A deterministic algorithm for nonlinear, fatigue‐based structural health monitoring

Abstract

The irregularity of peak and valley stress values of loading histories is the main impediment for accurate fatigue‐based structural health monitoring. Since the available fatigue material data (e.g., S‐N curves) have been derived by cyclic loading tests, and the existing damage accumulation models can be implemented on structures under cyclic loading, cycle‐counting algorithms for the transformation of a spectrum loading into an equivalent cyclic one are necessary for deterministic fatigue damage estimation and life prediction. The existing four cycle‐counting algorithms have an inherent disadvantage; the sequence of the derived cycles is unknown, and the loading sequence effect on the fatigue damage estimation and life prediction cannot be accounted for (linear damage summation). The present work proposes a new damage estimation algorithm containing two modules: a new cycle‐counting algorithm and a new damage summation algorithm. Unlike the existing methods, the proposed algorithm takes into account the loading sequence effect and has a solid physical base because it simulates the nonlinear damage accumulation with a multi‐linear damage summation procedure. With the aid of a new concept of inserting fictitious loading cycles in the irregular spectrum, the proposed cycle counting module counts loading cycles that correspond to loading loops with an algorithm that is easily applicable in engineering practice. According to the author's knowledge, nonlinear damage accumulation estimation in structures under an irregular loading spectrum is carried out for the first time. The effect of the loading sequence to high‐low two‐stage random loading, low‐high two‐stage random loading, decreasing amplitude multi‐stage random loading, increasing amplitude multi‐stage random loading, and alternating amplitude random loading is examined and discussed.

Method for statistical evaluation of cumulative damage models applied to block loading

“…New fatigue damage accumulation models are still published each year. Most recent examples are the works Pavlou, 18 Bjørheim, 19 Yu et al, 20 and Zhu et al 21 But over the course of the last 70 years, not a single one has been widely accepted as an improvement over the much disputed Miner rule. Remarkably, the new models always appear to outperform selected models to which they are compared.…”

Nonlinear fatigue life prediction model based on the theory of the S‐N fatigue damage envelope

“…However, even with the aid of a counting method, direct implementation of the proposed model to irregular loading spectra yields numerical error accumulation in long loading histories. To this end, a multilinear damage summation technique for utilizing nonlinear models in spectrum loading and a new counting method has recently been proposed by Pavlou 9 and can be adopted by the proposed damage function.…”

“…The exponent q σ, m ð Þ is accepted to be a function of the stress amplitude by all the existing research. 9,15,16,39 Both the final expression of the function q σ,m ð Þ and the number of material parameters m with their respective values depends upon the theoretical or experimental method which is adopted to develop a function, as there are both theoretical and experimental methods of defining damage. As the theoretical approach proposed by Pavlou 38 is adopted herein, the governing parameters for the resulting expression with its material parameters are related to the nature of the S-N curve.…”

“…7 This is due to the perspective that an accumulation model is required to design for VAL, that it is generally simple to follow, and that the formula yields acceptable life prediction for uniform random loading histories. [8][9][10][11] The inherent error or uncertainty in Miner's rule for decreasing load amplitude spectra could result in catastrophic consequences. However, it is commonly accounted for through the application of a Design Fatigue Factor, used in conjunction with a design S-N curve which already has a low probability of failure (2.3% in DNVGL), 12,13 resulting in a more conservative design due to the application of Miner's rule.…”

Fatigue reliability of wind turbines: historical perspectives, recent developments and future prospects

“…( 8), there are also some improved models (double linear or non-linear) with higher prediction accuracy. For instance, Pavlou [91] used the S-N fatigue damage envelope theory in fatigue-based structural health monitoring of an offshore wind turbine structure. More details about the advances in cumulative fatigue damage can be found in Refs.…”