Nonstationary Oscillations Research Articles

An ensemble multi-scale framework for long-term forecasting of air quality.

The significance of accurate long-term forecasting of air quality for a long-term policy decision for controlling air pollution and for evaluating its impacts on human health has attracted greater attention recently. This paper proposes an ensemble multi-scale framework to refine the previous version with ensemble empirical mode decomposition (EMD) and nonstationary oscillation resampling (NSOR) for long-term forecasting. Within the proposed ensemble multi-scale framework, we on one hand apply modified EMD to produce more regular and stable EMD components, allowing the long-range oscillation characteristics of the original time series to be better captured. On the other hand, we provide an ensemble mechanism to alleviate the error propagation problem in forecasts caused by iterative implementation of NSOR at all lead times and name it improved NSOR. Application of the proposed multi-scale framework to long-term forecasting of the daily PM2.5 at 14 monitoring stations in Hong Kong demonstrates that it can effectively capture the long-term variation in air pollution processes and significantly increase the forecasting performance. Specifically, the framework can, respectively, reduce the average root-mean-square error and the mean absolute error over all 14 stations by 8.4% and 9.2% for a lead time of 100 days, compared to previous studies. Additionally, better robustness can be obtained by the proposed ensemble framework for 180-day and 365-day long-term forecasting scenarios. It should be emphasized that the proposed ensemble multi-scale framework is a feasible framework, which is applicable for long-term time series forecasting in general.

Application of singular spectrum analysis to nonstationary time series in flow-induced vibrations of a circular cylinder

In numerical simulations of flow-induced vibrations (FIV) of a circular cylinder, abundant time series data are available, including cylinder displacement and acting forces. Singular spectrum analysis (SSA) is employed to deal with nonstationary multi-component time series produced in two FIV cases with proper interpretation in physics. In the first case, the cylinder displacement time series is decomposed into two oscillatory components using SSA. The instantaneous frequencies of these two components are obtained by Hilbert transform (HT) and found to be in agreement with the wavelet transform of the cylinder displacement. In the second case, three oscillatory components are extracted from the cylinder displacement time series by SSA. The dominant component is characterized by steady oscillations at the vortex shedding frequency, which suggests a relatively steady vortex shedding process behind the rear cylinder. In contrast, the second component, which is closely associated with the alternate boundary layer separations from the front cylinder, features in the increasing amplitude with time. This implies that the unsteady flow field in the gap might be attributed to the nonstationary cylinder oscillations. This work demonstrates that SSA, in conjunction with HT, enables a comprehensive time-frequency analysis of nonstationary time series obtained in FIV.

An improved rhythmicity analysis method using Gaussian Processes detects cell-density dependent circadian oscillations in stem cells.

Detecting oscillations in time series remains a challenging problem even after decades of research. In chronobiology, rhythms (for instance in gene expression, eclosion, egg-laying, and feeding) tend to be low amplitude, display large variations amongst replicates, and often exhibit varying peak-to-peak distances (non-stationarity). Most currently available rhythm detection methods are not specifically designed to handle such datasets, and are also limited by their use of P-values in detecting oscillations. We introduce a new method, ODeGP (Oscillation Detection using Gaussian Processes), which combines Gaussian Process regression and Bayesian inference to incorporate measurement errors, non-uniformly sampled data, and a recently developed non-stationary kernel to improve detection of oscillations. By using Bayes factors, ODeGP models both the null (non-rhythmic) and the alternative (rhythmic) hypotheses, thus providing an advantage over P-values. Using synthetic datasets, we first demonstrate that ODeGP almost always outperforms eight commonly used methods in detecting stationary as well as non-stationary symmetric oscillations. Next, by analyzing existing qPCR datasets, we demonstrate that our method is more sensitive compared to the existing methods at detecting weak and noisy oscillations. Finally, we generate new qPCR data on mouse embryonic stem cells. Surprisingly, we discover using ODeGP that increasing cell-density results in rapid generation of oscillations in the Bmal1 gene, thus highlighting our method's ability to discover unexpected and new patterns. In its current implementation, ODeGP is meant only for analyzing single or a few time-trajectories, not genome-wide datasets. ODeGP is available at https://github.com/Shaonlab/ODeGP.

Construction of a physical-mathematical model of oscillations of the unbalanced vibrator of the pneumatic sorting table

A physical-mathematical model of oscillations of unbalanced vibrators of a pneumatic sorting table as non-stationary oscillations of an impulse-loaded round plate with various options for fixing its contour has been built. The axisymmetric non-stationary oscillations of a round plate supported by a one-sided round base were considered in two ways of fixing its contour, namely, when it is tightly clamped and freely supported. It was assumed that the linearly elastic base resists only compression and does not perceive stretching. It is shown that for certain durations of the transverse force pulse in time, the amplitude of the deflection of the middle of the plate in the direction of action of the external pulse can be smaller than the amplitude of the deflection in the opposite direction. At the same time, in the second case, there is no contact of the plate with the base. It has been proven that this dynamic effect of the asymmetry of the elastic characteristic of the system also applies to bending moments and is more clearly manifested when the contour is freely supported than when it is tightly clamped. For rectangular and sinusoidal pulses, closed-loop solutions of the equations of motion of the plate during its contact with the base and after separation from the base were constructed. Compact formulas were derived for calculating the amplitudes of positive and negative deflections in both directions from the zero position of static equilibrium. Formulas have been obtained for calculating the time it takes for the plate to obtain extreme deflection values, which is achieved due to the selection of a special axisymmetric distribution of dynamic pressure on the plate. Under such a load, the plate simultaneously detaches from the base at all points, except for the contour points, which reduces the nonlinear boundary value problem to a sequence of two linear problems. Numerical integration of the differential equation was carried out to check the reliability of the constructed analytical solutions. Adequacy of the model was proven for the following values of initial parameters: modulus of elasticity, 2.1·1011 Pa; the Poisson ratio of the plate material, 0.25; plate thickness, 7...10 mm; the maximum pressure on the plate, 4·103 Pa; the bending stiffness of the plate, 6402.6667 N·m

Variational Bayesian Approach to Nonstationary and Oscillatory Slow Feature Analysis With Applications in Soft Sensing and Process Monitoring

Extraction of underlying patterns from measured variables is central to various data-driven control applications, such as soft-sensor modeling, statistical process monitoring, and fault detection and diagnosis. More often than not, the observed variables display nonstationary characteristics and oscillations due to the changes in operating conditions and problems in controller tuning. Such variations pose a great challenge to conventional feature extraction methods. Hence, we present a probabilistic drift-type nonstationary oscillating slow feature model that can separate oscillating patterns and nonstationary variations from measured data. Furthermore, the measurement noise of each variable is independently modeled to account for the fact that not all the observed variables have the same level of uncertainty. Finally, the feature extractor parameters are estimated under a variational Bayesian framework to incorporate the prior information and obtain corresponding posterior distributions. The proposed methodology is applied to solve a fouling monitoring problem for an industrial oil production process.

Trends, Shifting, or Oscillations? Stochastic Modeling of Nonstationary Time Series for Future Water‐Related Risk Management

AbstractHydrological time series often present nonstationarities such as trends, shifts, or oscillations due to anthropogenic effects and hydroclimatological variations, including global climate change. For water managers, it is crucial to recognize and define the nonstationarities in hydrological records. The nonstationarities must be appropriately modeled and stochastically simulated according to the characteristics of observed records to evaluate the adequacy of flood risk mitigation measures and future water resources management strategies. Therefore, in the current study, three approaches were suggested to address stochastically nonstationary behaviors, especially in the long‐term variability of hydrological variables: as an overall trend, shifting mean, or as a long‐term oscillation. To represent these options for hydrological variables, the autoregressive model with an overall trend, shifting mean level (SML), and empirical mode decomposition with nonstationary oscillation resampling (EMD‐NSOR) were employed in the hydrological series of the net basin supply in the Lake Champlain‐River Richelieu basin, where the International Joint Committee recently managed and significant flood damage from long consistent high flows occurred. The detailed results indicate that the EMD‐NSOR model can be an appropriate option by reproducing long‐term dependence statistics and generating manageable scenarios, while the SML model does not properly reproduce the observed long‐term dependence, that are critical to simulate sustainable flood events. The trend model produces too many risks for floods in the future but no risk for droughts. The overall results conclude that the nonstationarities in hydrological series should be carefully handled in stochastic simulation models to appropriately manage future water‐related risks.

Динамика плоского движения космического крана-манипулятора типа руки с учетом изгиба звеньев

The paper considers the plane motion dynamics of a three-link crane-manipulator consisting of two rods elastic in bending and a massive solid body attached to them at their end (load capture). All links are interconnected by hinge joints with the given (controlled) relative rotation angles. The first link is also connected to the mobile base. The system mathematical model was developed to calculate its non-stationary oscillations and dynamic loading of links at arbitrary in time and large relative angles of the links rotation as the solid bodies. The rods bending deformations (elastic transverse displacements and rotation angles of the axes) were considered to be insignificant (linear). Each rod ending was represented by the Ritz method using two given shape functions with the unknown coefficients, which were taken as the generalized coordinates. In this case, the “cantilever” bending forms of each rod with the given transverse displacement and angle of rotation at their ends were used. A simplified version was considered: each rod bending was represented by only one given form of its bending by a single moment applied at the end. System oscillation equations were obtained based on the principle of probable displacements in the generalized coordinates (four equations or two in a simplified form). Since rotation angles at the ends of the elastic rods were added to the given rotation angles of the non-deformable rods, total angles were left under the signs of sines and cosines without linearization for convenience of calculations and increasing accuracy. As a result, such equations of non-stationary oscillations remained non-linear. They were integrated by numerical methods using standard programs in one of the computer algebra systems. Examples are provided with the comparative results estimates obtained in the two-term and one-term approximations of the function in regard to the bending form of the system bending rod joints.

Nonstationary Delay in the Development of Oscillations of a Magnetostrictive Transducer under Conditions of Multiplication of the Excitation Frequency

A numerical study of the delay in the excitation of oscillations of a magnetostrictive transducer in the frequency multiplication mode based on the model of coupled oscillators is presented. The non-stationary nature of the oscillations excited after the amplitude jump is revealed. The phenomenon is interpreted on the basis of the dynamic potential model. A numerical study of the development of oscillations in time has been carried out, and phase portraits of oscillations have been constructed. The fractal-like nature of nonstationary oscillations is established, which manifests itself in the preservation of the degree of their chaoticity with a change in the value of the calculation step in time.

Characterizing and forecasting climate indices using time series models

The objective of the current study is to present a comparison of techniques for the forecasting of low-frequency climate oscillation indices with a focus on the Great Lakes system. A number of time series models have been tested including the traditional autoregressive moving average (ARMA) model, dynamic linear model (DLM), generalized autoregressive conditional heteroskedasticity (GARCH) model, as well as the nonstationary oscillation resampling (NSOR) technique. These models were used to forecast the monthly El Niño-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) indices which show the most significant teleconnection with the net basin supply (NBS) of the Great Lakes system from a preliminary study. The overall objective is to predict future water levels, ice extent, and temperature, for planning and decision making purposes. The results showed that the DLM and GARCH models are superior for forecasting the monthly ENSO index, while the forecasted values from the traditional ARMA model presented a good agreement with the observed values within a short lead time ahead for the monthly PDO index.

Forced Oscillation Identification and Filtering From Multi-Channel Time-Frequency Representation

Location of non-stationary forced oscillation (FO) sources can be a challenging task, especially under resonance condition with natural system modes. In this case, the magnitudes of the oscillations could be greater in places distant from the source and the oscillation spreads over a large region of the power system. Detection, frequency identification and filtering of FO oscillatory components constitutes an initial and critical step for the application of oscillation source location (OSL) methods. Specifically, this step has a major impact on the performance of the OSL method, such as the Dissipating Energy Flow (DEF) method. In this paper we develop a systematic methodology for detection, identification and filtering of non-stationary FO based on multi-channel time-frequency (TF) representation (TFR). We compare three TF approaches applied together with the DEF method: short-time Fourier transform (STFT), STFT-based synchrosqueezing transform (FSST) and second order FSST (FSST2). We have used simulated signals and real world PMU data to show that the proposed method provides a systematic framework for the identification and filtering of power systems non-stationary forced oscillations.

Time-Dependent 4D Quantum Harmonic Oscillator and Reacting Hydrogen Atom

With the help of low-dimensional reference equations (ordinary differential equations) and the corresponding coordinate transformations, the non-stationary 4D quantum oscillator in an external field is reduced to an autonomous form. The latter, in particular, reflects the existence of a new type of dynamical symmetry that reduces the equation of motion of a non-stationary oscillator to an autonomous form that does not change with time. By imposing an additional constraint on the wave function of the isotropic oscillator, we have obtained the total wave functions of the reacting hydrogen atom in two different cases: (a) when the non-stationary frequency has two asymptotic values and there is no external field; and (b) when, in addition to the non-stationary frequency, an external force acts on the hydrogen atom. The transition S-matrix elements of various elementary atomic–molecular processes are constructed. The probabilities of quantum transitions of the hydrogen atom to others, including new bound states, are studied in detail, taking into account the influence of external forces.

A unified damping controller for non-stationary forced oscillation

Forced disturbances (FDs) with non-stationary frequencies can sequentially resonate from electromechanical modes (EMs) to sub/super synchronous modes (SSMs) and thus lead to non-stationary forced oscillations (FOs). Previous FO damping controllers designed for specified frequency bands may not be able to suppress the non-stationary FOs. This paper proposes a unified FO damping controller design method to deal with all oscillations caused by non-stationary FOs. The model of a power system with non-stationary FOs is obtained by a continuous model detection and identification of measured signals, which does not require any value of the system parameters. Accordingly, four stability indices, i.e., robustness, interaction, frequency, and damping ratio of the EMs and SSMs, can be calculated from the estimated model. At each operating point, these indices are monitored and used to optimally design the unified FO damping controller. The effectiveness of the proposed unified FO damping controller is verified in the modified Southeast Australian power system with converter controlled-based generations under various operating points and FO conditions.

Modeling and Control of Instabilities in Combustion Processes

This paper treats the control of nonstationary oscillations of acoustic pressure in the combustion instability process, which appears in the combustion chamber. Two models of nonstationary combustion process control are presented, where first of them is a classic model, which applies the Rayleigh criterium of phase matching between heat-release rate and acoustic pressure. The second model is an alternative van der Pol model exhibiting selfexciting oscillations due to the feedback with a negative damping. The paper outlines the model of fuel control, which is successfully applied for quenching of selfexcited oscillations. Efficiency of fuel control to quench selfexcited oscillations is shown in the phenomenon of competitive quenching, where the influence of various control parameters is explained.

Detailed Investigation on Nonstationary Behavior in a Frequency-Tunable Gyrotron

As a terahertz (THz) radiation source, the frequency-tunable gyrotron is promising in application and attractive to researchers. In this article, the nonstationary phenomenon in a frequency-tunable gyrotron operating in different regimes—gyromonotron, transition, and gyro-backward-wave oscillator (BWO)—has been investigated in detail by 3-D particle in cell (PIC) simulation. Simulated results demonstrate that among the three regimes, gyromonotron has the strongest capability to keep stationary, and nonstationary oscillations are most likely to occur in the transition regime. Moreover, in the gyro-BWO regime, the capability of the system to maintain steady-state operation gets slightly improved with the increase in the axial mode. The corresponding interpretation is based on detuning frequency and feedback mechanism. Finally, the effect of the velocity spread on the nonstationary behavior has also been studied. Investigations reveal that the stability of stationary oscillations would be weakened when velocity spread is considered. The results in this article may be of benefit of a deeper insight into the nonstationary phenomenon in a frequency-tunable gyrotron.

Non-stationary oscillations of an instantly loaded oscillator under conditions of nonlinear resistance

The motion of an oscillator instantaneously loaded with a constant force under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, are considered. Using the first integral of the equation of motion and the Lambert function, compact formulas for calculating the ranges of oscillations are derived. In order to simplify the search for the values of the Lambert function, asymptotic formulas are given that, with an error of less than one percent, express this special function in terms of elementary functions. It is shown that as a result of the action of the resistance force, including dry friction, the oscillation process has a finite number of cycles and is limited in time, since the oscillator enters the stagnation region, which is located in the vicinity of the static deviation of the oscillator caused by the applied external force. The system dynamic factor is less than two. Examples of calculations that illustrate the possibilities of the stated theory are considered. In addition to analytical research, numerical computer integration of the differential equation of motion was carried out. The complete convergence of the results obtained using the derived formulas and numerical integration is established, which confirms that using analytical solutions it is possible to determine the extreme displacements of the oscillator without numerical integration of the nonlinear differential equation. To simplify the calculations, the literature is also recommended, where tables of the Lambert function are printed, allowing you to find its value for interpolating tabular data. Under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, the process of oscillations of an instantly loaded oscillator has a limited number of cycles. The dependences obtained in this work using the Lambert function make it possible to determine the range of oscillations without numerical integration of the nonlinear differential equation of motion both for an oscillator with quadratic viscous resistance and dry friction, and for an oscillator with quadratic resistance and positional and dry friction.
 Keywords: nonlinear oscillator, instantaneous loading, quadratic viscous resistance, Lambert function, oscillation amplitude.

Towards dynamic property control of bridge spans

Regulation of the dynamic properties of bridge spans is a priority field of this research, which solves the problem of increasing the obsolescence and physical periods of bridge structures manifested both at the design stage of the load redistribution in the load bearing and during long-term operation.Over the past 40 years, technical bridge diagnostics has shown that the durability and safe long-term operation can be ensured by the improved calculations, operation and stress and strain control under the excess and over-calculated live loads.The aim of this work is to control the dynamic deformation and amplitude-frequency characteristics of bridge spans under harmonic random (non-stationary) oscillations of the span-vehicle system due to changes in the energy and stress state of the structure. The dynamic behavior of the span-vehicle system is based on the control for the amplitude-frequency characteristics of random oscillations by averaged values, the required spectral density being provided.The use of dynamic dampers for the system element control and the rigidity of junctions provide antiphase oscillations of the bridge span elements such as beams and decks, that leads to the unaccounted inertial forces.Another important element of the joint work imbalance of the bridge span elements during the dynamic load, are various defects, both in the deck design and load-bearing elements. It is assumed that the deck is a transfer layer (element) of vibrations induced by a vehicle in the beams. It is shown that the control for the dynamic properties is required in the case of a coincidence between the vehicle and beam stiffness and mass at the center of the system rigidity.The attention is paid to the conditions and dependencies between the dynamic load parameters and the stress-strain state of the bridge beams at the elastic and elastoplastic stages, with respect to the additional inertia of the system. This approach is the pilot in the Russian and foreign bridge construction in terms of experimental studies and testing of bridges for continuous random traffic.The dynamic testing of bridge spans for random traffic flow contributes to the creation of vibration diagnostic express laboratories necessary for the operation and maintenance of bridges.

Non-stationary oscillation of a string on the Winkler foundation subjected to a discrete mass–spring system non-uniformly moving at a sub-critical speed

We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass–spring system non-uniformly moving at a given sub-critical speed. The speed of the mass–spring system is assumed to be a slowly time-varying function. To describe a non-vanishing free oscillation we use an analytic approach based on the method of stationary phase and the method of multiple scales. The moving oscillator is characterized by a partial frequency, which can be greater or less than the cut-off frequency. Accordingly, a sub-critical uniformly accelerated motion generally has two stages. At the first stage there exists a trapped mode, and, therefore, a part of the wave energy is localized near the moving oscillator and does not propagate away. For this stage we obtain the analytic solution in a simple form describing non-vanishing free oscillation and verify it numerically. For the second stage there is no trapped mode, and all the wave energy propagate away. This stage is investigated numerically, and some unexpected results are obtained. Additionally, we consider the case of the oscillator with a destabilizing spring. The dynamics of the system in the latter case is quite different from the case of commonly used stabilizing spring, since the system loses the stability during an accelerated motion. We also take into consideration the forced oscillation caused by an external load being a superposition of harmonics with time-varying parameters (the amplitude and the frequency).

Numerical study of the vertical vibration of a vehicle model with variable speed

The paper deals with the numerical analysis of the general model of vehicle oscillations considering the non-stationarity of random excitation. The model parameters of the applied railway vehicle are deterministic functions. The non-stationary random function will be modelled by the variable speed of the vehicle and the vertical unevenness of the track. The so-called evolutionary Gaussian random process will be considering. The proposed comparative study of the dynamics of the vertical motion of the analysed railway vehicle will be realized using Monte Carlo simulation and a numerical procedure based on the theory of Markov processes. The originality of the article can be found in the implementation and algorithmization of the principles of solving non-stationary oscillation problems of machines. A universal methodology applicable in the dynamics of machines of various purposes is presented.

Towards the dynamic coefficient

For the first time, this paper studies the fundamental conditions of the dynamics of bridge spans under non-stationary oscillations with regard to the mass inertia of the span–vehicle system. Based on the dynamic analysis of the stress-strain state of spans under changing live load, the mechanical and energy principles of additional dynamic load characterized by the dynamic coefficient, are formulated and substantiated. It is found that the dynamic coefficient slightly depends on the system vibrations due to the temporary nature of its application. The amplitudefrequency characteristics of the dynamic stress-strain state are considered in the mode of stable oscillations only. Theoretical and experimental studies of road bridges of various designs and lengths confirm the relationship between the dynamic coefficient and the parameters of damping and resonance. It is found that the dynamic coefficient reflecting the energy balance of the system allows considering the critical ratios of the equilibrium amplitudes and dynamic stiffness of the spans under the changing effect of the live load as well as the presence of road defects and span bearing elements in terms of the well-known Hurwitz criterion.

КОЛИВАННЯ ІМПУЛЬСНО НАВАНТАЖЕНОГО ОСЦИЛЯТОРА ЗІ СТЕПЕНЕВИМ ПОЗИЦІЙНИМ ТЕРТЯМ

Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an instantaneous force pulse are described. The power dependence of the positional friction force on the displacement of the system, which generalizes the known models, is accepted. The corresponding dynamics problems were solved precisely by the method of adding and approximated by the method of energy balance. In the study, using periodic Ateb-functions, an exact analytical solution of the nonlinear differential equation of motion was constructed. Compact formulas for calculating oscillation ranges and half-cycle durations are derived. It is shown that the decrease in the amplitude of oscillations, as well as under the action of the force of linear viscous resistance, follows the law of geometric progression. The denominator of the progression is less than one and depends on the positional friction constants, in particular on the nonlinearity index. Thus, we have not only a decrease in the amplitude of oscillations, but also an increase in the durations of half-cycles, which is characteristic of nonlinear systems with a rigid force characteristic. Approximate displacement calculations use Pade-type approximations for periodic Ateb-functions. The error of these approximations is less than one percent. From the obtained analytical relations, as separate cases, the known dependences covered in the theory of oscillations for linear positional friction follow. It is shown that even in the case of nonlinear positional friction the process of oscillations caused by an instantaneous momentum has many oscillations and is not limited in time. In the case of power positional friction, the oscillation ranges of the pulse-loaded oscillator can be calculated by elementary formulas. The calculation of displacements in time is associated with the use of periodic Ateb-functions, the values of which are not difficult to determine by known asymptotic formulas. Calculations confirm that the obtained approximate formula does not give large errors. In order to verify the adequacy of the obtained analytical solutions, numerical computer integration of the original nonlinear differential equation of motion was performed. The results of the calculation, which lead to analytical and numerical solutions of the Cauchy problem, are well matched.