Abstract
Abstract In every aspect of scientific research, model predictions need calibration and validation as their representativity of the record measurement. In the literature, there are a myriad of formulations, empirical expressions, algorithms and software for model efficiency assessment. In general, model predictions are curve fitting procedures with a set of assumptions that are not cared for sensitively in many studies, but only a single value comparison between the measurements and predictions is taken into consideration, and then the researcher makes the decision as for the model efficiency. Among the classical statistical efficiency formulations, the most widely used ones are bias (BI), mean square error (MSE), correlation coefficient (CC) and Nash-Sutcliffe efficiency (NSE) procedures, all of which are embedded within the visual inspection and numerical analysis (VINAM) square graph as measurements versus predictions scatter diagram. The VINAM provides a set of verbal interpretations and then numerical improvements embracing all the previous statistical efficiency formulations. The fundamental criterion in the VINAM is 1:1 (45°) main diagonal along which all visual, science philosophical, logical, rational and mathematical procedures boil down for model validation. The application of the VINAM approach is presented for artificial neural network (ANN) and adaptive network-based fuzzy inference system (ANFIS) model predictions.
Highlights
Models are the reflection tools of the reality for simulation, prediction, automation and optimum management studies at the service to men, and they are required to produce outputs as close as possible to the measurements in an efficient manner
The main purpose of this paper is to present visual inspection and numerical analysis (VINAM) methodology for effective model efficiency and ideal validation, and if necessary, modification or calibration of the model predictions to comply with the measurements
Rather than depending on such expressions without visual impressions, this paper presents an effective model efficiency evaluation methodology by means of the visual inspection and numerical analysis (VINAM) square template concept
Summary
Models are the reflection tools of the reality for simulation, prediction, automation and optimum management studies at the service to men, and they are required to produce outputs as close as possible to the measurements in an efficient manner. Whatever are the model types (analytical, probabilistic, statistical, stochastic or numerical) in practical studies, there are two sequences for comparison as the measurement series and corresponding model prediction series. There are other versions including empirical relationships, stochastic and more complex numerical solution algorithms. All these techniques have a visual basis, which can be appreciated by means of shapes in the forms of mathematical functions, flow charts, geometry, algorithms, and block diagrams. Any idea based on a geometrical shape provides visual inspections, examinations and inference deductions, perhaps at early stages verbally, but such statements can be converted to mathematical expressions after understanding the science philosophical, logical and rational fundamentals. Human philosophical thinking and logical rational trimming of blurted ideas lead to a set of logical rule bases, which are precedencies of mathematical equations and expressions by a set of convenient symbols
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