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A Framework of Data-Enabled Science for Evaluation of Material Damage Based on Acoustic Emission

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Abstract

Analytics of ‘Big Data’ has been so promising that it is thought to be a new frontier for innovation, competition, and productivity in science and business. Vast amounts of material damage data constitute a unique set of “Big Data” which are generated from damage events when materials are under applied stress, and their occurrence is strongly related to the source physics. Such data forms fundamental “information infrastructure” such that the ensemble of these events can be used as the basis for evaluating the state of material damage, thereby making data-enabled material damage evaluation a new frontier for innovation. Presently, data-enabled digital analytics of material damage is in its infancy and is much needed to advance our understanding of damage physics, which has, for the most part, been overlooked by the classical deterministic approaches. In this article, we propose a framework of data-enabled science for evaluating material damage that includes the introduction of a 3S principle to guide the efforts, and a global damage variate D, which is a multivariate data matrix of random damage with its rows and columns being observations (spectrum) and scale (time series) vectors, respectively, of the real world damage. This multivariate damage data matrix facilitates the systematic employment of standard methods of multivariate statistics and data mining techniques. The proposed framework was implemented by examples taken from typical engineering materials using acoustic emission. The examples revealed that; (1) damage events are interactive and significantly correlated; (2) they form different ensembles in different loading stages implicating damage mechanisms, and (3) their phenomenological behavior can be modeled numerically. The information entropy of multiscale damage matrices revealed a trajectory of damage state that provides a new means to quantify real world material damage. We also highlight some promising research topics related to other digital analytics that can be used for the investigation of material damage.

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Notes

  1. There are several different versions of these “V”s in “Big Data” related literature, but they are no more than a verbal description of the features of so called “Big Data”, and do not scientifically contribute to the problem solving.

  2. It is a luxury to have the knowledge of real stress and properties as they vary with the material microstructure which is not independent.

  3. For details, readers are suggested to our earlier work [63].

  4. It shall be discussed separately in a different work.

Abbreviations

\(D\) :

Multiscale and spectrum matrix of damage matrix

\(\bar{D}\) :

Probability space of random damage

\(L_{k}\) :

Summation of the \(k\)th row of \(D\) matrix

\(M\) :

Total number of observation intervals, or the number of row vectors of \(D\)

\(N\) :

Total number of divisions of magnitude scales of ERD, or the number of column vectors of \(D\)

\(X\) :

Column vector of \(D\). Each column vector is a time series of ERD of same scale, the elements in each of these columns are the independently observed quantity of ERD

\(Y\) :

Row vector of \(D\). Each row vector is an observation made in the same observation window. Because it covers ERD entire scale from the smallest to the largest, it is also the spectrum vector

\(Z\) :

Principal component, also as PC

\(\Omega \) :

Subset of damage variables, consisting of variables of timing, quantity, rate of occurrence, and the amplitude of the acquired ERD

\(a_{o}\), \(b_{o}\), and \(c_{o}\) :

Regression coefficients

\(f_k^D (t)\) :

Andrews function

\(g\) :

Unity condition

\(h\) :

Score function, \(h=\langle \varepsilon \rangle \)

\(\hbox {Index}\{\cdot \}\) :

Index function that counts for the number of the acquired events

\(n\) :

Sample size

\(p\) :

Gibbs probability of ERD occurrence

p-value:

Statistic significance of a hypothesis test

\(s\) :

Entropy, probabilistic entropy, information entropy, Shannon entropy

\(s^*\) :

Predicted entropy based principle of maximum entropy

\(x\) :

Acquired damage event, it is a function of all the measurable physical features of ERD

\(y\) :

The element of \(Y\) spectrum (observation) vector

\(z\) :

The scale of acquired ERD in unit of decibel (dB)

\(\bar{p}\) :

The mean of an observation vector of \(\bar{D}\)

\(\hat{p}\) :

Predicted value according to \(\bar{D}\)

\(\alpha \) :

\(D\) matrix element, number of acquired \(x\)

\(\rho _{_{JH}}\) :

Coefficients of autocorrelation

\(\rho _{_{XX}}\) :

Coefficients of autocorrelation

\(\upsigma \) :

Applied stress

\(\uptau \) :

Time of measurement

\(\upvarepsilon \) :

Score

\(\langle \varepsilon \rangle \) :

Observed average score

EDA:

Exploratory data analysis

ERD:

Events of random damage

KDD:

Knowledge discovery and data mining

NDE:

Nondestructive evaluation

PC:

Principal component

PCA:

Principal component analysis

TDS:

Trajectory of damage state

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Acknowledgments

Qi wishes to thank for the partial financial support provided by a Grant, 11272234, of the Chinese National Natural Science Foundation, and an endowed visiting chair-professorship at Tianjin University of Science and Technology by the municipal government of Tianjin, China.

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  1. School of Mechanical Engineering, Tianjin University of Science and Technology, Tianjin, China

    Gang Qi

  2. Department of Mechanical Engineering, The University of Memphis, Memphis, TN , 38152, USA

    Gang Qi & Steven F. Wayne

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Qi, G., Wayne, S.F. A Framework of Data-Enabled Science for Evaluation of Material Damage Based on Acoustic Emission. J Nondestruct Eval 33, 597–615 (2014). https://doi.org/10.1007/s10921-014-0255-7

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