Solder joint defects classification using the Log-Gabor Filter, the Discrete Wavelet Transform and the Discrete Cosine Transform

Inspection of solder joints has been a critical process in the electronic manufacturing industry to reduce manufacturing cost, improve yield, and ensure project quality and reliability. This paper proposes the use of the Log-Gabor filter bank, Discrete Wavelet Transform and Discrete Cosine Transform for feature extraction of solder joint images on Printed Circuit Boards (PCBs). A distance based on the Mahalanobis Cosine metric is also presented for classification of five different types of solder joints. From the experimental results, this methodology achieved high accuracy and a well generalised performance. This can be an effective method to reduce cost and improve quality in the production of PCBs in the manufacturing industry.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Beat phenomena in metal nanowires, and their implications for resonance-based elastic property measurements

The elastic properties of 1D nanostructures such as nanowires are often measured experimentally through actuation of the nanowire at its resonance frequency, and then relating the resonance frequency to the elastic stiffness using elementary beam theory. In the present work, we utilize large scale molecular dynamics simulations to report a novel beat phenomenon in [110]oriented Ag nanowires. The beat phenomenon is found to arise from the asymmetry of the lattice spacing in the orthogonal elementary directions of the [110] nanowire, i.e. the [-110] and [001] directions, which results in two different principal moments of inertia. Because of this, actuations imposed along any other direction are found to decompose into two orthogonal vibrational components based on the actuation angle relative to these two elementary directions, with this phenomenon being generalizable to <110> FCC nanowires of different materials (Cu, Au, Ni, Pd and Pt). The beat phenomenon is explained using a discrete moment of inertia model based on the hard sphere assumption, the model is utilized to show that surface effects enhance the beat phenomenon, while the effect is reduced with increasing nanowires cross-sectional size or aspect ratio. Most importantly, due to the existence of the beat phenomena, we demonstrate that in resonance experiments only a single frequency component is expected to be observed, particularly when the damping ratio is relatively large or very small. Furthermore, for a large range of actuation angles, the lower frequency is more likely to be detected than the higher one, which implies that experimental predictions of Young’s modulus obtained from resonance may in fact be under predictions. The present study therefore has significant implications for experimental interpretations of Young’s modulus as obtained via resonance testing.

Synthesis of discrete allyl-functional polyethylene glycol for efficient hydrophilization of dihydr (polydimethylsiloxane)

Amphiphilic poly(ethylene glycol)-block-pol (dimethylsiloxane)-block-poly(ethylene glycol)(PEG-block-PDMS block-PEG) triblock copolymers have been successfully prepared via hydrosilylation using discrete and polydisperse PEG of various chain lengths. Facile synthesis of discrete PEG (dPEG) is achieved via systematic tosylation and etherification of lower glycols. Amphiphilicity of the dPEG block-PDMS-block-dPEG triblock copolymer is illustrated by dynamic light scattering (DLS) and measurement of the critical micelle concentration (CMC).

Discrete loading of the foot during hurdle drills: A pilot investigation

Introduction: Lower limb function in hurdling is patently asymmetrical. The lead limb undertakes the preparatory and landing steps while the trail limb contends with the hurdle and recovery steps. Discrete loading profiles of these steps will reflect the asymmetrical function and may provide useful insight into injury mechanisms. A pilot study was undertaken to determine the loading profiles of the hurdle, landing and recovery steps of elite male hurdlers. Equivalent data for steps between hurdles, where the running action is more symmetrical, were used for the purpose of comparison, simultaneously minimising the confounding effect of speed. Methodology: In-shoe pressures were recorded (FScan, 200 Hz) for four elite male hurdlers while they completed a routine hurdle drill at a self-selected fast but sub-race speed. The drill comprised of three consecutive hurdles. Data for the hurdle, landing and recovery steps of the first and second hurdles, along with data for the running steps between hurdles 1 and 2, and 2 and 3, were used for the purpose of analysis. Peak pressures within 1cm2 masks were determined for the hallux, first, central and fifth metatarsals (T1, M1, M2–4 and M5 respectively). Peak pressure (kPa) and loading duration (ms) for the hurdle, landing and recovery steps are reported as a percentage of the respective limb-matched values for between-hurdle steps. Results/discussion: For between-hurdle steps, T1, M1 and M2–4 peak pressures were 312/357, 356/306 and 362/368 kPa, lead/trail limbs respectively. For the hurdle, landing and recovery steps, pressures at T1 and M1 increased. For T1 the increases were in the order of 17%, 36% and 8% (hurdle, landing and recovery steps, respectively) while the corresponding increases at M1 were 7%, 54% and 20%. Pressures at M2–4 were similar for all steps, while M5 loaded erratically. For the between-hurdle steps, the loading durations at T1, M1 and M2–4, were 160/162, 170/142 and 190/191 ms, respectively. For the landing step, loading duration decreased for T1, M1and M2–4 (−8%, −19% and −18%, respectively). In the hurdle step, loading duration decreased for the metatarsals but not for T1. Conclusions: The hurdling action leads to regional pressure increases that act for shorter durations in comparison to the between-hurdle running steps. These changes are most notable at the first metatarsal, a common site of foot injury.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Separable and non-separable discrete wavelet transform based texture features and image classification of breast thermograms

Highly sensitive infrared cameras can produce high-resolution diagnostic images of the temperature and vascular changes of breasts. Wavelet transform based features are suitable in extracting the texture difference information of these images due to their scale-space decomposition. The objective of this study is to investigate the potential of extracted features in differentiating between breast lesions by comparing the two corresponding pectoral regions of two breast thermograms. The pectoral regions of breastsare important because near 50% of all breast cancer is located in this region. In this study, the pectoral region of the left breast is selected. Then the corresponding pectoral region of the right breast is identified. Texture features based on the first and the second sets of statistics are extracted from wavelet decomposed images of the pectoral regions of two breast thermograms. Principal component analysis is used to reduce dimension and an Adaboost classifier to evaluate classification performance. A number of different wavelet features are compared and it is shown that complex non-separable 2D discrete wavelet transform features perform better than their real separable counterparts.

The velocity synchronous discrete Fourier transform for order tracking in the field of rotating machinery

Diagnostics of rotating machinery has developed significantly in the last decades, and industrial applications are spreading in different sectors. Most applications are characterized by varying velocities of the shaft and in many cases transients are the most critical to monitor. In these variable speed conditions, fault symptoms are clearer in the angular/order domains than in the common time/frequency ones. In the past, this issue was often solved by synchronously sampling data by means of phase locked circuits governing the acquisition; however, thanks to the spread of cheap and powerful microprocessors, this procedure is nowadays rarer; sampling is usually performed at constant time intervals, and the conversion to the order domain is made by means of digital signal processing techniques. In the last decades different algorithms have been proposed for the extraction of an order spectrum from a signal sampled asynchronously with respect to the shaft rotational velocity; many of them (the so called computed order tracking family) use interpolation techniques to resample the signal at constant angular increments, followed by a common discrete Fourier transform to shift from the angular domain to the order domain. A less exploited family of techniques shifts directly from the time domain to the order spectrum, by means of modified Fourier transforms. This paper proposes a new transform, named velocity synchronous discrete Fourier transform, which takes advantage of the instantaneous velocity to improve the quality of its result, reaching performances that can challenge the computed order tracking.

Order tracking for discrete-random separation in variable speed conditions

The transmission path from the excitation to the measured vibration on the surface of a mechanical system introduces a distortion both in amplitude and in phase. Moreover, in variable speed conditions, the amplification/attenuation and the phase shift, due to the transfer function of the mechanical system, varies in time. This phenomenon reduces the effectiveness of the traditionally tachometer based order tracking, compromising the results of a discrete-random separation performed by a synchronous averaging. In this paper, for the first time, the extent of the distortion is identified both in the time domain and in the order spectrum of the signal, highlighting the consequences for the diagnostics of rotating machinery. A particular focus is given to gears, providing some indications on how to take advantage of the quantification of the disturbance to better tune the techniques developed for the compensation of the distortion. The full theoretical analysis is presented and the results are applied to an experimental case.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

Shrinking the keys of discrete-log-type lossy trapdoor functions

To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(λ 2) group elements for a reduction from the decisional Diffie-Hellman assumption (where λ is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(λ) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption. Our first construction achieves this result at the expense of a long common reference string of Θ(λ 2) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(λ), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction. The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.

Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Multiphase experiments with at least one later laboratory phase. I. orthogonal designs

The paper provides a systematic approach to designing the laboratory phase of a multiphase experiment, taking into account previous phases. General principles are outlined for experiments in which orthogonal designs can be employed. Multiphase experiments occur widely, although their multiphase nature is often not recognized. The need to randomize the material produced from the first phase in the laboratory phase is emphasized. Factor-allocation diagrams are used to depict the randomizations in a design and the use of skeleton analysis-of-variance (ANOVA) tables to evaluate their properties discussed. The methods are illustrated using a scenario and a case study. A basis for categorizing designs is suggested. This article has supplementary material online.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.