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The methodology pages explain how models are developed so that the user can understand their structure, followed by a detailed description of how to apply them in problem-solving and analysis.
During the structuring phase, each stage is considered, providing a general overview of how models are built, with a focus on key aspects that are essential for understanding a model's structure.
Once the model is structured, the user is guided through its step-by-step application: from identifying the appropriate model, recognizing and associating the variables, to performing the necessary calculations and/or analyses.
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Organization of the material
Description
The methodology serves as the foundation for all the content on these pages, so it is recommended to study it before moving on to the other topics. While this section explains the method and provides guidelines for working with the methodology, the remaining topics contain specific information for each area without detailing how to apply the methodology.
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How models are structured
Description
The method is based on creating various models that aim to describe and, as far as possible, explain the behavior of systems. To do this, the fundamental principles governing the behavior of the studied systems are identified. When certain basic principles are unknown, a phenomenological solution is used, which at least provides a basic model to analyze the system.
Once the fundamental principles are identified, the necessary variables to describe the systems behavior over time are derived from them. Additionally, equations that these variables must satisfy are identified. If its not possible to derive an equation based on fundamental principles, empirical modeling is used, in which case the model is termed phenomenological.
Before using the model to study situations of interest, it is essential to empirically verify its validity. This is achieved by studying an event for which its behavior is theoretically predicted, including an error range. The situation is then recreated, and measurements are taken, which should yield results within the calculated error range.
If the model does not align with certain variable ranges, a validity range is defined to avoid its application in situations where the calculated results diverge from the observed ones.
A validated model can be used to study a situation, design solutions to specific problems, or assess potential future risks.
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Summary of the modeling process
Description
In summary, the steps to follow for modeling are:
• Identify the behaviors and properties to be explained.
• Determine the causes or mechanisms that originate them.
• Identify the variables that describe these behaviors.
• Develop a mathematical model based on fundamental principles.
• If this is not possible, define a phenomenological model to explain the observations.
• Empirically validate the proposed model.
• Generalize the model for application in different contexts.
• Use the model to study, predict, and assess specific situations.
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How to use models
Description
Once models have been defined, they can be used to study physical systems. The first task is to select the appropriate model for a specific case. This choice can be complex, as using the wrong model may lead to inaccurate results, even if it bears some similarities to the correct one. To avoid this, it is essential to thoroughly understand each models mechanisms, principles, and variables. If any of these aspects do not match the system, the model should be discarded.
After identifying the model, the next step is to identify the variables and link them to observable elements in the physical system. It is crucial to interpret the variables correctly; an initial check is to ensure that the units match. If several variables share the same unit, it is important to understand the underlying mechanism and correctly associate each variable with its corresponding observable in the real situation.
With the variables identified and associated, the models network can then be used to distinguish between known variables and those that can be calculated using the models equations. Finally, any variables that remain unmeasured and cannot be calculated directly in the current situation are identified. In these cases, the models network can be examined to determine if other variables might allow calculation of the missing variable.
In many cases, model parameterization is the ultimate goal. In others, it serves as a starting point for further analysis, such as variation analysis or error propagation studies, where results are forecasted with associated errors to verify the models accuracy.
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Summary of model usage
Description
In summary, the steps to apply modeling are as follows:
• Gain a detailed understanding of the models associated with the physical system.
• Identify the appropriate model for the specific case.
• Verify that the mechanics and principles of the model do not contradict the physical system.
• Identify the model's variables and the system's observable elements.
• Associate the model's variables with the system's observables.
• Determine the known values of the system's observables.
• Calculate unknown variables using the models network.
• Calculate the error range of the variables and compare with measured data to validate the model's accuracy.
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