Estimation of Parameters of PTRC SRGM using Non-informative Priors

Reliability is an essentially important characteristic of software. The reliability of software has been assessed by considering Poisson Type occurrence of software failures and the failure intensity of one parameter say (η_1 ) Rayleigh class. Here, it is assumed that the software contains fixed number of inherent faults say (η_0 ). The scale parameter of Rayleigh density (η_1 ) and fixed number of inherent faults contained in software are the parameters of interest. The failure intensity and mean failure function of this Poisson Type Rayleigh Class (PTRC) Software Reliability Growth Model (SRGM) have been studied. The estimates of above parameters can be obtained by using maximum likelihood method. Bayesian technique has been used to about estimates of η_0 and η_1 if prior knowledge about these parameters is available. The prior knowledge about these parameters is considered in the form of non- informative priors for both the parameters. The proposed Bayes estimators are compared with their corresponding maximum likelihood estimators on the basis of risk efficiencies under squared error loss. The Monte Carlo simulation technique is used for calculating risk efficiencies. It is seen that both the proposed Bayes estimators can be preferred over corresponding MLEs for the proper choice of the values of execution time.

Estimation of parameters characterizing a steady-state synthesis process with nonlinear microorganism growth kinetics

The paper describes a theoretical basis developed for estimating the parameters of a steady-state biotechnological process characterized by nonlinear microorganism growth kinetics. This study aimed to obtain a common methodological basis for estimating input parameters that determine actual technology implementation, taking into account all possible restrictions on the concentration of incoming substrate Sf (g/l) and dilution rate D (h-1 ). The theory development was based on a mathematical model describing one of the most common processes of lactic acid production. This mathematical model includes three mass balance equations (for biomass, substrate, and product), as well as an equation of microorganism growth kinetics. The study established relations for calculating the ultimate value of the dilution rate D ult at a given Sf , relations for the maximum and minimum values of Sf , as well as Sf and D providing the maximum productivity value QP, g/(l·h), where QP = PD (P – product concentration, g/l). These relations were designed to calculate the parameters of possible process implementation for two options at the same value of QP: two values of D calculated for a given Sf and two values of Sf calculated for a given D. A numerical experiment is described using the constants of the mathematical model confirmed by foreign studies. This numerical experiment is illustrated using an Sf-D dependence pattern determining an acceptable value range for Sf and D, with the separate calculation of parameters according to Sf sections. For each of these sections, calculation formulas are provided. It is concluded that the developed theoretical basis is sufficiently general in nature to be applied to biotechnological processes that involve other kinetic relations, as well as microorganism strains creating by-products and using raw materials that are employed to reproduce the substrate in the process of synthesis.

A Proposal for Parameter-Free Surrogate Building Algorithm Using Artificial Neural Networks

Surrogate models, capable of emulating the robust first principle based models, facilitate the online implementation of computationally expensive industrial process optimization. However, the heuristic estimation of parameters governing the surrogate building often renders them erroneous or under-trained. Current work aims at presenting a novel parameter free surrogate building approach, specifically focusing on Artificial Neural Networks. The proposed algorithm implements Sobol sampling plan and intelligently designs the configuration of network with simultaneous estimation of optimal transfer function and training sample size to prevent overfitting and enabling maximum prediction accuracy. A novel Sample Size Determination algorithm based on a potential concept of hypercube sampling technique adds to the speed of surrogate building algorithm, thereby assuring faster convergence. Surrogates models for a highly nonlinear industrial sintering process constructed using the novel algorithm resulted in 7 times faster optimization.

Identification of Dynamical Systems Through the Structure of Auto-regression With Exogenous Variable by Decreasing Gradient and Least Squares

In this article was made the identification of dynamic systems of first and second order more common in electronics such as low and high pass filters of the first order, pass-band filter and direct current motor through the structure of auto-regression with exogenous variable. The proposed dynamical systems are initially modeled by a continuous-time transfer function using physical laws. Subsequently, a step entry signal was applied and the data for the identification process was recorded in discrete time. The estimation of parameters was performed with the method of decreasing gradient and least squares. It was obtained as a result that the least squares method could not find a model for the first-order high-pass filter, but the decreasing grade method allowed to model all the proposed systems.

Distributed Super Nested Arrays: Reduce the Mutual Coupling between Array Antennas

In array, mutual coupling between the antennas is inevitable, which has an adverse effect on the estimation of parameters. To reduce the mutual coupling between the antennas of distributed nested arrays, this paper proposes a new array called the distributed super nested arrays, which have the good characteristics of the distributed nested arrays and can reduce the mutual coupling between the antennas. Then, an improved multiscale estimating signal parameter via rotational invariance techniques (ESPRIT) algorithm is presented for the distributed super nested arrays to improve the accuracy of direction-of-arrival (DOA) estimation. Next, we analyze the limitations of the spatial smoothing algorithm used by the distributed super nested arrays when there are multiple-source signals and the influence of the baseline length of distributed super nested arrays on the accuracy of DOA estimation. The simulation results show that the distributed super nested arrays can effectively reduce the mutual coupling between the array antennas, improve the DOA estimation performance, and significantly increase the number of detectable source signals.

Synthesis of the optimal algorithm and structure of contactless optical device for estimating the parameters of statistically uneven surfaces

The production of parts and (or) finished products in electronics, mechanical engineering and other industries is inextricably linked with the control of the accuracy and cleanliness of the processed surfaces. Currently existing meters of parameters of statistically uneven surfaces, both contact and non-contact have some disadvantages, as well as limitations due to methods and design features of measurement. Speckle interferometric methods for measuring parameters of statistically uneven surfaces make it possible to get away from some disadvantages inherent in existing methods and measurements. The use of methods of statistical radio engineering, methods of optimization of statistical solutions and estimates of parameters of predictive distributions for optimal radio engineering system synthesis is promising for the analysis and processing optical-electronic coherent laser space-time signals (speckle images) form with the laser radiation scattered by statistically uneven surfaces. This work synthesizes the optimal algorithm and structure for analyzing the parameters of statistically-temporal surfaces based on spatio-temporal processing of optical speckle interference signals and images using modern methods of optimal synthesis of radio engineering and coherent optoelectronic systems. In this work, an algorithm for processing optical signals scattered by statistically uneven surfaces is synthesized and investigated for problems of optimal estimation of parameters and statistical characteristics of statistically uneven surfaces. A block diagram of the optical contactless device for evaluating the parameters of statistically uneven surfaces is proposed. The limiting errors of estimation parameters of statistically uneven surfaces and the optimal installation angles of the emitters and the optical receiver are investigated. Equations are obtained for estimating the root-mean-square height of the ridges and the correlation radius of small-scale statistically uneven surfaces in the approximation of small perturbations. The proposed method for evaluating the parameters of statistically uneven surfaces allows to increase the accuracy of measurements, to conduct a non-contact assessment of the parameters - even statistically uneven surfaces that have geometric surface irregularities or located in hard-to-reach places, for example, grooves, holes, as well as products of cylindrical, spherical and other shapes.

Mathematical Analysis of the TB Model with Treatment via Caputo-Type Fractional Derivative

In this study, we formulate a noninteger-order mathematical model via the Caputo operator for the transmission dynamics of the bacterial disease tuberculosis (TB) in Khyber Pakhtunkhwa (KP), Pakistan. The number of confirmed cases from 2002 to 2017 is considered as incidence data for the estimation of parameters or to parameterize the model and analysis. The positivity and boundedness of the model solution are derived. For the dynamics of the tuberculosis model, we find the equilibrium points and the basic reproduction number. The proposed model is locally and globally stable at disease-free equilibrium, if the reproduction number ℛ 0 < 1 . Furthermore, to examine the behavior of the various parameters and different values of fractional-order derivative graphically, the most common iterative scheme based on fundamental theorem and Lagrange interpolation polynomial is implemented. From the numerical result, it is observed that the contact rate and treatment rate have a great impact on curtailing the tuberculosis disease. Furthermore, proper treatment is a key factor in reducing the TB transmission and prevalence. Also, the results are more precise for lower fractional order. The results from various numerical plots show that the fractional model gives more insights into the disease dynamics and on how to curtail the disease spread.