Capturing a Change in the Covariance Structure of a Multivariate Process

This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift.

New Methodology of Designation the Precise Aircraft Position Based on the RTK GPS Solution

The paper presents the results of research on improving the accuracy of aircraft positioning using RTK-OTF (Real Time Kinematic–On The Fly) technique in air navigation. The paper shows a new solution of aircraft positioning for the application of the differential RTK-OTF technique in air navigation. In particular, a new mathematical model is presented which makes it possible to determine the resultant position of an aircraft based on the solution for the method of least squares in a stochastic process. The developed method combines in the process of alignment of GPS (Global Positioning System) observations, three independent solutions of the aircraft position in OTF mode for geocentric coordinates XYZ of the aircraft. Measurement weights as a function of the vector length and the mean vector length error, respectively, were used in the calculations. The applied calculation method makes it possible to determine the resultant position of the aircraft with high accuracy: better than 0.039 m with using the measurement weight as a function of the vector length and better than 0.009 m with the measurement weight as a function of the mean error of the vector length, respectively. In relation to the classical RTK-OTF solution as a model of the arithmetic mean, the proposed method makes it possible to increase the accuracy of determination of the aircraft position by 45–46% using the measurement weight as a function of the vector length, and 86–88% using the measurement weight as a function of the mean error of the vector length, respectively. The obtained test results show that the developed method improves to significantly improve the accuracy of the RTK-OTF solution as a method for determining the reference position in air navigation.

Upper troposphere circulation anomalies over Asia-Pacific region associated with the interannual variation of Indian summer monsoon

Monthly mean vector wind and geopotential heights at 200 hPa of 67 radiosonde stations from Asia Pacific regions for the period 1963-1988 are used to examine the composite circulation anomaly patterns for the month of May and the monsoon season (June- September) with respect to good monsoon years and bad monsoon years (both associated with ENSO and not associated with ENSO). There are significant differences in the anomalous circulation features between good and bad monsoon years. During the month of May an anomalous anticyclonic (cyclonic) circulation over-central Asia and an anomalous cyclonic (anticyclonic) circulation over Pacific ocean were observed during good (bad) monsoon years. These anomalies persist in the subsequent monsoon season. The key mechanisms of the development of these anomalous circulation patterns and their consequences are discussed.

An Adaptive Covariance Scaling Estimation of Distribution Algorithm

Optimization problems are ubiquitous in every field, and they are becoming more and more complex, which greatly challenges the effectiveness of existing optimization methods. To solve the increasingly complicated optimization problems with high effectiveness, this paper proposes an adaptive covariance scaling estimation of distribution algorithm (ACSEDA) based on the Gaussian distribution model. Unlike traditional EDAs, which estimate the covariance and the mean vector, based on the same selected promising individuals, ACSEDA calculates the covariance according to an enlarged number of promising individuals (compared with those for the mean vector). To alleviate the sensitivity of the parameters in promising individual selections, this paper further devises an adaptive promising individual selection strategy for the estimation of the mean vector and an adaptive covariance scaling strategy for the covariance estimation. These two adaptive strategies dynamically adjust the associated numbers of promising individuals as the evolution continues. In addition, we further devise a cross-generation individual selection strategy for the parent population, used to estimate the probability distribution by combing the sampled offspring in the last generation and the one in the current generation. With the above mechanisms, ACSEDA is expected to compromise intensification and diversification of the search process to explore and exploit the solution space and thus could achieve promising performance. To verify the effectiveness of ACSEDA, extensive experiments are conducted on 30 widely used benchmark optimization problems with different dimension sizes. Experimental results demonstrate that the proposed ACSEDA presents significant superiority to several state-of-the-art EDA variants, and it preserves good scalability in solving optimization problems.

THEORETICAL AND EXPERIMENTAL INVESTIGATION OF ESTIMATING CHANGE POINT IN MULTIVARIATE PROCESSES VIA SIMULTANEOUS COVARIANCE MATRIX AND MEAN VECTOR

The identification of change points in statistical process control (SPC) data is the critical criterion for multivariate techniques when output is out-of-control condition. Therefore, monitoring all independent variables is essential and demands targeted attention to avoid errors at the systems control stage. However, estimating change-point in multivariate control charts is the main problem when these correlated quality characteristics monitor together. Therefore, we proposed a combination of an ensemble learning-based model of artificial neural networks with support vector machines to monitor process mean vector and covariance matrix shifts simultaneously to estimate the change point in a multivariable system. The performance of the final model indicated an estimated changing point with one sample over 6,000 simulated cases with a probability of 98 percent, which is a significantly high accuracy rating. Finding suggests the outcome of the project confirms that the proposed model can provide a precise estimating the change point by monitoring the mean vector and the covariance matrix simultaneously and, helps to identify those variable(s) responsible for an out-of-control condition. For further validation of the model, the performance of the proposed model has been compared with previous reported which confirms a better performance of the proposed model. Finally, the model was applied to monitor the performance of the solar hydrogen production system and the model identify the variables which have negative effects on the performance of the system.

Ridgelized Hotelling’s T2 test on mean vectors of large dimension

In this paper, a ridgelized Hotelling’s [Formula: see text] test is developed for a hypothesis on a large-dimensional mean vector under certain moment conditions. It generalizes the main result of Chen et al. [A regularized Hotelling’s [Formula: see text] test for pathway analysis in proteomic studies, J. Am. Stat. Assoc. 106(496) (2011) 1345–1360.] by relaxing their Gaussian assumption. This is achieved by establishing an exact four-moment theorem that is a simplified version of Tao and Vu’s [Random matrices: universality of local statistics of eigenvalues, Ann. Probab. 40(3) (2012) 1285–1315] work. Simulation results demonstrate the superiority of the proposed test over the traditional Hotelling’s [Formula: see text] test and its several extensions in high-dimensional situations.