Parameters robust

The simplex algorithm is conceptually a very simple method. It is reasonably fast for small numbers of parameters, robust and reliable. For high dimensional tasks with many parameters, however, it quickly becomes painfully slow. Also, the simplex algorithm does not deliver any statistical information about the parameters, e.g. it is possible to fit parameters that are completely independent of the data. The algorithm delivers a value without indicating its uselessness. 

Robustness is defined as a measure of how well the method will remain unaffected by small variations in the parameters. Robustness can be assured by setting appropriate system suitability. However, it is important that these parameters be set properly. Some parameters which could be used to demonstrate robustness are the varying age of columns, column brands, temperature, pH of mobile phase, and the different amounts of mobile phase modifiers. 

Advantages Distinct rate constants, real time measurement Fast, easy assay setup Thermo- dynamic parameters Robust assay design, HTS compatible... 

In our knowledge robust estimators have not been applied in nonlinear dynamic real plant data yet. The first comparative study among some robust estimators in DR has been presented by Ozyurt and Pike (2004). They conclude that the estimators based on Cauchy and Hampel distributions give promising results, however did not consider dynamic systems. Other earlier studied has been accomplished by Basu and Paliwal (1989) in autoregressive parameter robust estimation issues, showing that for their case the Welsch estimator produced the best results. 

Contrary to t3q>ically deterministic mathematical models available in the literamre, real-world apphcations are usually surrounded with uncertainty. The two main approaches for dealing with uncertainty are stochastic programming and robust optimization. For developing stochastic programming models, probability distributions of uncertain parameters should be known in advance. However, in many practical situations, there is no information or enough information for obtaining probability distribution of uncertain parameters. Robust optimization models are viable answers to these situations via providing solutions that are always... 

The D-HMQC Cq parameter robustness makes of this technique a perfect tool for the investigation of boro-phosphate-based system. Figure 4.4 shows the B P D-HMQC spectra obtained in 2011 on ultrafast quenched 45Li20-xB203-(55 —x)P20s composition line [48,49]. The... 

KUB 95] Kubica F., Livet T., Le Iron X., Bucharles A., Parameter-robust flight control system for a flexible aircraft . Control Engineering Practice, vol. 3, n° 9, pp. 1209-1215, 1995. 

In order to test the economic performance of the project to variations in the base case estimates for the input data, sensitivity analysis is performed. This shows how robust the project is to variations in one or more parameters, and also highlights which of the inputs the project economics is more sensitive to. These inputs can then be addressed more specifically. For example if the project economics is highly sensitive to a delay in first production, then the scheduling should be more critically reviewed. 

The Fresnel equations predict that reflexion changes the polarization of light, measurement of which fonns the basis of ellipsometry [128]. Although more sensitive than SAR, it is not possible to solve the equations linking the measured parameters with n and d. in closed fonn, and hence they cannot be solved unambiguously, although their product yielding v (equation C2.14.48) appears to be robust. 

The MPC control problem illustrated in Eqs. (8-66) to (8-71) contains a variety of design parameters model horizon N, prediction horizon p, control horizon m, weighting factors Wj, move suppression factor 6, the constraint limits Bj, Q, and Dj, and the sampling period At. Some of these parameters can be used to tune the MPC strategy, notably the move suppression faclor 6, but details remain largely proprietary. One commercial controller, Honeywell s RMPCT (Robust Multivariable Predictive Control Technology), provides default tuning parameters based on the dynamic process model and the model uncertainty. 

The models must be considered to be approximations. Therefore, the goals of robustness and uniqueness are rarely met. The nonlinear nature of the physical model, the interaction between the database and the parameters, the approximation of the unit fundamentals, the equipment boundaries, and the measurement uncertainties all contribute to the limitations in either of these models. 

The first task considered is the robust estimation of fitting parameters. Following to Peter Huber, the consideration is built at the assumption that the density function of the experimental random errors (8) can be presented in the following form ... 

The criteria chai acterizing the robustness of parameters of retention model for the changing of experimental data number were proposed to estimate the prediction capability of the models. 

This is a multivariable robust eontrol problem that ealeulates the optimal Hrx, eontroller. The MATLAB eommand hinf opt undertakes a number of iterations by varying a parameter 7 until a best solution, within a given toleranee, is aehieved. 

It is inherently safer to develop processes with wide safe operating limits that are less sensitive to variations in critical safety operating parameters, as shown in Figure 4.3. Sometimes this type of process is referred to as a forgiving or robust process. If a process must be controlled within a very small temperature band in order to avoid... 

It does not calculate source emission rates. While it handles jets, it does so simply and docs not calculate the details of the jet motions and thermodynamics. It should not be used for strongly buoyant plumes. The error diagnostics are limited to checking the consistency of input parameters. Run time error diagnostics are missing but are rarely needed due to its robustness. 

A target purity of 99 % was established for both extract and raffinate. According to the simulation results, one can predict that a variation of the feed concentration range between 7.5 and 11 g will meet the required purity. The system was designed for a feed concentration equal to 10 g The influence of change in feed concentration on the purity of both extract and raffinate illustrates the robustness of SMB, and that the process tolerates fluctuations when critical parameters are stressed during process validation. 

Using computer-aided numerical calculations, one can readily simulate and identify critical parameters for process validation. Thus, one can evaluate the robustness of the process during its design. To ensure performance, optimization of the process and evaluation of critical parameters can be determined before actual operating conditions. 

Simple models (fewer parameters) are more robust, but more complex models will usually provide a better fit. 

The Optimization Xpert Automated design of experiments that builds on the foundation established in Setup Xpert and allows users to further optimize the combination of processing parameters to determine a robust good parts processing window. 

The robustness of an analytical procedure is a measure of its capacity to remain unaffected by small, but deliberate, variations in method parameters this provides an indication of its reliability during normal usage. 

Based on comparison of three traditional equivalence parameters with cracking energy density, the maximum principal strain corresponded the closest to the cracking energy density. Thus, Mars and Fatemi judged that the maximum principal strain is the most robust and meaningful of the traditional parameters considered in their work. 

The present investigations were largely motivated to show the serial-screening capabilities of the reactor concept used. The speed of process-parameter changes, consumption of small volumes only, preciseness of kinetic information, and robustness were major micro reactor properties utilized. 

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