed. All our algorithms use two simulations and two-timescale stochastic approximation. As an application setting, we consider the important problem of admission control of packets in communication networks under dependent service times. We consider a discrete time slotted queueing model of the system and consider two different scenarios - one where the service times have a dependence on the system state and the other where they depend on the number of arrivals in a time slot. Under our settings, the simulated objective function appears ill-behaved with multiple local minima and a unique global minimum characterized by a sharp dip in the objective function in a small region of the parameter space. We compare the performance of our algorithms on these settings and observe that the two SF algorithms show the best results overall. In fact, in many cases studied, SF algorithms converge to the global minimum.

Target reliability based design optimization of anchored cantilever sheet pile walls

In this study, the stability of anchored cantilever sheet pile wall in sandy soils is investigated using reliability analysis. Targeted stability is formulated as an optimization problem in the framework of an inverse first order reliability method. A sensitivity analysis is conducted to investigate the effect of parameters influencing the stability of sheet pile wall. Backfill soil properties, soil - steel pile interface friction angle, depth of the water table from the top of the sheet pile wall, total depth of embedment below the dredge line, yield strength of steel, section modulus of steel sheet pile, and anchor pull are all treated as random variables. The sheet pile wall system is modeled as a series of failure mode combination. Penetration depth, anchor pull, and section modulus are calculated for various target component and system reliability indices based on three limit states. These are: rotational failure about the position of the anchor rod, expressed in terms of moment ratio; sliding failure mode, expressed in terms of force ratio; and flexural failure of the steel sheet pile wall, expressed in terms of the section modulus ratio. An attempt is made to propose reliability based design charts considering the failure criteria as well as the variability in the parameters. The results of the study are compared with studies in the literature.

Strength design of composite beam using gradient and particle swarm optimization

This work addresses the optimum design of a composite box-beam structure subject to strength constraints. Such box-beams are used as the main load carrying members of helicopter rotor blades. A computationally efficient analytical model for box-beam is used. Optimal ply orientation angles are sought which maximize the failure margins with respect to the applied loading. The Tsai-Wu-Hahn failure criterion is used to calculate the reserve factor for each wall and ply and the minimum reserve factor is maximized. Ply angles are used as design variables and various cases of initial starting design and loadings are investigated. Both gradient-based and particle swarm optimization (PSO) methods are used. It is found that the optimization approach leads to the design of a box-beam with greatly improved reserve factors which can be useful for helicopter rotor structures. While the PSO yields globally best designs, the gradient-based method can also be used with appropriate starting designs to obtain useful designs efficiently. (C) 2006 Elsevier Ltd. All rights reserved.

A novel approach for large-scale polypeptide folding based on elastic networks using continuous optimization

We present a new computationally efficient method for large-scale polypeptide folding using coarse-grained elastic networks and gradient-based continuous optimization techniques. The folding is governed by minimization of energy based on Miyazawa–Jernigan contact potentials. Using this method we are able to substantially reduce the computation time on ordinary desktop computers for simulation of polypeptide folding starting from a fully unfolded state. We compare our results with available native state structures from Protein Data Bank (PDB) for a few de-novo proteins and two natural proteins, Ubiquitin and Lysozyme. Based on our simulations we are able to draw the energy landscape for a small de-novo protein, Chignolin. We also use two well known protein structure prediction software, MODELLER and GROMACS to compare our results. In the end, we show how a modification of normal elastic network model can lead to higher accuracy and lower time required for simulation.

Novel composite coded pattern for small angle measurement using imaging method -art.no.62891D

A novel approach for measurement of small rotation angles using imaging method is proposed and demonstrated. A plane mirror placed on a precision rotating table is used for imaging the newly designed composite coded pattern. The imaged patterns are captured with the help of a CCD camera. The angular rotation of the plane mirror is determined from a pair of the images of the pattern, captured once before and once after affecting the tilt of the mirror. Both simulation and experimental results suggest that the proposed approach not only retains the advantages of the original imaging method but also contributes significantly to the enhancement of its measuring range (+/- 4.13 degrees with accuracy of the order of 1 arcsec).

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. II. Results of parametric study

Based on a method presented in detail in a previous work by the authors, similar solutions have been obtained for the steady inviscid quasi‐one‐dimensional nonreacting flow in the supersonic nozzle of a CO2–N2 gasdynamic laser system, with either H2O or He as the catalyst. It has been demonstrated how these solutions could be used to optimize the small‐signal gain coefficient on a specified vibrational‐rotational transition. Results presented for a wide range of mixture compositions include optimum values for the small‐signal gain, area ratio, reservoir temperature, and a binary scaling parameter, which is the product of reservoir pressure and nozzle shape factor.

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. I. Theory

Based on a method proposed by Reddy and Daum, the equations governing the steady inviscid nonreacting gasdynamic laser (GDL) flow in a supersonic nozzle are reduced to a universal form so that the solutions depend on a single parameter which combines all the other parameters of the problem. Solutions are obtained for a sample case of available data and compared with existing results to validate the present approach. Also, similar solutions for a sample case are presented.

Optimization of two-dimensional NMR by matched accumulation

It is well known that in the time-domain acquisition of NMR data, signal-to-noise (S/N) improves as the square root of the number of transients accumulated. However, the amplitude of the measured signal varies during the time of detection, having a functional form dependent on the coherence detected. Matching the time spent signal averaging to the expected amplitude of the signal observed should also improve the detected signal-to-noise. Following this reasoning, Barna et al. (J Magn. Reson.75, 384, 1987) demonstrated the utility of exponential sampling in one- and two-dimensional NMR, using maximum-entropy methods to analyze the data. It is proposed here that for two-dimensional experiments the exponential sampling be replaced by exponential averaging. The data thus collected can be analyzed by standard fast-Fourier-transform routines. We demonstrate the utility of exponential averaging in 2D NOESY spectra of the protein ubiquitin, in which an enhanced SIN is observed. It is also shown that the method acquires delayed double-quantum-filtered COSY without phase distortion.

Stochastic Approximation Algorithms for Constrained Optimization via Simulation

We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.

Constrained optimization of heat exchangers

Optimizing a shell and tube heat exchanger for a given duty is an important and relatively difficult task. There is a need for a simple, general and reliable method for realizing this task. The authors present here one such method for optimizing single phase shell-and-tube heat exchangers with given geometric and thermohydraulic constraints. They discuss the problem in detail. Then they introduce a basic algorithm for optimizing the exchanger. This algorithm is based on data from an earlier study of a large collection of feasible designs generated for different process specifications. The algorithm ensures a near-optimal design satisfying the given heat duty and geometric constraints. The authors also provide several sub-algorithms to satisfy imposed velocity limitations. They illustrate how useful these sub-algorithms are with several examples where the exchanger weight is minimized.

Shape optimization of RC flexural members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm (Goldberg and Samtani 1986) has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. Three design examples-a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads-have been optimized. The results show a significant savings (40-56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.

Two timescale analysis of the Alopex algorithm for optimization

Alopex is a correlation-based gradient-free optimization technique useful in many learning problems. However, there are no analytical results on the asymptotic behavior of this algorithm. This article presents a new version of Alopex that can be analyzed using techniques of two timescale stochastic approximation method. It is shown that the algorithm asymptotically behaves like a gradient-descent method, though it does not need (or estimate) any gradient information. It is also shown, through simulations, that the algorithm is quite effective.