Cutting angle method - a tool for constrained global optimization

Cutting angle method (CAM) is a deterministic global optimization technique applicable to Lipschitz functions f: Rn → R. The method builds a sequence of piecewise linear lower approximations to the objective function f. The sequence of solutions to these relaxed problems converges to the global minimum of f. This article adapts CAM to the case of linear constraints on the feasible domain. We show how the relaxed problems are modified, and how the numerical efficiency of solving these problems can be preserved. A number of numerical experiments confirms the improved numerical efficiency.

Recrystallization in 304 austenitic stainless steel

A 304 austenitic stainless steel was deformed using hot torsion to study the evolution of dynamic recrystallization (DRX). The initial nucleation of dynamically recrystallization occurred by the bulging of pre-existing high angle grain boundaries at a strain much lower than the peak strain. At the
peak stress, only a low fraction of the prior grain boundaries were covered with new DRX grains. Beyond the peak stress, new DRX grains formed layers near the initial DRX and a necklace structure was developed. Several different mechanisms appeared to be operative in the formation of new high angle boundaries and grains. The recrystallization behaviour after deformation showed a classic transition from strain dependent to strain independent softening. This occurred at a strain beyond the
peak, where the fraction of dynamic recrystallization was only 50%.

Effect of thermomechanical parameters on the critical strain for ultrafine ferrite formation through hot torsion testing

A C–Mn–V steel was used to study ultrafine ferrite formation (1–3 μm) through dynamic strain-induced transformation (DSIT) using hot torsion experiments. A systematic study determined the critical strain for the start of DSIT (C,DSIT), although this may not lead to a fully ultrafine microstructure. Therefore, the strain to produce an ultrafine ferrite (UFF) as final microstructure (C,UFF) during deformation was also determined. In addition, the effect of thermomechanical parameters such as deformation temperature, prior austenite grain size, strain rate and cooling rate on C,DSIT and C,UFF has been evaluated. DSIT ferrite nucleated on prior austenite grain boundaries at an early stage of straining followed by intragranular nucleation at higher strains. The prior austenite grain size affected the distribution of DSIT ferrite nucleation sites at an early stage of transformation and the subsequent coarsening behaviour of the grain boundary and intragranular ferrite grains during post-deformation cooling. Also, C,DSIT and C,UFF increased with an increase in the prior austenite grain size and deformation temperature. The post-deformation cooling had a strong effect not only on C,UFF but also the UFF microstructure (i.e. final ferrite grain size and second phase characteristics).

Formation of a W-25%Cu nanocomposite during high pressure torsion

A coarse-grained W–25%Cu composite is subjected to high pressure torsion (HPT) at room temperature, 200 °C, and 400 °C, to different very large strains. The evolution of microstructure with increasing strain is investigated. It is shown that the HPT causes a strong refinement of W particles. No significant influence of the deformation temperature on the microstructure is revealed at small strains (64). A strong effect of the HPT temperature on the microstructure is found at larger strains (>64). It is demonstrated that the HPT can be successfully used to fabricate a W–25%Cu nanocomposite.

Miscibility, crystallization κinetics and real-time small-Angle x-ray scattering investigation of the semicrystalline morphology in thermosetting polymer blends of epoxy resin and poly(ethylene oxide)

Thermosetting polymer blends of poly(ethylene oxide) (PEO) and bisphenol-A-type epoxy resin (ER) were prepared using 4,4′-methylenebis(3-chloro-2,6-diethylaniline) (MCDEA) as curing agent. The miscibility and crystallization behavior of MCDEA-cured ER/PEO blends were investigated by differential scanning calorimetry (DSC). The existence of a single composition-dependent glass transition temperature (Tg) indicates that PEO is completely miscible with MCDEA-cured ER in the melt and in the amorphous state over the entire composition range. Fourier-transform infrared (FTIR) investigations indicated hydrogen-bonding interaction between the hydroxyl groups of MCDEA-cured ER and the ether oxygens of PEO in the blends, which is an important driving force for the miscibility of the blends. The average strength of the hydrogen bond in the cured ER/PEO blends is higher than in the pure MCDEA-cured ER. Crystallization kinetics of PEO from the melt is strongly influenced by the blend composition and the crystallization temperature. At high conversion, the time dependence of the relative degree of crystallinity deviated from the Avrami equation. The addition of a non-crystallizable ER component into PEO causes a depression of both the overall crystallization rate and the melting temperature. The surface free energy of folding σe displays a minimum with variation of composition. The spherulitic morphology of PEO in the ER/PEO blends exhibits typical characteristics of miscible crystalline/amorphous blends, and the PEO spherulites in the blends are always completely volume-filling. Real-time small-angle X-ray scattering (SAXS) experiments reveal that the long period L increases drastically with increasing ER content at the same temperatures. The amorphous cured ER component segregates interlamellarly during the crystallization process of PEO because of the low chain mobility of the cured ER. A model describing the semicrystalline morphology of MCDEA-cured ER/PEO blends is proposed based on the SAXS results. The semicrystalline morphology is a stack of crystalline lamellae; the amorphous fraction of PEO, the branched ER chains and imperfect ER network are located between PEO lamellae.

Efficient serial and parallel implementations of the cutting angle global optimisation technique

We examine efficient computer implementation of one method of deterministic global optimisation, the cutting angle method. In this method the objective function is approximated from values below the function with a piecewise linear auxiliary function. The global minimum of the objective function is approximated from the sequence of minima of this auxiliary function. Computing the minima of the auxiliary function is a combinatorial problem, and we show that it can be effectively parallelised. We discuss the improvements made to the serial implementation of the cutting angle method, and ways of distributing computations across multiple processors on parallel and cluster computers.

A new method for locating the global optimum : application of the cutting angle method to molecular structure prediction

Many problems in chemistry depend on the ability to identify the global minimum or maximum of a function. Examples include applications in chemometrics, optimization of reaction or operating conditions, and non-linear least-squares analysis. This paper presents the results of the application of a new method of deterministic global optimization, called the cutting angle method (CAM), as applied to the prediction of molecular geometries. CAM is shown to be competitive with other global optimization techniques for several benchmark molecular conformation problem. CAM is a general method that can also be applied to other computational problems involving global minima, global maxima or finding the roots of nonlinear equations.

Deformation behaviour of a cylinder under simultaneous compression and torsion

A number of experiments involving the compression of an Aluminum cylinder with concurrent die rotation were carried out. Two important features were observed: one was that die rotation reduced the degree of bulging and the other was that the compression load decreased. An upper bound analysis with a velocity field consisting of a compound exponential cusp representation was utilized to obtain an approximate analytical solution in a closed form. The theoretical result reproduced the reduction in bulging severity with die rotation as well as the changes in compression pressure.

Active temperature compensation for an accelerometer based angle measuring device

An angle measuring device using a high performance and very compact accelerometer provides a new and exciting method for producing highly compact and accurate angle measuring devices. Accelerometers are micro-machined and are able to measure acceleration to a very high accuracy. By using gravity as a reference these compact devices can also be used for measuring angles of rotation. The inherent problem with these devices is that their response characteristic changes with temperature which is detrimental to measurement accuracy. This paper describes an effective method to overcome this problem using a temperature sensor and intelligent software to compensate for this drift characteristic. In order to demonstrate the effectiveness of this work, experiments have been developed and conducted with the results and analysis provided at the end
of this paper for discussion.

A discussion on passive location discovery in emitter networks using angle-only measurements

In this paper we discuss the ghost node problem found when triangulation of 2 or more nodes is required. We present and discuss a simple algorithm, termed ABLE (Angle Based Location Estimation), that will position randomly placed emitters in a wireless sensor network using a mobile antenna array. The individual nodes in the network are relieved of the localization task by the mobile antenna system and require no modifications to account for location determination. Furthermore, no beacon nodes (i.e. nodes that know their own position) are required. We provide analysis that indicates a reasonably small number of measurements are required to guarantee the successful
localization of the emitting nodes and demonstrate our results through simulation.

The effect of multiple deformations on the formation of ultrafine grained steels

A C-Mn-Nb-Ti steel was deformed by hot torsion to study ultrafine ferrite formation through dynamic strain-induced transformation (DSIT) in conjunction with air cooling. A systematic study was carried out first to evaluate the effect of deformation temperature and prior austenite grain size on the critical strain for ultrafine ferrite formation (ε C,UFF) through single-pass deformation. Then, multiple deformations in the nonrecrystallization region were used to study the effect of thermomechanical parameters (i.e., strain, deformation temperature, etc.) on ε C,UFF. The multiple deformations in the nonrecrystallization region significantly reduced ε C,UFF, although the total equivalent strain for a given thermomechanical condition was higher than that required in single-pass deformation. The current study on a Ni-30Fe austenitic model alloy revealed that laminar microband structures were the key intragranular defects in the austenite for nucleation of ferrite during the hot torsion test. The microbands were refined and overall misorientation angle distribution increased with a decrease in the deformation temperature for a given thermomechanical processing condition. For nonisothermal multipass deformation, there was some contribution to the formation of high-angle microband boundaries from strains at higher temperature, although the strains were not completely additive.

Dynamic softening of ferrite during large strain warm deformation of a plain-carbon steel

The evolution of dynamic ferrite softening in a plain-carbon steel was investigated by torsion tests during warm deformation at 810 °C, in the two-phase (ferrite + austenite) region, and strain rate of 0.1 s−1 with different strains up to 50. The warm flow behaviour and ferrite microstructural parameters, such as grain size, misorientation angle across ferrite/ferrite boundaries, and the fraction of high-angle and low-angle grain/subgrain boundaries were quantified using electron back scatter diffraction. The results show that with increasing strain up to not, vert, similar2, the ferrite grain size and fraction of high-angle boundaries rapidly decrease and the fraction of low-angle boundaries increases. However, these parameters remain approximately unchanged with increasing strain from not, vert, similar2 to 50. The dynamic softening mechanism observed during large strain ferritic deformation is explained by dynamic recovery and continuous dynamic recrystallization.

Fuzzy terminal attitude guidance controller with angle only measurements

This paper introduces the concept of terminal attitude guidance as an alternative to precision guidance and uses fuzzy control ideas in designing a control strategy for a pursuer in countering a manoeuvreing target. The fuzzy controller uses only angle measurements in the control strategy and produces satisfactory results in comparison to the LQR or H∞ type guidance controllers, although they were addressed in a precision guidance context. Both 2D and 3D cases have been considered.

Microstructural evolution during hot deformation of duplex stainless steel

The microstructure evolution during hot deformation of a 23Cr-5Ni-3Mo duplex stainless steel was investigated in torsion. The presence of a soft δ ferrite phase in the vicinity of austenite caused strain partitioning, with accommodation of more strain in the δ ferrite. Furthermore, owing to the limited number of austenite/austenite grain boundaries, the kinetics of dynamic recrystallisation (DRX) in austenite was very slow. The first DRX grains in the austenite phase formed at a strain beyond the peak and proceeded to <15% of the microstructure at the rupture strain of the sample. On the other hand, the microstructure evolution in δ ferrite started by formation of low angle grain boundaries at low strains and the density of these boundaries increased with increasing strain. There was clear evidence of continuous dynamic recrystallisation in this phase at strains beyond the peak. However, in the δ ferrite phase at high strains, most grains consisted of δ/δ and δ/γ boundaries.

Passive angle measurement based localization consistency via geometric constraints

In this paper, we examine the geometric relations between various measured parameters and their corresponding errors in angle-measurement based emitter localization scenarios. We derive a geometric constraint formulating the relationship among the measurement errors in such a scenario. Using this constraint, we formulate the localization task as a constrained optimization problem that can be performed on the measurements in order to provide the optimal values such that the solution is consistent with the underlying geometry.