Robustness of Maximin Space-filling Designs

In this report, we first have a review of the maximin space-filling design methods that is often applied and discussed in the literature (for example, Müller (2007)). Then we will discuss the robustness of the maximin space-filling design against model misspecification via numerical simulation. For this purpose, we will generate spatial data sets on a n x n grid and design points are selected from the n2 locations. The predictions at the unsampled locations are made based on the observations at these design points. Then the mean of the squared prediction errors are estimated as a measure of the robustness of the designs against possible model misspecification. Surprisingly, according to the simulation results, we find that the maximin space-filling designs may be robust against possible model misspecification in the sense that the mean of the squared prediction error does not increase significantly when the model is misspecified. Although the results were obtained based on simple models, this result is very inspiring. It will guide further numerical and theoretical studies which will be done as future work.

SIMULTANEOUS SPECTROPHOTOMETRIC DETERMINATION OF PHENYLEPHRINE HYDROCHLORIDE AND NAPHAZOLINE HYDROCHLORIDE IN EYE DROPS BY CHEMOMETRIC TECHNIQUES AND ARTIFICIAL NEURAL NETWORK

Three multivariate calibration-prediction techniques, partial least squares (PLS), principal component regression (PCR) and artifi cial neural networks (ANN), have been applied without separation in the spectrophotometric multi-component analysis of phenylephrine hydrochloride and naphazoline hydrochloride. A set of 25 synthetic mixtures of phenylephrine hydrochloride and naphazoline hydrochloride has been evaluated to determine the predictability of PLS, PCR and ANN. The absorbance data matrix was obtained by measuring zero-order absorbances between 230-300 nm at intervals of 3 nm. The suitability of the models was determined on the basis of root mean square error (RMSE), root mean squared cross validation error (RMSECV) and root mean squared prediction error (RMSEP) values of calibration and validation data. The results showed a very good correlation between true values and the predicted concentration values. Therefore, the methods developed can be used for routine drug analysis without chemical pre-treatment.

Narrowband Interference Cancellation using Set-membership Adaptive Predictor for GPS Receiver

The global positioning system (GPS) provides accurate positioning and timing information that is useful in various civil and military applications. The adaptive filtering predictor for GPS jamming suppression applications is proposed. This research uses the gLab-G software to substitute for the hardware receiver to record the GPS signal waveform. The normalized least-mean-square (NLMS) and set-membership NLMS (SM-NLMS) filtering methods are employed for continuous wave interference suppression. Simulation results reveal that our proposed methods can provide the better performances when the interference-to-noise ratios (INR) are varied from 20 to 50 dB. The anti-jamming performances are evaluated via extensive simulation by computing mean squared prediction error (MSPE) and signal-to-noise ratio (SNR) improvements.

Distributional Robustness of K-class Estimators and the PULSE

While causal models are robust in that they are prediction optimal under arbitrarily strong interventions, they may not be optimal when the interventions are bounded. We prove that the classical K-class estimator satisfies such optimality by establishing a connection between K-class estimators and anchor regression. This connection further motivates a novel estimator in instrumental variable settings that minimizes the mean squared prediction error subject to the constraint that the estimator lies in an asymptotically valid confidence region of the causal coefficient. We call this estimator PULSE (p-uncorrelated least squares estimator), relate it to work on invariance, show that it can be computed efficiently as a data-driven K-class estimator, even though the underlying optimization problem is non-convex, and prove consistency. We evaluate the estimators on real data and perform simulation experiments illustrating that PULSE suffers from less variability. There are several settings including weak instrument settings, where it outperforms other estimators.

A Predictive Model to Detect the Impending Electric Submersible Pump Trips and Failures

Trips and failures are common occurrences in the Electric Submersible Pump (ESP) systems. The random nature of these trips and failures will lead to low industry run-life and high workover costs for ESP companies and operators. To perform early detection and take corrective actions to handle the potential incidents, ESP operation data collected from downhole and surface sensors are used to perform diagnostics and prognostics to identify trips and failures. In this study, Principal Component Analysis (PCA) method serves as a pre-processing method to retain the most essential principal components to reevaluate the initial ESP system. For a single well system, the Squared Prediction Error (SPE) and Hotelling T-square statistic (T2) equations are employed for numerical visualization in the new principal component space and therefore detection of the potential ESP trips or failures. For the whole well group, the score plot of three principal components provides a solution that enables to distinguish different clusters of stable operation, trip and failure regions, and diagnose the upcoming ESP trips and failures. In this way, the predictive model is bulit to continuously analyze the ESP operation and automatically perform health monitoring for any ESP system. This paper concludes that the predictive model has the potential to construct a real-time proactive surveillance system to identify dynamic anomalies and therefore predict developing trips or failures in the ESP system.

Data Driven Detection of Different Dissolved Oxygen Sensor Faults for Improving Operation of the WWTP Control System

Sensor faults frequently occur in wastewater treatment plant (WWTP) operation, leading to incomplete monitoring or poor control of the plant. Reliable operation of the WWTP considerably depends on the aeration control system, which is essentially assisted by the dissolved oxygen (DO) sensor. Results on the detection of different DO sensor faults, such as bias, drift, wrong gain, loss of accuracy, fixed value, or complete failure, were investigated based on Principal Components Analysis (PCA). The PCA was considered together with two statistical approaches, i.e., the Hotelling’s T2 and the Squared Prediction Error (SPE). Data used in the study were generated using the previously calibrated first-principle Activated Sludge Model no.1 for the Anaerobic-Anoxic-Oxic (A2O) reactors configuration. The equation-based model was complemented with control loops for DO concentration control in the aerobic reactor and nitrates concentration control in the anoxic reactor. The PCA data-driven model was successfully used for the detection of the six investigated DO sensor faults. The statistical detection approaches were compared in terms of promptness, effectiveness, and accuracy. The obtained results revealed the way faults originating from DO sensor malfunction can be detected and the efficiency of the detection approaches for the automatically controlled WWTP.

Customized yet Standardized Temperature Derivatives: A Non-Parametric Approach with Suitable Basis Selection for Ensuring Robustness

Previous studies have demonstrated that non-parametric hedging models using temperature derivatives are highly effective in hedging profit/loss fluctuation risks for electric utilities. Aiming for the practical applications of these methods, this study performs extensive empirical analyses and makes methodological customizations. First, we consider three types of electric utilities being exposed to risks of “demand,” “price,” and their “product (multiplication),” and examine the design of an appropriate derivative for each utility. Our empirical results show that non-parametrically priced derivatives can maximize the hedge effect when a hedger bears a “price risk” with high nonlinearity to temperature. In contrast, standard derivatives are more useful for utilities with only “demand risk” in having a comparable hedge effect and in being liquidly traded. In addition, the squared prediction error derivative on temperature has a significant hedge effect on both price and product risks as well as a certain effect on demand risk, which illustrates its potential as a new standard derivative. Furthermore, spline basis selection, which may be overlooked by modeling practitioners, improves hedge effects significantly, especially when the model has strong nonlinearities. Surprisingly, the hedge effect of temperature derivatives in previous studies is improved by 13–53% by using an appropriate new basis.

Considerations on the Castrop formula for calculation of intraocular lens power

Background To explain the concept of the Castrop lens power calculation formula and show the application and results from a large dataset compared to classical formulae. Methods The Castrop vergence formula is based on a pseudophakic model eye with 4 refractive surfaces. This was compared against the SRKT, Hoffer-Q, Holladay1, simplified Haigis with 1 optimized constant and Haigis formula with 3 optimized constants. A large dataset of preoperative biometric values, lens power data and postoperative refraction data was split into training and test sets. The training data were used for formula constant optimization, and the test data for cross-validation. Constant optimization was performed for all formulae using nonlinear optimization, minimising root mean squared prediction error. Results The constants for all formulae were derived with the Levenberg-Marquardt algorithm. Applying these constants to the test data, the Castrop formula showed a slightly better performance compared to the classical formulae in terms of prediction error and absolute prediction error. Using the Castrop formula, the standard deviation of the prediction error was lowest at 0.45 dpt, and 95% of all eyes in the test data were within the limit of 0.9 dpt of prediction error. Conclusion The calculation concept of the Castrop formula and one potential option for optimization of the 3 Castrop formula constants (C, H, and R) are presented. In a large dataset of 1452 data points the performance of the Castrop formula was slightly superior to the respective results of the classical formulae such as SRKT, Hoffer-Q, Holladay1 or Haigis.

IOL formula constants – strategies for optimization and defining standards for presenting data

Purpose: To present strategies for optimization of lens power formula constants and to show options how to present the results adequately. Methods: A dataset of N=1601 preoperative biometric values, lens power data and postoperative refraction data was split into a training set and a test set using a random sequence. Based on the training set we calculated the formula constants for established lens calculation formulae with different methods. Based on the test set we derived the formula prediction error as difference of the achieved refraction from the formula predicted refraction. Results: For formulae with 1 constant it is possible to back-calculate the individual constant for each case using formula inversion. However, this is not possible for formulae with more than 1 constant. In these cases, more advanced concepts such as nonlinear optimization strategies are necessary to derive the formula constants. During cross-validation, measures such as the mean absolute or the root mean squared prediction error or the ratio of cases within mean absolute prediction error limits could be used as quality measures. Conclusions: Different constant optimization concepts yield different results. To test the performance of optimized formula constants a cross-validation strategy is mandatory. We recommend performance curves, where the ratio of cases within absolute prediction error limits is plotted against the mean absolute prediction error.