A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.

Pre-harvest Treatment of Zn ＆ B Affects the Fruit Quality and Storability of Sweet Orange

Physico-chemical composition of sweet orange （Citrus sinensis L.） cv. blood red was determined in relation to different storage conditions and micronutrients application at department of horticulture, Agricultural University Peshawar, Pakistan during 2006-2007 and 2007-2008. The post-harvest quality of sweet orange was evaluated for 60 days storage with 20 days intervals. Fruit were harvested after the foliar application of zinc and boron in two consecutive seasons. The harvested fruits were stored at an ambient temperature （ATS） of 25 ＋ 2 ℃ and at low temperature storage （LTS） of 15 ± 2 ℃ with 60%-70% relative humidity （RH） for 60 days. Sweet oranges stored at LTS maintained better fruit quality than ATS. The foliar application of zinc and boron significantly enhanced fruit juice content, total soluble solids （TSS）, ascorbic acid （AA） and non-reducing sugar （NRS） of fruit. However, fruit juice content, TSS and AA were observed significantly higher, when the fruit was treated with high zinc （1%） and low boron （0.02%）. The percent of weight loss, disease incidence, TSS and reducing sugar （RS） increased with increasing the storage durations. A reduction was noted in fruit juice, AA and NRS with increasing the storage durations.