Multiple parameters fusion of electromagnetic nondestructive inspection data for evaluation of fatigue damage in steel elements

Abstract

The use of electromagnetic nondestructive testing methods to assess damage and fatigue changes is a subject of numerous studies. However, the observed signals are influenced by many factors. Thus, making a proper assessment on the basis of single parameters’ behavior is complicated task. Therefore, in this paper, an approach of multiple parameters fusion for evaluation of damage was presented. The range of material changes in steel sample after successive stages of fatigue process was monitored using Magnetic Barkhausen Noise and AC magnetization method in a selected two-dimensional region. The acquired data was then processed for the need of signals parametrization. The procedures in time, frequency and time-frequency domains were applied. Then the selection of representative features was carried out before the information was combined via multivariate regression. Finally, the obtained function was used to achieve the two-dimensional maps of evaluated damage for successive fatigue periods.

Keywords

Fatigue evaluation nondestructive evaluation magnetic Barkhausen noise AC magnetization method multi-source data fusion

1. Introduction

Fatigue is named as a one of the major cause of mechanical damages [1, 2, 3]. Assessment of a fatigue level and prediction of failure of steel structures is an important issue. However, the estimation process necessitates having the information about several factors such as geometry, mechanical properties, the history of loading and the critical load value or cracking growth on the tested material [4]. In practical cases these requirements are hard to fulfill, therefore the need for nondestructive (NDT) methods supporting the process emerges [4]. In reference to the existing relationship between mechanical and electromagnetic properties, electromagnetic testing methods such as Barkhausen noise (BN), hysteresis loop (BH), eddy current or magnetic flux leakage technique can become a natural solution [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. It is known that the fatigue process can be generally divided into three stages [3]. First is responsible for rearrangements of dislocations, influencing the mobility of domain wall movement. The second (transient) one reflects in initiation and growth of mircocraks as the last stage brings rapid growth of damage resulting in rearrangement of local stress levels and then local reorganization of magnetic microstructure. Numerous works were carried out on the influence of fatigue process on magnetic properties in all three stages. However not all observed behaviors are still understood [2, 5, 7, 8]. Coercivity and remanence values were found to be strongly correlated with the number of fatigue cycles, increasing or decreasing in the first and the last stage while almost remained unchanged in the middle one [8]. Similar behavior was observed for BN activity defined in the form of number of peaks [5]. Moreover, BN emission is influence by stress level while creep reflects in BH loop characteristic behavior [3, 8]. Nevertheless, the various factors i.e. the loading frequency and the maximum force value or production technology affects the initial value of the magnetic parameters as well as theirs change rate along the fatigue process. Magnetic methods allow to obtain complementary information. However, they require to be combined to get the full image of the materials state. Therefore, it is reasonable to create multivariate classification and decision rules based on the numerous of the measured signals parameters [1, 6, 10]. The importance of the multisource inspection and multivariate data fusion for assessment of a structure’s condition is rapidly growing. Most commonly applied procedures involve, but are not limited to, features extraction from measured data, features selection, data transformation and fusion, followed by decision making [1, 6, 10]. Data processing methods should be considered according to two aspects, data mining and knowledge extraction, resulting in wide set of features describing the observed phenomena and then fusion of data for building the more complete and/or accurate image of examined object state. Signals of electromagnetic NDT methods preserve wide range of information about the magnetization process. Therefore, considering their complicated nature, feature extraction procedures play an important role in the further stage of condition assessment. In case of BN, the quantitative analysis is mostly carried out in time domain ( $t$ -domain) basing on features such as RMS, energy, or numerous other statistical parameters calculated directly from raw signal or its envelope [1, 2, 5, 6, 9]. Frequently the changes of material properties affect not only characteristics of the BN time response, but influence the dynamics of the magnetization process, resulting in shape and scale changes of the BN envelope. Therefore, the frequency domain ( $f$ -domain) analysis is also carried out [13]. In such cases, the profile of the power spectrum can be considered in similar manner as the envelope of the BN signal, resulting in set of statistical parameters [6]. Besides the variation of frequency characteristics of the single BN burst under different material properties, the rate of the influence may also depend on the given temporary magnetization conditions. For that reason time-frequency (tf-domain) or time-scale representations of BN signal found their application in the process of material state assessment [11, 12]. In case of AC magnetization method, the ferromagnetic properties of the material affect and the shape of the measured signals (corresponding to induction and strength of magnetic field) and results in arising of higher harmonics components in the waveforms. Therefore, both $t$ - and $f$ -domain analysis can be performed in order to evaluate the changes rate. The second aspect of the multi-source inspection systems is to select the valuable information and then combine it to create the final result. Various methods such as principal or independent component analysis, partial least squares, fuzzy logic, supported vector machines, artificial neural network or Bayesian inference are used for multivariate function modelling, and further for classification or decision making [1, 6, 10, 14].

Recently, the multiple parameters data fusion procedure was applied for evaluation of damage stage under static loaded steel samples basing on results of two electromagnetic methods (Barkhausen noise and AC magnetization ACM process observation) allowing observation of dynamics of the magnetization process [6]. In this paper both methods data were used for knowledge extraction and multivariate information fusion for the need of evaluation of the fatigue progress.

Figure 1.

The measurement and multivariate data fusion procedure diagram.

2. Multi-source fatigue process observation

2.1 Examined sample

The experiment was carried out for a planar specimen made of standard construction carbon steel S355J2G3 (according to EN 10025-2:2004 standards). The sample was 2 mm thick, 250 mm long and 45 mm wide with a necking of 30 mm in the middle part (Fig. 1). The achieved during the tensile tests minimum yield strength and tensile strength of this material was around 355 MPa and 580 MPa respectively while the evaluated fatigue limit (endurance limit) was around 360 MPa. The sample prior the fatigue process was annealed for one hour in 300 ${}^{\circ}$ C and then furnace cooled. Then the sample was tensile deformed in a longitudinal direction.

2.2 Measuring methods and experimental setup

In order to conduct the test, a hydraulic mechanical system was utilized operating at loading frequency of 4 Hz. The stress amplitude was controlled and kept at constant level with maximum value below 350 MPa and R $\approx$ 0.43 resulting in high cycle fatigue character. The testing time was divided into several predefined loading intervals. In order to monitor more precisely the state of the fatigue changes in the material, after each loading period the sample was examined in two dimensions over the selected area of the surface (ROI) using both NDT inspection methods. The measurements were made using a laboratory based system setup described in details in [6]. The system allows to acquire signals of magnetic BN and ACM signals corresponding to magnetic induction $B(U_{B})$ and tangential component of magnetic field $H(U_{H})$ . In both cases a sinusoidal magnetizing field was utilized with a frequency of 30 and 40 Hz respectively in case of BN and ACM method.

3. Data integration using multivariate regression

3.1 Data processing and feature extraction

In order to analyze the acquired signals, feature extraction procedures were implemented in the $t$ , $f$ and tf regimes resulting in over 60 parameters (Fig. 1). The stochastic nature of the BN signal requires the use of complex data analysis algorithms to determine its numerical representation. First, statistical analysis and characteristic values were computed directly from the obtained BN signal $U_{BN}$ . Consequently, parameters such as BN burst’s standard deviations ( $BN_{\textit{STD}})$ or energy ( $BN_{EN}$ ) were obtained. Further, for all BN bursts the envelopes $BN_{E}$ were calculated, which were then used to compute a set of parameters such as peak value ( $BN_{PV}$ ), position ( $BN_{PP}$ ) and width ( $BN_{\textit{WRMS}}$ ), as well as median ( $BN_{\textit{MEDIAN}}$ ), interquartile range ( $BN_{\textit{IQR}}$ ), skewness ( $BN_{S}$ ), or full width at half module ( $BN_{\textit{FWHM}}$ ) value. Due to the influence of stress on the shape and dynamics of the burst as well as the activity of BN, the procedures of frequency and time-frequency analysis were also applied. For that reason the Fast Fourier Transform and Short Time Fourier Transform were calculated in order to obtain respectively the $f$ and tf representations of BN signal. Then frequency spectrum characteristics were analyzed and the features set corresponding to the set obtained for BN envelope was achieved (e.g. $BN_{f\_\textit{PMAX}}$ , $BN_{f\_\textit{fMAX}}$ , $BN_{f\_\textit{STD}}$ , etc.). In case of tf-domain, classical features such as value of power maximum ( $BN_{tf\_\textit{PMAX}}$ ) and its position on $f$ ( $BN_{tf\_\textit{fMAX}}$ ) and $t$ ( $BN_{tf\_\textit{tMAX}}$ ) axes were calculated. Additionally inherent features of tf representation were also computed such as concentration measure $BN_{tf\_M}$ defined as:

$\displaystyle BN_{tf\_M}=\left({\sum_{k=1}^{K}\sum_{l=1}^{K}\sqrt{P_{tf}(k,l)}% }\right)^{2},$ (1)

where $P_{tf}$ is the matrix of power spectrogram (uniform distribution of $P_{tf}$ results in $BN_{tf\_M}$ high value).

As a result, it is possible to obtain information about the dynamics of the magnetization process, and indirectly about the structure of the material under investigation. The use of the ACM method is related to the monitoring of minor parameters of the BH hysteresis loop. Determination of loop parameters, such as coercivity $H_{c}$ , remanence $B_{r}$ as well as initial ( $\mu_{i}$ ), maximum ( $\mu_{\max}$ ), differential ( $\mu_{\textit{diff}}$ ) or at saturation point ( $\mu_{s}$ ) permeability, makes it possible to detect material changes. Frequency representation (signal spectrum envelope) and harmonics of measured signals ( $B_{h}$ and $H_{h}$ ) also provide useful information. The observed loop changes depend on the state of the material damage in the area under investigation. Finally, two dimensional distributions of the acquired signals parameters were obtained. This allowed to monitor the changes across the fatigue progress simultaneously in various parts of the examined sample. Selected results are presented in Fig. 2. In the initial phase of the process only minor variation in the distributions could be noticed. Pre-process material state is reflecting only in BN peaks number, however all results present rather uniform distributions. This state was observed until around 3 $\cdot$ 10 ${}^{5}$ of cycles. The growth of BN activity was then visible in the form of respectively lighter and darker areas depicted in the top part on both sides of the $BN_{E\_\textit{IQR}}$ and $BN_{tf\_M}$ distributions. This can be explained by arising of the micro-stress areas in the sample, which next lead to occurrence of deformations. It resulted in concentration of BN peaks in narrow time span affecting increasing of IQR and decreasing of tf spectrum concentration measure. Next, along the fatigue process, that BN high energy areas move down to bottom part of the distributions, which allows to monitor changes in micro-stress occurrence. On the other hand, the $H$ harmonic distortion coefficient $H_{\textit{THD}}$ can provide one with the information about the development and growth of the deformations in the sample. As a result darker bands are visible in the plots obtained after 4.5 $\cdot$ 10 ${}^{5}$ and 5.1 $\cdot$ 10 ${}^{5}$ cycles. In order to visualize the global condition of the sample, the statistical analysis of 2D parameters distribution were carried out (selected results are presented in Fig. 3). The achieved curves confirm earlier observation. The initial, almost constant level of BN energy, started to monotonically grow from around 3 $\cdot$ 10 ${}^{5}$ until 4.5 $\cdot$ 10 ${}^{5}$ cycles, where deformations were observed reflecting in higher parameters variation range. Further the full width at half module of the BN ${}_{\textit{FWHM}}$ signal profile decrease significantly. In the same time the fast growth of $H_{\textit{THD}}$ and $\mu_{\textit{diff}}$ and first harmonic of $B$ can be seen. The obtained characteristics provide one with the complementary information. The resulting database contained over 4.5 $\cdot$ 10 ${}^{4}$ of features vectors set. Taking into consideration of the observed changes of materials structure, the fatigue process data was divided into four state levels with additional one referring to state before the process. During the first state, only global changes of parameters distribution are observed. In the second and third, referring to stress concentration area growth and initiation of microcracks, local changes of parameters can be noticed, where, in the fourth stage, deformations also arise.

Figure 2.

Selected features distributions obtained for different stage of the fatigue process: a) before loading and after b) 2.4 $\cdot$ 10 ${}^{5}$ , c) 3.0 $\cdot$ 10 ${}^{5}$ , d) 3.6 $\cdot$ 10 ${}^{5}$ , e) 4.5 $\cdot$ 10 ${}^{5}$ and f) 5.1 $\cdot$ 10 ${}^{5}$ of fatigue cycles; $BN_{N}$ , $BN_{E\_\textit{IQR}}$ and $BN_{tf\_M}$ – Barkhausen Noise peaks number, envelope’s Inter Quartile Range and concentration measure of tf spectrum representation; $H_{\textit{THD}}$ – $H$ harmonic distortion, $\mu_{\textit{diff}}$ – differential permeability.

Figure 3.

Results of the selected parameters distribution calculated along with the progress of the fatigue process.

Figure 4.

The results of defined multivariate data integration model obtained for testing subset of database.

Figure 5.

The results of fatigue progress evaluation based on multivariate fusion; (0–1) refers to predefined stages of the process expressed in normalized scale.

3.2 Feature selection

On that basis, the local evaluation of the fatigue process can further be carried out. However the extensive number of features can result in worse data generalization ability of the algorithm. Therefore before processing of the final data integration, a selection of representative group of features was performed. The procedure was carried in two following steps. First, the features correlated with other ones as well as having lower information content and presenting lower sensitivity to noises were discounted in the further process. Next, on the reduced set of 45 parameters, an unsupervised feature selection graph-based filter Inf-FS was applied which allows to define the features importance ranking [14]. Finally, the representative features set based on ranking was evaluated using final multivariate data integration algorithm.

3.3 Fatigue process evaluation model

In order to integrate the multiple parameters the multivariate regression analysis was carried out. During the process various definitions of integration function model were considered according to equation:

$\displaystyle y=\beta_{0}+\sum_{i=1}^{n}\beta_{i}x_{i}^{m}$ (2)

The $n$ parameter refers to the features number while $m$ to the exponent value. The optimization of the $\beta$ coefficients was preceded for different number of features and for the selected subsets from the obtained features database (around 40%). The selection of features vectors for the process was controlled so the representatives of different fatigue stages were used. Each time the quality of the model was validated using the remaining part of the database. Finally the model using $n=$ 18 (BN:{ $BN_{\textit{MEDIAN}}$ , $BN_{E\_\textit{MAX}}$ , $BN_{E\_\textit{WRMS}}$ , $BN_{E\_\textit{FWHM}}$ , $BN_{E\_\textit{MEAN}}$ , $BN_{E\_\textit{IQR}}$ , $BN_{f\_\textit{WRMS}}$ , $BN_{tf\_\textit{PMAX}}$ }, ACM: { $H_{\textit{THD}}$ , $B_{\textit{THD}}$ , $H_{h1,h2,h5,h7}$ , $B_{h2,h3}$ , $B_{S}$ , $\mu_{S}$ }) and $m$ of 1/2 was utilized. The result of the multivariate regression is presented in Fig. 4. It can be noticed that generally the model allows finding almost linear relationship for the set of selected features. The dash line represents the mean value of response $y$ obtained for test subset of database. The obtained R ${}^{2}$ determinant and adjusted R ${}^{2}$ are at fair level and both equal to 0.73. Next, the obtained model responses $y$ for selected features sets collected at each stage of fatigue process were reshaped to form the damage evaluation maps (Fig. 5). One can noticed clearly visible successive changes of the evaluated damage areas from stage to stage.

4. Conclusions

In this paper the results of the high cycle fatigue progress was evaluated using multisource data integration by multivariate regression. The results of the two nondestructive inspection methods were analyzed in order to calculate the wide features database. The use of multiple feature description of successive stages of fatigue process can bring complementary information allowing more precise evaluation of the real damage. Taking into consideration that the maximum level of stressing force did not exceed the fatigue limit causing significant plastic deformation in the material, the fatigue evaluation results are promising and confirms that the further work can be continued in the subject. Additional research is planned to carry out considering the advance methods for preliminary assessment of features robustness and final selection of theirs set under various conditions of fatigue process. Moreover the broader range of data integration models also is going to be used.

Footnotes

Acknowledgments

The author would like to express his gratitude to Prof. Tomasz Chady from West Pomeranian University of Technology in Szczecin for discussion and support during the measurements.

References

Sorsa

Leiviskä

Santa-aho

and Lepistö

, Quantitative prediction of residual stress and hardness in case-hardened steel based on the Barkhausen noise measurements, NDT&E Int.46 (2012), 100–106.

Sagar

S.P.

Parida

Das

Dobmann

and Bhattacharya

D.K.

, Magnetic Barkhausen emission to evaluate fatigue damage in low carbon structural steel, Int. Journal of Fatigue27 (2005), 317–322.

Maleque

M.A.

and Salit

M.S.

, Materials Selection and Design: Mechanical Failure of Metals, Springer (2013), 17–38.

Dobmann

, Probability of detection – the approach to combine probabilistic fracture mechanics with NDT – where we are? Badania Nieniszcza̧ce i Diagnostyka1–2 (2016), 27–33.

Palma

E.S.

Mansur

T.R.

Ferreira Silva

Jr and Alvarenga

Jr, Fatigue damage assessment in ANSI 8620 steel using Barkhausen noise, Int. Journal of Fatigue27 (2005), 659–665.

Psuj

, Fusion of Multiple Parameters of Magnetic Testing Results for Damage Assessment of Loaded Steel Structures, Studies in Applied Electromagnetics and Mechanics40 (2015), 192–199.

Soultan

et al., Mechanical Barkhausen noise during fatigue of iron, NDT&E Int.39 (2006), 493–498.

C.C.H.

Tang

Jiles

D.C.

and Biner

S.B.

, Evaluation of fatigue damage using a magnetic measurement technique, IEEE Trans. on Magn.35 (1999), 3977–3979.

Lindgren

and Lepist

, Effect of cyclic deformation on Barkhausen noise in a mild steel, NDT&E Int.36 (2003), 401–409.

10.

Dion

Kumar

and Ramuhalli

, Multi-Sensor Data Fusion for High-Resolution Material Characterization, in: AIP Conf. Proc., Rev. of Quantitative Nondestructive Evaluation, Vol. 894, 2007, pp. 1189–119.

11.

Padovese

L.R.

Martin

and Millioz

, Time-frequency and time-scale analysis of Barkhausen noise signals, Proc. of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering223 (2009), 577–588.

12.

Miesowicz

Staszewski

W.J.

and Korbiel

, Analysis of Barkhausen noise wavelet-based fractal signal processing for fatigue crack detection, Int. Journal of Fatigue83 (2016), 109–116.

13.

Mirai

Iliana

and Yoshifuru

, Frequency fluctuation signal processing and its application to the Barkhausen signals, Int. Journal of Applied Electromagnetics and Mechanics52 (2016), 371–379.

14.

Roffo

Melzi

and Cristani

, Infinite Feature Selection, in: IEEE Int. Conf. on Computer Vision (ICCV), Chile, 2015.