Stochastic process models for linear structure behavior

Vibration characteristics of a powerplant, an important parameter to evaluate the booming noise and the durability of each parts of an automobile is a major field of simulation analysis using the finite element method (FEM). Overall vibration characteristics, however, depend heavily on the joint properties when it comes to the analysis of complicated structures like a powerplant where a number of parts are incorporated. Among other characteristics, it is extremely difficult to conduct accurate identification of the damping characteristics of the joint area, which had been the result of inaccurate analyses. This paper reports a newly established method to solve these problems through the application of frequency response function (FRF) data and FEM models. Also described is the result of application of the method to the evaluation of a transversely-mounted in-line four-cylinder engine in a front-wheel drive layout. The application revealed that the joint properties can be identified fairly accurately, which in turn allows reliable prediction of vibration level.

The evaluation of the structural performance and durability using only measurement data without any baseline data is practical. One measurement data type is the frequency response function (FRF) data set, which does not provide enough information about the health state because of the noise included in the data. Proper orthogonal modes (POMs) extracted from the FRF data in a prescribed frequency range are utilized as an index to recognize the existence of damage. The POMs represent the principal axes of inertia formed by the distribution of data on the modal coordinate curve. This work proposes a damage detection method to trace damage based on the POM energy curvature at the element of the finite element model. The validity of the proposed method is illustrated by a numerical experiment and an experimental test.

Summary An efficient approach to identify multiple cracks in a slender beam using the frequency response function data is presented. It is formulated in a general form from the dynamic stiffness equation of motion for a structure and then applied to a slender beam. The cracks are modeled by rotational springs and the frequency response function is computed based on a spectral element model by the spectral finite element. The procedure gives a linear relationship explicitly between the changes of the measured frequency response function and crack parameters. The inverse problem is solved iteratively for the depths and locations of the cracks through the sensitivity-based model updating. Some numerically simulated tests on beam examples are provided for validating the feasibility of the method to identify the cracks. The results are generally agreement with the target values. Finally, the effect of noise on the damage identification is discussed in the numerical examples.

A ‘Sub-PolyMAX’ method is proposed in this paper not only for estimating modal parameters, but also for identifying structural flexibility by processing the impact test data in narrow frequency bands. The traditional PolyMAX method obtains denominator polynomial coefficients by minimizing the least square (LS) errors of frequency response function (FRF) estimates over the whole frequency range, but FRF peaks in different structural modes may have different levels of magnitude, which leads to the modal parameters identified for the modes with small FRF peaks being inaccurate. In contrast, the proposed Sub-PolyMAX method implements the LS solver in each subspace of the whole frequency range separately; thus the results identified from a narrow frequency band are not affected by FRF data in other frequency bands. In performing structural identification in narrow frequency bands, not in the whole frequency space, the proposed method has the following merits: (1) it produces accurate modal parameters, even for the modes with very small FRF peaks; (2) it significantly reduces computation cost by reducing the number of frequency lines and the model order in each LS implementation; (3) it accurately identifies structural flexibility from impact test data, from which structural deflection under any static load can be predicted. Numerical and laboratory examples are investigated to verify the effectiveness of the proposed method.

Damage detection in an offshore platform using incomplete noisy FRF data by a novel Bayesian model updating method

This paper presents the adaptation of the Cross Ambiguity Function Mapping (CAF- Mapping) algorithm for use in acoustics. The CAF-Mapping algorithm provides a useful means of generating a geographic visualization of acoustic data. Modifications of the algorithm for use in acoustics are explained, including use of acoustic modeling to generate propagation time differences, nonlinear grid spacing for frequency differences, location seeding using either three sensors or two sensors and two data samples, and frequency normalization. The algorithm allows discrimination between multiple acoustic signals with spatial or velocity vector variance. The presentation compares simulation results for several different types of data, then provides results that track a likely group of pygmy blue whale (Balaenoptera musculus brevicauda) using data from the Comprehensive Test Ban Treaty (CTBT) sensors off the coast of Australia. The author's affiliation with The MITRE Corporation is provided for identification purposes only and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions, or viewpoints expressed by the author. [Approved for Public Release; Distribution Unlimited Case 19-1301. Copyright 2019, The MITRE Corporation.]This paper presents the adaptation of the Cross Ambiguity Function Mapping (CAF- Mapping) algorithm for use in acoustics. The CAF-Mapping algorithm provides a useful means of generating a geographic visualization of acoustic data. Modifications of the algorithm for use in acoustics are explained, including use of acoustic modeling to generate propagation time differences, nonlinear grid spacing for frequency differences, location seeding using either three sensors or two sensors and two data samples, and frequency normalization. The algorithm allows discrimination between multiple acoustic signals with spatial or velocity vector variance. The presentation compares simulation results for several different types of data, then provides results that track a likely group of pygmy blue whale (Balaenoptera musculus brevicauda) using data from the Comprehensive Test Ban Treaty (CTBT) sensors off the coast of Australia. The author's affiliation with The MITRE Corporation is provided for identification purposes onl...

In experimental modal analysis, the use of characterized excitation and the choice of window functions are fundamental to the estimation of system frequency response function (FRF) data. It greatly influences the quality of the resulting FRF measurements. Discussed are combination methods of several commonly-used excitation signals with window function, which is relative to lightly damped systems. Study shows that burst random signal with Rectangular works well for lightly damped structures, and pure random with Hanning will bring about higher error. A modal testing of white car body was done. Experimental parameters analysis are given to demonstrate the study result presented above. So it poses a practicable method for improving the accuracy of frequency response function (FRF) measurements of lightly damped structure by using proper excitation signal with appropriate window function.

An experimental verification of a parameter estimation algorithm for finite-element (FE) model updating for damage quantification of a concrete beam with extensive damage is presented using the measured frequency response function (FRF) data. The intact stage of the beam and four progressive damage stages are investigated to update the FE model to quantify the damage across the beam. The method uses a subset of measured FRF data for FE model updating via a quasi-linear sensitivity equation of structural response. A least-squares algorithm with an appropriate weighting technique is used for parameter estimation. Proper selection of excitation frequency ranges for model updating is addressed. Predicted equivalent stiffnesses demonstrate the success and robustness of the method in damage quantification, even when using only a subset of the measured FRF data.

Damage indices based on structural dynamic characteristics are often used to detect damage in the structures. In this study, a new index for identifying damages in base-isolated structures is proposed using the frequency response function (FRF). Since calculation of the FRF data is time- and memory-consuming for problems of large size, the two-dimensional principal component analysis technique is employed to decrease the data size. The damage indices calculated, representing the health state of the structure, are stored in a database, which are then used to detect the damage location and severity by utilizing the lookup table method. The proposed damage detection method is applied to four concrete frame models, one of which is fixed at the base and the others are isolated by elastomeric bearings. The FRF data are polluted with three different noise values (5%, 10% and 15%) in order to evaluate the uncertainty of measurements. The accuracy of the proposed indices is compared with each other for various parameters such as noise values, bearings characteristics, base conditions and different damage scenarios. The results show the precision of the proposed method.

Regression is one of the most widely used of all statistical tools. Linear modelling in its widest sense is both well developed and well understood, and there is in addition a variety of useful techniques for checking the assumptions involved. However, there are cases where such models cannot be applied because of intrinsic nonlinearity in the data. Nonparametric regression aims to provide a means of modelling such data. Even where the suitability of linear models has not yet been brought into question, smoothing techniques are still useful by enhancing scatterplots to display the underlying structure of the data, without reference to a parametric model. This can in turn lead to further useful suggestions of, or checks on, appropriate parametric models. In this chapter, the main ideas of nonparametric regression are introduced and illustrated on several different types of data. The emphasis throughout is on the exploration of data, although technical and inferential issues will be raised for discussion in later chapters.

Measurement of Frequency Response Functions (FRFs) on the Millennium Bridge in London was a key part in the validation of the retrofit solution for excessive sway vibration caused by walking pedestrians during the bridge opening in June 2000. The measured FRFs were employed to verify the analytical response analysis and to estimate and confirm analytical predictions of natural frequencies, modal damping ratios, mode shapes and modal masses corresponding to various configurations of prototype viscous and tuned mass dampers. These results were used to experimentally assess the effectiveness of the proposed retrofit solution. Although FRF measurement technology is fairly standard in many engineering disciplines, its application on the Millennium Bridge was quite problematic and required some unique solutions which are described in this paper. Modal testing of the Millennium Bridge clearly demonstrated that it was possible to measure good quality FRFs around a frequency as low as 0·5 Hz, which was the natural frequency of the first lateral mode of vibration. This was achieved by designing, constructing and installing a bespoke hydraulic shaker featuring a translatory moving mass of 1000 kg. As the shaker was not able to produce perfectly sinusoidal excitation for stepped-sine testing, FRFs were successfully estimated using the so-called Resolver method in conjunction with an Hc estimator. The standard H1 FRF estimator, which is used in the vast majority of modern digital spectrum analysers nowadays, was demonstrably unable to produce meaningful FRF estimates when using the Resolver approach. The FRF estimation and curve-fitting performed in situ proved to be crucial for the success of the modal testing of the Millennium Bridge. By evaluating the estimates of the experimental FRFs and the corresponding modal properties during the testing programme on site, a number of test errors were spotted. This, in turn, enabled immediate repetition of measurements and/or evaluation of the structural behaviour which would have been impossible if the FRF data analysis had been performed after the testing had been completed.

This paper presents frequency response function (FRF) expansion techniques that minimize the difference between the analytical and predicted FRF matrices to satisfy the FRF constraints. The measured FRF relationships at a small number of locations were used as constraints. The expansion method is useful for estimating the rotational FRFs that are difficult to measure or apply using frequency-based substructuring (FBS) techniques. The validity of the proposed method, including the effects of external noise, was confirmed using numerical examples. An FBS algorithm was also derived by incorporating the FRFs of each substructure, and the compatibility conditions were transformed into FRFs with pseudomasses at the joint nodes. A discrepancy between the FRFs of the synthesized system estimated using the proposed method and the analysis results of the entire system was observed in the numerical example, and the reasons for the discrepancy were investigated and discussed. It is estimated that the proposed FBS method can be enhanced by combining it with other dynamic substructuring techniques and supplementing additional information, such as measured FRFs.

A prototype of a computerized patient record

ABSTRACTIn this paper, the capabilities of an enhanced sensitivity relation for the structural model updating are validated using a subset of the measured frequency response function (FRF) and natural frequency data of a laboratory concrete beam. The sensitivity relation of FRF is expressed implicitly as a function of the change of the mode shapes and incomplete measured natural frequencies of the damaged structure. In order to achieve more accurate parameters estimation results, an enhanced sensitivity relation is proposed by incorporating the measured natural frequencies of the damaged structures in the mathematical formulation. Solution of sensitivity equations by Least Square algorithm yields to the damage parameters. The method is applied to experimental data of a pin-roller concrete beam subjected to the extensive damage cases. The experimental results prove robust model updating results by the proposed method.

Biomedical questions are often complex and address multiple topics simultaneously. Answering them requires the comprehensive evaluation of several different types of data. They are often available, but in distributed and heterogeneous data sources; this hampers their global evaluation. We developed a software architecture to create and maintain updated a Genomic and Proteomic Data Warehouse (GPDW), which integrates several of the main of such dispersed data. It uses a modular and multi-level global data schema based on abstraction and generalization of integrated data features. Such a schema eases integration of data sources evolving in data content, structure and number, and assures provenance tracking of all the integrated data. Thanks to the developed software architecture and adopted data schema, the GPDW has been kept updated easily and progressively extended with additional data types and sources; it is publicly usable at http://www.bioinformatics.dei.polimi.it/GPKB/.