This article reviews the development of the original modal assurance criterion (MAC) together with other related assurance criteria that have been proposed over the last twenty years. Some of the other assurance criteria that will be discussed include the coordinate modal assurance criterion (COMAC), the frequency response assurance criterion (FRAC), coordinate orthogonality check (CORTHOG), frequency scaled modal assurance criterion (FMAC), partial modal assurance criterion (PMAC), scaled modal assurance criterion (SMAC), and modal assurance criterion using reciprocal modal vectors (MACRV). In particular, the thought process that relates the original MAC development to ordinary coherence and to orthogonality computations will be explained. Several uses of MAC that may not be obvious to the casual observer (modal parameter estimation consistency diagrams and model updating are two examples) will be identified. The common problems with the implementation and use of modal assurance criterion computations will also be identified. The development of the modal assurance criterion 1-2 over twenty years ago has led to a number of similar assurance criteria used in the area of experimental and analytical structural dynamics. It is important to recognize the mathematical similarity of these varied criteria in order to be certain that conclusions be correctly drawn from what is essentially a squared, linear regression correlation coefficient. The modal assurance criterion is a statistical indicator, just like ordinary coherence, which can be very powerful when used correctly but very misleading when used incorrectly. This article will first review the historical development of the modal assurance criterion. Other similar assurance criteria will then be identified although the list is not intended to be comprehensive. Typical uses of the modal assurance criterion will be discussed and finally, typical abuses will be identified.

The modal assurance criterion–twenty years of use and abuse

Experimental verification of a novel system identification technique that can detect defects at the element level is successfully accomplished The method can be used for inservice health assessment of real structures without disrupting normal operations This study conclusively verifies the method Analytical verification of the proposed algorithm has been successfully completed by the research team at the University of Arizona Vo and Haldar (2004) experimentally verified the method by conducting tests on fixed-ended and simply supported defect-free and defective beams The purpose of this research was to validate the method by conducting experiments with more realistic structures A three-story one-bay steel frame, built to 1/3 scale to fit the experimental facility, was considered The frame was excited by harmonic or impulsive excitation forces The transverse acceleration responses were collected using capacitive accelerometers The angular displacement responses were measured using an autocollimator The dynamic responses of the frames were collected by a data acquisition system with simultaneous sampling capability Using only experimentally collected response information and completely ignoring the excitation information, the stiffness of all the structural elements were identified The method identified the defect-free frame very accurately Defects, in terms of removing a beam, reducing cross sectional area over a small segment of a beam, and cutting notches in a beam, were introduced The method correctly identified the defect location in all cases Additional sensors were placed

Damage assessment potential of a novel system identification technique - experimental verification

https://cronfa.swan.ac.uk/Record/cronfa25256/Download/0025256-11022016171447.pdf

Automatic mode tracking for flight dynamic analysis using a spanning algorithm

/pdf/open-crack-damage-assessments-of-aluminum-panels-using-1a1kvtp64r.pdf

Open-crack damage assessments of aluminum panels using structural intensity-based techniques

Tobe, Randy Joseph. Ph.D. College of Engineering and Computer Science, Wright State University, 2010. Structural Health Monitoring of a Thermal Protection System for Fastener Failure with a Validated Model. Air vehicles flying at hypersonic speeds encounter extreme thermal, aerodynamic and acoustic loads. To maintain the structural integrity of the flight vehicle, a thermal protection system shields the main structure from these loads. Therefore, maintaining the health of the thermal protection system is critical for a successful mission and vehicle safety. One of the more common types of failure in a mechanically attached thermal protection system is fastener failure. Since reducing vehicle turnaround between flights is desired, creating an automated system to perform structural health monitoring on the fastener health of the thermal protection system is needed. This can be completed by analyzing changes in the dynamic characteristics of the system due to fastener failure. While much of the recent experimental research focuses on using sensors to detect high-frequency dynamic changes in the system to detect damage, this research focuses on investigating fastener failure damage where only low-frequency dynamics are available. This involves validating a finite element model with low-frequency experimental dynamic tests to ensure the geometry, boundary conditions, material properties, and finite element mesh properly capture the physical characteristics of the structure. The damage states are then simulated with the finite element model to obtain a better understanding of how the damages cause low-frequency dynamic changes without requiring a vast amount of experimental data. The damage detection metrics include previously developed modal parameters—the MAC, PMAC, and COMAC—in addition to two newly developed damage metrics—the normalized coordinate modal assurance criterion and the normalized coordinate modal assurance criterion summation. The new damage metrics investigate how mode shape normalization can provide a distributed prediction for where damage is located.

/pdf/structural-health-monitoring-of-a-thermal-protection-system-3cdu3x2r10.pdf

Structural Health Monitoring of a Thermal Protection System for Fastener Failure with a Validated Model

This paper reviews the concepts behind and the need for a measure of the accuracy of mode shapes. Experimental-to-analytical Anaytical-to-Analytical, and Experimental-to-Experimental mode shape comparisons are made daily by the dynamics community. The problem is that the conventional measure of mode shape accuracy, the Modal Assurance Criteria (MAC), is used to assess the correlation or coherence between two modes or operating shapes. This measure computes the least squares deviation of the shape points from a straight-line correlation. However, the anti-nodes of the mode shape dominate this computation. Observation of small errors in modes shapes result in the conclusion that changes in mode shapes are most easily detected in the region of the node points and the spatial movement of same. Certainly the MAC will not be sensitive to small changes in nodal position since the MAC's properties are dominated by the larger anti-nodal information. This paper proposes the use of the inverse of the mode shapes to form the basis function for the MAC calculation. This new measure wW be called the IMAC (Inverse Modal Assurance Criteria). That is, the complex arithmetic inverse of the mode shape is used in the conventional MAC calculation. Examples will be given of comparative sensitivities of the MAC and IMAC to small mode shape errors.

Increasing the sensitivity of the modal assurance criteria (MAC) to small mode shape changes : The IMAC

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

L. D. Mitchell

Author Tools

Chat about Author

Papers

Increasing the sensitivity of the modal assurance criteria (MAC) to small mode shape changes : The IMAC