Variance-based sensitivity analysis with the uncertainties of the input variables and their distribution parameters. (English) Zbl 07549511
Summary: For the structural systems with both the uncertainties of input variables and their distribution parameters, three sensitivity indices are proposed to measure the influence of input variables, distribution parameters and their interactive effects. With those sensitivity indices, analysts can make a decision that whether it is worth to accumulate data of one distribution parameter to reduce its uncertainty. Due to the large computational cost, the analytical solutions are derived for quadratic polynomial output responses. Whereas for the complex models, state dependent parameter (SDP) method is utilized to solve the proposed sensitivity indices efficiently.
MSC:
| 65C60 | Computational problems in statistics (MSC2010) |
Keywords:
analytical solution; distribution parameter; input variable; sensitivity indices; state dependent parameter methodReferences:
| [1] | Au, S. K.; Beck, J. L., A new adaptive important sampling scheme for reliability calculation, Structural Safety, 21, 2, 139-163 |
| [2] | Borgonovo, E., Measuring uncertainty importance: investigation and comparison of alternative approaches, Risk Analysis, 26, 1349-1361 |
| [3] | Breitkpf, P.; Naceur, H.; Rassineux, A.; Villon, P., Moving least squares response surface approximation: formulation and metal forming applications, Computers & Structures, 83, 1411-1428 |
| [4] | Bucher, C. G., A fast and efficient response surface approach for structural reliability problems, Structural Safety, 7, 57-66 |
| [5] | Cheng, C. H.; Mon, D. L., Fuzzy system reliability analysis by interval of confidence, Fuzzy Sets and Systems, 56, 1, 29-35 |
| [6] | Chun, M. H.; Han, S. J.; Tak, N. I., An uncertainty importance measure using a distance metric for the change in a cumulative distribution function, Reliability Engineering and System Safety, 94, 596-603 |
| [7] | Der Kiureghuan, A.; Ditlevsen, O., Aleatory or epistemic? Does it matter?, Reliability Engineering and System Safety, 31, 105-112 |
| [8] | Dubois, D.; Prade, H., Possibility Theory: An Approach to Computerized Processing of Uncertainty, New York: Plenum, New York |
| [9] | Grooteman, F., Adaptive radial-based importance sampling method for structural reliability, Structural Safety, 30, 6, 533-542 |
| [10] | Guo, J.; Du, X. P., Sensitivity analysis with mixture epistemic and aleatory uncertainties, AIAA Journal, 45, 2337-2349 |
| [11] | Haaker, M. P. R.; Verheijen, P. J. T., Local and global sensitivity analysis for a reactor design with parameter uncertainty, Chemical Engineering Research and Design, 82, 591-598 |
| [12] | Hanss, M.; Turrin, S., A fuzzy-based approach to comprehensive modeling and analysis of systems with epistemic uncertainties, Structural Safety, 32, 6, 433-441 |
| [13] | Hao, W. R.; Lu, Z. Z.; Wei, P. F., Importance measure of correlated variables in polynomial output, Chinese Journal of Theoretical and Applied Mechanics, 44, 167-173 |
| [14] | Hao, W. R.; Lu, Z. Z.; Wei, P. F., A new method on ANN for variance based importance measure analysis of correlated input variables, Structural Safety, 38, 56-63 |
| [15] | Helton, J. C., Alternative representations of epistemic uncertainty, Reliability Engineering and System Safety, 85, 1-10 |
| [16] | Helton, J. C.; Johnson, J. D.; Sallaberry, C. J., Survey of sampling-based method for uncertainty and sensitivity analysis, Reliability Engineering and System Safety, 91, 1175-1209 |
| [17] | Hoang, N. H.; Langseth, M.; Porcaro, R., The effect of the riveting process and aging on the mechanical behaviour of an aluminium self-piercing riveted, European Journal of Mechanics - A/Solids, 30, 617-630 · Zbl 1278.74007 |
| [18] | Hofer, E.; Kloos, M.; Krzykacz-Hansmann, B., An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties, Reliability Engineering and System Safety, 77, 229-238 |
| [19] | Homma, T.; Saltelli, A., Importance measures in global sensitivity analysis of nonlinear models, Reliability Engineering and System Safety, 52, 1-17 |
| [20] | Iman, R. L.; Hora, S. C., A robust measure of uncertainty importance for use in fault tree system analysis, Risk Analysis, 10, 401-406 |
| [21] | Kaymaz, I., Application of Kriging method to structural reliability problems, Structural Safety, 27, 133-151 |
| [22] | Klir, G. J.; Wierman, M. J., Uncertainty-Based Information Elements of Generalized Information Theory, Heidelberg: Physica-Verlag, Heidelberg · Zbl 0935.68023 |
| [23] | Krzykacz-Hausmann, B., An approximate sensitivity analysis of results from complex computer models in the presence of epistemic and aleatory uncertainties, Reliability Engineering and System Safety, 91, 1210-1218 |
| [24] | Kucherenko, S.; Rodriguez-Fernandez, M.; Pantelides, C., Monte Carlo evaluation of derivative based global sensitivity measures, Reliability Engineering and System Safety, 94, 1135-1148 |
| [25] | Li, L. Y.; Lu, Z. Z.; Feng, J.; Wang, B. T., Moment independent importance measure of basic variable and its state dependent parameter solution, Structural Safety, 8, 40-47 |
| [26] | Li, L. Y.; Lu, Z. Z.; Zhou, C. C., Importance analysis for models with correlated input variables by the state dependent parameters method, Computers & Mathematics with Applications, 62, 4547-4556 · Zbl 1236.62169 |
| [27] | Liu, J. S., Monte Carlo Strategies in Scientific Computing, New York: Springer-Verlag, New York · Zbl 1132.65003 |
| [28] | Ratto, M.; Pagano, A.; Young, P. C., State dependent parameter meta-modelling and sensitivity analysis, Computer Physics Communications, 177, 863-876 |
| [29] | Ratto, M.; Pagano, A.; Young, P. C., Non-parametric estimation of conditional moments for sensitivity analysis, Reliability Engineering and System Safety, 94, 237-243 |
| [30] | Ratto, M.; Tarantola, S.; Saltelli, A.; Young, P. C.; Hanson, K. M.; Hemez, F. M., Accelerated estimation of sensitivity indices using state dependent parameter models, 61-70 |
| [31] | Ricotti, M. E.; Zio, E., Neural network approach to sensitivity and uncertainty analysis, Reliability Engineering and System Safety, 64, 59-71 |
| [32] | Saltelli, A., Sensitivity analysis for importance assessment, Risk Analysis, 22, 579-590 |
| [33] | Sankararaman, S.; Mahadevan, S., Distribution type uncertainty due to sparse and imprecise data, Mechanical Systems and Signal Processing, 37, 1-2, 182-198 |
| [34] | Sankararaman, S.; Mahadevan, S., Separating the contributions of variability and parameter uncertainty in probability distributions, Reliability Engineering and System Safety, 112, 187-199 |
| [35] | Shafer, G., A Mathematical Theory of Evidence, Princeton, NJ: Princeton University Press, Princeton, NJ · Zbl 0359.62002 |
| [36] | Sobol, I. M., Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation, 55, 271-280 · Zbl 1005.65004 |
| [37] | Sun, S.; Fu, G. T.; Djordjevic, S.; Khu, S. T., Separating aleatory and epistemic uncertainties: probabilistic sewer flooding evaluation using probability box, Journal of Hydrology, 420-421, 360-372 |
| [38] | Young, P. C.; Rao, T. S., Developments in Time Series Analysis, Time variable and state dependent modelling of nonstationary and nonlinear time series, 374-413, London: Chapman and Hall, London · Zbl 0880.62100 |
| [39] | Young, P. C.; Fitzgerald, W. J.; Smith, R. L.; Walden, A. T.; Young, P. C., Nonlinear and Nonstationary Signal Processing, Stochastic, dynamic modelling and signal processing: Time variable and state dependent parameter estimation, 74-114, Cambridge: Cambridge University Press, Cambridge · Zbl 0973.93057 |
| [40] | Zador, J.; Zsely, I.; Turanyi, T., Local and global uncertainty analysis of complex chemical kinetic systems, Reliability Engineering and System Safety, 91, 1232-1240 |
| [41] | Zhao, Y. G.; Ono, T., Moment method for structural reliability, Structural Safety, 23, 1, 47-75 |
| [42] | Zhao, Y. G.; Ono, T., On the problems of the fourth moment method, Structural Safety, 26, 3, 343-347 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
