Random Functions

Pugachev, V.S.

doi:10.1016/b978-0-08-010421-8.50014-x

Cited by 21 publications

(10 citation statements)

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“…For ease of comparison of results for the harmonic and random vibrations, let us take the same data as in [8] and present the results obtained in [8] for the harmonic excitation in the linear approximation. Let…”

Section: Numerical Data and Results In The Case Of Harmonic Excitationmentioning

confidence: 99%

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Vibrations of a floating beam on marine waves

Товстик

2015

Vestnik St.Petersb. Univ.Math.

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Small vertical vibrations of a horizontal floating towed beam on marine waves are consid ered. The beam bending stiffness, attached mass of water, and water resistance forces are taken into account. The theory of small gravitational waves is adopted in the wave action description. It is assumed that the water motion is plane harmonic or stationary random. The directions of propagation and towing of beams coincide [11, Fig. 6].

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Section: Numerical Data and Results In The Case Of Harmonic Excitationmentioning

confidence: 99%

“…Suppose that for a fixed x 0 the function ξ 0 (x 0 , t) is a stationary random process with spectral density s ξ (ω). Let us write its integral canonical decomposition [8] with the integrand of the form (2.5),…”

Section: Mathematical Modelmentioning

confidence: 99%

Vibrations of a floating beam on marine waves

Товстик

2015

Vestnik St.Petersb. Univ.Math.

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“…Thereupon, when forming realizable in practice algorithms of the forecasting, different simplifications and limitations on the properties of a random sequence are used. For example, a number of suboptimal nonlinear extrapolation methods with a limited order of a stochastic relation on the basis of approximation of a posteriori density of probabilities of an estimated vector by orthogonal Hermite polynomial expansion or in the form of the Edgeworth series is offered by Pugachev (1965). The solution to the non-stationary Kolmogorov equation (in particular, the case of the Stratanovich differential equation to describe the Markovian processes) is obtained provided that a drift coefficient is a linear function of condition, and the diffusion coefficient is equal to constant.…”

Section: Methodsmentioning

confidence: 99%

Method of individual forecasting of sow reproductive performance on the basis of a non-linear canonical model of a random sequence

et al. 2020

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Improvement of sow reproductive performance is a key factor determining the efficiency of the pig production cycle and profitability of pork production. This article presents the solution of an important scientific and practical problem of individual forecasting of sow reproduction . The population used for the present study is from a pig farm managed by the Limited Liability Company (LLC) ‘Tavriys’kisvyni’ located in Skadovsky district (Kherson region, Ukraine). The experimental materials used for this study consisted of 100 inds. of productive parent sows of the Large White breed.The litter size traits – the total number of piglets born (TNB), number of piglets born alive (NBA) and number of weaned piglets (NW) – were monitored in the first eight parities over an eleven year period (2007–2017). The method of the forecasting of sow litter size is developed based on the non-linear canonical model of the random sequence of a litter size change. The proposed method allows us to take maximum account of stochastic peculiarities of sow reproductive performance and does not impose any restrictions on the random sequence of a litter size change (linearity, stationarity, Markov property, monotony, etc.). The block diagram of the algorithm presented in this work reflects the peculiarities of calculation of the parameters of a predictive model. The expression for the calculation of an extrapolation error allows us to estimate the necessary volume of a priori and a posteriori information for achieving the required quality of solving the forecasting problem. The results of the numerical experiment confirmed the high accuracy of the proposed method of forecasting of sow reproduction. The method offered by us almost doubles the accuracy of forecasting of sow litter size compared to the use of the Wiener and Kalman methods. Thus, average forecast error decreases across the range of features TNB (1.71), NBA (1.68) and NW (1.25 piglets). Apparently, this may reflect a higher level of manifestation of the genetically determined level of individual sow fertility at the moment of piglet weaning. The higher adequacy of the developed mathematical model with regard to NW can be also due to the fact that the relations between sow litter size in different farrowings primarily have a non-linear character, which is taken into maximum account in our offered model. Given non-linearity, on the other hand, turns out to be a significant factor determining a lower estimation of the repeatability value for NW compared to the estimations for TNB and NBA. The use of the developed method will help to improve the efficiency of pig farming.

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“…Despite the irregular nature of external loads with correlation functions of type (6), under certain operating conditions of c~ the loads are amplified in the drive.…”

Section: T = Ti + T~ (9-4)mentioning

confidence: 99%

“…If ct >>15, the load vibrations will be very irregular, and the correlation function can be simplified (6). In coal-and rock-cutting with bits it has been shown that usually c~/15 ~.…”

Section: T = Ti + T~ (9-4)mentioning

confidence: 99%

Theoretical principles of load formation in the drive mechanisms of mining machinery

Dokukin

Krasnikov

1966

Soviet Mining Science

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The external load on a mining machine, determined by the forces of resistance, is one of the principal conditions for establishing the main parameters of the machine, i.e., the strengths of its elements and the operating routine (depth of cut, speed of cut, width of web, etc.).As shown in [1], during operation the initial external loads acting on the cutting tool are transformed in the various elements of the transmission according to definite laws. The loads on these elements can thus be either greater or less than the initial external loads.The type and magnitude O f the load on any element of the drive (in the electric motor, on the transmission elements, etc.) can be determined if we know the external forces and dynamic (operative) characteristics of the drive. In this case the load on any element in the drive can be found from the symbolic expressionwhere A t is the "system operator," which indicates which operation must be performed on the external load function x(t) i so as to obtain the load acting in the i-th element of the drive.It is assumed here that we know the external resistance forces and that these are given as functions of time.The magnitudes and types of the loads in the drive elements can thus be affected by changes in the dynamic parameters of the machine and also in the operating conditions corresponding to various external loads.In this connection the following problems may arise in the construction of modern high-productivity mining machines with high reliability indexes: a)for the most representative characteristics of the external load, to choose optimal parameters for the drive so as to obtain a permissible level of dynamic loading on the elements or on the weakest link of the drive, together with the required level of reliability; b)given the permitted level of dynamic loading of the drive, to choose the operating conditions so that they shall correspond to the best technical indices (productivity, coal grade, power capacity, etc.) for the given properties of the rock in the given conditions; c) in the construction of automatic machines, to arrange that the power expended by the motor is constant, and to introduce control corrections for the dynamic loading of the drive which shall enable the equipment to operate with high reliability in fulfilling its main technological requirements.Owing to the effect of various random factors which are decisive in the process of forming the resistance of the rock to the cutting tool of a cutter-loader, digger, etc., a complete analytical solution of these problems is possible using the theory of random functions, with the use of electronic computers.In connection with experiments on new mining techniques, various oscillograms are used by researchers to characterize the formation of the external loads on the cutting tools. 37

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Random Functions

Cited by 21 publications

References 0 publications

Vibrations of a floating beam on marine waves

Vibrations of a floating beam on marine waves

Method of individual forecasting of sow reproductive performance on the basis of a non-linear canonical model of a random sequence

Theoretical principles of load formation in the drive mechanisms of mining machinery

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