Design of Aerodynamic Ball Levitation Laboratory Plant

This paper presents the development of a new Aerodynamic Ball Levitation Laboratory Plant at the Center of Modern Control Techniques and Industrial Informatics (CMCT&II). The entire design process of the plant is described, including the component selection process, the physical construction of the plant, the design of a printed circuit board (PCB) powered by a microcontroller, and the implementation of its firmware. A parametric mathematical model of the laboratory plant is created, whose parameters are then estimated using a nonlinear least-squares method based on acquired experimental data. The Kalman filter and the optimal state-space feedback control are designed based on the obtained mathematical model. The designed controller is then validated using the physical plant.

Velocity Estimation via Wheel Circumference Identification

The article presents a velocity estimation algorithm through the wheel encoder-based odometry and wheel circumference identification. The motivation of the paper is that a proper model can improve the motion estimation in poor sensor performance cases. For example, when the GNSS signals are unavailable, or when the vision-based methods are incorrect due to the insufficient number of features, furthermore, when the IMU-based method fails due to the lack of frequent accelerations. In these situations, the wheel encoders can be an appropriate choice for state estimation. However, this type of estimation suffers from parameter uncertainty. In the paper, a wheel circumference identification is proposed to improve the velocity estimation. The algorithm listens to the incoming sensor measurements and estimates the wheel circumferences recursively with a nonlinear least squares method. The experimental results demonstrate that with the application of the identified parameters in the wheel odometry model, accurate velocity estimation can be obtained with high frequency. Thus, the presented algorithm can improve the motion estimation in the driver assistant functions of autonomous vehicles.

Statistical modeling of the novel COVID-19 epidemic in Iraq

Objectives This study aimed to apply three of the most important nonlinear growth models (Gompertz, Richards, and Weibull) to study the daily cumulative number of COVID-19 cases in Iraq during the period from 13th of March, 2020 to 22nd of July, 2020. Methods Using the nonlinear least squares method, the three growth models were estimated in addition to calculating some related measures in this study using the “nonlinear regression” tool available in Minitab-17, and the initial values of the parameters were deduced from the transformation to the simple linear regression equation. Comparison of these models was made using some statistics (F-test, AIC, BIC, AICc and WIC). Results The results indicate that the Weibull model is the best adequate model for studying the cumulative daily number of COVID-19 cases in Iraq according to some criteria such as having the highest F and lowest values for RMSE, bias, MAE, AIC, BIC, AICc and WIC with no any violations of the assumptions for the model’s residuals (independent, normal distribution and homogeneity variance). The overall model test and tests of the estimated parameters showed that the Weibull model was statistically significant for describing the study data. Conclusions From the Weibull model predictions, the number of cumulative confirmed cases of novel coronavirus in Iraq will increase by a range of 101,396 (95% PI: 99,989 to 102,923) to 114,907 (95% PI: 112,251 to 117,566) in the next 24 days (23rd of July to 15th of August 15, 2020). From the inflection points in the Weibull curve, the peak date when the growth rate will be maximum, is 7th of July, 2020, and at this time the daily cumulative cases become 67,338. Using the nonlinear least squares method, the models were estimated and some related measures were calculated in this study using the “nonlinear regression” tool available in Minitab-17, and the initial values of the parameters were obtained from the transformation to the simple linear regression model.

Identification and assessment of regression models of the learning curve for automotive manufacturing

The problem of identification and assessment of the reliability of regression models of the learning curve for the automotive industry is considered. For regression analysis, four learning curve models of a given type are used: Wright's, Stanford-B, Deyong's, and exponential. The parameters of the learning curve models are determined using a nonlinear least squares method. The estimation of the significance and reliability of the regression models is carried out. It is shown that the models of learning curves in the automotive industry are well approximated by the Stanford-B power function.

Circadian Profile of Salivary Melatonin Secretion in Hypoxic Ischemic Encephalopathy

Purpose. In the present study, the salivary melatonin secretion in the hypoxic ischemic encephalopathy (HIE) children was measured. The logit model was fitted to the data to obtain the salivary dim light melatonin onsets (DLMOs), and the results were compared with the values estimated from the classic threshold method with a linear interpolation and those previously published for the blood measurements. Materials and Methods. 9 patients suffering from HIE aged from 65 to 80 months were included in the study. The melatonin levels were assessed by a radioimmunoassay (RIA). The diurnal melatonin secretion was estimated using a nonlinear least squares method. Student’s t-test and the Mann–Whitney U test were used for the comparisons of the obtained parameters. Results. The circadian profiles of the melatonin secretion for both calculation methods do not differ statistically. The DLMO parameters obtained in the blood and saliva samples in children with hypoxic ischemic encephalopathy were similar.

Prediksi Akhir Pandemi COVID-19 di Indonesia dengan Simulasi Berbasis Model Pertumbuhan Parametrik

This research aims to predict the end of the COVID-19 pandemic in Indonesia based on parametric growth models. The models are chosen by considering their fitness with the data of Taiwan which is believed to have passed over the peak of the pandemic and have gone through all phases in the growth curves. The models are parameterized using the nonlinear least squares method. The deviation and confidence interval of each parameter is estimated using the k-fold cross-validation and the bootstrap techniques. Using the total cases per million population data from March 2 to June 18, 2020, it was found that two growth models fit the data, i.e. logistic and modified Gompertz, where the latter performs better. Using the information about the deviation of each model parameter, a simulation model is developed to predict the time at which the total cases curve starts to flatten, which is an indication of the end of the pandemic. It was found with 95% confidence level that based on the modified Gompertz model the pandemic will end somewhere between March 9 – September 7, 2021 with total cases per million of 206 - 555. Meanwhile, based on the logistic growth model, the end of the pandemic is between August 28 – September 23, 2020 with total cases per million of 180 - 375. This model can be extended by making comparative scenario with Taiwan based on measures that represent the quality of the pandemic mitigation such as test ratio and the intensity of social restriction.

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems

Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, which renders the inference of parameter values for complex dynamic models challenging. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms. In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.

Linear least squares method in nonlinear parametric inverse problems

A generalization of the linear least squares method to a wide class of parametric nonlinear inverse problems is presented. The approach is based on the consideration of the operator equations, with the selected function of parameters as the solution. The generalization is based on the two mandatory conditions: the operator equations are linear for the estimated parameters and the operators have discrete approximations. Not requiring use of iterations, this approach is well suited for hardware implementation and also for constructing the first approximation for the nonlinear least squares method. The examples of parametric problems, including the problem of estimation of parameters of some higher transcendental functions, are presented.