Load estimation with uncertainties from opportunistic sampling data: A semiparametric approach

We consider estimating the total load from frequent flow data but less frequent concentration data. There are numerous load estimation methods available, some of which are captured in various online tools. However, most estimators are subject to large biases statistically, and their associated uncertainties are often not reported. This makes interpretation difficult and the estimation of trends or determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for obtaining reliable load estimates that minimizes the biases and makes use of informative predictive variables. The key step to this approach is in the development of an appropriate predictive model for concentration. This is achieved using a generalized rating-curve approach with additional predictors that capture unique features in the flow data, such as the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and the discounted flow. The latter may be thought of as a measure of constituent exhaustion occurring during flood events. Forming this additional information can significantly improve the predictability of concentration, and ultimately the precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach for two rivers delivering to the Great Barrier Reef, Queensland, Australia. One is a data set from the Burdekin River, and consists of the total suspended sediment (TSS) and nitrogen oxide (NO(x)) and gauged flow for 1997. The other dataset is from the Tully River, for the period of July 2000 to June 2008. For NO(x) Burdekin, the new estimates are very similar to the ratio estimates even when there is no relationship between the concentration and the flow. However, for the Tully dataset, by incorporating the additional predictive variables namely the discounted flow and flow phases (rising or recessing), we substantially improved the model fit, and thus the certainty with which the load is estimated.

An extended regression approach to estimating loads and their uncertainties in Great Barrier Reef catchments

There are numerous load estimation methods available, some of which are captured in various online tools. However, most estimators are subject to large biases statistically, and their associated uncertainties are often not reported. This makes interpretation difficult and the estimation of trends or determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for obtaining reliable load estimates by minimizing the biases and making use of possible predictive variables. The load estimation procedure can be summarized by the following four steps: - (i) output the flow rates at regular time intervals (e.g. 10 minutes) using a time series model that captures all the peak flows; - (ii) output the predicted flow rates as in (i) at the concentration sampling times, if the corresponding flow rates are not collected; - (iii) establish a predictive model for the concentration data, which incorporates all possible predictor variables and output the predicted concentrations at the regular time intervals as in (i), and; - (iv) obtain the sum of all the products of the predicted flow and the predicted concentration over the regular time intervals to represent an estimate of the load. The key step to this approach is in the development of an appropriate predictive model for concentration. This is achieved using a generalized regression (rating-curve) approach with additional predictors that capture unique features in the flow data, namely the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and cumulative discounted flow. The latter may be thought of as a measure of constituent exhaustion occurring during flood events. The model also has the capacity to accommodate autocorrelation in model errors which are the result of intensive sampling during floods. Incorporating this additional information can significantly improve the predictability of concentration, and ultimately the precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach using the concentrations of total suspended sediment (TSS) and nitrogen oxide (NOx) and gauged flow data from the Burdekin River, a catchment delivering to the Great Barrier Reef. The sampling biases for NOx concentrations range from 2 to 10 times indicating severe biases. As we expect, the traditional average and extrapolation methods produce much higher estimates than those when bias in sampling is taken into account.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

Quality of life changes during conformal radiation therapy for prostate carcinoma

BACKGROUND: The objective of this study was to describe prospectively quality of life (QOL) before and after radiotherapy for patients with prostate carcinoma. METHODS: Forty-three patients with T1-T3 prostate carcinoma who underwent conformal external beam radiation therapy were randomized either to the complete European Organization for Research and Treatment of Cancer (EORTC) QOL questionnaire (EORTC QLQ-C30) or the Medical Outcomes Study Group Short Form Health Survey (SF-36) at baseline, at 3 weeks and 6 weeks after initial treatment, and at 6 weeks and 5 months after the completion of radiotherapy. The measures were self-reported patient QOL, and values are given as the mean +/- standard error of the mean. Changes in QOL are described from baseline to the end of treatment in both questionnaire groups. RESULTS: Emotional role functioning, as measured with the SF-36 questionnaire, significantly improved from 68.2 +/- 9.9 at baseline to 93.3 +/- 5.2 at the end of therapy (P = 0.02). The EORTC QLQ-C30 questionnaire revealed consistent values of emotional functioning during treatment (72.7 +/- 5.9 at baseline) but showed a significant improvement 6 weeks after therapy (89.0 +/- 4.4; P = 0.01). Role functioning deteriorated from 80.1 +/- 6.5 at baseline to 62.5 +/- 8.8 at the end of radiotherapy (P = 0.02). Symptoms of fatigue were shown to increase significantly from 26.9 +/- 6.0 at baseline to 37.7 +/- 7.6 at the end of therapy (P = 0.02). No significant changes in the other dimensions were observed in either questionnaire. CONCLUSIONS: After radiotherapy for prostate carcinoma, patients experience a temporary deterioration of fatigue and role functioning, as measured with the EORTC QLQ-C-30. Despite physical deterioration, the authors observed an improvement in emotional functioning scores with both questionnaires. This may have been due to psychological adaptation and coping.

Combination of Kalman filter and least error square techniques in power system

An algorithm based on the concept of combining Kalman filter and Least Error Square (LES) techniques is proposed in this paper. The algorithm is intended to estimate signal attributes like amplitude, frequency and phase angle in the online mode. This technique can be used in protection relays, digital AVRs, DGs, DSTATCOMs, FACTS and other power electronics applications. The Kalman filter is modified to operate on a fictitious input signal and provides precise estimation results insensitive to noise and other disturbances. At the same time, the LES system has been arranged to operate in critical transient cases to compensate the delay and inaccuracy identified because of the response of the standard Kalman filter. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations and a laboratory test are presented to highlight the usefulness of the proposed method. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

Measurement error of rearfoot kinematics during running between a 100Hz and 30Hz camera

Background: Measurement accuracy is critical for biomechanical gait assessment. Very few studies have determined the accuracy of common clinical rearfoot variables between cameras with different collection frequencies. Research question: What is the measurement error for common rearfoot gait parameters when using a standard 30Hz digital camera compared to 100Hz camera? Type of study: Descriptive. Methods: 100 footfalls were recorded from 10 subjects ( 10 footfalls per subject) running on a treadmill at 2.68m/s. A high-speed digital timer, accurate within 1ms served as an external reference. Markers were placed along the vertical axis of the heel counter and the long axis of the shank. 2D coordinates for the four markers were determined from heel strike to heel lift. Variables of interest included time of heel strike (THS), time of heel lift (THL), time to maximum eversion (TMax), and maximum rearfoot eversion angle (EvMax). Results: THS difference was 29.77ms (+/- 8.77), THL difference was 35.64ms (+/- 6.85), and TMax difference was 16.50ms (+/- 2.54). These temporal values represent a difference equal to 11.9%, 14.3%, and 6.6% of the stance phase of running gait, respectively. EvMax difference was 1.02 degrees (+/- 0.46). Conclusions: A 30Hz camera is accurate, compared to a high-frequency camera, in determining TMax and EvMax during a clinical gait analysis. However, relatively large differences, in excess of 12% of the stance phase of gait, for THS and THL variables were measured.

Error and uncertainty of adult age estimation of the pubic symphysis in an Australian sub-population using computed tomography

After attending this presentation, attendees will gain awareness of: (1) the error and uncertainty associated with the application of the Suchey-Brooks (S-B) method of age estimation of the pubic symphysis to a contemporary Australian population; (2) the implications of sexual dimorphism and bilateral asymmetry of the pubic symphysis through preliminary geometric morphometric assessment; and (3) the value of three-dimensional (3D) autopsy data acquisition for creating forensic anthropological standards. This presentation will impact the forensic science community by demonstrating that, in the absence of demographically sound skeletal collections, post-mortem autopsy data provides an exciting platform for the construction of large contemporary ‘virtual osteological libraries’ for which forensic anthropological research can be conducted on Australian individuals. More specifically, this study assesses the applicability and accuracy of the S-B method to a contemporary adult population in Queensland, Australia, and using a geometric morphometric approach, provides an insight to the age-related degeneration of the pubic symphysis. Despite the prominent use of the Suchey-Brooks (1990) method of age estimation in forensic anthropological practice, it is subject to intrinsic limitations, with reports of differential inter-population error rates between geographical locations1-4. Australian forensic anthropology is constrained by a paucity of population specific standards due to a lack of repositories of documented skeletons. Consequently, in Australian casework proceedings, standards constructed from predominately American reference samples are applied to establish a biological profile. In the global era of terrorism and natural disasters, more specific population standards are required to improve the efficiency of medico-legal death investigation in Queensland. The sample comprises multi-slice computed tomography (MSCT) scans of the pubic symphysis (slice thickness: 0.5mm, overlap: 0.1mm) on 195 individuals of caucasian ethnicity aged 15-70 years. Volume rendering reconstruction of the symphyseal surface was conducted in Amira® (v.4.1) and quantitative analyses in Rapidform® XOS. The sample was divided into ten-year age sub-sets (eg. 15-24) with a final sub-set of 65-70 years. Error with respect to the method’s assigned means were analysed on the basis of bias (directionality of error), inaccuracy (magnitude of error) and percentage correct classification of left and right symphyseal surfaces. Morphometric variables including surface area, circumference, maximum height and width of the symphyseal surface and micro-architectural assessment of cortical and trabecular bone composition were quantified using novel automated engineering software capabilities. The results of this study demonstrated correct age classification utilizing the mean and standard deviations of each phase of the S-B method of 80.02% and 86.18% in Australian males and females, respectively. Application of the S-B method resulted in positive biases and mean inaccuracies of 7.24 (±6.56) years for individuals less than 55 years of age, compared to negative biases and mean inaccuracies of 5.89 (±3.90) years for individuals greater than 55 years of age. Statistically significant differences between chronological and S-B mean age were demonstrated in 83.33% and 50% of the six age subsets in males and females, respectively. Asymmetry of the pubic symphysis was a frequent phenomenon with 53.33% of the Queensland population exhibiting statistically significant (χ2 - p<0.01) differential phase classification of left and right surfaces of the same individual. Directionality was found in bilateral asymmetry, with the right symphyseal faces being slightly older on average and providing more accurate estimates using the S-B method5. Morphometric analysis verified these findings, with the left surface exhibiting significantly greater circumference and surface area than the right (p<0.05). Morphometric analysis demonstrated an increase in maximum height and width of the surface with age, with most significant changes (p<0.05) occurring between the 25-34 and 55-64 year age subsets. These differences may be attributed to hormonal components linked to menopause in females and a reduction in testosterone in males. Micro-architectural analysis demonstrated degradation of cortical composition with age, with differential bone resorption between the medial, ventral and dorsal surfaces of the pubic symphysis. This study recommends that the S-B method be applied with caution in medico-legal death investigations of unknown skeletal remains in Queensland. Age estimation will always be accompanied by error; therefore this study demonstrates the potential for quantitative morphometric modelling of age related changes of the pubic symphysis as a tool for methodological refinement, providing a rigor and robust assessment to remove the subjectivity associated with current pelvic aging methods.

Prevalence and predictors of refractive error in a genetically isolated population : the Norfolk Island Eye Study

BACKGROUND: We aimed to determine the prevalence and associations of refractive error on Norfolk Island. DESIGN: Population-based study on Norfolk Island, South Pacific. PARTICIPANTS: All permanent residents on Norfolk Island aged ≥ 15 years were invited to participate. METHODS: Patients underwent non-cycloplegic autorefraction, slit-lamp biomicroscope examination and biometry assessment. Only phakic eyes were analysed. MAIN OUTCOME MEASURES: Prevalence and multivariate associations of refractive error and myopia. RESULTS: There were 677 people (645 right phakic eyes, 648 left phakic eyes) aged ≥ 15 years were included in this study. Mean age of participants was 51.1 (standard deviation 15.7; range 15-81). Three hundred and seventy-six people (55.5%) were female. Adjusted to the 2006 Norfolk Island population, prevalence estimates of refractive error were as follows: myopia (mean spherical equivalent ≥ -1.0 D) 10.1%, hypermetropia (mean spherical equivalent ≥ 1.0 D) 36.6%, and astigmatism 17.7%. Significant independent predictors of myopia in the multivariate model were lower age (P < 0.001), longer axial length (P < 0.001), shallower anterior chamber depth (P = 0.031) and increased corneal curvature (P < 0.001). Significant independent predictors of refractive error were increasing age (P < 0.001), male gender (P = 0.009), Pitcairn ancestry (P = 0.041), cataract (P < 0.001), longer axial length (P < 0.001) and decreased corneal curvature (P < 0.001). CONCLUSIONS: The prevalence of myopia on Norfolk Island is lower than on mainland Australia, and the Norfolk Island population demonstrates ethnic differences in the prevalence estimates. Given the significant associations between refractive error and several ocular biometry characteristics, Norfolk Island may be a useful population in which to find the genetic basis of refractive error.

Development of optical ray tracing model of a standard parabolic trough collector

Parabolic trough concentrator collector is the most matured, proven and widespread technology for the exploitation of the solar energy on a large scale for middle temperature applications. The assessment of the opportunities and the possibilities of the collector system are relied on its optical performance. A reliable Monte Carlo ray tracing model of a parabolic trough collector is developed by using Zemax software. The optical performance of an ideal collector depends on the solar spectral distribution and the sunshape, and the spectral selectivity of the associated components. Therefore, each step of the model, including the spectral distribution of the solar energy, trough reflectance, glazing anti-reflection coating and the absorber selective coating is explained and verified. Radiation flux distribution around the receiver, and the optical efficiency are two basic aspects of optical simulation are calculated using the model, and verified with widely accepted analytical profile and measured values respectively. Reasonably very good agreement is obtained. Further investigations are carried out to analyse the characteristics of radiation distribution around the receiver tube at different insolation, envelop conditions, and selective coating on the receiver; and the impact of scattered light from the receiver surface on the efficiency. However, the model has the capability to analyse the optical performance at variable sunshape, tracking error, collector imperfections including absorber misalignment with focal line and de-focal effect of the absorber, different rim angles, and geometric concentrations. The current optical model can play a significant role in understanding the optical aspects of a trough collector, and can be employed to extract useful information on the optical performance. In the long run, this optical model will pave the way for the construction of low cost standalone photovoltaic and thermal hybrid collector in Australia for small scale domestic hot water and electricity production.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.