An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.

Coalescence of secondary dispersions in fibrous beds

SUMMARY A study has been made of the coalescence of secondary dispersions in a fibrous bed. The literature pertaining to the formation, hydrodynamic behaviour and methods of separation of droplets less than one hundred micrometres in diameter has been reviewed with particular reference to fibrous bed coalescers. The main operating parameters were identified as inlet drop size distribution, phase ratio, superficial velocity and the thickness and voidage of the bed . A recirculatory rig with interchangeable fibrous bed pads was designed and operated with toluene-water dispersions generated by a combination of centrifugal pumps . Inlet drop sizes were analysed using a Coulter Counter and outlet drops were sized photographically. A novel technique, involving conductivity measur ements at different planes in the bed, was developed to measure hold up distribution. Single phase flow and two phase flow pressure drops were correlated by a Blake-Kozeny type equation. Exit drop size was independent of inlet drop size distribution and phase ratio but a function of superficialvelocity and packing thickness. Average bed hold up was independent of inlet drop size distribution and phase ratio, but decreased with increase in superficial velocity. Hold up was not evenly distributed in the bed, the highest value occurred at the inlet followed by a sharp -2 drop at approximately 1.2 x 10 m. Hold up remained constant throughout the rest of the bed until the exit plane, where it increased. From the results, a mechanism is postulated involving: (a) Capture of the inlet drops followed by interdrop coalescence until an equilibrium value is reached. (b) Equilibrium size droplets flowing as rivulets through the intermediate portion of the bed, and (c) Each rivulet forms droplets at the exit face, which detach by a 'drip point' mechanism.

Coalescence of secondary dispersions

A study has been made of the coalescence of secondary dispersions in beds of woven meshes. The variables investigated were superficial velocity, bed depth, mesh geometry and fibre material; the effects of presoaking the bed in the dispersed phase before operation were also considered. Equipment was design~d to generate a 0.1% phase ratio toluene in water dispersion whose mean drop size was determined using a Coulter Counter. The coalesced drops were sized by photography and a novel holographic technique was developed to evaluate the mean diameter of the effluent secondary drops. Previous models describing single phase flow in porous media are reviewed and it was found that the experimental data obtained in this study is best represented by Keller's equation which is based on a physical model similar to the internal structure of the meshes. Statistical analysis of two phase data produced a correlation, for each mesh tested, relating the pressure drop to superficial velocity and bed depth. The flow parameter evaluated from the single phase model is incorporated into a theoretical comparison of drop capture mechanisms which indicated that direct and indirect interception are predominant. The resulting equation for drop capture efficiericy is used to predict the initial, local drop capture rate in a coalescer. A mathematical description of the saturation profiles was formulated and verified by average saturation data. Based 6n the Blake-Kozeny equation, an expression is derived analytically to predict the two phase pressure drop using the parameters which characterise the saturation profiles. By specifying the local saturation at the inlet face for a given velocity, good agreement between experimental pressure drop data and the model predictions was obtained.

Sequential pyrolysis of willow SRC at low and high heating rates:implications for selective pyrolysis

The main aim of the work is to investigate sequential pyrolysis of willow SRC using two different heating rates (25 and 1500 °C/min) between 320 and 520 °C. Thermogravimetric analysis (TGA) and pyrolysis - gas chromatography - mass spectroscopy (Py-GC-MS) have been used for this analysis. In addition, laboratory scale processing has been undertaken to compare product distribution from fast and slow pyrolysis at 500 °C. Fast pyrolysis was carried out using a 1 kg/h continuous bubbling fluidized bed reactor, and slow pyrolysis using a 100 g batch reactor. Findings from this study show that heating rate and pyrolysis temperatures have a significant influence on the chemical content of decomposition products. From the analytical sequential pyrolysis, an inverse relationship was seen between the total yield of furfural (at high heating rates) and 2-furanmethanol (at low heating rates). The total yield of 1,2-dihydroxybenzene (catechol) was found to be significant higher at low heating rates. The intermediates of catechol, 2-methoxy-4-(2-propenyl)phenol (eugenol); 2-methoxyphenol (guaiacol); 4-Hydroxy-3,5-dimethoxybenzaldehyde (syringaldehyde) and 4-hydroxy-3-methoxybenzaldehyde (vanillin), were found to be highest at high heating rates. It was also found that laboratory scale processing alters the pyrolysis bio-oil chemical composition, and the proportions of pyrolysis product yields. The GC-MS/FID analysis of fast and slow pyrolysis bio-oils reveals significant differences. © 2011 Elsevier Ltd. All rights reserved.

Sequential grouping of pure-tone percepts evoked by the segregation of components from a complex tone

A sudden change applied to a single component can cause its segregation from an ongoing complex tone as a pure-tone-like percept. Three experiments examined whether such pure-tone-like percepts are organized into streams by extending the research of Bregman and Rudnicky (1975). Those authors found that listeners struggled to identify the presentation order of 2 pure-tone targets of different frequency when they were flanked by 2 lower frequency “distractors.” Adding a series of matched-frequency “captor” tones, however, improved performance by pulling the distractors into a separate stream from the targets. In the current study, sequences of discrete pure tones were substituted by sequences of brief changes applied to an otherwise constant 1.2-s complex tone. Pure-tone-like percepts were evoked by applying 6-dB increments to individual components of a complex comprising harmonics 1–7 of 300 Hz (Experiment 1) or 0.5-ms changes in interaural time difference to individual components of a log-spaced complex (range 160–905 Hz; Experiment 2). Results were consistent with the earlier study, providing clear evidence that pure-tone-like percepts are organized into streams. Experiment 3 adapted Experiment 1 by presenting a global amplitude increment either synchronous with, or just after, the last captor prior to the 1st distractor. In the former case, for which there was no pure-tone-like percept corresponding to that captor, the captor sequence did not aid performance to the same extent as previously. It is concluded that this change to the captor-tone stream partially resets the stream-formation process, and so the distractors and targets became likely to integrate once more. (PsycINFO Database Record (c) 2011 APA, all rights reserved)

Sequential, Bayesian geostatistics:a principled method for large data sets

The principled statistical application of Gaussian random field models used in geostatistics has historically been limited to data sets of a small size. This limitation is imposed by the requirement to store and invert the covariance matrix of all the samples to obtain a predictive distribution at unsampled locations, or to use likelihood-based covariance estimation. Various ad hoc approaches to solve this problem have been adopted, such as selecting a neighborhood region and/or a small number of observations to use in the kriging process, but these have no sound theoretical basis and it is unclear what information is being lost. In this article, we present a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm. By imposing sparsity in a well-defined framework, the algorithm retains a subset of “basis vectors” that best represent the “true” posterior Gaussian random field model in the relative entropy sense. This allows a principled treatment of Gaussian random field models on very large data sets. The method is particularly appropriate when the Gaussian random field model is regarded as a latent variable model, which may be nonlinearly related to the observations. We show the application of the sequential, sparse Bayesian estimation in Gaussian random field models and discuss its merits and drawbacks.

Projected sequential Gaussian processes: flexible interpolation for large data sets

Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential framework for inference in such projected processes is presented, where the observations are considered one at a time. We introduce a C++ library for carrying out such projected, sequential estimation which adds several novel features. In particular we have incorporated the ability to use a generic observation operator, or sensor model, to permit data fusion. We can also cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the variogram parameters is based on maximum likelihood estimation. We illustrate the projected sequential method in application to synthetic and real data sets. We discuss the software implementation and suggest possible future extensions.

Coalescence of secondary dispersions in packed beds

A study has been made of the coalescence of secondary dispersions in beds of monosized glass ballotini. The variables investigated were superficial velocity, bed depth, ballotini size and dispersed phase concentration. Equipment was designed to generate a toluene ln water dispersion with phase ratios from 0.1 - 1.0 v/v % and whose mean drop size was determined using a Coulter Counter. The coalesced drops were sized by photography and the mean diameter of the effluent drops was determined using a Malvern Particle Size Analyser. Previous models describing single phase flow in porous media are reviewed and it was found that the experimental data obtained in this study is best represented by the Carman-Kozeny equations. Relative permeability correlations were used to predict the saturation profiles across the bed from measured two phase pressure drop data. Theoretical comparison of drop capture mechanisms indicated that direct and indirect interception are predominant. The total capture efficiency for the bed can also be evaluated using Spielman and Fitzpatrick's correlation.The resulting equation is used to predict the initial, local drop capture rate in a coalescer. A mathematical description of the saturation profiles is formulated and verified by the saturation profiles obtained by relative permeability. Based on the Carman-Kozeny equation, an expression is derived analytically to .predict the two phase pressure drop using the parameters which characterise the saturation profiles. By specifying the local saturation at the inlet face for a given velocity and phase ratio, good agreement between experimental pressure drop data and the model predictions was obtained. An attempt to predict the exit drop size has been made using an analogy for flow through non cylindrical channels.