Prediction of Full Field Dynamic Strain from Limited Sets of Measured Data

Abstract

Dynamic response is an important consideration for design of structures due to operating or occasional loadings. The resulting dynamic stress strain is also of concern for fatigue and structural health monitoring. Typically, the actual loading and structural condition (boundary conditions, environmental condition, geometry, mechanical properties, etc.) are not necessarily known. Much effort is expended in attempting to identify the loads and appropriate model for prediction of these types of events. At best, the forces and actual boundary conditions are approximate and have an effect on the overall predicted response and resulting stress-strain that is identified for subsequent evaluation.Experimental data can only be obtained from limited sets of points, such as those typically collected with accelerometers. These are normally used in the evaluation the state of a structure in service condition. More recently, Digital Image Correlation (DIC) and Dynamic Photogrammetry (DP) have become very important techniques to measure the surface response. These are non-contact and full-field techniques, which allow that much more simultaneous data to be measure. The sets of limited surface data that are collected can be used in conjunction with an expansion algorithm to obtain full field information. The finite element model mass and stiffness matrices are used to obtain the normal constitutive relations as well as the modal characteristics. This information is used to develop the expansion algorithm and for the stress recovery during the back substitution process typically employed.

Underwater Dynamic Response at Limited Points Expanded to Full-Field Strain Response

“…The SEREP technique has been presented in earlier work cited in the references; only summarizing equations are list below. The relationship between the full set of DOF and a reduced set of degree-of-freedom is given as [12] fX n g ¼…”

“…There are some approaches that focus on predicting the full-field response from limited sets of measurement. Avitabile and Pingle [12,13] used noncontact measurement technique, with digital image correlation and dynamic photogrammetry, as well as full-field techniques to measure the surface response. Both the full-field displacement and strain of an analytical box-beam model and a base-upright structure was determined in that work.…”

“…The actual expansion process has been presented in Refs. [12] and [25]. The basic theoretical approach is summarized below and utilizes concepts from model reduction and model expansion as the underlying methodology for the expansion approach used for this work.…”

Fatigue assessment of offshore wind turbines on monopile foundations using multi‐band modal expansion

“…Other virtual sensing techniques will use strain sensors or accelerometers to catch and extrapolate higher frequent motion to predict the stress history of a structure. These virtual sensing techniques can be divided in the model‐based robust observers , the Kalman filter‐based techniques , the joint input‐state filtering techniques and the MDE technique . The aforementioned techniques have been applied on a wide range of civil and mechanical structures.…”

“…one sensor/one mode, two sensors/two modes, three sensors/three modes and three sensors/two modes). To quantify the correlation between the measured and predicted signals in the time domain, the time response assurance criterion (TRAC) is used . The TRAC is defined according to equation .…”