Nonstationary Intensity Research Articles

Comparative Performance of Non-Stationary Intensity-Duration-Frequency (NS-IDF) Models for Selected Gauge Stations in the Niger Delta

This study focused on a comparative analysis of developed Non-stationary rainfall intensity-duration-frequency (NS-IDF) models with existing IDF models for the Niger Delta with Uyo, Benin, Port Harcourt, and Warri as selected stations. Applied was 24-hourly (daily) annual maximum series (AMS) data with downscaling models also used to downscale the time series data. Uyo and Benin had statistically significant trends with Port Harcourt and Warri showing mild trends. The best linear behavioural parameter extremes model integrating time as co-variate was selected for each station for computation of the General extreme value (GEV) distribution fitted NS-IDF models with the open-access R-studio software. The Non-stationary intensity values were higher than computed stationary ones, with significant differences at a 5% significance level for a given return period. For example, for 2 and 10-year return periods for 1-hour storms the differences of 22.71% & 17.0%, 15.24% & 9.40%, 5.09% & 4.04%, and 6.15% & 4.43% for Uyo, Benin, Port Harcourt and Warri, respectively were recorded. While, the percentage difference in intensities was very high between the Non-stationary and existing, Stationary IDF models. For a return period of 2 years at 15 and 60 min durations, the differences were 97.9 & 3.2%, 240.6 & 67.2%, 78.2 & 0%, and 121.6 & 50.1% for Uyo, Benin, Port Harcourt and Warri, respectively. Such extreme value difference in intensity underestimates the peak flood and exagerate the flood risk. The general NS-IDF calibrated models showed very good match and fit with R<sup>2</sup> = 0.977, 0.999, 0.999 & 0.999, and MSE accuracy = 193.5, 1.011, 4.1552 & 1.011 for Uyo, Benin, Port Harcourt, and Warri, respectively. Erosion and flood control facilities in the Niger Delta require upgrading using the calibrated general NS-IDF models to accommodate extra-value rainfall intensities due to climate change.

Hydrologic regionalization of non-stationary intensity–duration–frequency relationships for Indian mainland

Abstract Intensity–duration–frequency (IDF) curve is one of the important hydrologic tools used for the design of hydraulic infrastructure. The static return period assumption of precipitation extremes is invalid in a changing climate environment, and the underestimation of rainfall intensity may lead to the failure of infrastructure in extreme events. This study first developed the non-stationary (NS) IDF curves for six selected locations in India based on sub-daily station data based on time-dependent estimates of five combinations of Generalized Extreme Value (GEV) distribution parameters. Then, in order to identify the critical regions of rainfall non-stationarity, the IDF curves were developed for 357 grid points over India using the daily gridded data for the period 1951–2016 at 1° × 1° resolution. The comparison of spatial patterns of rainfall intensity estimates under stationary and non-stationary showed that about 23% of grids showed an overestimation of NS rainfall over their stationary counterparts by at least 15%. About 32 grid locations which showed at least 15% overestimation of rainfall under an NS case displayed a significantly increasing rainfall trend. The majority of the grids with larger deviation of non-stationary rainfall estimates over stationary values are located in India's eastern regions and coastal belts.

STOCHASTIC MODEL FOR FORECASTING OF CRUISE OR FERRY SHIP ARRIVAL AT SEAPORT FOR INFRASTRUCTURE ASSESSMENT

The topic of the research is the development of new models and methods to assess the efficiency of port operations of sea passenger ports and terminals in order to effectively plan the work and accurate forecasting of infrastructure development. It is noted that changes in cruise and ferry route networks, especially relevant in the conditions of passenger traffic recovery after the gradual lifting of restrictions due to Covid-19, will directly affect port congestion. It is proposed to include into the sphere of decision-making on management of the sea passenger port the models based on consideration of probabilistic processes of cruise or ferry vessels calls. The Baltic Sea region is chosen as an object of research. The main modern directions in the sphere of sea passenger transportations confirming the gradual recovery of the route networks operation are presented. The flow of cruise and ferry vessels of the sea passenger port “Passenger port St. Petersburg “Marine Facade” is chosen as an object of research. The analysis of loading of berths, the analysis of the size of cruise and ferry ships, the route networks of ferry and cruise lines are carried out. As a result of the research a new stochastic model is presented and comparison with known distribution laws is carried out. Based on the data obtained, a confidence zone for making decisions on port congestion is determined. This area is formed on the basis of an assessment of the study of the dynamics of ship traffic nonstationary intensity, followed by the application of correlation-regression analysis and the characteristics of the random function describing the intervals between individual arrivals of cruise and ferry ships. The proposed model includes the ability to consider different priorities, primarily in terms of vessel length. Digital transport model is built in AnyLogic environment for port congestion study. The received data are used for optimization experiments in AnyLogic software environment with the purpose of complex estimation of the seaport operation for a year. Based on the optimization experiment and simulation, data are generated considering different distribution laws and used for decision making in case of uncertainty for infrastructure modernization. The presented model can be used for substantiation of management decisions both on strategic and tactical levels for assessing the efficiency of investment projects on development of sea passenger ports and terminals.

Optical Drills by Dynamic High-Order Bessel Beam Mixing

One of the key trends in laser material processing is the usage of structured laser beams. Collimated and focused Gaussian beams are the most common tools; however, more exotic beams can be beneficial too. For instance, Bessel beams with elongated focal area and self-healing properties, or vortex beams with helical wave fronts and a dark area along the optical axis are being increasingly used. Here, we propose and experimentally demonstrate dynamical ``optical drill'' beams presenting nonstationary intensity distributions that resemble a spinning mechanical drill. Optical drills appear as the spatiotemporal interference of two Bessel-vortex beams of different topological charges and different carrier frequencies. By mixing a pair of high-order Bessel beams, synthesized using a liquid crystal spatial light modulator, optical drills of tuned helicities are experimentally observed, and the simplest cases of matter processing (fluorescence) with such beams are demonstrated. Optical drill beams are expected to be useful in material processing by light or in cell and particle manipulation in biomedical applications.

Convergence Bounds for Limited Processor Sharing Queue with Impatience for Analyzing Non-Stationary File Transfer in Wireless Network

The data transmission in wireless networks is usually analyzed under the assumption of non-stationary rates. Nevertheless, they strictly depend on the time of day, that is, the intensity of arrival and daily workload profiles confirm this fact. In this article, we consider the process of downloading a file within a single network segment and unsteady speeds—for arrivals, file sizes, and losses due to impatience. To simulate the scenario, a queuing system with elastic traffic with non-stationary intensity is used. Formulas are given for the main characteristics of the model: the probability of blocking a new user, the average number of users in service, and the queue. A method for calculating the boundaries of convergence of the model is proposed, which is based on the logarithmic norm of linear operators. The boundaries of the rate of convergence of the main limiting characteristics of the queue length process were also established. For clarity of the influence of the parameters, a numerical analysis was carried out and presented.

Nonstationary Intensity Statistics in Diffusive Waves.

It is a long-standing belief that, in the diffusion regime, the intensity statistics is always stationary and its probability distribution follows a negative exponential decay. Here, we demonstrate that, in fact, in reflection from strong disordered media, the intensity statistics changes through different stages of the diffusion. We present a statistical model that describes this nonstationary property and takes into account the evolving balance between recurrent scattering and near field coupling. The predictions are further verified by systematic experiments in the optical regime. This statistical nonstationary is akin to the nonequilibrium but steady-state diffusion of particulate systems.

Climate change and its influence on design rainfall at-site in New South Wales State, Australia

AbstractQuantification of rainfall is needed for planning, designing and operation of water engineering projects. Although there is lot of research on design rainfall in the literature, there is a lack of research considering the impact of climate change on design rainfall. This study focuses on the assessment of the impact of climate changes on design rainfall using data from New South Wales (NSW), Australia. Future stationary and non-stationary intensity–frequency–duration (IFD) curves have been estimated using generalized extreme value (GEV) distribution. The maximum-likelihood estimation method is employed to estimate the parameters of the GEV models. It has been found that the consideration of the climatic change on the rainfall data of the selected station confirms that the simulation exhibits non-stationary behaviour on the IFD curve data. In addition, the results show that when the future period increases, the relative differences between the stationary and non-stationary IFD curves generally increase. Comparison of the new IFD curves estimated in this study with the Australian Rainfall and Runoff (ARR) IFD curves demonstrates that there is a better match between the ARR IFD curves and the new stationary IFD curves compared with the non-stationary IFD curves.

Numerical Simulation of Seismic Waves with Peak Arrival Time and Amplitude-Frequency Correlation

To improve the accuracy with which the non-stationary intensity characteristics of artificial acceleration-time-history curves are determined, a method of adjusting the frequency correlation between the artificial peak arrival time and amplitude spectrum is proposed. A calculation method for determining the peak arrival time to reflect the physical meaning of the phase-difference spectrum was first deduced. Subsequently, the amplitude-distribution characteristics corresponding to the peak arrival times for different durations of natural earthquakes were analyzed. In accordance with the distribution characteristics of the reference amplitude, the frequency distribution of the artificial peak arrival time was divided into four parts: the beginning, strong-earthquake, attenuation, and tail sections. By adjusting the arrival frequency of peak points for the different earthquake durations considered, the corresponding relationship between the artificial peak arrival time and amplitude spectrum was determined to be more consistent with the general law of natural earthquakes. The sample calculation described in this paper demonstrates that adjusting the frequency correspondence between the artificial peak arrival time and amplitude spectrum greatly improves the accuracy of the non-stationary intensity characteristics of artificial acceleration-time-history curves.

Does nonstationarity in rainfall require nonstationary intensity–duration–frequency curves?

Abstract. In Canada, risk of flooding due to heavy rainfall has risen in recent decades; the most notable recent examples include the July 2013 storm in the Greater Toronto region and the May 2017 flood of the Toronto Islands. We investigate nonstationarity and trends in the short-duration precipitation extremes in selected urbanized locations in Southern Ontario, Canada, and evaluate the potential of nonstationary intensity–duration–frequency (IDF) curves, which form an input to civil infrastructural design. Despite apparent signals of nonstationarity in precipitation extremes in all locations, the stationary vs. nonstationary models do not exhibit any significant differences in the design storm intensity, especially for short recurrence intervals (up to 10 years). The signatures of nonstationarity in rainfall extremes do not necessarily imply the use of nonstationary IDFs for design considerations. When comparing the proposed IDFs with current design standards, for return periods (10 years or less) typical for urban drainage design, current design standards require an update of up to 7 %, whereas for longer recurrence intervals (50–100 years), ideal for critical civil infrastructural design, updates ranging between ∼ 2 and 44 % are suggested. We further emphasize that the above findings need re-evaluation in the light of climate change projections since the intensity and frequency of extreme precipitation are expected to intensify due to global warming.

Model for the Formation of Acoustic Self-Oscillations in a Chamber with a Jet Flowing Through its Nozzle

This paper describes free acoustic oscillations of gas in a chamber with a jet flowing through its nozzle in the case of nonstationary intensity component of vortex sheet flowing down from the edge of the nozzle. There is established feedback between acoustic oscillations and oscillations induced by a corresponding vortex sheet component. It is shown that, in the presence of given feedback, there could be instability of acoustic oscillations, which would result in acoustic self-oscillations in the chamber. The boundaries of the domain in which instability is formed are determined by developing a mathematical model of stable acoustic oscillations in the chamber with account for the influence of the vortex sheet.

Formation of periodic phase structures in a photopolymerizable layer by nonstationary light beams

Photopolymerization of a composite containing a nonpolymerizable component under the action of nonstationary optical radiation is studied. It is shown that the diffusion displacement of the nonpolymerizable component at the illuminated region boundary is caused by the appearance of the monomer concentration gradient, which, in turn, is induced by nonuniform photoinitiation. The action of radiation with a nonstationary intensity distribution makes it possible to form a periodic refractive index structure in the volume of the photopolymerizable material. The possibility of optical formation of polymer phase gratings by moving the shadow boundary stepwise along the polymerizable layer is studied numerically and experimentally.

Medical image registration using sparse coding of image patches

Image registration is a basic task in medical image processing applications like group analysis and atlas construction. Similarity measure is a critical ingredient of image registration. Intensity distortion of medical images is not considered in most previous similarity measures. Therefore, in the presence of bias field distortions, they do not generate an acceptable registration. In this paper, we propose a sparse based similarity measure for mono-modal images that considers non-stationary intensity and spatially-varying distortions. The main idea behind this measure is that the aligned image is constructed by an analysis dictionary trained using the image patches. For this purpose, we use “Analysis K-SVD” to train the dictionary and find the sparse coefficients. We utilize image patches to construct the analysis dictionary and then we employ the proposed sparse similarity measure to find a non-rigid transformation using free form deformation (FFD). Experimental results show that the proposed approach is able to robustly register 2D and 3D images in both simulated and real cases. The proposed method outperforms other state-of-the-art similarity measures and decreases the transformation error compared to the previous methods. Even in the presence of bias field distortion, the proposed method aligns images without any preprocessing.

Evaluation of Relative Entropy for Distributed Passive Detection of Weak Acoustic Signals

Passive detection of weak signals in noise is formulated without assuming a parametric distribution of the received signal statistics. A binary likelihood-ratio test as to whether the probability densities of two candidate noise populations are the same, or significantly different, leads to the comparison of relative entropy with a Neyman-Pearson detection threshold. The method is demonstrated using the acoustical intensity of narrowband signals at the hydrophones of a bottom-mounted horizontal line array, which was deployed during the Transverse Acoustic Variability Experiment. Receiver operating characteristics of the relative entropy detector are compared with those for the mean signal-to-noise ratio on a set of hydrophones. It is found that at large false-alarm rates the relative entropy detector has comparatively inferior performance while remaining competitive in the region of small false-alarm probability. Relative entropy detection is insensitive to statistical dependence among the sensors, but is sensitive to data having nonstationary intensity statistics characteristic of the ocean environment in which it was tested.

Sparse‐induced similarity measure: mono‐modal image registration via sparse‐induced similarity measure

Similarity measure is an important key in image registration. Most traditional intensity-based similarity measures (e.g. sum-of-squared-differences, correlation coefficient, mutual information and correlation ratio) assume a stationary image and pixel-by-pixel independence. These similarity measures ignore the correlation among pixel intensities; hence, a perfect image registration cannot be achieved especially in the presence of spatially varying intensity distortions and outlier objects that appear in one image but not in the other. It is supposed here that non-stationary intensity distortion (such as bias field) has a sparse representation in the transformation domain. Based on this assumption, a novel similarity measure is proposed here based on sparse representation in a mono-modal setting. The zero norm (l 0 ) in the transform domain is introduced as a new similarity measure in the presence of non-stationary intensity distortion. The present study defines a sparsity similarity measure that indicates the complexity of the residual image between two registered images in the transform domain such as discrete cosine transform or wavelet. It is attempted here to analytically and statistically illustrate that the proposed similarity measure has important properties such as metric properties in vector space, from correntropy perspective. This measure produces accurate registration results on both artificial and real-world problems which are examined in the present study.

Robust Huber similarity measure for image registration in the presence of spatially-varying intensity distortion

Similarity measure is an important part of image registration. The main challenge of similarity measure is lack of robustness to different distortions. A well-known distortion is spatially-varying intensity distortion. Its main characteristic is correlation among pixels. Most traditional intensity based similarity measures (e.g., SSD, MI) assume stationary image and pixel to pixel independence. Hence, these similarity measures are not robust against spatially-varying intensity distortion. Here, we suppose that non-stationary intensity distortion has a sparse representation in transform domain, i.e. its distribution has high peak at origin and a long tail. We use two viewpoints of Maximum Likelihood (ML) and Robust M-estimator. First, using the ML view, we propose robust Huber similarity measure (RHSM) in spatial transform domain as a new similarity measure in a mono-modal setting. In fact, RHSM is a combination of ℓ2 and ℓ1 norms. To demonstrate robustness of the proposed similarity measure, image registration is treated as a non-linear regression problem. In this view, covariance matrix of estimated parameters is obtained based on the one-step M-estimator. Then with minimizing Fisher information function, robust similarity measure of RHSM is introduced. This measure produces accurate registration results on both artificial as well as real-world problems that we have examined.

Dynamic processes and their influence on the transformation of the passive admixture in the sea of Azov

In this model, we apply a nonlinear three-dimensional sigma-coordinate model to study the waves and currents in the Sea of Azov generated by different fields of wind forcing: a constant wind, a quickly varying real wind obtained using the data of reanalysis applying the SKIRON model, and the wind resulting from their combined forcing. This mathematical model was also applied to study the transformation of the passive admixture appearing under the influence of wind fields in the Sea of Azov considered here. We compared the results of numerical calculations with the field data obtained under the wind forcing at a number of hydrological stations. We found the regularities of the water transport driven by onshore and offshore winds, the velocities of the currents, and the characteristics of the evolution of polluted regions at different depths as functions of the nonstationary wind intensity and the velocities of the stationary currents.

Fractal dynamics of light scattering intensity fluctuation in disordered dusty plasmas

Dynamic light scattering (DLS) technique is a simple and yet powerful technique for characterizing particle properties and dynamics in complex liquids and gases, including dusty plasmas. Intensity fluctuation in DLS experiments often studied using correlation analysis with assumption that the fluctuation is statistically stationary. In this study, the temporal variation of the nonstationary intensity fluctuation is analyzed directly to show the existence of fractal characteristics by employing wavelet scalogram approach. Wavelet based scale decomposition approach is used to separate non-scaling background noise (without dust) from scaling intensity fluctuation from dusty plasma. The Hurst exponents for light intensity fluctuation in dusty plasma at different neutral gas pressures are determined. At low pressures, weaker damping of dust motions via collisions with neutral gases results in stronger persistent behavior in the fluctuation of DLS time series. The fractal scaling Hurst exponent is demonstrated to be useful for characterizing structural phases in complex disordered dusty plasma, especially when particle configuration or sizes are highly inhomogeneous which makes the standard pair-correlation function difficult to interpret. The results from fractal analysis are compared with alternative interpretation of disorder based on approximate entropy and particle transport using mean square displacement.

Exact simulation of Hawkes process with exponentially decaying intensity

We introduce a numerically efficient simulation algorithm for Hawkes process with exponentially decaying intensity, a special case of general Hawkes process that is most widely implemented in practice. This computational method is able to exactly generate the point process and intensity process, by sampling interarrival times directly via the underlying analytic distribution functions without numerical inverse, and hence avoids simulating intensity paths and introducing discretisation bias. Moreover, it is flexible to generate points with either stationary or non-stationary intensity, starting from any arbitrary time with any arbitrary initial intensity. It is also straightforward to implement, and can easily extend to multi-dimensional versions, for further applications in modelling contagion risk or clustering arrival of events in finance, insurance, economics and many other fields. Simulation algorithms for one dimension and multi-dimension are represented, with numerical examples of univariate and bivariate processes provided as illustrations.

Small work-load mode in a queueing system with random nonstationary intensity

We consider a queueing system of M t R|GI|1|∞ type with doubly stochastic Poisson arrival stream. The case of a small work load in such a system is studied. We derive an asymptotic expansion in the work-load smallness parameter of the distribution function of the virtual waiting time.

Nonstationary Vibration Control for Buildings by Using Time-Varying Weight.

There are many studies on vibration control for building using an active dynamic absorber. When applying active vibration control, it is most important problem to achieve higher performance within a certain constraint on actuator. However, it is difficult to solve this problem by using a stationary controller because seismic wave has nonstationary characteristics. This study presents a controller design method based on the nonstationary optimal control. In this technique, the characteristics of nonstationary intensity such as a seismic wave is considered by using the time-varying criterion function. Time-varying weight corresponds to the envelop function which gives noncriterion function. Time-varying weight corresponds to the envelop function which gives non stationary intensity of a seismic wave. And this controller is designed by solving the time-varying Riccati equations. By considering uncertain characteristics of seismic wave, a modification method is presented, in which the time varying feedback gain is varied continuously depending on the mean square value of seismic wave. To compare the performance with a stationary control, numerical calculations and simulations were carried out. As a result, the effectiveness of nonstationary optimal control was shown.