Prediction-error framework

Parametric linear system identification as a research discipline originated in the late 1960s and developed along two lines that are still dominant today. The first line is the prediction error framework, where a system model is identified by minimizing the difference between the measured system response and the response predicted by... 

In addition, the chapter will provide an overview of htunan reliability quantification techniques, and the relationship between these techniques and qualitative modeling. The chapter will also describe how human reliability is integrated into chemical process quantitative risk assessment (CPQRA). Both qualitative and quantitative techniques will be integrated within a framework called SPEAR (System for Predictive Error Analysis and Reduction). 

To alleviate this biased estirrratiorL resampling methods, such as cross-validation and bootstrapping, can be employed to more accurately estimate prediction error. In the next sections, these techniques are described as well as the impUcations of their use in the framework of model selection and performance assessment. 

In this paper, the building of a statistical model to diagnose the fault condition of gearboxes based on a framework of Time Domain Averaging across all Scales - IDAS, proposed by HALIM et al. (2008), is undertaken. This model pays special attention to statistical analysis using the concept of squared prediction errors, which allows the most likely condition of gearboxes to be estimated. 

A Bayesian statistical framework for model npdating and predictions for linear or nonlinear dynamic systems that explicitly treats prediction-error and other model... 

Many problems with MNDO involve cases where the NDO approximation electron-electron repulsion is most important. AMI is an improvement over MNDO, even though it uses the same basic approximation. It is generally the most accurate semi-empirical method in HyperChem and is the method of choice for most problems. Altering part of the theoretical framework (the function describing repulsion between atomic cores) and assigning new parameters improves the performance of AMI. It deals with hydrogen bonds properly, produces accurate predictions of activation barriers for many reactions, and predicts heats of formation of molecules with an error that is about 40 percent smaller than with MNDO. 

The use of a model of human error allows a systematic approach to be adopted to the prediction of human failures in CPI operations. Although there are difficulties associated with predicting the precise forms of mistakes, as opposed to slips, the cognitive approach provides a framework which can be used as part of a comprehensive qualitative assessment of failure modes. This can be used during design to eliminate potential error inducing conditions. It also has applications in the context of CPQRA methods, where a comprehensive qualitative analysis is an essential precursor of quantification. The links between these approaches and CPQRA will be discussed in Chapter 5. 

Although Figure 4 provides a conceptually simple framework for minimizing the variance of Pp from its set point, there is a much simpler relationship which can be used to relate the manipulated input APj to the purity error. In particular, Equations 9-12 can be combined to eliminate Dk, ak + P, and the minimum variance prediction of Dk+1. In addition, if g is evaluated using the process model described by Equation 7 and if the term (1 - B) 1 is expanded to yield 1 + B + B2 +. .., then the following relation results ... 

In Tables 4,5 we summarize all known corrections to the ground-state energy of hydrogen-like U and Pb ions including the complete set of the SESE corrections obtained in the present paper. The inaccuracy assigned to our results for SESE a) (red) + SESE b), c) corrections remains the main source of the total error in the theoretical Lamb shift prediction. We expect that the inaccuracy can be essentially diminished within the framework of the method described above. 

The study presented herein has a number of implications. First, this study implies that it is possible to obtain accurate predictions of the thermodynamic behavior of mixtures within a multiparameter, corresponding-states framework using empirically determined exponents for the characterization parameters of the reference system in a first-order truncation of the conformal solution method expression for the Helmholtz free energy. This result is important to the continuing effort to develop a highly accurate multiparameter, corresponding-states framework for correlation of fluid properties, and to the industrial use of such a correlation. Second, this study demonstrates that there is a need to study separately rather than collectively (as herein) the errors introduced by the various major approximations introduced into the correlation meth-... 

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