PRELIMINARY DESIGN OF ANALOG DISCRETE UNIFORM NOISE GENERATOR

The paper presents the basic idea of ​​the construction of an analog discrete uniform noise generator. The source of noise is a carbon resistor, the noise is linearly strongly amplified and limited to around zero. The probability density function (PDF) of the carbon resistor thermal noise in that region is square. By narrowing the symmetric allowable gap (interval) around zero, PDF of the noise approaches a uniform distribution. The factor of deviation from the uniform distribution is correctly and precisely defined. This quantity has been shown to be practically negligible. In addition, the paper discusses the application of the proposed ditheter noise, both in the two-bit and in the multi-bit stochastic digital measurement method (SDMM). It has been shown that noise is more suitable for application in multi-bit SDMM, because it is less sensitive to deviations from the uniform distribution. Commercially available track-and-hold circuits provide at least an order of magnitude wider bandwidth of the described generator compared to the standard solution that uses numerical random number generator and a corresponding D/A converter. However, the realization of such a generator requires hard engineering work, and therefore goes beyond the scope of this paper.

Hypothetical Control of Fatal Quarrel Variability

Wars, terrorist attacks, as well as natural catastrophes typically result in a large number of casualties, whose distributions have been shown to belong to the class of Pareto’s inverse power laws (IPLs). The number of deaths resulting from terrorist attacks are herein fit by a double Pareto probability density function (PDF). We use the fractional probability calculus to frame our arguments and to parameterize a hypothetical control process to temper a Lévy process through a collective-induced potential. Thus, the PDF is shown to be a consequence of the complexity of the underlying social network. The analytic steady-state solution to the fractional Fokker-Planck equation (FFPE) is fit to a forty-year fatal quarrel (FQ) dataset.

Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts

The repair rate is a very important parameter for system maintainability and can be defined as a frequency of successfully performed repair actions on a failed component per unit of time. This paper analyzes the integral characteristics of a stochastic repair rate for corresponding values of availability in a system operating under maintenance contracts. The probability density function (PDF) of the repair rate has been studied extensively and it was concluded that it is not a symmetric function so its mean value does not correspond to its maximum. Based on that, the equation for the envelope line of the PDF maximums of the repair rate has been provided. Namely, instead of repair rate PDF equations, we can use envelope line parameters for certain calculations, which are expressed in a simpler mathematical form. That will reduce time required for calculations and prediction and enhance reactions in failure events. Further, for the analytical and numerical evaluation of a system performance, the annual repair rate PDFs are analyzed, such as particular solutions of corresponding differential equation, while the existence of a singular solution is considered and analyzed under different conditions. Moreover, we derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize the behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed.

Comparison between Accelerated Tests and Natural Exposures for Organic Coating Protective Systems Based on EIS Parameters

The equivalent relationship between accelerated tests and natural exposures has been extensively studied over the past several years to estimate the service life of a barrier organic coating protective system. Herein, based on the probability density function (PDF) theory, a mathematical expression that describes the limit value of the low-frequency impedance (RL) of a barrier organic coating protective system as a function of the elapsed time is proposed in form of Arrhenius formula under certain assumptions, and the degradation coefficient is defined. This expression was consistent with the results of the accelerated tests. The equivalent relationship between accelerated tests and natural exposures, established based on the equivalence principle, was utilized to predict the service life of the coated Al alloy in an ocean atmospheric environment.

Error Uncertainty Analysis in Planar Closed-Loop Structure with Joint Clearances

For planar closed-loop structures with clearances, the angular and positional error uncertainties are studied. By using the vector translation method and geometric method, the boundaries of the errors are analyzed. The joint clearance is considered as being distributed uniformly in a circle area. A virtual link projection method is proposed to deal with the clearance affected length error probability density function (PDF) for open-loop links. The error relationship between open loop and closed loop is established. The open-loop length PDF and the closed-loop angular error PDF both approach being Gaussian distribution if there are many clearances. The angular propagation error of multi-loop structures is also investigated by using convolution. The positional errors of single and multiple loops are both discussed as joint distribution functions. Monte Carlo simulations are conducted to verify the proposed methods.

Simultaneous Joint Lower and Upper record values Probability Laws for Absolutely Continuous or Discrete Data

This paper investigates the probability density function (pdf) of the \((2n-1)\)-vector \((n\geq 1)\) of both lower and upper record values for a sequence of independent random variables with common \textit{pdf} \(f\) defined on the same probability space, provided that the lower and upper record times are finite up to \(n\). A lot is known about the lower or the upper record values when they are studied separately. When put together, the challenges are far complicated. The rare results in the literature still present some flaws. This paper begins a new and complete investigation with a few number of records: (n=2\) and \(n=3\). Lessons from these simple cases will allow addressing the general formulation of simultaneous joint lower-upper records.

Product of κ-μ and α-μ Distributions and Their Composite Fading Distributions

In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-μ fading distribution and α-μ fading distribution is considered. The novel exact series formulas for the product of two i.n.i.d. fading distributions κ-μ and α-μ are derived instead of Fox H-function to solve the problem that Fox H function with multiple RVs cannot be implemented in professional mathematical software packages as MATHEMATICA and MAPLE. Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) are deduced to represent provided product expressions and generalized composite multipath shadowing models. At last, these analytical results are validated with Monte Carlo simulations, it shows that for provided κ-μ/α-μ model nonlinear parameter has more important influence than multipath component in PDF and CDF when the ratio between the total power of the dominant components and<br>the total power of the scattered waves is same. <br>

Product of κ-μ and α-μ Distributions and Their Composite Fading Distributions

In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-μ fading distribution and α-μ fading distribution is considered. The novel exact series formulas for the product of two i.n.i.d. fading distributions κ-μ and α-μ are derived instead of Fox H-function to solve the problem that Fox H function with multiple RVs cannot be implemented in professional mathematical software packages as MATHEMATICA and MAPLE. Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) are deduced to represent provided product expressions and generalized composite multipath shadowing models. At last, these analytical results are validated with Monte Carlo simulations, it shows that for provided κ-μ/α-μ model nonlinear parameter has more important influence than multipath component in PDF and CDF when the ratio between the total power of the dominant components and<br>the total power of the scattered waves is same. <br>

Variational Sparse Bayesian Learning for Estimation of Gaussian Mixture Distributed Wireless Channels

In this paper, variational sparse Bayesian learning is utilized to estimate the multipath parameters for wireless channels. Due to its flexibility to fit any probability density function (PDF), the Gaussian mixture model (GMM) is introduced to represent the complicated fading phenomena in various communication scenarios. First, the expectation-maximization (EM) algorithm is applied to the parameter initialization. Then, the variational update scheme is proposed and implemented for the channel parameters’ posterior PDF approximation. Finally, in order to prevent the derived channel model from overfitting, an effective pruning criterion is designed to eliminate the virtual multipath components. The numerical results show that the proposed method outperforms the variational Bayesian scheme with Gaussian prior in terms of root mean squared error (RMSE) and selection accuracy of model order.

Robot Manipulator Control with Inverse Kinematics PD-Pseudoinverse Jacobian and Forward Kinematics Denavit Hartenberg

This paper presents the development of vision-based robotic arm manipulator control by applying Proportional Derivative-Pseudoinverse Jacobian (PD-PIJ) kinematics and Denavit Hartenberg forward kinematics. The task of sorting objects based on color is carried out to observe error propagation in the implementation of manipulator on real system. The objects image captured by the digital camera were processed based on HSV-color model and the centroid coordinate of each object detected were calculated. These coordinates are end effector position target to pick each object and were placed to the right position based on its color. Based on the end effector position target, PD-PIJ inverse kinematics method was used to determine the right angle of each joint of manipulator links. The angles found by PD-PIJ is the input of DH forward kinematics. The process was repeated until the square end effector reached the target. The experiment of model and implementation to actual manipulator were analyzed using Probability Density Function (PDF) and Weibull Probability Distribution. The result shows that the manipulator navigation system had a good performance. The real implementation of color sorting task on manipulator shows the probability of success rate cm is 94.46% for euclidian distance error less than 1.2 cm.