Parameter identification

In this chapter, the model is evaluated and examined that was proposed in the previous chapter. Sticking to the model might be boring to mechanical engineers and robotics researchers, this process is especially important for solving activeness problem. Because of its simplicity, the model is sensitive to the difference of parameters. The system is extended from material to machine in the next part, design. Before that, it is essential to make clear compensation method and level of unreliability. 

Aside from the activeness problem, there is a hmdamental problem for modelling. Most of the polymer scientists believe that the model should not be so much simple, because gel is a complex system. Some researchers noted that the model might be reasonable because it went well with experimental results. The descriptive power of the model is made clear as a result in the comse of this book. We believe that the model is acceptable for polymer scientists at certain approximation level. 

In this chapter, the condition is kept simple. Deformation response of the gel to spatially miiform static electric field is investigated. This strategy was selected to remove the effect of other factors like modelling error of electric field or meshing of the gel. 

The parameters to be identified are a,d, and b in equations (2.7) and (2.10). Parameter a represents the adsorption speed of molecules while parameter d represents the dissociation speed of molecules. We name a for adsorption parameter and d for dissociation parameter. Parameter b represents the stress generation when the adsorption rate is given. We normalized and set parameter b so that 

Otake Electroactive Polymer Gel Robots, STAR 59, pp. 35—60. springerlink.com Springer-Verlag Berlin Heidelberg 2010 

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Figure 2 Schematic flow chart of the OSD parameters identification method Our specific dissimilarity criterion is defined as ...

Table 2.3 is used to classify the differing systems of equations, encountered in chemical reactor applications and the normal method of parameter identification. As shown, the optimal values of the system parameters can be estimated using a suitable error criterion, such as the methods of least squares, maximum likelihood or probability density function. 

Chapter 2 is employed to provide a general introduction to signal and process dynamics, including the concept of process time constants, process control, process optimisation and parameter identification. Other important aspects of dynamic simulation involve the numerical methods of solution and the resulting stability of solution both of which are dealt with from the viewpoint of the simulator, as compared to that of the mathematician. 

Our approach to determine the properties of heterogeneous media utilizes mathematical models of the measurement process and, as appropriate, the flow process itself. To determine the desired properties, we solve an associated system and parameter identification problem (also termed an inverse problem) to estimate the properties from the measured data. 

In this chapter, we describe the approaches used to mathematically model the flow of immiscible fluid phases through permeable media. We summarize the elements of system and parameter identification, and then describe our methods for determining properties of heterogeneous permeable media. 

With the conventional experimental design, information about spatial variations of the permeability is not available. With MRI, we can obtain information within the sample, so that we may determine the spatial distribution of the permeability. Clearly, the computational procedure required to estimate the entire distribution will not be as simple as that reflected by Eq. 4.1.7. We will use the principles of system and parameter identification, discussed in the following section, to determine the various macroscopic properties from experiments. 

We refer to system and parameter identification as the principles to determine the most appropriate equations, and properties within those equations, to describe physical phenomena. In particular, we refer to parameter identification as the estimation of properties within a specified model from observations of states or... 

The parameter identification problem associated with the conventional permeability experiments is within the first class (with m= 1). By contrast, the problems we consider here are within the second and third classes these areJunctional estimation problems. Ultimately, however, these are solved with finite-dimensional representations, although an essential aspect of the solution of these infinite-dimensional (function) estimation problems is the selection of the appropriate representations. 

We have developed a method to spatially resolve permeability distributions. We use MRI to determine spatially resolved velocity distributions, and solve an associated system and parameter identification problem to determine the permeability distribution. Not only is such information essential for investigating complex processes within permeable media, it can provide the means for determining improved correlations for predicting permeability from other measurements, such as porosity and NMR relaxation [17-19]. 

Displacement experiments can be relatively complex and time-consuming, so the experimental design can be a critical issue. Using suitable system and parameter identification methods, we obtain the best estimates of properties from the available data. It is most desirable to have some measures of the accuracy with which the properties are estimated. If that level of accuracy is less than desired, one can consider other ways of conducting the experiments so that additional information about the properties may be obtained. 

We presented a novel method to determine spatially resolved permeability distributions. We used MRI to measure spatially resolved flow velocities, and estimated the permeability from the solution of an associated system and parameter identification problem. 

DM Gibon, ME Taylor, WA Colburn. Curve fitting and unique parameter identification. I Pharm Sci 76 658-659, 1987. 

Validation Parameter Identification Impurities (Quantitation) Impurities (Limit) Assay... 

O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, and J.P. Steyer. Dynamical model development and parameter identification for anaerobic wastewater treatment process. Biotechnol. Bioeng., 75(4) 424-438, 2001. 

Validation parameter Identification Testing for impurities Quantitative Limit test Assay... 

Pseudo-experimental data can be generated by solving the model. Equations 1-4, for a chosen set of parameters and initial conditions, and then adding random noise to the model solution. For a given choice of measurement variables, the simulated data is then used in the parameter estimation problem. This procedure provides a means by which to evaluate the measurements that are required and the amount of measurement noise that is tolerable for parameter identification. 

Method Performance Parameter Identification Test Impurity Test Limit Impurity Quantitative Test Impurity Test Assay Test... 

Abstract This paper is concerned with the experimental identification of some chemo-poroelastic parameters of a reactive shale from data obtained in pore pressure transmission - chemical potential tests. The parameter identification is done by matching the observed pressure response with a theoretical solution of the experiment. This solution is obtained within the framework of Biot theory of poroelasticity, extended to include physico-chemical interactions. Results of an experiment on a Pierre II shale performed in a pressure cell are reported and analyzed. 

Bock, H. G., Recent advances in parameter identification techniques for O.D.E., in Numerical Treatment of Inverse Problems for Differential and Integral Equations, Springer-Verlag, 1981. 

Bristol, E. H., "Pattern Recognition an Alternative to Parameter Identification in Adaptive Control," Automatica, 1977, 13, 197. 

Modeling, Parameter Identification, and Adaptive Control of Anticoagulant Drug Therapy... 

Nonlinear and dynamic models of desorption are used in the sequel. Mathematical justification of the boundary-value problems for the TDS-degassing method of metal saturated with hydrogen is given in [6,7]. The work [4] was a starting point of the results presented here. Algorithm of parameter identification for the model of hydrogen permeability of metals for the concentration pulses method [5] is presented in [8],... 

ErH2 -> Er). Then diffusion may be considered as relatively fast and therefore ordinary differential equations are sufficient. This significantly simplifies solving the inverse problems of parameter identification. Although models with fast diffusion may also correspond to the low-temperature flux peak atoms of H easily diffuse in ErH2 (may be, even easier than in Er even at higher temperatures). 

This switch doesn t influence on diagram of J. The advantages are the low number of parameters (they can be estimated using a little experimental data). Model curves satisfactorily approximate the experimental data if distribution is taken into account. Also we bear in mind that the algorithms of parameter identification are locally convergent. The parameter estimations of simple models should be taken as the initial approximation for more complex models. 

The samples without defensive film coat were studied by the method of concentration pulses (MCP) at pressure 0.2 Torr within the range of temperatures 370 -596 °C in order to determine the hydrogen permeability parameters of stainless steel (12X18H10T). The knowledge of these parameters allowed to simplify the problem of parameter identification for titanium nitride. The samples with titanium nitride covering were studied by method of permeability at pressures 0.5-249 Torr and the temperatures 380-670 °C. 

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