scholarly journals Investigating errors when forecasting processes with uncertain dynamics and observation noise by the self-adjusting brown's zero-order model

2021 ◽  
Vol 6 (9 (114)) ◽  
pp. 47-53
Author(s):  
Boris Pospelov ◽  
Evgenіy Rybka ◽  
Mikhail Samoilov ◽  
Olekcii Krainiukov ◽  
Yurii Kulbachko ◽  
...  

This paper reports a study into the errors of process forecasting under the conditions of uncertainty in the dynamics and observation noise using a self-adjusting Brown's zero-order model. The dynamics test models have been built for predicted processes and observation noises, which make it possible to investigate forecasting errors for the self-adjusting and adaptive models. The test process dynamics were determined in the form of a rectangular video pulse with a fixed unit amplitude, a radio pulse of the harmonic process with an amplitude attenuated exponentially, as well as a video pulse with amplitude increasing exponentially. As a model of observation noise, an additive discrete Gaussian process with zero mean and variable value of the mean square deviation was considered. It was established that for small values of the mean square deviation of observation noise, a self-adjusting model under the conditions of dynamics uncertainty produces a smaller error in the process forecast. For the test jump-like dynamics of the process, the variance of the forecast error was less than 1 %. At the same time, for the adaptive model, with an adaptation parameter from the classical and beyond-the-limit sets, the variance of the error was about 20 % and 5 %, respectively. With significant observation noises, the variance of the error in the forecast of the test process dynamics for the self-adjusting and adaptive models with a parameter from the classical set was in the range from 1 % to 20 %. However, for the adaptive model, with a parameter from the beyond-the-limit set, the variance of the prediction error was close to 100 % for all test models. It was established that with an increase in the mean square deviation of observation noise, there is greater masking of the predicted test process dynamics, leading to an increase in the variance of the forecast error when using a self-adjusting model. This is the price for predicting processes with uncertain dynamics and observation noises.

2018 ◽  
Vol 56 ◽  
pp. 130-135
Author(s):  
M. V. Tserenyuk ◽  
O. M. Tserenyuk

In addition to assessing the absolute performance of animals, the impact of certain technological approaches, breeding influence and other external organized factors on the consolidation of pigs groups on certain grounds should be evaluated. Breeding consolidation is a desirable breeding process that is realized through more motivated consolidation of intra-breeding structural units for maintaining a significant level of intergroup differentiation and variability. If the issue relates to the rearing young animals that are introduced into the herd, this is the most urgent issue that needs to be monitored. The purpose of the research is to determine the consociality of the main signs of reproductive ability of the gilts, which are checked at different rates of artificial insemination of sows of the main herd. The research was carried out at the Shubs`ke farm in the Bogoduhivsky District of Kharkiv Oblast at the pig farm for the pure breeding of the Welsh breed pigs (breeding reproductive status from 2014). In order to evaluate the optimal multiplicity (from single to triple), a gilts with a total of 30 heads was selected. The main indicators of reproductive ability of gilts (multiplicity, weight of nest at birth and excommunication and keeping piglets before weaning on day 28) were evaluated. Recalculation on the weight of the litter at weaning at the weight of the nest at extermination in 60 days was carried out in accordance with the current instruction on the boning of pigs. The results of researches were worked out according to traditional methods by the method of variation statistics. Consolidation of individual indicators of reproductive capacity of gilts was calculated to the total number of evaluated animals. In the previous stage of the research, it was found that the use of multiple insemination of gilts compared to single insemination is positively reflected at the level of their reproductive ability. A decrease in the percentage of non-productive inseminants in animal groups has been established. Triple insemination of gilts allows for 1.14 piglets to be obtained more compared to single insemination of the same pigs (p < 0.01). Also, for three times insemination of gilts, in comparison with single insemination, larger nest for weaning were obtained (by 14.24 kg, converted to 60th day p < 0.01). At the same time, the reduction in the keeping of piglets to weaning for increase frequency of insemination of gilts. According to the multiplicity of gilts, the most consolidated level of symptoms per group was obtained for single insemination. Increasing the multiplicity of insemination negatively affected the consolidation of the multiplicity of the piglets (as for determining the coefficients of phenotypic consolidation due to the mean square deviation, so, and for determining the coefficient of variability). The least consolidated in terms of multiplicity were uterus for double insemination. It should also be noted that there is little difference, in general, on the indicators of the theonotypical consolidation of the multiplicity of piglets between different groups of animals. So this difference between the most contrasting groups was 0.447 points for determining the coefficients due to the mean square deviation and 0.397 points for the determination due to the coefficient of variability, respectively. By weight of the same litters at birth, the most consolidated group was gilts, which was inseminated twice. The least consolidated are trimmed three times, respectively. The difference as a whole, according to the indicators of the theonotype consolidation of the mass of the litter’s piglets at birth, between different groups of pigs was even smaller. The difference between the most contrasting groups was 0.270 points for determining the coefficients due to the mean square deviation and 0.260 points for the determination due to the coefficient of variability, respectively. On the basis of the mass of the litter at weaning, the most consolidated level of symptoms was obtained in the group of gilts for triple insemination. The least consolidated group, respectively, was gilts for single insemination. At the same time, on the basis of the weight of the litter at weaning, the slightest differences were obtained after the consolidation of the signs between different groups of pigs. The difference between the most contrasting groups was 0.173 points for determining the coefficients due to the mean square deviation and 0.248 points for the determination due to the coefficient of variation, respectively. At different rates of insemination of gilts, there are no significant differences between the groups between the groups in terms of the consolidation of signs of reproductive ability. Also, there was no clear effect on increasing the multiplicity of insemination of gilts to the consolidation of their signs of reproductive qualities.


Author(s):  
Valdecir de Godoy Borges ◽  
RJ Lato Sensu

Brownian motion is small particles suspended in a liquid tend to move in pseudorandom or stochastic paths through the liquid, even if the liquid in question is inert. By Einstein's theories for Brownian motion referring to the 1905 works, equilibrium relations and viscous friction, osmotic pressure reaching the diffusion coefficient of Brownian particles. In the fluid medium, we will address the deviation (diffusion equation and basically the relationship between the mean square deviation of the particle position and the fluid temperature, the higher the temperature, the greater the mean square deviation, that is, directly proportional to the constant of the diffusion). The importance of this study is the movement of particles and molecules in the fluid medium, whether these molecules are lipids, proteins, we know that viruses and bacteria are having a certain movement in the organism and its systems, we will tend to study their movement within vessels and between fluids body, with two densities and particular conditions, knowing the likely displacement, we will know therapeutic interventions that are probably more effective. The aim of this work is to demonstrate through mathematical applications the Brownian motion.


2014 ◽  
Vol 8 (1) ◽  
pp. 85-91 ◽  
Author(s):  
Qiang Xu ◽  
Jian-Yun Chen ◽  
Chunfeng Zhao ◽  
Jing Li ◽  
Hongyuan Yue

In this paper, an improved model is presented for analysis of failure probability of the interlayer sliding belts under seismic loads. Firstly, using the theory of the Markov chain, the relation between failure probabilities of specified interlayer sliding belts and elements in this interlayer sliding belt is deduced. Then, the failure function is proposed according to the destructive characteristic of concrete, the pseudo excitation method is utilized in order to obtain the probability distribution of element stresses in specified interlayer sliding belts, and the improved response surface method based on weighted regression is used to calculate the failure probability of elements in specified interlayer sliding belts. Finally, an algorithm is established to calculate the failure probability of the specified interlayer sliding belts. In this paper, the mean value and variance of the tensile strength of elements are changed when interlayer sliding belt is developed. The numerical results show that the conditional failure probability in specified interlayer sliding belts at the head of the dam tends to decrease. However, the tendency of conditional failure probability in the other specified interlayer sliding belts is complicated. And the interlayer sliding belt at head of the concrete gravity dam is the most dangerous. In addition, the tendencies of the mean value and mean square deviation of stresses in different specified interlayer sliding belts are similar. The mean value of stress in different specified interlayer sliding belts tends to decrease but the tendency of mean square deviation changes from decrease to increase. The range of the mean value and the mean square deviation of stress in specified interlayer sliding belts at the heel of the dam is the greatest of all.


2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Alejandro Castañeda-Miranda ◽  
M. de Icaza-Herrera ◽  
Víctor M. Castaño

The temperature readings for all the 365 days and the 24 hours may be fitted through a 3 × 3 matrix (the so-called T-matrix). The mean square deviation between this fit and the actual meteorological measurements is smaller than three degrees Celsius. Four entries of this (nonsymmetric) matrix may be fixed by other means, leaving only five independent components. However, the same method applied to the humidity measurements produces a larger mean square deviation. A strong stochastical connection is found between the T-temperature matrix and the U-humidity matrix. The computer program, in C, may be used to adjust a (2M + 1) × (2m + 1) matrix simply by changing the arguments at the command line and has been tested with m and M ranging from zero to 11 (eleven) (more than 24 readings per day are necessary for larger values of m). The physical meaning of these constants is given only in the case m = M = 1. Our results have also been connected to fundamental cosmological properties: Earth’s orbit, the ecliptic angle, and the latitude of Querétaro (or whatever geographical location is chosen). A separate program calculates the angular position of the Sun as measured in the sky of Querétaro, to determine the length of the day or the mean value of the solar cosine. This work introduces several new variables which happen to be stochastically connected.


1980 ◽  
Vol 102 (1) ◽  
pp. 67-72
Author(s):  
H. M. Behery ◽  
E. A. Vaughn ◽  
M. Lee

This study is mainly directed towards blends of cotton and polyester which are cotton-rich blends. Measurements taken from dyed tracer fibers within the yarn and from physical testing indicate that only yarn count significantly affects several of the migration parameters. Coarser or lower count yarns exhibit slower rates of migration as measured by the mean migration intensity, and also showed a reduced tendency towards migration as measured by the root-mean-square deviation. Yarn count was the most significant parameter affecting yarn quality. Fiber fineness significantly affected thick places, break factors, single-end strengths and elongations. Polyester staple length significantly affected evenness and imperfections. Blend level significantly affected thick places, elongations, neps, and break factors.


2006 ◽  
Vol 15-17 ◽  
pp. 627-632
Author(s):  
Hong Yan

The non-homogeneous metal flow during the extrusion process is well controlled by introducing a reflecting non-equilibrium parameter of metal flow —— the mean-square deviation of velocity ( SDV ) in this paper. The finite deformation elastoplastic finite element method is used to carry out the numerical simulation research on the profile extrusion process with the different extrusion parameters (such as extrusion ratio, frictional factor). The varied laws of the extrusion pressure, SDV and stress-strain fields with the extrusion parameters are obtained. It is a theoretic consideration to optimize the technological parameters in the profile extrusion process.


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