Parameter identification algorithm

Identify the "interval" of the required unmeasured parameters (N ) (see Identification algorithm). 

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],... 

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 estimation of parameters D, b, s, a, a2 in model (11) - (17) of the hydrogen transfer in stainless steel was made by the identification algorithm based on the Fourier series. The detailed description of the algorithm is in [3, 4]. The experimental data got by the concentration pulses method were used for identification. In addition the estimations of s, X = Db1/2 were received by isotherms for the permeability method [3, 4]. Below we describe the identification algorithm based on the Fourier series. 

At this step of the work we evaluated the fitting performances of six further rate equations, derived from assumed reaction mechanisms and congruent with previous findings obtained with power law rate equations. Among them, it has been reported the model named Centi modified, which represents our proposal to take into account the effect of O2 partial pressure on the overall kinetics under the same hypotheses of the model of Centi [24]. The results of parameters identification, carried out for each temperature investigated, are reported in Tab.3b and show different performances of the models. The model Centi modified does not produce effective results, since the relevant values are still very low and the minimisation algorithm estimated some unacceptable parameters value (for example, a negative value for K no at 450°C). 

Following these results, in this paper, two hybrid meta-hemistic algorithms, based on GA and FA, are proposed for parameter identification of an E. coli fed-batch cultivation process. The algorithms performances are compared to the pure GA and FA and the results are analyzed. 

Each algorithm has its own influential parameters that affect its performance in terms of solution quality and computational time. In order to increase the performance of the FA and GA, it is necessary to provide the adjustments of the parameters depending on the problem domain. With the appropriate choice of the algorithm settings the accuracy of the decisions and the execution time can be optimized. Parameters of the FA and GA are tuned on the basis of a large number of pre-tests according to the parameter identification problem, considered here. 

Genetic Algorithm Parameters. For the considered here model parameter identification, the type of the basic operators in GA are as follows ... 

A series of parameter identification procedures for the considered model Eqs. (l)-(4), using FA, GA, FA-GA and GA-FA, are performed. Because of the stochastic characteristics of the applied algorithm, the algorithms have been nm at least 30 times in order to carry out meaningful statistical analysis. 

In this paper, a hybrid meta-heuristic approach, which is a combination between two meta-heuristics, FA and GA is applied to the problem of parameter identification of an E. coli fed-batch cultivation process model. The proposed hybrid FA-GA and GA-FA algorithms are collaborative combinations of the FA and GA techniques. 

A comparison of pure FA, pure GA and hybrids FA-GA and GA-FA were done. Some adjustments of the considered meta-heuristics, according to the regarded problem, were performed to improve the optimization capability and the decision speed. Numerical and simulation results from model parameter identification based on the proposed algorithms reveal that correct and consistent results can be obtained using the discussed meta-heuristics. 

Roeva, O., Trenkova, T. Genetic algorithms and firefly algorithms for non-linear bioprocess model parameters identification. In Proceedings of the 4th International Joint Conference on Computational InteUigence (ECTA), Barcelona, Spain, 5-7 October 2012, pp. 164-169 (2012)... 

Juang, J. N. and Suzuki, H. An eigen-system realization algorithm in frequency domain for modal parameter identification. Journal cf Vibration, Acoustics, Stress and Reliability in Design 110(1) (1988), 24-29. 

The free parameters of the model are fitted to experimental data (the 0-I-D-P-fluorescence rise of dark-adapted tobacco leaves) by means of the multiple shooting algorithm PARFIT as developed by Bock [2] for parameter identification in systems of nonlinear differential equations. We use a multiple experiment structure for measurements at different light intensities. The initial trajectory and the results are shown in Figs. 2 and 3. 

The least-squares problem has been solved by a generalized Gaufi -Newton method [26,53]. The algorithm of the inverse problem of kinetic parameter identification is available as a code called PARFIT. Nowak and Deuflhard [27] have developed a software package PARKIN for the identification of kinetic parameters. 

Chapter 12 considers the combination of optimal control with state and parameter estimation. The separation principle is developed, which states that the design of a control problem with measurement and model uncertainty can be treated by first performing a Kalman filter estimate of the states and then developing the optimal control law based upon the estimated states. For linear regulator problems, the problem is known as the linear quadratic Gaussian (LQG) problem. The inclusion of model parameter identification results in adaptive control algorithms. 

In section Structural Parametric Identification by Extended Kalman Filter, online structural parametric identification using the EKF will be briefly reviewed. In section Online Identification of Noise Parameters, an online identification algorithm for the noise parameters in the EKF is introduced. Then, in section Outlier-Resistant Extended Kalman Filter, an online outlier detection algorithm is presented, and it is embedded into the EKF. This algorithm allows for robust structural identification in the presence of possible outliers. In section Online Bayesian Model Class Selection, a recursive Bayesian model class section method is presented for non-parametric identification problems. 

In this section, a Bayesian probabilistic approach is presented for online estimation of the noise parameters of the process noise and measurement noise. Sectimi ParameterizatiOTi and Bayesian Formulation introduces the parameterization of the noise covariance matrices and the Bayesian formulation. Thereafter, the online identification algorithm is presented in section Online Estimation of Noise Parameters. ... 

The EKF has by far been the most extensively used identification algorithm, for the case of nonlinear systems, over the past 30 years, and has been applied for a number of civil engineering applications, such as structural damage identification, parameter identification of inelastic structures, and so forth. It is based on the propagation of a Gaussian random variable (GRV) through the first-order linearization of the state-space model of the system. Despite... 

Furukawa T, Yagawa G (1997) Inelastic constitutive parameter identification using an evolutionary algorithm with continuous individuals. Int J Numer Methods Eng 40 1071-1090... 

The ambient, shaker, and drop weight data from scenario 8 of the progressive damage test have been employed as benchmark data for system identification methods for operational modal analysis. Peeters and Ventura (2003) compare the modal parameter estimates obtained by seven different research teams in the framework of this benchmark. In addition, new modal parameter estimation techniques have been validated on the benchmark data. The best reported result was obtained by applying a subspace identification algorithm (Reynders and De Roeck 2008) and a maximum likelihood algorithm... 

In the present study, we propose a tuning method for PID controllers and apply the method to control the PBL process in LG chemicals Co. located in Yeochun. In the tuning method proposed in the present work, we first find the approximated process model after each batch by a closed-loop Identification method using operating data and then compute optimum tuning parameters of PID controllers based on GA (Genetic Algorithm) method. 

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