Model predictions and measured

When implemented at the miniplant reactor scale, there was good agreement between the model predictions and measurements of residual monomer as shown in Figure 4. 

Figure 7. Comparison of model predictions and measured displacement after 48 month of heating.

In most cases, graphical comparisons clearly show the existence or absence of systematic deviations between model predictions and measurements. It is evident that a quantitative measure of the differences between calculated and measured values is an important criterion for the adequacy of a model. Hence, the difference between the values of the objective function J achieved by considered meta-heuristic algorithms is negligible the d3mamics of the process variables (experimental data and modeled data) for FA-GA result, are presented only. 

The comparisons of model predictions and measurements of the mole fraction of CO2 at the exhaust of the fuel and the electrolyte channels, for various flow rates are shown respectively in Fig. 5.22 and Fig. 5.23. For both cases MTPM and MMS predictions are in excellent agreement with measured values. DGM and MFM also work well in reproducing... 

Kalman filter is well known as an efficient recursive filter that can optimally estimate the states of linear dynamic systems from a series of noisy measurements [20]. For nonlinear systems, extended Kalman filters [21,22] have been developed and validated by many studies to be effective in real applications [17, 23-25]. Unlike model-based estimators which heavily rely upon the plant models, a specific feature of a Kalman filter is that it finds the stochastic relations between model predictions and sensor measurements, and then estimates system states in an optimal approach. By utilizing this feature of the Kalman filter, a slowly time-varying state can be treated as a constant and its variation can be estimated by comparing the model predictions and measurements in a stochastic manner. 

In Step 3 of the calibration, we will use Aspen HYSYS to vary several activity factors in order to minimize the objective function. We define the objective function as the weighting sum of the absolute deviations from the model prediction and measure data. We can select terms in the objective function by going to the Objective section of the Calibration Control Tab. We show this interface in Figure 5.84. 

Figure 2 Comparison of original and improved mWM model predictions and measured shear viseosity and uniaxial/planar extensional viseosity. Solid symbol represent experimental data and lines correspond to model predictions.

Fig. 19. Comparison of the predictions of k-e model and experimental data for a confined swirling flow, (a) Flow configuration where 4. is the primary inlet, D = 25 mm, and B is the secondary inlet, = 31 mm, = 59 mm and the step height, H = 31.5 mm. (b) Predicted and measured streamline values where r/H is the ratio of the radial distance from the centerline to the step height.

The response produced by Eq. (8-26), c t), can be found by inverting the transfer function, and it is also shown in Fig. 8-21 for a set of model parameters, K, T, and 0, fitted to the data. These parameters are calculated using optimization to minimize the squarea difference between the model predictions and the data, i.e., a least squares approach. Let each measured data point be represented by Cj (measured response), tj (time of measured response),j = 1 to n. Then the least squares problem can be formulated as ... 

Aside from the fundamentals, the principal compromise to the accuracy of extrapolations and interpolations is the interaction of the model parameters with the database parameters (e.g., tray efficiency and phase eqiiilibria). Compromises in the model development due to the uncertainties in the data base will manifest themselves when the model is used to describe other operating conditions. A model with these interactions may describe the operating conditions upon which it is based but be of little value at operating conditions or equipment constraints different from the foundation. Therefore, it is good practice to test any model predictions against measurements at other operating conditions. 

In making a preliminary comparison between predicted and measured burning rates, Nachbar has shown that the present analysis does not predict the observed effect of pressure on the burning rate. In fact, the model predicts... 

Qu W, Mudawar I (2002) Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. Int J Heat Mass Transfer 45 3933-3945 Qu W, Mudawar I (2004) Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 47 2045-2059 Quiben JM, Thome JR (2007a) Flow pattern based two-phase pressure drop model for horizontal tubes. Part I. Diabatic and adiabatic experimental study. Int. J. Heat and Fluid Flow. 28(5) 1049-1059... 

In order to evaluate system performance it is useful to plot SR as a function of fo. This may be compared to simulations or model predictions and deviations indicate that there are problems. When this occurs, what are the diagnostics that can be examined There is a great deal of information in the wavefront sensor measurements and provision should be made to store them. Zemike decomposition of the residuals helps to identify if there are problems... 

In the above two equations, the superscripts exp and EoS indicate that the state variable has been obtained from the experimental equilibrium surface or by EoS calculations respectively. The value of % which is used is the maximum between the Equations 14.27 and 14.29a or 14.27 and 14.29b. Equation 14.27 accounts for the uncertainty in the measurement of the experimental data, whereas Equations 14.29a and 14.29b account for the deviation between the model prediction and the experimental equilibrium surface. The minimum of

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Fig. 1. N/C and N/O ratios are shown as a function of luminosity relative to the initial solar values. The lower hatched line in each plot is the standard model prediction and the upper hatched line is the predicted value for an initial rotational velocity of 300 km s 1 [6]. Our measurements show that the low ratios seen in aOri are not commonly seen in supergiants. Instead the ratios indicate extensive mixing as predicted by the rotation models.

State estimators are basically just mathematical models of the system that are solved on-line. These models usually assume linear DDEs, but nonlinear equations can be incorporated. The actual measured inputs to the process (manipulated variables) are fed into the model equations, and the model equations are integrated. Then the available measured output variables are compared with the predictions of the model. The differences between the actual measured output variables and the predictions of the model for these same variables are used to change the model estimates through some sort of feedback. As these differences between the predicted and measured variables are driven to zero, the model predictions of all the state variables are changed. 

Difficulties in obtaining good quantitative agreement between predicted and measured distribution results are indicative that model refinements as well as an improved property database will be needed before accurate quantitative predictions of not only overall polarization curve but also detailed distributions within a DMFC may be obtained. 

Figure 9.10 PLS-1 model for the average particle size in chambers 2 and 3. Sensors C and D were used in this model based on four PLS components. The model was validated with segmented cross validation with 10 segments. Predicted versus measured (top) and predicted and measured (bottom).

Figure 9.11 Predicted and measured plot for granule moisture contents, calibrated on data from 5 months of production. Sensor B was used in this model (eight PLS components). Cray curve measured, black curve predicted.

Therefore, a flexible method to evaluate physical and chemical system parameters is still needed (2, 3). The model identification technique presented in this study allows flexibility in model formulation and inclusion of the available experimental measurements to identify the model. The parameter estimation scheme finds the optimal set of parameters by minimizing the sum of the differences between model predictions and experimental observations. Since some experimental data are more reliable than others, it is advantageous to assign higher weights to the dependable data. 

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