کمی‌‌سازی عدم اطمینان در تخمین ویژگی‌های مودال طیف امپدانس الکترومکانیکی وصله پیزوالکتریک مستطیلی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 پژوهشکده فناوری نو، دانشگاه صنعتی امیرکبیر، تهران، ایران - دانشکده مهندسی مکانیک، دانشگاه صنعتی امیرکبیر، تهران، ایران

2 پژوهشکده فناوری نو، دانشگاه صنعتی امیرکبیر، تهران، ایران دانشکده مهندسی مکانیک، دانشگاه صنعتی امیرکبیر، تهران، ایران

3 پژوهشکده فناوری نو، دانشگاه صنعتی امیرکبیر، تهران، ایران

4 دانشکده مهندسی مکانیک و مکاترونیک، دانشگاه صنعتی شاهرود، شاهرود، ایران

5 دانشکده مهندسی مکانیک، دانشگاه صنعتی امیرکبیر، تهران، ایران

چکیده

روش امپدانس الکترومکانیکی از جمله روش‌های مؤثر جهت شناسایی آسیب در حوزه تعمیر و نگهداری بر خط به شمار می‌رود. در این روش از قابلیت وصله‌های پیزوالکتریک جهت عملگری و حسگری هم‌زمان استفاده می‌شود. تخمین طیف امپدانس الکترومکانیکی به کمک مدل‌های عددی یا تحلیلی مزایای ویژه‌‌ای در فرایند شناسایی آسیب فراهم می‌آورد. این در حالی است که وجود منابع عدم اطمینان مختلف منجر به اختلاف قابل‌توجه بین نتایج مدل‌های عددی و نتایج تجربی می‌شود. ازاین‌رو کمی سازی عدم اطمینان در پاسخ ارتعاشاتی فرکانس بالای وصله پیزوالکتریک ضرورت پیدا می‌کند. در این تحقیق به بررسی احتمالاتی تخمین طیف امپدانس الکترومکانیکی پرداخته می‌شود. در این راستا از مدل‌های جایگزین مبتنی بر بسط آشوبناک چندجمله‌ای جهت تحلیل احتمالاتی ویژگی‌های مودال طیف امپدانس استفاده شد. ممان‌های احتمالاتی و توزیع احتمال کمیت‌های پاسخ مورد نظر به‌صورت تحلیلی توسط مدل‌های جایگزین محاسبه شدند. تحلیل حساسیت سراسری جهت رتبه‌بندی اهمیت متغیرهای احتمالاتی بر واریانس مقادیر پاسخ از طریق پس‌پردازش ضرایب مدل‌های آشوبناک چندجمله‌ای و با هزینه محاسباتی بسیار کم امکان‌پذیر است. طبق نتایج، به‌ازای مقادیر عدم اطمینان رایج در خواص و هندسه وصله پیزوالکتریک، ضریب تغییرات در دامنه فرکانس‌های قله (%50/70) بسیار بیشتر از فرکانس‌های مودال (%4/20) است. به‌علاوه، فرکانس‌های مودال بیشترین حساسیت را به خواص مکانیکی (مدول نرمی و چگالی) و دامنه‌های مودال بیشترین حساسیت را به ضریب میرایی مکانیکی، ضریب گذردهی الکتریکی و ثابت پیزوالکتریک دارند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Uncertainty Quantification in the Assessment of the Characteristics of the Electromechanical Impedance Spectrum of a Rectangular Piezoelectric Patch

نویسندگان [English]

  • Mohammad Ehsani 1 2
  • Mahnaz Shamshirsaz 3
  • Naserodin Sepehry 4
  • Mojtaba Sadighi 5
1 New Technologies Research Center (NTRC), Amirkabir University of Technology, Tehran|Department of Mechanical Engineering, Amirkabir University of Technology, Tehran
2 New Technologies Research Center (NTRC), Amirkabir University of Technology, Tehran|Department of Mechanical Engineering, Amirkabir University of Technology, Tehran
3 New Technologies Research Center (NTRC), Amirkabir University of Technology, Tehran
4 Faculty of Mechanical and Mechatronic Engineering, Shahrood University of Technology, Shahrood
5 Department of Mechanical Engineering, Amirkabir University of Technology, Tehran
چکیده [English]

Electromechanical impedance spectroscopy can be used for damage localization by estimating the electromechanical impedance spectrum with numerical or analytical models. The existence of several sources of uncertainty, however, leads to a significant mismatch between the numerical and experimental results. Therefore, uncertainty quantification for high-frequency coupled electromechanical vibration response of the piezoelectric patch is necessary. Polynomial chaos expansion is an efficient method for assessing uncertainty when dealing with time-consuming models. For the probabilistic analysis of modal features of the impedance spectrum, surrogate models derived by polynomial chaos expansion were used. The statistical moments and probability distributions of the quantity of interest were computed analytically using surrogate models. By post-processing the coefficients of polynomial chaos expansion models with relatively minimal computing cost, global sensitivity analysis was performed to rank the relevance of input variable variation on response variance. According to the results, due to the common uncertainties in the material properties and geometry of the piezoelectric patch, the coefficient of variation in the peak amplitudes is substantially higher than the peak frequencies. In addition, modal frequencies are most sensitive to mechanical properties (compliance and density), whereas modal amplitudes are most sensitive to mechanical damping, electrical permittivity, and the piezoelectric constant.

کلیدواژه‌ها [English]

  • Structural health monitoring
  • Piezoelectric patch
  • Uncertainty quantification
  • Polynomial chaos expansion
  • Global sensitivity analysis

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نشریه مهندسی مکانیک امیرکبیر
دوره 54، شماره 10
دی 1401
صفحه 2351-2376

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