Probabilistic modeling and sizing of embedded flaws in ultrasonic non-destructive inspections for fatigue damage prognostics and structural integrity assessment Xuefei Guan a,n , Jingdan Zhang a , Shaohua Zhou a , El Mahjoub Rasselkorde b , Waheed Abbasi b a Corporate Technology, Siemens Corporation, 755 College Rd. E., Princeton, NJ 08540, USA b Siemens Energy, Inc., 841 Old Frankstown Road, Pittsburgh, PA 15239, USA article info Article history: Received 10 January 2013 Received in revised form 4 September 2013 Accepted 9 September 2013 Available online 17 September 2013 Keywords: Probability of detection Non-destructive evaluation Ultrasonic inspection Fatigue life prediction Bayesian Flaw sizing abstract The paper presents a systematic method and procedure for probabilistic fatigue life prediction using non- destructive testing data under uncertainty. The procedure is developed using uncertainty quantification models for detection, sizing, fatigue model parameters and inputs. The probability of detection model is based on a classical log-linear model coupling the actual flaw size with the NDE reported size. Using probabilistic modeling and Bayes theorem, the distribution of the actual flaw size is derived for both NDE data without flaw indications and NDE data with flaw indications. Fatigue damage and structural integrity assessment are suggested based on the developed method and procedure. A turbine rotor example with realistic NDE inspection data is presented to demonstrate the overall methodology. Calculation and interpretation of the results based on risk recommendations for industrial applications are given. The influence of the NDE detection threshold to the assessment results, and error analysis of the assessment results are discussed in detail. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Steel and alloy structures are essential parts of civil, aviation, marine, and power generation systems. NDE has been an effective measure to evaluate the manufacturing quality and operation integrity of those structures and systems since the early 1970s [1–3]. Most widely used NDT/E techniques include ultrasonic inspection, magnetic particle inspection, electromagnetic inspec- tion, radiographic inspection, penetrant inspection, acoustic emis- sion, and visual inspection [4–7]. In particular, state-of-the-art ultrasonic NDE techniques provide an opportunity to obtain the information about internal flaws of a structure, such as voids and cracks, without damaging the structure [1]. This information can be integrated with fracture mechanics and material properties, allowing for fatigue life prediction and risk management [8,9]. Scheduled NDEs are sometimes mandatory for structures experiencing time-dependent degradations. Inservice or field inspections are more difficult than inspections in manufacturing phases, and uncertainties in flaw identification and sizing can be much larger due to the more complex conditions for testing [10]. The quality of NDE depends on many uncertain factors, including the sensitivity of inspection instrument, the service condition of the target structure being inspected, the variability of material proper- ties, operation procedure and personnel, and so on. Scientific quantification of these uncertainties must be made in order to produce reliable and informative inspection results. Traditionally, deterministic treatment of the uncertainty uses safety factors [11,12]. The determination of safety factors relies on experiences and expert judgment, which is not a trivial task for normal engineers without strong field knowledge. No universal equations and parameters are available for quantifying uncertainties of a given inspection. Prob- abilistic methods provide a rational approach for uncertainty man- agement and quantification. However, few studies have been found to provide a complete and systematic procedure for probabilistic modeling and uncertainty quantification in the overall process of ultrasonic NDE-based fatigue life and reliability assessment. The objective of this study is to develop a systematic method for reliable fatigue life prediction using ultrasonic NDE inspection data under uncertainty. The study is organized as follows. First, probability of detection (POD) modeling is presented using a classical log-linear sizing model to couple the ultrasonic NDE reported flaw size and the actual flaw size. Next, the probabilistic model for actual flaw size is developed. Following that, the overall procedure of probabilistic Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ndteint NDT&E International 0963-8695/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ndteint.2013.09.003 n Corresponding author. Tel.: þ609 734 6554; fax: þ609 734 6565. E-mail address: xuefei.guan@siemens.com (X. Guan). NDT&E International 61 (2014) 1–9