Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models

Nicholas A. Nechval; Vadims Danovics; Natalija Ribakova

doi:doi:10.11648/j.ajtas.s.2016050201.15

| Peer-Reviewed

Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models

Nicholas A. Nechval, Vadims Danovics, Natalija Ribakova

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 2-1)

Received: 17 January 2016 Accepted: 19 January 2016 Published: 4 February 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The main aim of this paper is to present more accurate stochastic fatigue models for solving the fatigue reliability problems, which are attractively simple and easy to apply in practice for situations where it is difficult to quantify the costs associated with inspections and undetected cracks. From an engineering standpoint the fatigue life of a structure consists of two periods: (i) crack initiation period, which starts with the first load cycle and ends when a technically detectable crack is presented, and (ii) crack propagation period, which starts with a technically detectable crack and ends when the remaining cross section can no longer withstand the loads applied and fails statically. Periodic inspections of fatigued structures, which are common practice in order to maintain their reliability above a desired minimum level, are based on the conditional reliability of the fatigued structure. During the period of crack initiation, when the parameters of the underlying lifetime distributions are not assumed to be known, for effective in-service inspection planning (with decreasing intervals as alternative to constant intervals often used in practice for convenience in operation), the pivotal quantity averaging (PQA) approach is offered. During the period of crack propagation (when the damage tolerance situation is used), the approach, based on an innovative crack growth equation, to in-service inspection planning (with decreasing intervals between sequential inspections) is proposed to construct more accurate reliability-based inspection strategy in this case. To illustrate the suggested approaches, the numerical examples are given.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 2-1) This article belongs to the Special Issue Novel Ideas for Efficient Optimization of Statistical Decisions and Predictive Inferences under Parametric Uncertainty of Underlying Models with Applications
DOI	10.11648/j.ajtas.s.2016050201.15
Page(s)	29-39
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Fatigued Structure, Crack, Initiation, Propagation, In-Service Inspection Planning, Innovative Approaches

References

[1]	N. Iyyer, S. Sarkar, R. Merrill, and N. Phan, “Aircraft life management using crack initiation and crack growth models - P-3C Aircraft experience,” International Journal of Fatigue, vol. 29, pp. 15841607, 2007.
[2]	R. E. Barlow, L. C. Hunter, and F. Proschan, “Optimum checking procedures,” Journal of the Society for Industrial and Applied Mathematics, vol. 11, 10781095, 1963.
[3]	H. Luss and Z. Kander, “Inspection policies when duration of checkings is non-negligible,” Operational Research Quarterly, vol. 25, pp. 299309, 1974.
[4]	B. Sengupta, “Inspection procedures when failure symptoms are delayed,” Operational Research Quarterly, vol. 28, pp. 768776, 1977.
[5]	A. G. Munford and A. K. Shahani, “A nearly optimal inspection policy,” Operational Research Quarterly, vol. 23, pp. 373379, 1972.
[6]	A. G. Munford and A. K. Shahani, (1973). “An inspection policy for the Weibull case,” Operational Research Quarterly, vol. 24, pp. 453458, 1973.
[7]	P. R. Tadikamalla, “An inspection policy for the gamma failure distributions,” Operational Research Quarterly, vol. 30, pp. 7778, 1979.
[8]	A. G. Munford, “Comparison among certain inspection policies,” Management Science, vol. 27, pp. 260267, 1981.
[9]	N. A. Nechval, K. N. Nechval, G. Berzins, M. Purgailis, and U. Rozevskis, “Stochastic fatigue models for efficient planning inspections in service of aircraft structures,” in K. Al-Begain, A. Heindl, and M. Telek (Eds.), Analytical and Stochastic Modeling Techniques and Applications, Lecture Notes in Computer Science (LNCS), vol. 5055.. Berlin, Heidelberg: Springer-Verlag, 2008, pp. 114127.
[10]	K. N. Nechval, N. A. Nechval, G. Berzins, M. Purgailis, U. Rozevskis, and V. F. Strelchonok, “Optimal adaptive inspection planning process in service of fatigued aircraft structures,” in K. Al-Begain, D. Fiems, and G. Horvath (Eds.), Analytical and Stochastic Modeling Techniques and Applications, Lecture Notes in Computer Science (LNCS), vol. 5513. Berlin, Heidelberg: Springer-Verlag, 2009, pp. 354369.
[11]	N. A. Nechval, K. N. Nechval, and M. Purgailis, “Inspection policies in service of fatigued aircraft structures,” in S. I. Ao and L. Gelman (Eds.), Electrical Engineering and Applied Computing, Lecture Notes in Electrical Engineering, vol. 90. Berlin, Heidelberg: Springer Science+Business Media B. V., 2011, pp. 459472.
[12]	N. A. Nechval, G. Berzins, M. Purgailis, and K. N. Nechval, “Improved estimation of state of stochastic systems via invariant embedding technique,” WSEAS Transactions on Mathematics, vol. 7, pp. 141159, 2008.
[13]	N. A. Nechval, K. N. Nechval, and M. Purgailis, “Prediction of future values of random quantities based on previously observed data,” Engineering Letters, vol. 9, pp. 346359, 2011.
[14]	K. C. Kapur and L. R. Lamberson, Reliability in Engineering Design. New York: Wiley, 1977.
[15]	J. L. Bogdanoff and F. Kozin, Probabilistic Models of Cumulative Damage. New York: Wiley, 1985.
[16]	Y. K. Lin and J. N. Yang, “On statistical moments of fatigue crack propagation,” Engineering Fracture Mechanics, vol. 18, 243256, 1985.
[17]	J. N. Yang, W. H. His, and S. D. Manning, “Stochastic crack propagation with applications to durability and damage tolerance analyses,” Technical Report, Flight Dynamics Laboratory, Wright-Patterson Air Force Base, AFWAL-TR-85-3062, 1985.
[18]	J. N. Yang and S. D. Manning, “Stochastic crack growth analysis methodologies for metallic structures,” Engineering Fracture Mechanics, vol. 37, pp. 11051124, 1990.
[19]	N. A. Nechval, K. N. Nechval, and E. K. Vasermanis, “Statistical models for prediction of the fatigue crack growth in aircraft service,” in A. Varvani-Farahani and C. A. Brebbia (Eds.), Fatigue Damage of Materials 2003. Southampton, Boston: WIT Press, 2003, pp. 435445.
[20]	N. A. Nechval, K. N. Nechval, and E. K. Vasermanis, “Estimation of warranty period for structural components of aircraft,” Aviation, vol. VIII, pp. 39, 2004.
[21]	D. Straub and M. H. Faber, “Risk based inspection planning for structural systems,” Structural Safety, vol. 27, pp. 335355, 2005.
[22]	D. A. Virkler, B. M. Hillberry, and P. K. Goel, “The statistic nature of fatigue crack propagation,” ASME Journal of Engineering Materials and Technology, vol. 101, pp. 148153, 1979.
[23]	H. Ghonem and S. Dore, “Experimental study of the constant probability crack growth curves under constant amplitude loading,” Engineering Fracture Mechanics, vol. 27, pp. 125, 1987.
[24]	H. Itagaki, T. Ishizuka, and P. Y. Huang, “Experimental estimation of the probability distribution of fatigue crack growth lives,” Probabilistic Engineering Mechanics, vol. 8, pp. 2534, 1993.
[25]	R. Paris and F. Erdogan, “A critical analysis of crack propagation laws,” Journal of Basic Engineering, vol. 85, pp. 528534, 1963.
[26]	Military Specification, Airplane Damage Tolerance Requirements. MIL-A-83444 (USAF), 1974.

Cite This Article

Plain Text BibTeX RIS

APA Style

Nicholas A. Nechval, Vadims Danovics, Natalija Ribakova. (2016). Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models. American Journal of Theoretical and Applied Statistics, 5(2-1), 29-39. https://doi.org/10.11648/j.ajtas.s.2016050201.15

Copy | Download

ACS Style

Nicholas A. Nechval; Vadims Danovics; Natalija Ribakova. Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models. Am. J. Theor. Appl. Stat. 2016, 5(2-1), 29-39. doi: 10.11648/j.ajtas.s.2016050201.15

Copy | Download

AMA Style

Nicholas A. Nechval, Vadims Danovics, Natalija Ribakova. Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models. Am J Theor Appl Stat. 2016;5(2-1):29-39. doi: 10.11648/j.ajtas.s.2016050201.15

Copy | Download

@article{10.11648/j.ajtas.s.2016050201.15,
  author = {Nicholas A. Nechval and Vadims Danovics and Natalija Ribakova},
  title = {Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {2-1},
  pages = {29-39},
  doi = {10.11648/j.ajtas.s.2016050201.15},
  url = {https://doi.org/10.11648/j.ajtas.s.2016050201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2016050201.15},
  abstract = {The main aim of this paper is to present more accurate stochastic fatigue models for solving the fatigue reliability problems, which are attractively simple and easy to apply in practice for situations where it is difficult to quantify the costs associated with inspections and undetected cracks. From an engineering standpoint the fatigue life of a structure consists of two periods: (i) crack initiation period, which starts with the first load cycle and ends when a technically detectable crack is presented, and (ii) crack propagation period, which starts with a technically detectable crack and ends when the remaining cross section can no longer withstand the loads applied and fails statically. Periodic inspections of fatigued structures, which are common practice in order to maintain their reliability above a desired minimum level, are based on the conditional reliability of the fatigued structure. During the period of crack initiation, when the parameters of the underlying lifetime distributions are not assumed to be known, for effective in-service inspection planning (with decreasing intervals as alternative to constant intervals often used in practice for convenience in operation), the pivotal quantity averaging (PQA) approach is offered. During the period of crack propagation (when the damage tolerance situation is used), the approach, based on an innovative crack growth equation, to in-service inspection planning (with decreasing intervals between sequential inspections) is proposed to construct more accurate reliability-based inspection strategy in this case. To illustrate the suggested approaches, the numerical examples are given.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models
AU  - Nicholas A. Nechval
AU  - Vadims Danovics
AU  - Natalija Ribakova
Y1  - 2016/02/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.s.2016050201.15
DO  - 10.11648/j.ajtas.s.2016050201.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 29
EP  - 39
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2016050201.15
AB  - The main aim of this paper is to present more accurate stochastic fatigue models for solving the fatigue reliability problems, which are attractively simple and easy to apply in practice for situations where it is difficult to quantify the costs associated with inspections and undetected cracks. From an engineering standpoint the fatigue life of a structure consists of two periods: (i) crack initiation period, which starts with the first load cycle and ends when a technically detectable crack is presented, and (ii) crack propagation period, which starts with a technically detectable crack and ends when the remaining cross section can no longer withstand the loads applied and fails statically. Periodic inspections of fatigued structures, which are common practice in order to maintain their reliability above a desired minimum level, are based on the conditional reliability of the fatigued structure. During the period of crack initiation, when the parameters of the underlying lifetime distributions are not assumed to be known, for effective in-service inspection planning (with decreasing intervals as alternative to constant intervals often used in practice for convenience in operation), the pivotal quantity averaging (PQA) approach is offered. During the period of crack propagation (when the damage tolerance situation is used), the approach, based on an innovative crack growth equation, to in-service inspection planning (with decreasing intervals between sequential inspections) is proposed to construct more accurate reliability-based inspection strategy in this case. To illustrate the suggested approaches, the numerical examples are given.
VL  - 5
IS  - 2-1
ER  -

Copy | Download

Author Information

Nicholas A. Nechval

Department of Mathematics, Baltic International Academy, Riga, Latvia
Vadims Danovics

Department of Marketing, University of Latvia, Riga, Latvia
Natalija Ribakova

Department of Marketing, University of Latvia, Riga, Latvia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Nicholas A. Nechval, Vadims Danovics, Natalija Ribakova. (2016). Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models. American Journal of Theoretical and Applied Statistics, 5(2-1), 29-39. https://doi.org/10.11648/j.ajtas.s.2016050201.15

Copy | Download

ACS Style

Nicholas A. Nechval; Vadims Danovics; Natalija Ribakova. Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models. Am. J. Theor. Appl. Stat. 2016, 5(2-1), 29-39. doi: 10.11648/j.ajtas.s.2016050201.15

Copy | Download

AMA Style

Nicholas A. Nechval, Vadims Danovics, Natalija Ribakova. Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models. Am J Theor Appl Stat. 2016;5(2-1):29-39. doi: 10.11648/j.ajtas.s.2016050201.15

Copy | Download

@article{10.11648/j.ajtas.s.2016050201.15,
  author = {Nicholas A. Nechval and Vadims Danovics and Natalija Ribakova},
  title = {Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {2-1},
  pages = {29-39},
  doi = {10.11648/j.ajtas.s.2016050201.15},
  url = {https://doi.org/10.11648/j.ajtas.s.2016050201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2016050201.15},
  abstract = {The main aim of this paper is to present more accurate stochastic fatigue models for solving the fatigue reliability problems, which are attractively simple and easy to apply in practice for situations where it is difficult to quantify the costs associated with inspections and undetected cracks. From an engineering standpoint the fatigue life of a structure consists of two periods: (i) crack initiation period, which starts with the first load cycle and ends when a technically detectable crack is presented, and (ii) crack propagation period, which starts with a technically detectable crack and ends when the remaining cross section can no longer withstand the loads applied and fails statically. Periodic inspections of fatigued structures, which are common practice in order to maintain their reliability above a desired minimum level, are based on the conditional reliability of the fatigued structure. During the period of crack initiation, when the parameters of the underlying lifetime distributions are not assumed to be known, for effective in-service inspection planning (with decreasing intervals as alternative to constant intervals often used in practice for convenience in operation), the pivotal quantity averaging (PQA) approach is offered. During the period of crack propagation (when the damage tolerance situation is used), the approach, based on an innovative crack growth equation, to in-service inspection planning (with decreasing intervals between sequential inspections) is proposed to construct more accurate reliability-based inspection strategy in this case. To illustrate the suggested approaches, the numerical examples are given.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Innovative Planning in-Service Inspections of Fatigued Structures Under Parametric Uncertainty of Lifetime Models
AU  - Nicholas A. Nechval
AU  - Vadims Danovics
AU  - Natalija Ribakova
Y1  - 2016/02/04
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.s.2016050201.15
DO  - 10.11648/j.ajtas.s.2016050201.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 29
EP  - 39
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2016050201.15
AB  - The main aim of this paper is to present more accurate stochastic fatigue models for solving the fatigue reliability problems, which are attractively simple and easy to apply in practice for situations where it is difficult to quantify the costs associated with inspections and undetected cracks. From an engineering standpoint the fatigue life of a structure consists of two periods: (i) crack initiation period, which starts with the first load cycle and ends when a technically detectable crack is presented, and (ii) crack propagation period, which starts with a technically detectable crack and ends when the remaining cross section can no longer withstand the loads applied and fails statically. Periodic inspections of fatigued structures, which are common practice in order to maintain their reliability above a desired minimum level, are based on the conditional reliability of the fatigued structure. During the period of crack initiation, when the parameters of the underlying lifetime distributions are not assumed to be known, for effective in-service inspection planning (with decreasing intervals as alternative to constant intervals often used in practice for convenience in operation), the pivotal quantity averaging (PQA) approach is offered. During the period of crack propagation (when the damage tolerance situation is used), the approach, based on an innovative crack growth equation, to in-service inspection planning (with decreasing intervals between sequential inspections) is proposed to construct more accurate reliability-based inspection strategy in this case. To illustrate the suggested approaches, the numerical examples are given.
VL  - 5
IS  - 2-1
ER  -

Copy | Download