This paper considers the data-based identification of industrial robots using an instrumental variable method that uses off-line estimation of the joint velocities and acceleration signals based only on the measurement of the joint positions. The usual approach to this problem relies on a `tailor-made' prefiltering procedure for estimating the derivatives that depends on good prior knowledge of the system's bandwidth. The paper describes an alternative Integrated Random Walk SMoothing (IRWSM) method that is more robust to deficiencies in such a priori knowledge and exploits an optimal recursive algorithm based on a simple integrated random walk model and a Kalman filter with associated fixed interval smoothing. The resultant IDIM-IV instrumental variable method, using this approach to signal generation, is evaluated by its application to an industrial robot arm and comparison with previously proposed methods.
In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum likelihood and other approach has to be applied. We depart from the H-method of maximum likelihood suggested by Kagan (1976) where the likelihood function is replaced by a function called informant which is an approximation of the likelihood function in some Hilbert space. For this method only some functionals of the distribution are required, such as probability generating function or characteristic function. We adopt this method for the case of discrete stable distributions and in a simulation study show the performance of this method.
The well-known bottleneck of systems pharmacology, i. e., systems biology applied to pharmacology, refers to the model parameters determination from experimentally measured datasets. This paper represents the development of our earlier studies devoted to inverse (ill-posed) problems of model parameters identification. The key feature of this research is the introduction of control (or periodic forcing by an input signal being a drug intake) of the nonlinear model of drug-induced enzyme production in the form of a system of ordinary differential equations. First, we tested the model features under periodic dosing, and subsequently, we provided an innovative method for a parameter estimation based on the periodic dosing response measurement. A numerical example approved the satisfactory behavior of the proposed algorithm.
The parameters estimated from traditional A/Ci curve analysis are dependent upon some underlying assumptions that substomatal CO2 concentration (Ci) equals the chloroplast CO2 concentration (Cc) and the Ci value at which the A/Ci curve switches between Rubisco- and electron transport-limited portions of the curve (Ci-t) is set to a constant. However, the assumptions reduced the accuracy of parameter estimation significantly without taking the influence of Ci-t value and mesophyll conductance (gm) on parameters into account. Based on the analysis of Larix gmelinii's A/Ci curves, it showed the Ci-t value varied significantly, ranging from 24 Pa to 72 Pa and averaging 38 Pa. t-test demonstrated there were significant differences in parameters respectively estimated from A/Ci and A/Cc curve analysis (p<0.01). Compared with the maximum ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate (Vcmax), the maximum electron transport rate (Jmax) and Jmax/Vcmax estimated from A/Cc curve analysis which considers the effects of gm limit and simultaneously fits parameters with the whole A/Cc curve, mean Vcmax estimated from A/Ci curve analysis (Vcmax-Ci) was underestimated by 37.49%; mean Jmax estimated from A/Ci curve analysis (Jmax-Ci) was overestimated by 17.8% and (Jmax-Ci)/(Vcmax-Ci) was overestimated by 24.2%. However, there was a significant linear relationship between Vcmax estimated from A/Ci curve analysis and Vcmax estimated from A/Cc curve analysis, so was it Jmax (p<0.05). and W. Zeng ... [et al.].
The paper presents iterated algorithm for parameter estimation of non-linear regression model. The non-linear model is firstly approximated by a polynomial. Afterwards, parameter estimation based on measured data is taken as the initial value for the proposed iterated algorithm. As the estimation method, the well-known Least Square Estimation (LSE), artificial neural networks (ANN) or Bayesian methodology (BM) can be used. With respect to the knowledge of initial parameters the measured data are transformed to meet best the non-linear regression criteria (orthogonal data projection). The original and transformed data are used in the next step of the designed iterated algorithm to receive better parameter estimation. The iteration is repeated until the algorithm converges into a final result. The proposed methodology can be applied on all non-linear models that could be approximated by a polynomial function. The illustrative examples show the convergence of the designed iterated algorithm.
This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves. The main purpose of semi-linear credibility theory is the estimation of µ0(θ) = E[f0(Xt+1)|θ] (the net premium for a contract with risk parameter θ) by a linear combination of given functions of the observable variables: X ′ = (X1, X2, . . . , Xt). So the estimators mainly considered here are linear combinations of several functions f1, f2, . . . , fn of the observable random variables. The approximation to µ0(θ) based on prescribed approximating functions f1, f2, . . . , fn leads to the optimal non-homogeneous linearized estimator for the semi-linear credibility model. Also we discuss the case when taking fp = f for all p to find the optimal function f. It should be noted that the approximation to µ0(θ) based on a unique optimal approximating function f is always better than the one in the semi-linear credibility model based on prescribed approximating functions: f1, f2, . . . , fn. The usefulness of the latter approximation is that it is easy to apply, since it is sufficient to know estimates for the structure parameters appearing in the credibility factors. Therefore we give some unbiased estimators for the structure parameters. For this purpose we embed the contract in a collective of contracts, all providing independent information on the structure distribution. We close this paper by giving the semi-linear hierarchical model used in the applications chapter.
This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated in a small simulation study.
Knowledge of soil hydraulic and thermal properties is essential for studies involving the combined effects of soil temperature and water input on water flow and redistribution processes under field conditions. The objective of this study was to estimate the parameters characterizing these properties from a transient water flow and heat transport field experiment. Real-time sensors built by the authors were used to monitor soil temperatures at depths of 40, 80, 120, and 160 cm during a 10-hour long ring infiltration experiment. Water temperatures and cumulative infiltration from a single infiltration ring were monitored simultaneously. The soil hydraulic parameters (the saturated water content θ s , empirical shape parameters α and n, and the saturated hydraulic conductivity Ks) and soil thermal conductivity parameters (coefficients b1 , b2 , and b3 in the thermal conductivity function) were estimated from cumulative infiltration and temperature measurements by inversely solving a two-dimensional water flow and heat transport using HYDRUS-2D. Three scenarios with a different, sequentially decreasing number of optimized parameters were considered. In scenario 1, seven parameters (θ s , Ks , α, n, b1 , b2 , and b3) were included in the inverse problem. The results indicated that this scenario does not provide a unique solution. In scenario 2, six parameters (Ks , α, n, b1 , b2 , and b3) were included in the inverse problem. The results showed that this scenario also results in a non-unique solution. Only scenario 3, in which five parameters (α, n, b1 , b2 , and b3) were included in the inverse problem, provided a unique solution. The simulated soil temperatures and cumulative infiltration during the ring infiltration experiment compared reasonably well with their corresponding observed values.
When we apply ecological models in environmental management, we must assess the accuracy of parameter estimation and its impact on model predictions. Parameters estimated by conventional techniques tend to be nonrobust and require excessive computational resources. However, optimization algorithms are highly robust and generally exhibit convergence of parameter estimation by inversion with nonlinear models. They can simultaneously generate a large number of parameter estimates using an entire data set. In this study, we tested four inversion algorithms (simulated annealing, shuffled complex evolution, particle swarm optimization, and the genetic algorithm) to optimize parameters in photosynthetic models depending on different temperatures. We investigated if parameter boundary values and control variables influenced the accuracy and efficiency of the various algorithms and models. We obtained optimal solutions with all of the inversion algorithms tested if the parameter bounds and control variables were constrained properly. However, the efficiency of processing time use varied with the control variables obtained. In addition, we investigated if temperature dependence formalization impacted optimally the parameter estimation process. We found that the model with a peaked temperature response provided the best fit to the data., H. B. Wang, M. G. Ma, Y. M. Xie, X. F. Wang, J. Wang., and Obsahuje bibliografii
Diabetes mellitus (DM) is a disease affecting millions of people worldwide, and its medical care brings an economic wear to patients and public health systems. Many efforts have been made to deal with DM, one of them is the full-automation of insulin delivery. This idea consists in design a closed-loop control system to maintain blood glucose levels (BGL) within normal ranges. Dynamic models of glucose-insulin-carbohydrates play an important role in synthesis of control algorithms, but also in other aspects of DM care, such as testing glucose sensors, or as support systems for health care decisions. Therefore, there are several mathematical models reproducing glycemic dynamics of DM, most of them validated with nominal parameters of standardized patients. Nevertheless, individual patient-oriented models could open the possibility of having closed-loop personalized therapies. This problem can be addressed through the information provided by open-loop therapy based on continuous glucose monitoring and subcutaneous insulin infusion. This paper considers the problem of identifying particular parameters of a compartmental model of glucose-insulin dynamics in DM; the goal is fitting the model response to historical data of a diabetic patient collected during a time period of her/his daily life. At this time, Sorensen model is one of the most complete compartmental models representing the complex dynamics of the glucose-insulin metabolism. This is a system of 19 ordinary differential equations (ODEs), thus the identification of its parameters is a non-easy task. In this contribution, parameter identification was performed via three evolutionary algorithms: differential evolution, ant colony optimization and particle swarm optimization. The obtained results show that evolutionary algorithms are powerful tools to solve problems of parametric identification. Also, a comparative analysis of the three algorithms was realized throw a wilcoxon sign-rank test, in which colony optimization had the better performance. The model obtained with the estimated parameters could be used to in type 1 diabetes mellitus (T1DM) care, such as in the design of full-automation of insulin infusion.