MATLAB modelling approach

With these five equations (Eqs. 23-42 to 23-46), two of them partial differential equations, the limits of the analytical approach and the goals of this book are clearly exceeded. However, at this point we take the occasion to look at how such equations are solved numerically. User-friendly computer programs, such as MAS AS (Modeling of Anthropogenic Substances in Aquatic Systems, Ulrich et al., 1995) or AQUASIM (Reichert, 1994), or just a general mathematical tool like MATLAB and MATHE-MATICA, can be used to solve these equations for arbitrary constant or variable parameters and boundary conditions. 

In the present work, two methods are chosen to conduct variable selection. The first is t-test, which is a simple univariate method that determines whether two samples from normal distributions could have the same mean when standard deviations are unknown but assumed to be equal. The second is subwindow permutation analysis (SPA) which was a model population analysis-based approach proposed in our previous work [14]. The main characteristic of SPA is that it can output a conditional P value by implicitly taking into account synergistic effects among multiple variables. With this conditional P value, important variables or conditionally important variables can be identified. The source codes in Matlab and R are freely available at [46]. We apply these two methods on a type 2 diabetes mellitus dataset that contains 90 samples (45 healthy and 45 cases) each of which is characterized by 21 metabolites measured using a GC/MS instrument. Details of this dataset can be found in reference [32]. 

Having determined the optimal model order for the given segment of signal, the model can be estimated using one of the following MATLAB functions arburg, arcov (uses a covariance approach), armcov (uses a modified covariance approach), or aryule (uses the Yule-Walker equations... 

Biahmou et al. [42] have developed an approach for deriving behavior models from 3D models in MATLAB/SimMechanics that have been created with CATIA V5. After updating the geometrical model, the behavioral model is to be updated by the user. In order to free the user from this task and achieve a structured and right synchronization of changes in partial models of a system, the application of ontologies has been addressed to identify the update sequence of models [43]. 

Biahmou et al. have elaborated an approach presenting the federation of the systems CATIA V5 and Matlab SimMechanics in the past [42]. In early development phases, the behavioral partial model can be derived from the geometrical one using the CAMAT (CATIA-MATLAB-Translator). A co-simulation is conducted, whereby the nominal values are sent to acmators within CATIA V5. The sensors capture values, which are sent back to the MATLAB SimMechanics model [42]. A drawback of that approach is the fact that methods must be developed to ensure the update of the different partial models involved. From this point of view, conventional autonomous tools used today and the processes based on them are not appropriate to tackle all challenges of product development. A middle way between integrated and autonomous environments is necessary (see Sect. 13.6) [43]. 

The proposed matrix-based approach is illustrated by manual derivation of results for small, well-known examples. For more complex system models, software such as CAMP-G/MATLAB together with the Symbolic Math Toolbox can be used. 

In the case of linear system models, the combination of CAMP-G, MATLAB, and the Symbolic Math Toolbox can generate state space matrices as well as transfer functions in symbolic form from a bond graph. MATLAB in conjunction with the Symbolic Math Toolbox can also be used for the incremental bond graph approach presented in Chapter 4. 

In addition to a formal specification, we need a technique to analyze the fault tolerance behavior of a component in a formal way. Approaches such as [19] verify formalized fault trees against formal implementation models. Furthe-more, several fault injection analyzes that rely on model checking like [3] and [9] have been presented. In this paper we focus on a fault injection based-technique [16], [10] that is called model-based safety analysis MBS A. The MBS A processes functional requirements and provides complete results as cut-sets and allows to define custom faulty behavior in the implementation model, which is specified using Matlab/Statefiow. Cut-sets are unique combinations of malfunctions occurrences that can cause a system failure. A cut-set is said to be minimal if no event can be removed from the set and the combination of malfunctions still leads to a failure[ll]. 

We have presented an approach to prove the compliance of an implementation to a safety specification. Our approach currently supports Matlab/Stateflow models. The safety properties are specified using safety contracts. Therefore, a safety view of a system can be built, which allows to reason about the correct refinement of safety requirements (by using virtual integration techniques for contracts) and an correct fulfillment of these requirements by an implementation. This reduces verification effort, since integration tests can be replaced to a certain extent. 

Duller et al. presented a systematic approach to employ EIS for determining the structure and parameters of a VRLA battery model [45]. They focused on the interpretation of the impedance data in an ECM and described its MATLAB/Simulink... 

ABSTRACT Availability and reliability evaluation of redundant systems under periodic maintenance is one of the difficulties in the field of reliability engineering. In order to overcome the disadvantages of existing evaluation methods, an instantaneous availability analytic approach for such systems is deduced, considering fault detection rate, fault isolation rate and repair rate. Limitations of this approach are discussed. Furthermore, a simulation model is devised to accomplish the evaluation of instantaneous availability and MTBCF. The validity of this simulation method is proved. And a simulation tool for availability and reliability evaluation of redundant systems periodically maintained is developed with MATLAB. At last, a case is studied. 

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