Sains Malaysiana 43(3)(2014): 475–481

Suatu Kajian Perintis Menggunakan Pendekatan Kalut bagi Pengesanan Sifat dan

Peramalan Siri Masa Kepekatan PM

(A Pilot Study using Chaotic Approach to Determine Characteristics and Forecasting of PM₁₀ Concentration Time Series)

NOR ZILA ABD HAMID¹* & MOHD SALMI MD NOORANI²

¹Jabatan Matematik, Fakulti Sains dan Matematik, Universiti Pendidikan Sultan Idris

35900 Tanjung Malim, Perak, Malaysia

²Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi

43600 Bangi, Selangor, Malaysia

Diserahkan: 16 Mei 2013/Diterima: 15 Julai 2013

ABSTRAK

Peramalan kepekatan PM₁₀ adalah penting kerana menyedut udara mengandungi PM₁₀ boleh membawa kepada pelbagai penyakit kronik seperti kanser dan bronkitis. Kajian ini merupakan kajian perintis menggunakan pendekatan kalut bagi meramal PM₁₀ di Malaysia. Data yang dikaji adalah siri masa PM₁₀ mengikut jam yang dicerap di stesen penanda aras yang terletak dalam daerah Jerantut di negeri Pahang. Pendekatan kalut mempunyai dua langkah iaitu pembinaan semula ruang fasa dan proses peramalan. Melalui langkah 1, ruang fasa pelbagai-matra dibina menggunakan parameter masa tunda τ = 7 dan matra pembenaman m = 4 yang masing-masing diperoleh daripada kaedah maklumat purata bersama dan kaedah Cao. Hasil daripada gambarajah ruang fasa dan juga plot parameter kaedah Cao mempamerkan bahawa data bersifat kalut. Melalui langkah 2, peramalan satu jam ke hadapan selama sebulan siri masa PM₁₀ dijalankan menggunakan kaedah penghampiran setempat. Nilai pekali kolerasi antara data ramalan dan data sebenar hanyalah 0.5692. Namun, graf perbandingan menunjukkan bahawa data ramalan adalah hampir dengan data sebenar dengan nilai ralat punca min kuasa dua peramalan adalah 7.6814. Ini menunjukkan kesesuaian penggunaan kaedah penghampiran setempat dalam meramal siri masa PM₁₀ dan ia merupakan petanda positif bahawa pendekatan kalut ini boleh diguna pakai ke atas siri masa bahan pencemar di Malaysia.

Kata kunci: Kaedah penghampiran setempat; Malaysia; pendekatan kalut; peramalan; PM₁₀

ABSTRACT

Forecasting of PM₁₀ concentration is important as breathing air containing PM₁₀ can lead to chronic diseases such as cancer and bronchitis. This study is a pilot study using chaotic approach to forecast PM₁₀ in Malaysia. Studied data is a time series of observed hourly PM10 at benchmark station located in the district of Jerantut in Pahang state. Chaotic approach has two steps, namely the phase space reconstruction and the forecasting process. Through step 1, multi-dimensional phase space is reconstructed using the parameters of the delay time τ = 7 and embedding dimension m = 4, respectively, derived from the average mutual information and Cao method. The results from the phase space diagram and parameter plot of Cao method demonstrates that the data are chaotic. Through step 2, 1 h ahead forecasting for a month PM₁₀ time series is carried out using the local approximation method. Correlation coefficient value between the actual and forecasted data is only 0.5692. However, comparison graphs show that forecasted data are close to the actual data with root mean square error value 7.6814. This demonstrates the suitability of the local approximation method to forecast the time series of PM₁₀ and it's a positive sign that this chaotic approach is applicable to the time series of pollutants in Malaysia.

Keywords: Chaotic approach; forecast; local approximation method; Malaysia; PM₁₀

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*Pengarang untuk surat-menyurat; email: nor_zila@yahoo.com