بررسی عدم قطعیت پارامترهای خاک بر عدم قطعیت پروفیل رطوبتی با استفاده از نظریه‌ی مجموعه‌های فازی

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری/ آبیاری و زهکشی . دانشگاه فردوسی مشهد

2 استاد/ گروه مهندسی آب .دانشگاه فردوسی مشهد

چکیده

عدم قطعیت ابزاری برای سنجش اعتماد پذیری سیستم یا پارامترهای آن می‌باشد. در بررسی حرکت آب در خاک غیر اشباع پارامترهای زیادی موثر هستند، که اندازه‌گیری یا برآورد آن‌ها دشوار بوده و به نوعی دارای عدم قطعیت می‌باشند. در این پژوهش، بر اساس نظریه‌ی مجموعه‌های فازی، رویکردی جایگزین برای بیان نادقیقی پارامترهای مدل و پیش بینی عدم قطعیت در شبیه‌سازی مدل به کار گرفته شد. ابتدا معادله ریچاردز به عنوان یک مدل قطعی برای حرکت آب در خاک به صورت عددی حل گردید. برای به دست آوردن عدم قطعیت در شبیه سازی این مدل، متغیرهای ورودی (θs، θr ، Ks ، α و n) به عنوان توابع فازی معرفی شدند. پس از ساختن توابع فازی مناسب برای هر یک از ورودی‌ها، برای هر برش β مشخص مقادیر مرزی برای این پارامترها به دست آمد، با استفاده از این مقادیر و با درنظر گرفتن قیدهای خاص، مقادیر بیشینه و کمینه رطوبت در زمان و مکان مشخص با استفاده از حل عددی معادله ریچاردز به دست آمد. نتایج نشان داد که عدم قطعیت در شبیه سازی پروفیل رطوبتی خاک در فاز اشباع کمترین و در فاز پیشروی بیش‌ترین مقدار را به خود اختصاص می‌دهد که علت این امر بیش‌ترین اثر عدم قطعیت ذاتی پارامترهای ورودی و نتیجه این عدم قطعیت در پروفیل رطوبتی در فاز پیشروی است. شکل توابع فازی به دست آمده برای رطوبت خاک در زمان مشخص، در عمق‌های مختلف خاک متفاوت بود که متاثر از نقش پارامترهای اولیه در هر زمان و مکان خاص در نتایج خروجی رطوبت می‌باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Uncertainty analysis of soil parameters in soil moisture profile uncertainty using fuzzy set theory

نویسندگان [English]

  • M. Khorami 1
  • B. Ghahraman 2
1 Ph.D. Student in Irrigation and drainage, Department of Water Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
2 Professor, Department of Water Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
چکیده [English]

Uncertainty is the measure of the reliability associated with a particular set of results. There are a lot of effective parameters in water movement through the unsaturated zone and obtaining measurement or estimation of them are difficult and have a kind of uncertainty.In this study, a methodology based on fuzzy set theory is presented to express imprecision of input data, in terms of fuzzy number, to quantify the uncertainty in prediction. Richards’ equation as a certain model was solved numerically .To estimate uncertainty in model; input parameters (θs, θr, Ks, α and n) were introduced as fuzzy parameters. After introducing suitable fuzzy membership functions for input parameters, at different β level cuts in input parameters, there will be boundaries for each parameter, then the mathematical operation on fuzzy sets are performed at different β- cut levels and result interval boundaries for the moisture in specific time and location. Corresponding to different β- cuts, fuzzy membership functions were derived for soil moisture at any time and depth. The results showed that uncertainty in simulating soil moisture profile is minimum in saturated phase and it is maximum in advance phase, that’s because of maximum number of parameters that taking part with maximum uncertainty in this phase. The shape of fuzzy membership function for soil moisture in specific time is varying for different depths because the rule of effective initial parameters in any time and depth are different.

کلیدواژه‌ها [English]

  • Unsaturated zone
  • Numerical Solution
  • Richard’s equation
  • HYDRUS

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