Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors

In order to discuss the application and mode of the forced modulation function in a sensor, the optical fibre emphasis function was established by referring to the geometric method, the tilt factor and the shape factor of the reflecting surface. These were introduced for the first time, and the corresponding mathematical model was established. The method of numerical simulation is systematically studied and multimode optical fibre parameters (including optical fibre of axial spacing, optical fibre core diameter and numerical aperture) are adopted. The reflective surface inclination and shape factors on the RIM–FOS intensity modulation characteristics are studied according to the obtained light quasi-Gaussian distribution model, establishing a general three-intensity modulation function of fibre optic sensor. The results show that the intensity modulation characteristic of specular reflection is obviously better than that of the diffuse reflection surface, and the peak value of the modulation function is five times that of diffuse reflection. The intensity modulation characteristic decreases with increase in the roughness of the reflection surface. The system can not only complete the RIM–FOS characteristic simulation and characteristic testing functions, but can also start-up the test and not be affected by the ambient light interference and power fluctuation of the light source. The test stability is good with high repeatability.

Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function

PurposeGear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.Design/methodology/approachAn approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.FindingsThe comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.Originality/valueThe research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

Parameter Estimation of the Lotka–Volterra Model with Fractional Order Based on the Modulation Function and Its Application

The Lotka–Volterra model is widely applied in various fields, and parameter estimation is important in its application. In this study, the Lotka–Volterra model with universal applicability is established by introducing the fractional order. Modulation function is multiplied by both sides of the Lotka–Volterra model, and the model is converted into linear equations with parameters to be estimated by the fractional integration method. The parameters are obtained by solving the equations. The state of the system is estimated by shifted Chebyshev polynomial. Last, the implementation program of the model is compiled. The concrete implementation method of the improved model is proposed by an example in this study.

Mathematical modeling of the correlation function and the energy spectra of the noise modulation function

Рассмотрены и проанализированы вопросы, связанные с математическим моделированием корреляционных функций и энергетических спектров функции помеховой модуляции. Показано, что при воздействии на сигнал узкополосной мультипликативной помехи в энергетическом спектре функции помеховой модуляции присутствует дискретная составляющая, мощность которой зависит от глубины фазовых искажений. При импульсно-флуктуационной модулирующей помехе с детерминированным тактовым интервалом энергетический спектр функции помеховой модуляции представляет собой сумму непрерывной и дискретной частей. The issues related to mathematical modeling of correlation functions and energy spectra of the noise modulation function are considered and analyzed. It is shown that when a signal is affected by a narrow-band multiplicative interference, a discrete component is present in the energy spectrum of the interference modulation function, the power of which depends on the depth of the phase distortion. In the case of pulse-fluctuating modulating interference with a deterministic clock interval, the energy spectrum of the interference modulation function is the sum of the continuous and discrete parts.

Analysis of the effect of fast and slow multiplicative noise on the distortion of the radiation pattern of the «array-receiver» system.

The effect of fast and slow multiplicative noise on the distortion of the beam pattern of the «array-receiver» system in the conditions of the smoothing effect of the receiver and taking into account the time of relative lag from the grating elements was analyzed. Expressions are obtained for instantaneous beam patterns of the «array-receiver» system in the absence and presence of multiplicative noise. It is shown that in the case of action of multiplicative noise the beam pattern of the «array-receiver» system is obtained by averaging the instantaneous pattern on the grating correctness at a time interval equal to the signal duration. Influence of periodic multiplicative noise on distortion of beam pattern of system «array-receiver» is investigted. It is shown that for all signals except frequency-modulated, the beam pattern expression is maximized at the time t0=0. It is also shown that the beam pattern distortion of the «array-receiver» system when exposed to periodic multiplicative noise is less than for the separately considered phased antenna array. The degree of reduction of distortion from smoothing action of matched receiver filter is determined; and the distortion is less, the greater the ratio of the spectrum width of the noise modulation function to the signal spectrum width. Analysis of the influence of fluctuation multiplicative noise on the distortion of beam pattern of «array-receiver» system for the case of matching with signal of receiver filter is performed. The power-average beam pattern of the «array-receiver» system is determined through the energy spectrum of the noise modulation function. It is noted that multiplicative noise, all other things being equal, has less effect on the beam-receiver pattern of the system when using broadband pulse signals without intra-pulse modulation and at the same time resolution in range. It is noted that in case of deep phase distortions for gratings with reversible phases, the distortion of the beam pattern of the «array-receiver» system caused by multiplicative noise is significantly more than those distortions associated with the extremity of the signal spectrum width. The newly smoothing effect of the receiver reduces the expansion of the beam lobe caused by multiplicative noise. An expression is obtained for the average power of the beam pattern of the «array-receiver» system with normally distributed phase distortions of the signal. The effect of the signal duration on beam distortions caused by multiplicative noise was quantified.

The Grammatical Incorporation of Demonstratives in an Emerging Tactile Language

In this article, we analyze the grammatical incorporation of demonstratives in a tactile language, emerging in communities of DeafBlind signers in the US who communicate via reciprocal, tactile channels—a practice known as “protactile.” In the first part of the paper, we report on a synchronic analysis of recent data, identifying four types of “taps,” which have taken on different functions in protacitle language and communication. In the second part of the paper, we report on a diachronic analysis of data collected over the past 8 years. This analysis reveals the emergence of a new kind of “propriotactic” tap, which has been co-opted by the emerging phonological system of protactile language. We link the emergence of this unit to both demonstrative taps, and backchanneling taps, both of which emerged earlier. We show how these forms are all undergirded by an attention-modulation function, more or less backgrounded, and operating across different semiotic systems. In doing so, we contribute not only to what is known about demonstratives in tactile languages, but also to what is known about the role of demonstratives in the emergence of new languages.

CHANGES IN SOLAR ACTIVITY DURING THE WOLF MINIMUM—NEW INSIGHTS FROM A HIGH-RESOLUTION 14C RECORD BASED ON DANISH OAK

ABSTRACT We present a new biennial record of radiocarbon (14C) measured in Danish oak. The new record covers the years 1251–1378 CE, thereby spanning the Grand Solar Minimum known as the Wolf Minimum. Two oak samples from every other year were measured at the AMS facility at Aarhus University (Denmark), resulting in an average precision of 1.4‰ for the record. Spectral analysis of the new record revealed two peaks at 27 and 9.1 years, which could indicate the Hale cycle was lengthened and the Schwabe cycle shortened during the Wolf Minimum, but it is also possible that the amplitude of the Schwabe cycle was too small to be accurately identified with the acquired precision of this record. The record was bandpass filtered to investigate the variability of the amplitude in different bands, which showed a dampening of the amplitude during the second half of the Wolf Minimum in bands centered on the Schwabe and the Hale cycle, respectively. A reconstruction of the solar modulation function, Φ, also showed a periodicity of ca. 9 years, and indicated that the Wolf Minimum was preceeded by one cycle of decreased solar activity.