Analysis of moisture change process in the maize grain with the use of statistical methods

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1 Annals of Warsaw University of Life Sciences SGGW Agriculture No 54 (Agricultural and Forest Engineering) 2009: (Ann. Warsaw Univ. of Life Sci. SGGW, Agricult. 54, 2009) Analysis of moisture change process in the maize grain with the use of statistical methods KATARZYNA SZWEDZIAK, JOANNA RUT Department of Agricultural and Forest Technology, Opole University of Technology Abstract: Analysis of moisture change process in the maize grain with the use of statistical methods. Investigations on specification of moisture change process in the maize grain are presented. A statistical data analysis was carried out with the use of the multiple, linear and non-linear regression models, enabling to determine degree of connection between particular variables. The obtained models were compared with the use of comparative statistics. Key words: statistical modeling, regression, sorbent, moisture content, maize grain. INTRODUCTION Majority of phenomena, such as moisture exchange or heat exchange influence substantially the mass of grain. Proper storing of grain is determined by excellent knowledge of its physical and biological properties. The basic aim of grain storage is preserving the grain usability over the longest possible time. This aim can be achieved by creating the conditions, which reduce the vital processes of grain and preclude development of pests and microorganisms [Pabis et al. 1974]. The storage of dry grain (of moisture reduced to 10 14%) has bin used most often. At this moisture the grain physiological processes are very slow, and no mould, bacteria or mites can be developed. To preclude development of insects in the grain mass, one should reduce moisture to 8 10%. Usually, drying of grain is applied, which is practically not economical, but sometimes essential. Another method is storing of cool grain, by decreasing its temperature. The development of insects in the stored grain is reduced at temperature below 17 C, thus, the grain cooling method can be used to prevent development of pests. Another method involves the grain storage in anaerobic conditions, when the vital activity of grain mass is maximally restricted (anabiosis) by cutting off the oxygen [Pohorecki et al. 1979]. The grain drying process calls for a big amount of expensive thermal energy, therefore, knowledge of moisture change process with the use of a natural sorbent (grain of the same species) can contribute to proper and economical drying of agricultural products [Hart 1967]. In scientific references there were proposed several models of moisture transport in the cereal grain, based on the models of Strumiłło or Pabis [Strumiłło 1975; Pabis et al. 1974], with the use of various functions describing course of the process. It was proved experimentally, that application of a harmonic function with

2 66 K. Szwedziak, J. Rut damping enabled to illustrate the process of moisture giving up and absorption [Szwedziak 2004]. However, no comprehensive dynamic characteristic of water content change in the mixture of wet grain (sorbate) and dry grain (sorbent) with consideration to temperature have been developed. Advancement of investigations in agriculture makes necessary searching for new solutions and improvement of the existing ones by application of statistical methods as a tool for data analysis. AIM OF INVESTIGATIONS The investigations aimed at determination of statistical solutions describing the change in moisture content in the maize grain mass. The statistical analysis of the multiple, linear and non-linear regression models was used for this purpose. MATERIAL AND METHODS There were carried out 6 series of investigations on the moisture exchange between maize grains in 4 replications, in the mixture of wet grain (sorbate) and dry grain (sorbent) with consideration to temperature. The investigations were performed in the containers of capacity 8 kg, fully filled with the properly mixed material and then closed. Both fractions were mixed by pouring with the use of a pouring mixer, until the state of equilibrium was obtained, i.e. when further mixing did not caused the qualitative changes in the system. It was proved that 10 subsequent pouring resulted in sufficient time of mixing [Boss and Tukiendorf 1989]. The mixture, where a given component particle can be found with the same probability as in all points is called the random mixture [Boss 1987]. The maize of variety Veritis was used in investigations; it is cultivated for grain and silage and has well filled, long-green corn cobs resistant to weather variation. Moisture exchange between the maize grains was investigated basing on the moisture content change in the mixed material. The moisture content was determined by drying method according to PN-ISO 712:2002 Standard in the mixture samples of 50 g, weighed with accuracy of ±0.01 g. The water content was determined in [kg H 2 O/kg d.m.]. The samples were taken every 3 hours over the period of 129 hours. The grain mass temperature was measured during experiment. ANALYSIS OF RESULTS AND DISCUSSION The obtained results were analyzed statistically with the use of multiple, linear and non-linear regression models, using the regression modeling with consideration to temperature (B C model) and also with no consideration to temperature (A D model). The obtained models are presented below: Model A: u = τ Model B: u = τ t Model C: u = τ τ τt t τt Model D: u = τ τ 2 gdzie: u wilgotność, τ czas, t temperatura The obtained models were compared with the use of comparative statistics. The determination coefficient gives no information about significance of particular variables. This value increases constantly when variables are added to

3 Analysis of moisture change process in the maize grain the model. However, it is evident that an increase in R 2 is often accompanied by the lack of significance of the added independent variables [Stanisz 2007]. The corrected determination coefficient was not introduced with respect to application of Akaike criterion (AIC), which is a more precise information criterion [Akaike 1973]. This criterion introduces a penalty for the reliability function, so that the simpler models can be preferred. In the case of fitting a model of q parameters to the data, this criterion is defined as D αqφ, where D is deviation, while φ is dispersion parameter [Stanisz 2007]. It can be pointed out that α 2 leads to minimal prediction errors, however, if φ is constant, the value α 4 is more proper, since it corresponds approximately to parameter testing on the level 0.05 [Olson 2002]. We select the model, for which this expression is minimal. The time needed for calculation of AIC statistics can be longer than for other criteria, but usually the obtained results are more precise [Stanisz 2007]. The obtained results are presented in Table 1. All the models are illustrated graphically (Fig. 1) together with empirical data. The best description of the course of moisture change was found for model C of highest value of coefficient R 2 = 0.89 and of the least value of Akaike criterion AIC = TABLE 1. Results of calculations Model Type of model R 2 AIC A Linear without temperature B Multiple with temperature C Non-linear with temperature D Non-linear without temperature Empirical data FIGURE 1. Models A, B, C and D Data

4 68 K. Szwedziak, J. Rut Surface diagram 3D Model C Differential temperature [ C] Time [h] FIGURE 2. Surface diagram of non-linear model with consideration to temperature (C model) Empirical values Model C 95% of confidence Data FIGURE 3. Model C with consideration to 95% of confidence interval

5 Analysis of moisture change process in the maize grain As a result of analysis on different forms of multiple, linear and non-linear models, there was selected the C model as a statistical model detecting a systematic trend in the data, and leaving out a random variability [Aczel 2005]. Model C is presented in Figure 2. The confidence interval of C model is presented in Figure 3. The confidence coefficient amounts to 0.95 which means, that the real value of moisture in investigated population is included in the determined confidence interval with probability of 95%. SUMMARY Majority of phenomena occurring in our environment is not isolated, but exists in various connections. The analysis with the use of statistical methods gives tools for verification of these recognized connections and for detection of not recognized hitherto interdependences. The statistical description allows for their better understanding and modification. Following statistical data analysis with the use of multiple, linear and non-linear regression models it was found, that the obtained non-linear model with consideration of temperature best describes the changes in moisture content of the maize grain. The selected model is a statistical model detecting a systematic trend of data, leaving out the random variability. REFERENCES ACZEL A. 2005: Statystyka w zarządzaniu pełny wykład, PWN Warszawa, ISBN X, s AKAIKE H. 1973: Information theory and an extension of the maximum likelihood princyple, In Proceedings of the 2nd International Symposium on Information, edited by Petrov B.N., and Czaki F., Budapest. BOSS J. 1987: Mieszanie materiałów ziarnistych, PWN Warszawa, ISBN , s BOSS J., TUKIENDORF M. 1989: Mieszanie systemem funnel-flow układu ziarnistego o różnych średnicach ziaren, Zeszyty Naukowe WSI w Opolu nr.151, z. 37. CIEŚLAK M. 2005: Prognozowanie gospodarcze, metody i prognozowanie, PWN Warszawa, ISBN , s HART J.R. 1967: Hysteresis effect In mixtures of wheat taken from the same sample but having different moisture contents, Cereal Chemistry, Vol. 41. KUFEL T. 2004: Ekonometria rozwiązywanie problemów z wykorzystaniem program GRETL, PWN Warszawa, ISBN , s MAGIERA R. 2007: Modele i metody statystyki matematycznej cz. II Wnioskowanie statystyczne, GiS Wrocław, ISBN: , s OLSON C.L. 1974: Comparative robustness of six tests multivariate analysis of ariance, Journal of the American Satatistical Assocation. PABIS S., PABIS J. 1974: Technologia suszenia i czyszczenia nasion, PWRiL Warszawa. POHORECKI R., WROŃSKI S. 1979: Kinetyka i termodynamika procesów inżynierii chemicznej, WNT Warszawa. STANISZ A. 2007: Przystępny kurs statystyki, modele liniowe i nieliniowe, Tom 2, StatSoft Polska Karków, ISBN , s STRUMIŁŁO Cz. 1975: Podstawy teorii i techniki suszenia, WNT Warszawa, s SZWEDZIAK K. 2006: Wpływ temperatury na jakość ziarna w procesie suszenia z wykorzystaniem sorbentów naturalnych, Inżynieria Rolnicza 11(86) Kraków, ISSN , s Streszczenie: Analiza procesu zmiany wilgoci w ziarnie kukurydzy z wykorzystaniem metod statystycznych. W artykule przedstawiono bada-

6 70 K. Szwedziak, J. Rut nia związane z charakterystyką procesu wilgoci w masie ziarna kukurydzy. Przeprowadzono statystyczną analizę danych za pomocą modeli regresji wielorakiej, liniowej i nieliniowej. Statystyczna metoda regresji pozwala na określenie stopnia, w jakim zmienne są ze sobą powiązane. Uzyskane modele porównano przy pomocy statystyk porównawczych. MS. received February 2009 Authors address: Katedra Techniki Rolniczej i Leśnej Politechnika Opolska Poland k.szwedziak@po.opole.pl j.rut@po.opole.pl