Response sensitivity analysis

Other computational issues in FE response sensitivity analysis... 

For real-world problems, the response simulation (computation of r for given 0) is typically performed using advanced mechanics-based nonlinear computational models developed based on the FE method. FE reliability analysis requires augmenting existing FE formulations for response-only calculation to compute the response sensitivities, Vef, to parameters 0. As already seen in Section 2, an accurate and efficient way to perform FE response sensitivity analysis is through the DDM. 

Barbato, M. Conte, J.P. 2005. Finite element response sensitivity analysis a comparison between force-based and displacement-based frame element models. Computer Methods in Applied Mechanics and Engineering, 194(12-16), 1479-1512. 

Barbato, M., Zona, A. Conte, J.P. 2007. Finite element response sensitivity analysis using three-field mixed formulation general theory and application to frame stmctures. International Journal for Numerical Methods in Engineering, 69(1), 114-161. 

Conte, J.P. 2001. Finite element response sensitivity analysis in earthquake engineering. In Spencer Hu (eds). Earthquake Engineering Frontiers in the New Millennium, 395 01. 

Gu, Q. Conte, J.P. 2003. Convergence studies in non-linear finite element response sensitivity analysis. Applications of Statistics and Probability in Civil Engineering, Proceedings of ICASP9, San Francisco, July 6-9. 

Conte, J.P., Vijalapura, P.K., Meghella, M. 2003. Consistent finite-element response sensitivity analysis. Journal of Engineering Mechanics (ASCE), 129 1380-1393. 

Iman RL, Helton JC, Campbell JE. An approach to sensitivity analysis of computer models Part II—Ranking of input variables, response surface validation, distribution effect and technique synopsis. / Quality Technol 1981 13 232-40. 

O-SCD Higher selectivity than AED Excellent sensitivity Linear response Odorant analysis Skilled operators (flame SCD) [33,40,45]... 

Figure 2. Contour sensitivity analysis illustrating the effect of compositional changes on the response around the optimal formulation.

In this example with only three components, the optimum could have been determined by simply overlaying the individual response contour plots. This approach would be difficult, if not impossible, if the formulation would have many responses or contain four or more components. By contrast, the combination of the desirability function and the Complex algorithm permits an optimization of a multiresponse formulation having many constrained components in addition to providing the basis for sensitivity analysis. 

Figure 5. Multiresponse sensitivity analysis of the overall desirability value showing the optimum and the compositional region complying with all response limits.

Parametric sensitivity analysis showed that for nonreactive systems, the adsorption equilibrium assumption can be safely invoked for transient CO adsorption and desorption, and that intrapellet diffusion resistances have a strong influence on the time scale of the transients (they tend to slow down the responses). The latter observation has important implications in the analysis of transient adsorption and desorption over supported catalysts that is, the results of transient chemisorption studies should be viewed with caution, if the effects of intrapellet diffusion resistances are not properly accounted for. 

For systems with large numbers of species and reactions, the dynamics of the reaction and the interactions between species can become quite complex. In order to analyze the reaction progress of species, various diagnostics techniques have been developed. Two of these techniques are reaction rate-of-production analysis and sensitivity analysis. A sensitivity analysis identifies the rate limiting or controlling reaction steps, while a rate-of-production analysis identifies the dominant reaction paths (i.e., those most responsible for forming or consuming a particular species). 

It appears that the formal theories are not sufficiently sensitive to structure to be of much help in dealing with linear viscoelastic response Williams analysis is the most complete theory available, and yet even here a dimensional analysis is required to find a form for the pair correlation function. Moreover, molecular weight dependence in the resulting viscosity expression [Eq. (6.11)] is much too weak to represent behavior even at moderate concentrations. Williams suggests that the combination of variables in Eq. (6.11) may furnish theoretical support correlations of the form tj0 = f c rjj) at moderate concentrations (cf. Section 5). However the weakness of the predicted dependence compared to experiment and the somewhat arbitrary nature of the dimensional analysis makes the suggestion rather questionable. 

Through modeling of global experiments it is possible to elucidate the mechanism and identify a number of rate coefficients that must be determined accurately. In this procedure sensitivity and reaction path analyses are essential tools. The sensitivity analysis identifies the bottlenecks in the chemical conversion process, that is the rate-controlling elementary reactions. Reaction path analysis provides information about the major reaction pathways responsible for the production and consumption of each species. 

Extraction scientist who is responsible for sample preparation should be certified prior to extracting real study samples. The validated extraction method has to be followed exactly. The raw data entries have to be documented promptly such as lot numbers of STD and QC, IS, extraction reagents, matrix, the IDs of automation tool and pipette, the time for study sample removal and return to storage and the completion of extraction. Instrument operator who is responsible for analysis has to perform SST test and assess sensitivity and carryover prior to initialing batch. Instrument operator has to... 

Sensitivity analysis can and should be used both iteratively and proactively during the course of developing an exposure model or a particular analysis. For example, sensitivity analysis can be used early in model development to determine which inputs contribute the most to variation in model outputs, to enable data collection to be prioritized to characterize such inputs. Furthermore, analysis of the model response to changes in inputs is a useful way to evaluate the appropriateness of the model formulation and to aid in diagnosing possible problems with a model. Thus, sensitivity analysis can be used to guide model development. 

Quantitative methods of sensitivity analysis and metrics for measuring sensitivity are widely available. The most commonly used sensitivity analysis methods are often relatively simple techniques that evaluate the local linearized sensitivity of model response at a particular point in the input domain. This type of approach is typically used if the model inputs are treated as point estimates, often representing the best guess as to the true but unknown value of each... 

Examples of mathematical methods include nominal range sensitivity analysis (Cullen Frey, 1999) and differential sensitivity analysis (Hwang et al., 1997 Isukapalli et al., 2000). Examples of statistical sensitivity analysis methods include sample (Pearson) and rank (Spearman) correlation analysis (Edwards, 1976), sample and rank regression analysis (Iman Conover, 1979), analysis of variance (Neter et al., 1996), classification and regression tree (Breiman et al., 1984), response surface method (Khuri Cornell, 1987), Fourier amplitude sensitivity test (FAST) (Saltelli et al., 2000), mutual information index (Jelinek, 1970) and Sobol s indices (Sobol, 1993). Examples of graphical sensitivity analysis methods include scatter plots (Kleijnen Helton, 1999) and conditional sensitivity analysis (Frey et al., 2003). Further discussion of these methods is provided in Frey Patil (2002) and Frey et al. (2003, 2004). 

Sensitivity analysis should be an integral component of the uncertainty analysis in order to identify key sources of variability, uncertainty or both and to aid in iterative refinement of the exposure model. The results of sensitivity analysis should be used to identify key sources of uncertainty that should be the target of additional data collection or research, to identify key sources of controllable variability that can be the focus of risk management strategies and to evaluate model responses and the relative importance of various model inputs and model components to guide model development. 

What are the key sources of uncertainty in the exposure assessment This question can also be posed as Which exposure factors contribute the most to the overall uncertainty in the inventory This insight can be used, in turn, to target resources to reduce the largest and most important uncertainties. There are various ways to answer this question, including various forms of sensitivity analysis. For example, in the context of a probabilistic uncertainty simulation for an overall exposure assessment, various statistical methods can be used to determine which input distributions are responsible for contributing the most to the variance of the output. 

Thermoeconomic optimization using differentially derived prices, permitting the analysis of the system s local and global responses to well specified small changes in the state of the system, and leading to sensitivity analysis and optimization techniques. 

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