Modeling and Life Prediction

Scientific models can take many shapes and forms, but they all seek to characterize response variables through relationships with appropriate factors. Traditional models can be divided into two main categories mathematical or theoretical models and statistical or empirical models. Mathematical models have the common characteristic that the response and predictor variables are assumed to be free of specification error and measurement uncertainty. Statistical models, on the other hand, are derived from data that are subject to various types of specification, observation, experimental, and/or measurement errors. In general terms, mathematical models can guide investigations, and statistical models are used to represent the results of these investigations. 

Mathematical models. Some specific situations lend themselves to the development of useful mechanistic models that can account for the principal features governing corrosion processes. These models are 

The multidisciplinary nature of corrosion science is reflected in the multitude of approaches to explaining and modeling fundamental corrosion processes that have been proposed. The following list gives some scientific disciplines with examples of modeling efforts that one can find in the literature  

The following examples illustrate the applications of computational mathematics to modeling some fundamental corrosion behavior that can affect a wide range of design and material conditions. 

A numerical model of crevice corrosion. Many mathematical models have been developed to simulate processes such as the initiation and propagation of crevice corrosion as a function of external electrolyte composition and potential. Such models are deemed to be quite important for predicting the behavior of otherwise benign situations that can progress into aggravating corrosion processes. One such model was published recently with a review of earher efforts to model crevice corrosion. The model presented in that paper was appHed to several experimental data 

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Ford, F. P., Modelling and life prediction of stress corrosion cracking in sensitized stainless steel in high temperature water , Proc. of ASME Fall Meeting, 1985... 

Computational design and life prediction codes should be developed explicitly for CMCs. Computational models and predictions should be validated by subelement and component tests that include representative thermomechanical loadings. Rigorous analyses of failure modes should then be performed. 

Major objectives of research in the Data Base and Life Prediction project element are understanding and application of predictive models for structural ceramic mechanical reliability, measurement techniques for longterm mechanical property behavior in structural ceramics, and physical understanding of time-dependent mechanical failure. Success in meeting these objectives will provide U.S. companies with the tools needed for accurately predicting the mechanical reliability of ceramic heat engine components, including the effects of applied stress, time, temperature, and atmosphere on the critical ceramic properties. 

Confidence intervals are essential for component strength and life prediction methods, and for methods verification in this program. Verification of the life prediction methods will be accomplished by comparing observed confirmatory specimen lives with predictions. There will be some uncertainty in the predictions, due to the size and number of specimens tested to generate the life prediction model parameters. Confidence intervals on the predictions will help quantify this uncertainty, and thereby determine (1) the expected deviation between measured and calculated lives, or (2) if the deviation is a result of modeling inaccuracies. Confidence intervals are also needed for component design to define the lower limits of reliable component operations. 

The above research papers partially answer the questions on both data and model for life prediction of high-reliability and long-life products. However, as described in Lee et al. (2014), explanation documents about the reason why select some specific prognosis algorithms still lack, which constrain the RUL prediction research into practical applications. Meanwhile, if we choose them blindly without reasonable basis, future life prediction activities will be extremely dangerous. 

The method has three stages initial battery aging experiment on the specimen cells to construct a database, then formulation of aging behavior, and then the actual evaluation and life prediction. Once the battery database is built by the end of second stage, the target battery model of any conditions new or used, can be evaluated at will in the third stage, possibly as a commercial service. 

Experimental data obtained from isothermal mass loss experiments, adiabatic and isothermal heat flow calorimetry can be used for kinetic modeling and the prediction of life and storage time of energetic materials under different environmental conditions. However, the models, that such predictions are based on, are often very complex and thus not a result of simple extrapolation procedures. For example, different chemical pathways and mechanisms of decomposition reactions as well as aspects of autocatalysis must be considered. ... 

Currently the expression of geotextile resistance to abrasion is limited to compliance with these and other related abrasion tests rather than acceleration and related modeling and the prediction of abrasion-related design life. 

There is, as always, a need for good quality data. Most of this is now available in electronic form and Chapter 11 lists some of the databases available. In spite of proclaimed good intentions, there is little systematic documentation of the successful application of plastics and their lifetimes, only examples of unexpected failure. There is a need for medium-term, lightly accelerated tests under intermediate conditions to validate the predictive models. While inspection of components at end-of-life is more prevalent than expected, there is a need for coupling it to predictive techniques to validate these techniques and to close the loop of life prediction. 

The application of thermodynamic models to the correlation and prediction of pharmaceutical solubility behaviour is an underutilized technique in today s process research and development environment. This is due to the relatively poor accuracy and limited predictive ability of the previous generation of models. Recent advances in computational chemistry and an increased focus on the life science sectors has led to the development of more appropriate models with significantly improved predictive capabilities. The NRTL-SAC and Local UNIFAC approaches will be discussed here with additional examples given in section 8. 

The analysis in Cremieux et al. (2005) yielded life expectancies for men and for women from 1981 to 1998 as predicted by a model and simulated with drug spending at 1981 levels (Fig. 12.1). Using methodology from Murphy and Topel (2005), life expectancy results from the Canadian pharmaceutical spending study can be evaluated in monetary terms. The value at age a of a statistical life is given by... 

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