Wind power forecasts using Gaussian processes and numerical weather prediction

Since wind at the earth's surface has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safe and economic use of wind energy. In this paper, we investigated a combination of numeric and probabilistic models: a Gaussian process (GP) combined with a numerical weather prediction (NWP) model was applied to wind-power forecasting up to one day ahead. First, the wind-speed data from NWP was corrected by a GP, then, as there is always a defined limit on power generated in a wind turbine due to the turbine controlling strategy, wind power forecasts were realized by modeling the relationship between the corrected wind speed and power output using a censored GP. To validate the proposed approach, three real-world datasets were used for model training and testing. The empirical results were compared with several classical wind forecast models, and based on the mean absolute error (MAE), the proposed model provides around 9% to 14% improvement in forecasting accuracy compared to an artificial neural network (ANN) model, and nearly 17% improvement on a third dataset which is from a newly-built wind farm for which there is a limited amount of training data. © 2013 IEEE.

Real-time error compensation of a three-axis machine tool using a laser tracker

The concept of measurement-enabled production is based on integrating metrology systems into production processes and generated significant interest in industry, due to its potential to increase process capability and accuracy, which in turn reduces production times and eliminates defective parts. One of the most promising methods of integrating metrology into production is the usage of external metrology systems to compensate machine tool errors in real time. The development and experimental performance evaluation of a low-cost, prototype three-axis machine tool that is laser tracker assisted are described in this paper. Real-time corrections of the machine tool's absolute volumetric error have been achieved. As a result, significant increases in static repeatability and accuracy have been demonstrated, allowing the low-cost three-axis machine tool to reliably reach static positioning accuracies below 35 μm throughout its working volume without any prior calibration or error mapping. This is a significant technical development that demonstrated the feasibility of the proposed methods and can have wide-scale industrial applications by enabling low-cost and structural integrity machine tools that could be deployed flexibly as end-effectors of robotic automation, to achieve positional accuracies that were the preserve of large, high-precision machine tools.

Short-term wind power forecasting using Gaussian processes

Since wind has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safety and economics of wind energy utilization. In this paper, we investigate a combination of numeric and probabilistic models: one-day-ahead wind power forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical Weather Prediction (NWP) model. Firstly the wind speed data from NWP was corrected by a GP. Then, as there is always a defined limit on power generated in a wind turbine due the turbine controlling strategy, a Censored GP was used to model the relationship between the corrected wind speed and power output. To validate the proposed approach, two real world datasets were used for model construction and testing. The simulation results were compared with the persistence method and Artificial Neural Networks (ANNs); the proposed model achieves about 11% improvement in forecasting accuracy (Mean Absolute Error) compared to the ANN model on one dataset, and nearly 5% improvement on another.

Estimation of computer waste quantities using forecasting techniques

Technology changes rapidly over years providing continuously more options for computer alternatives and making life easier for economic, intra-relation or any other transactions. However, the introduction of new technology “pushes” old Information and Communication Technology (ICT) products to non-use. E-waste is defined as the quantities of ICT products which are not in use and is bivariate function of the sold quantities, and the probability that specific computers quantity will be regarded as obsolete. In this paper, an e-waste generation model is presented, which is applied to the following regions: Western and Eastern Europe, Asia/Pacific, Japan/Australia/New Zealand, North and South America. Furthermore, cumulative computer sales were retrieved for selected countries of the regions so as to compute obsolete computer quantities. In order to provide robust results for the forecasted quantities, a selection of forecasting models, namely (i) Bass, (ii) Gompertz, (iii) Logistic, (iv) Trend model, (v) Level model, (vi) AutoRegressive Moving Average (ARMA), and (vii) Exponential Smoothing were applied, depicting for each country that model which would provide better results in terms of minimum error indices (Mean Absolute Error and Mean Square Error) for the in-sample estimation. As new technology does not diffuse in all the regions of the world with the same speed due to different socio-economic factors, the lifespan distribution, which provides the probability of a certain quantity of computers to be considered as obsolete, is not adequately modeled in the literature. The time horizon for the forecasted quantities is 2014-2030, while the results show a very sharp increase in the USA and United Kingdom, due to the fact of decreasing computer lifespan and increasing sales.

Clinical outcomes after implantation of a new hydrophobic acrylic toric IOL during routine cataract surgery

PURPOSE: To assess the clinical outcomes after implantation of a new hydrophobic acrylic toric intraocular lens (IOL) to correct preexisting corneal astigmatism in patients having routine cataract surgery. SETTING: Four hospital eye clinics throughout Europe. DESIGN: Cohort study. METHODS: This study included eyes with at least 0.75 diopter (D) of preexisting corneal astigmatism having routine cataract surgery. Phacoemulsification was performed followed by insertion and alignment of a Tecnis toric IOL. Patients were examined 4 to 8 weeks postoperatively; uncorrected distance visual acuity (UDVA), corrected distance visual acuity, manifest refraction, and keratometry were measured. Individual patient satisfaction with uncorrected vision and the surgeon’s assessment of ease of handling and performance of the IOL were also documented. The cylinder axis of the toric IOL was determined by dilated slitlamp examination. RESULTS: The study enrolled 67 eyes of 60 patients. Four to 8 weeks postoperatively, the mean UDVA was 0.15 logMAR G 0.17 (SD) and the UDVA was 20/40 or better in 88% of eyes. The mean refractive cylinder decreased significantly postoperatively, from -1.91 +/- 1.07 D to -0.67 +/- 0.54 D. No significant change in keratometric cylinder was observed. The mean absolute IOL misalignment from the intended axis was 3.4 degrees (range 0 to 12 degrees). The good UDVA resulted in high levels of patient satisfaction. CONCLUSION: Implantation of the new toric IOL was an effective, safe, and predictable method to manage corneal astigmatism in patients having routine cataract surgery.

A new non-contact optical device for ocular biometry

Background: A new commercially available device (IOLMaster, Zeiss Instruments) provides high resolution non-contact measurements of axial length (using partial coherent interferometry), anterior chamber depth, and corneal radius (using image analysis). The study evaluates the validity and repeatability of these measurements and compares the findings with those obtained from instrumentation currently used in clinical practice. Method: Measurements were taken on 52 subjects (104 eyes) aged 18-40 years with a range of mean spherical refractive error from +7.0 D to -9.50 D. IOLMaster measurements of anterior chamber depth and axial length were compared with A-scan applanation ultrasonography (Storz Omega) and those for corneal radius with a Javal-Schiötz keratometer (Topcon) and an EyeSys corneal videokeratoscope. Results: Axial length: the difference between IOLMaster and ultrasound measures was insignificant (0.02 (SD 0.32) mm, p = 0.47) with no bias across the range sampled (22.40-27.99 mm). Anterior chamber depth: significantly shorter depths than ultrasound were found with the IOLMaster (-0.06 (0.25) mm, p <0.02) with no bias across the range sampled (2.85-4.40 mm). Corneal radius: IOLMaster measurements matched more closely those of the keratometer than those of the videokeratoscope (mean difference -0.03 v -0.06 mm respectively), but were more variable (95% confidence 0.13 v 0.07 mm). The repeatability of all the above IOLMaster biometric measures was found to be of a high order with no significant bias across the measurement ranges sampled. Conclusions: The validity and repeatability of measurements provided by the IOLMaster will augment future studies in ocular biometry.

Optical quality and visual performance with customised soft contact lenses for keratoconus

Purpose: This study investigated how aberration-controlling, customised soft contact lenses corrected higher-order ocular aberrations and visual performance in keratoconic patients compared to other forms of refractive correction (spectacles and rigid gas-permeable lenses). Methods: Twenty-two patients (16 rigid gas-permeable contact lens wearers and six spectacle wearers) were fitted with standard toric soft lenses and customised lenses (designed to correct 3rd-order coma aberrations). In the rigid gas-permeable lens-wearing patients, ocular aberrations were measured without lenses, with the patient's habitual lenses and with the study lenses (Hartmann-Shack aberrometry). In the spectacle-wearing patients, ocular aberrations were measured both with and without the study lenses. LogMAR visual acuity (high-contrast and low-contrast) was evaluated with the patient wearing their habitual correction (of either spectacles or rigid gas-permeable contact lenses) and with the study lenses. Results: In the contact lens wearers, the habitual rigid gas-permeable lenses and customised lenses provided significant reductions in 3rd-order coma root-mean-square (RMS) error, 3rd-order RMS and higher-order RMS error (p ≤ 0.004). In the spectacle wearers, the standard toric lenses and customised lenses significantly reduced 3rd-order RMS and higher-order RMS errors (p ≤ 0.005). The spectacle wearers showed no significant differences in visual performance measured between their habitual spectacles and the study lenses. However, in the contact lens wearers, the habitual rigid gas-permeable lenses and standard toric lenses provided significantly better high-contrast acuities compared to the customised lenses (p ≤ 0.006). Conclusions: The customised lenses provided substantial reductions in ocular aberrations in these keratoconic patients; however, the poor visual performances achieved with these lenses are most likely to be due to small, on-eye lens decentrations. © 2014 The College of Optometrists.

Non-zero mean Gaussian process prior wind field models

This report outlines the derivation and application of a non-zero mean, polynomial-exponential covariance function based Gaussian process which forms the prior wind field model used in 'autonomous' disambiguation. It is principally used since the non-zero mean permits the computation of realistic local wind vector prior probabilities which are required when applying the scaled-likelihood trick, as the marginals of the full wind field prior. As the full prior is multi-variate normal, these marginals are very simple to compute.

Gaussian processes for classification: mean field algorithms:mean-field algorithms

We derive a mean field algorithm for binary classification with Gaussian processes which is based on the TAP approach originally proposed in Statistical Physics of disordered systems. The theory also yields an approximate leave-one-out estimator for the generalization error which is computed with no extra computational cost. We show that from the TAP approach, it is possible to derive both a simpler 'naive' mean field theory and support vector machines (SVM) as limiting cases. For both mean field algorithms and support vectors machines, simulation results for three small benchmark data sets are presented. They show 1. that one may get state of the art performance by using the leave-one-out estimator for model selection and 2. the built-in leave-one-out estimators are extremely precise when compared to the exact leave-one-out estimate. The latter result is a taken as a strong support for the internal consistency of the mean field approach.

Gaussian processes and SVM: Mean field results and leave-one-out

In this chapter, we elaborate on the well-known relationship between Gaussian processes (GP) and Support Vector Machines (SVM). Secondly, we present approximate solutions for two computational problems arising in GP and SVM. The first one is the calculation of the posterior mean for GP classifiers using a `naive' mean field approach. The second one is a leave-one-out estimator for the generalization error of SVM based on a linear response method. Simulation results on a benchmark dataset show similar performances for the GP mean field algorithm and the SVM algorithm. The approximate leave-one-out estimator is found to be in very good agreement with the exact leave-one-out error.

TAP for parity check error correcting codes

We employ the methods presented in the previous chapter for decoding corrupted codewords, encoded using sparse parity check error correcting codes. We show the similarity between the equations derived from the TAP approach and those obtained from belief propagation, and examine their performance as practical decoding methods.

Error-correcting codes on a Bethe-like lattice

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Bayesian error bars for regression

Regression problems are concerned with predicting the values of one or more continuous quantities, given the values of a number of input variables. For virtually every application of regression, however, it is also important to have an indication of the uncertainty in the predictions. Such uncertainties are expressed in terms of the error bars, which specify the standard deviation of the distribution of predictions about the mean. Accurate estimate of error bars is of practical importance especially when safety and reliability is an issue. The Bayesian view of regression leads naturally to two contributions to the error bars. The first arises from the intrinsic noise on the target data, while the second comes from the uncertainty in the values of the model parameters which manifests itself in the finite width of the posterior distribution over the space of these parameters. The Hessian matrix which involves the second derivatives of the error function with respect to the weights is needed for implementing the Bayesian formalism in general and estimating the error bars in particular. A study of different methods for evaluating this matrix is given with special emphasis on the outer product approximation method. The contribution of the uncertainty in model parameters to the error bars is a finite data size effect, which becomes negligible as the number of data points in the training set increases. A study of this contribution is given in relation to the distribution of data in input space. It is shown that the addition of data points to the training set can only reduce the local magnitude of the error bars or leave it unchanged. Using the asymptotic limit of an infinite data set, it is shown that the error bars have an approximate relation to the density of data in input space.

Global non-dynamic refinement of radial orbit error for altimetric earth satellites

The accuracy of altimetrically derived oceanographic and geophysical information is limited by the precision of the radial component of the satellite ephemeris. A non-dynamic technique is proposed as a method of reducing the global radial orbit error of altimetric satellites. This involves the recovery of each coefficient of an analytically derived radial error correction through a refinement of crossover difference residuals. The crossover data is supplemented by absolute height measurements to permit the retrieval of otherwise unobservable geographically correlated and linearly combined parameters. The feasibility of the radial reduction procedure is established upon application to the three day repeat orbit of SEASAT. The concept of arc aggregates is devised as a means of extending the method to incorporate longer durations, such as the 35 day repeat period of ERS-1. A continuous orbit is effectively created by including the radial misclosure between consecutive long arcs as an infallible observation. The arc aggregate procedure is validated using a combination of three successive SEASAT ephemerides. A complete simulation of the 501 revolution per 35 day repeat orbit of ERS-1 is derived and the recovery of the global radial orbit error over the full repeat period is successfully accomplished. The radial reduction is dependent upon the geographical locations of the supplementary direct height data. Investigations into the respective influences of various sites proposed for the tracking of ERS-1 by ground-based transponders are carried out. The potential effectiveness on the radial orbital accuracy of locating future tracking sites in regions of high latitudinal magnitude is demonstrated.