Nonstationary Model Research Articles

Interannual variations in the seasonal cycle of extreme precipitation in Germany and the response to climate change

Abstract. Annual maxima of daily precipitation sums can be typically described well with a stationary generalized extreme value (GEV) distribution. In many regions of the world, such a description does also work well for monthly maxima for a given month of the year. However, the description of seasonal and interannual variations requires the use of non-stationary models. Therefore, in this paper we propose a non-stationary modeling strategy applied to long time series from rain gauges in Germany. Seasonal variations in the GEV parameters are modeled with a series of harmonic functions and interannual variations with higher-order orthogonal polynomials. By including interactions between the terms, we allow for the seasonal cycle to change with time. Frequently, the shape parameter ξ of the GEV is estimated as a constant value also in otherwise instationary models. Here, we allow for seasonal–interannual variations and find that this is beneficial. A suitable model for each time series is selected with a stepwise forward regression method using the Bayesian information criterion (BIC). A cross-validated verification with the quantile skill score (QSS) and its decomposition reveals a performance gain of seasonally–interannually varying return levels with respect to a model allowing for seasonal variations only. Some evidence can be found that the impact of climate change on extreme precipitation in Germany can be detected, whereas changes are regionally very different. In general, an increase in return levels is more prevalent than a decrease. The median of the extreme precipitation distribution (2-year return level) generally increases during spring and autumn and is shifted to later times in the year; heavy precipitation (100-year return level) rises mainly in summer and occurs earlier in the year.

Non-stationary Bayesian spatial model for disease mapping based on sub-regions.

This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior to the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package fbesag equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary. Additionally, we model different causes of death in Brazil, where we use the new model to investigate the spatial stationarity of these causes.

A depth-variant seismic wavelet extraction method for basis pursuit inversion with an impedance trend constraint

The seismic images produced by prestack depth migration indicate more accurate subsurface structures than time images, resulting in a growing need for depth-domain inversion. However, due to the strong nonstationarity exhibited by depth-domain seismic data, time-domain inversion methods based on the convolutional model cannot be directly applied in the depth domain. To address this issue, we develop a method for extracting a depth-variant seismic wavelet, which is then combined with a nonstationary convolutional model to enable direct inversion of the depth-domain acoustic impedance (AI). First, we extend the Morlet wavelet to the depth domain and develop an orthogonal matching pursuit spectral decomposition method using the depth-domain Morlet wavelet. We then investigate the waveforms and wavenumber spectra similarities between the depth-domain Morlet wavelet and depth-domain Ricker wavelet and extract depth-variant Ricker wavelets from the depth-wavenumber spectrum. We add a depth-domain impedance trend constraint to the conventional basis pursuit inversion to enhance the lateral continuity of the inversion results. Then, we attain direct inversion of the depth-domain AI. Tests of synthetic and field data demonstrate that our method achieves high-accuracy inversion results while maintaining high computational efficiency, highlighting our approach’s effectiveness and strong reservoir characterization potential.

Dynamic Bayesian-Network-Based Approach to Enhance the Performance of Monthly Streamflow Prediction Considering Nonstationarity

In recognizing the pervasive nonstationarity of hydrometeorological variables, a paradigm shift towards alternative analytical methodologies is imperative for refining hydroclimatic data modeling and prediction. We introduce a novel approach leveraging nonstationary Graphical Modeling and Bayesian Networks (NGM-BNs) tailored for hydrometeorological applications. Demonstrated through monthly streamflow forecasting in the Kashgar River Basin of China, our method illuminates the temporal evolution of network relationships, underscoring the dynamism inherent in both input variables and modeling parameters. The key to our approach is identifying the most suitable time horizon (MST) for model updates, which is intricately problem-specific and crucial for peak performance. This methodology not only unveils changing predictor significance across varying flow conditions but also elucidates the fluctuating temporal links between variables, especially under the lens of climate change, for instance, the growing impact of snowmelt on the Kashgar Basin’s streamflow. Compared to stationary counterparts, our nonstationary Bayesian framework excels in capturing extreme events by adeptly accommodating temporal shifts, outperforming traditional models including both stationary and nonstationary variants of Support Vector Regression (SVR) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS).

Non-stationary buffeting responses of a twin-box girder suspension bridge with various evolutionary spectra

The effects of evolutionary wind spectra with different modulation functions on the nonstationary buffeting responses of suspension bridges are uncertain. After considering the nonlinear buffeting force of a twin-box girder, the buffeting responses of a cross-sea suspension bridge under four nonstationary wind speed models with two uniform modulation and two nonuniform modulation functions were investigated in this paper. Through the evolutionary spectral theory, the nonstationary wind speed models at the bridge site with four typical modulation functions were generated and then validated from the autocorrelation and power spectrum density. The results show that the mean and root-mean-square error (RMSE) values of vertical and horizontal wind speeds by using nonuniform modulation functions (NMF1 and NMF2) were much larger than those by using uniform modulation functions (uMF1 and uMF2). Moreover, most of the peak and RMSE values for the torsional and lateral displacement under the NMF1 are the largest, while the RMSE values of the vertical displacement without the modulation function are the largest. With the increase of the circular frequency γ or decrease of the initial phase θ in the cosine function of time-varying mean wind speeds, the RMS values in three displacement responses of the bridge deck become larger.

A novel framework for wind energy assessment at multi-time scale based on non-stationary wind speed models: A case study in China

Wind energy assessment at multi-time scale is essential for the effective utilization of offshore wind resources. Conventionally, energy assessment factors are estimated based on parametric models under the assumption of wind speed stationarity. However, given the subjection of seasonal variability and long-term trends, the hypothesis is violated, especially in the context of climate change. In this paper, to advance the conventional approach, wind speeds were modelled using the decomposition-based method to consider the non-stationarity, and a novel framework for the estimation of energy factors at multi-time scale was designed. Using long-term ERA5 data, wind energy potential across the sea area along Chinese continental coastline was investigated. It is demonstrated that the established non-stationary models are superior to commonly used stationary models, allowing the estimation of energy assessment factors at arbitrary time scales after one-time parametrization of parametric distributions. Results confirmed that wind energy exhibits apparently temporal and spatial variability. The difference between annual averaged wind power density at different nodes exceeds 1000 W/m2. Moreover, significant long-term trends of wind energy characteristics were detected. The increase can be up to 16 W/m2/year in Taiwan Strait, emphasizing that an adequate consideration of the non-stationarity of wind speed in future research is required.

Structural reliability analysis under stochastic seismic excitations and multidimensional limit state based on gamma mixture model and copula function

A novel method for analyzing the reliability of structures under non-stationary stochastic seismic excitations, considering the combined effect of multiple structural demand extreme values, is proposed. The spectral representation method is employed to establish a non-stationary stochastic seismic excitation model, and based on the theory of first-passage probability, multiple integral formulas for seismic reliability under multidimensional limit states are derived. The extreme value distribution is established using the Gamma mixture model (GMM). The equations for estimating the model parameters are derived based on both fractional moments and moment-generating functions, while the determination of the number of gamma distribution components is guided by the probability distribution and statistical characteristics of the samples. The joint probability density function (JPDF) for multiple demand extreme values is established by incorporating copula functions to account for correlation, and the fitting accuracy of different copula functions is assessed. The proposed method is illustrated using reinforced concrete (RC) frame structures. The results demonstrate that the fitting accuracy of extreme value distribution can be enhanced by adjusting the number of gamma distribution components in the GMM, which exhibits high accuracy in fitting both the main and tail regions. The presence of correlation can induce variations in the JPDF, thereby exerting an influence on the failure probability. Consequently, disregarding correlation is not conducive to reliability analysis.

Random noise attenuation of 3D multicomponent seismic data using a fast adaptive prediction filter

Random noise in seismic records affects the accuracy of effective signal identification, making it difficult for subsequent seismic data processing, imaging, and interpretation. Therefore, random noise attenuation has always been an important step in seismic data processing, especially for 3D data. In recent years, multicomponent exploration has been developed rapidly. However, the common method for processing multicomponent data is to process each component separately resulting in the correlation between multicomponent data being neglected. For 3D multicomponent data, we develop a multicomponent adaptive prediction filter (MAPF) based on noncausal regularized nonstationary autoregressive models to implement random noise attenuation in the t- x- y domain. The MAPF for multicomponent signals can be used to identify the potential correlations and differences between each pair of components, providing not only a robust analysis of the individual components but also effective information about the consistency and differences between each component with more information and constraints compared with traditional 1C prediction. Moreover, it can obtain smooth nonstationary prediction coefficients by solving the least-squares problem with shaping regularization. The example results demonstrate that the MAPF method is superior to the traditional adaptive prediction filtering method. Furthermore, because the multicomponent method requires more coefficients and takes a longer time to predict than the 1C method, we further develop a fast MAPF (FMAPF) combining the data pooling and coefficient reconstruction strategies. The example results demonstrate that the FMAPF method is effective at denoising and greatly improves computational efficiency. The method comes with a slight decrease in computational accuracy.

APPLICATIO STUDY ON KINETICS OF BIOMASS PYROLYSIS IN THE FIXED BED. 1. SIMULATION AND NUMERICAL ANALYSIS OF LIGNIN THERMAL DECOMPOSITION

A non-stationary model of the biomass thermolysis process was built based on three primary independent parallel reactions of the biomass active part conversion into gas, liquid phase and char, taking into account the secondary reactions of tar decomposition into char and light gas. It is shown that the main role in the production of mixed pyrolysis gas (primary gas and light gas) is played by the light gas generation rate due to the secondary reaction of tar decomposition into light gas. This reaction rate significantly exceeds the primary gas production rate due to the fact that the activation energy of the primary gas formation reaction lignin → gas is higher than the activation energy of the lignin → tar reactions. It was found that the rate of generation of the primary reaction lignin → char significantly outweighs the rate of tar → char production, so the latter reaction can be neglected. It is shown that as the temperature of lignin pellets increases, CO and light hydrocarbon C1.16H4 increase and carbon dioxide CO2 and H2О decrease. The consumption of volatile components in the pyrolyzer depends on the temperature distribution of biomass pellets across the pyrolyzer cross-section, which decreases towards the center of the retort, following the consumption of gaseous components decreases as they approach the axis of the pyrolyzer. The amount of mixed pyrolysis gas released and char depends on the radial coordinate r. At r = 0.047 m and time τ = 380 s, the amount of mixed pyrolysis gas is 90 % and char is 10 %, at r = 0.016 m and τ = 380 s = 83 % and = 17 %. Bibl. 13, Fig. 7.

Numerical modelling of the IMF influence on the large-scale structure of the ionosphere, including the poles displacement

The interplanetary magnetic field (IMF), frozen into the solar wind plasma, determines the level of geomagnetic activity and significantly affects the large-scale structure of the high-latitude ionosphere. Variations in the IMF components lead to non-stationarity of the magnetospheric convection electric field, causing changes in the spatio-temporal distribution of charged particles in the ionosphere. The situation is complicated by the fact that the geographic and geomagnetic poles do not coincide, which leads to universal time control (UT control) of the parameters of the high-latitude ionosphere. The effect of the poles displacement is most manifest in winter. Therefore, in this work, within the framework of a nonstationary mathematical model of the F-region of the ionosphere in Euler variables, taking into account the displacement between the geographic and geomagnetic poles, we study the influence of the interplanetary magnetic field components on the large-scale structure of the high-latitude ionosphere in winter. For this, the Weimer model of high-latitude electric potentials, which depends on the IMF, was used. As a result, of numerical modelling, it is shown that the IMF components affect the shape, size and spatio-temporal location of the main structural features of the high-latitude ionosphere depending on universal time. The obtained effect of ionisation tongue separation requires experimental confirmation. The obtained results demonstrate that the developed non-stationary three-dimensional model of the ionosphere in Euler variables can be applied to the study of ionospheric disturbances, including ionospheric disturbances associated with changes in the IMF components.

Stationary and dynamic mathematical modeling of autothermal reforming of diesel with aromatic compounds

The previously proposed stationary mathematical model provides a reliable description of n-hexadecane (diesel surrogate) reforming over the Rh/Ce0·75Zr0·25O2-δ/θ-Al2O3/FeCrAl structured catalyst. In its continuation this work represents the experimental studies and the model of the autothermal reforming process of hexadecane in a mixture with o-xylene and 1-methylnaphthalene. The reaction scheme is supplemented with reactions to account for steam reforming and oxidation of added aromatics compounds and selection of corresponding kinetic parameters is performed. The dynamic process of the reformer start until reaching the steady state is simulated by the non-stationary model in this work. The resulting mathematical and kinetic models provide a good description of the experiments performed with the reproduction of the dynamics of the observed outlet gas components concentrations and the catalyst temperature. The application of this model can be useful when considering the reforming of multicomponent mixtures or optimization of the dynamic start reformer process.

LAND-USE FILTERING FOR NONSTATIONARY SPATIAL PREDICTION OF COLLECTIVE EFFICACY IN AN URBAN ENVIRONMENT.

Collective efficacy-the capacity of communities to exert social control toward the realization of their shared goals-is a foundational concept in the urban sociology and neighborhood effects literature. Traditionally, empirical studies of collective efficacy use large sample surveys to estimate collective efficacy of different neighborhoods within an urban setting. Such studies have demonstrated an association between collective efficacy and local variation in community violence, educational achievement, and health. Unlike traditional collective efficacy measurement strategies, the Adolescent Health and Development in Context (AHDC) Study implemented a new approach, obtaining spatially-referenced, place-based ratings of collective efficacy from a representative sample of individuals residing in Columbus, OH. In this paper we introduce a novel nonstationary spatial model for interpolation of the AHDC collective efficacy ratings across the study area, which leverages administrative data on land use. Our constructive model specification strategy involves dimension expansion of a latent spatial process and the use of a filter defined by the land-use partition of the study region to connect the latent multivariate spatial process to the observed ordinal ratings of collective efficacy. Careful consideration is given to the issues of parameter identifiability, computational efficiency of an MCMC algorithm for model fitting, and fine-scale spatial prediction of collective efficacy.

Non-Stationary Low-Altitude UAV MIMO A2G Channel Model With Rotation and Arbitrary Trajectories

Non-Stationary Low-Altitude UAV MIMO A2G Channel Model With Rotation and Arbitrary Trajectories

Robustness of design flood estimates under nonstationary conditions: parameter sensitivity perspective

The changing frequency of flooding in global watersheds, driven by various human and natural factors like land use/cover changes and global warming, necessitates innovative approaches in flood frequency analysis and risk assessment. Nonetheless, the reliability of nonstationary frequency analysis models remains a concern given challenges in accurately measuring the uncertainty introduced by these methods and the impact on design flood values. In this study, deviation-based differential sensitivity indices, including single-parameter (SDDSI) and entire-parameter (EDDSI) measures were developed to assess the influence of parameter uncertainty in nonstationary models using Bayesian statistics and "equivalent reliability" nonstationary design. The Weihe River, the largest tributary of the Yellow River which is experiencing both climate change and heavy impact of human activities, is chosen to be the study area to investigate the impact of precipitation change and land use change on nonstationary flood frequency. Results show that in the One-At-A-Time (OAT) sensitivity analysis under a small uncertainty scenario (SUS) for parameter inputs, the shape parameter stands out as the most influential factor (SDDSI_SUS = 0.347) affecting the 100-year design flood in the Stationary Generalized Extreme Value (SGEV) model. For the Non-Stationary GEV (NGEV) models, the influence of this parameter is less pronounced, with SDDSI_SUS values of 0.095 and 0.093 for the SSP126 and SSP585 scenarios, respectively. Instead, attention turns to the regression coefficient of the grassland area, associated with the GEV scale parameter. In global sensitivity analysis under the posterior uncertainty scenario (PUS) for parameter inputs, the EDDSI_PUS values for SGEV, NGEV_SSP126, and NGEV_SSP585 models were 0.52, 1.41, and 1.30, respectively, inferring heightened sensitivity of NGEV models to perturbations from entire parameters. It is anticipated that incorporating additional evidence, such as historical flood data, is essential for accurate nonstationary hydrological design to mitigating the influence of parameter uncertainty. The sensitivity indices in this study provide significant insights for assessing the robustness of nonstationary hydrological design in flood risk management and applications.

A bi-level framework for real-time crash risk forecasting using artificial intelligence-based video analytics.

This study proposes a bi-level framework for real-time crash risk forecasting (RTCF) for signalised intersections, leveraging the temporal dependency among crash risks of contiguous time slices. At the first level of RTCF, a non-stationary generalised extreme value (GEV) model is developed to estimate the rear-end crash risk in real time (i.e., at a signal cycle level). Artificial intelligence techniques, like YOLO and DeepSort were used to extract traffic conflicts and time-varying covariates from traffic movement videos at three signalised intersections in Queensland, Australia. The estimated crash frequency from the non-stationary GEV model is compared against the historical crashes for the study locations (serving as ground truth), and the results indicate a close match between the estimated and observed crashes. Notably, the estimated mean crashes lie within the confidence intervals of observed crashes, further demonstrating the accuracy of the extreme value model. At the second level of RTCF, the estimated signal cycle crash risk is fed to a recurrent neural network to predict the crash risk of the subsequent signal cycles. Results reveal that the model can reasonably estimate crash risk for the next 20-25min. The RTCF framework provides new pathways for proactive safety management at signalised intersections.

SHyTCWaves: A stop-motion hybrid model to predict tropical cyclone induced waves

Waves produced by tropical cyclones (TCs) can be estimated using non-stationary wave models forced with time-varying wind fields. However, dynamical simulations are time and computationally demanding at regional-scale domains since high temporal and spatial resolutions are required to correctly simulate TC-induced wave propagation processes. Applications such as early warning systems, coastal risk assessments and future climate projections benefit from fast and accurate estimates of wave fields induced by close-to-real storm tracks geometry. The proposed SHyTCWaves methodology constitutes a novel tool capable of estimating the spatio-temporal variability of directional wave spectra produced by TCs in deep waters, using a hybrid approach and statistical techniques to reduce CPU time effort. This work demonstrates that TC-induced waves can be reconstructed using a stop-motion approach based on the addition of successive 6 h periods of time-varying storm conditions. The developed hybrid model reduces a TC track to a number of segments that are parameterized in terms of 10 representative TC features, and generates a library of cases dynamically pre-computed which allow to ensemble consecutive 6 h analog segments representing the original TC track. The metamodel has been compared and corrected with available satellite data, and its applicability is exemplified for TC Ofa in the South Pacific.

Research of nonstationary dynamic models of the organizational and technological process of railway transport technical vehicles repair

The problems of analytical and computer research of dynamic models of repair and operation of technical vehicles used in railway transport are among the urgent problems related to ensuring safety and stability of traffic, with the development of digital twins and the improvement of monitoring and diagnostic systems. The analysis of models described by various types of multidimensional nonlinear differential equations requires the use of modern methods of dynamical systems theory, numerical optimization and computer algebra. The purpose of the article is to conduct a qualitative and numerical analysis of mathematical models of organizational and technological processes (OTP) in railway transport, as well as the synthesis of new controlled OTP models. Nonstationary generalizations of a two-dimensional dynamic model describing the repair process of railway transport equipment are proposed. Various cases of using constant and time-dependent parameters are considered. The case of linear and exponential dependences of parameters on time is studied. For the studied models, trajectories are obtained taking into account the variation of constant parameters and taking into account the choice of parametric dependencies, a comparative analysis of the results is presented. The formulation of the problem of optimal control of the number of repaired and repaired railway wagons is proposed. Promising methods for solving this problem using numerical optimization methods, including those inspired by nature, are described. The results can be used in the tasks of constructing and analyzing mathematical models of dynamic systems, in the tasks of numerical modeling of transport systems and technological processes, in the tasks of optimizing the number of vehicles and improving the transportation process, as well as in the tasks of creating digital counterparts in the transport industry.

A Non-Stationary Channel Model for 6G Multi-UAV Cooperative Communication

This paper proposes a novel three-dimensional (3D) non-stationary multiple-unmanned aerial vehicle (multi-UAV) cooperative channel model for sixth generation (6G) wireless communication systems. In the proposed multi-UAV cooperative channel model, the channel impulse response (CIR) of sub-channel between each UAV and ground station (GS) is calculated, including line-of-sight (LoS), non-LoS (NLoS), as well as ground reflection transmissions. The relative distance and transmission relationship among sub-channels between multi-UAVs and GS are further modeled and analyzed. To simultaneously capture the cooperative non-stationarity of multi-UAV cooperative channels in space and time domains, a novel cooperation-based space-time (S-T) non-stationary algorithm is developed based on the birth-death (BD) process for the first time. Meanwhile, the UAV-related parameters, e.g., the height and 3D movement of UAVs, are considered. Some important channel statistical properties, such as space-time-frequency correlation function (STF-CF), Doppler power spectral density (DPSD), cooperative time stationary interval, and singular value spread (SVS), are obtained. Based on the simulation results, multi-UAV cooperative channel statistical properties are analyzed. Finally, the simulation results match well with the ray-tracing results, which validates the accuracy of the proposed multi-UAV channel model.

Investigation on wave-induced responses of heterogeneous seabed around a buried pipeline based on nonstationary random field model

The instability of the seabed poses a threat to the structural integrity and functionality of submarine pipelines. This numerical study investigates wave-induced responses in a heterogeneous seabed around a buried pipeline, considering spatial variability in soil properties through nonstationary random field models. Three scenarios of spatial variability for soil parameters changing with depth are simulated using both stationary and nonstationary random field models via the Karhunen-Loève expansion method. The discrete random fields are validated in terms of correlation structures and statistical characteristics. The stochastic finite element method, incorporating random fields and a poroelastic seabed model through a LiveLink code, is employed to examine probabilistic outcomes of dynamic soil responses and liquefaction zone distributions within a probabilistic framework. Contrastive analyses are conducted for seabed models with different random field scenarios, in addition to deterministic analyses. The results of the stochastic analysis show that the increasing trend of soil strength with depth has significant effects on the seabed responses and transient liquefaction characteristics around a pipeline.

Automatic reconstruction of geological reservoir models based on conditioning data constraints and BicycleGAN

For geological reservoir units with different sizes of pore spaces and relatively stronger anisotropic heterogeneities, Generative-Adversarial-Network-based (GAN) modeling methods can overcome limitation of numerical-simulation-based ones and support finely representation of nonstationary models. However, due to conditioning data weak constraints, GANs might ignore local detail features, with artifacts and noise during simulation. Some pre-processing strategies are strictly limited by the conditioning data distribution patterns, and corresponding processes should be updated frequently when new data are introduced, with relatively complicated operation. Therefore, the BicycleGAN framework was introduced in this paper. Based on bijective consistency between the latent vector and output, an image-to-image translation task with different dimensions is established, and multiple networks were coupled to realize finely representation of spatial attributes. Specifically, the mapping between conditioning data and output is established through the U-Net architecture, which not only local detail information is considered, but also reduce the impact of conditioning data distribution patterns. Meanwhile, the mapping between latent and actual test time distribution is also established by an encoding function to ensure simulation authenticities. In addition, a joint loss function combined with conditioning loss and prior loss is defined to ensure reconstruction accuracy of different facies types. Four kinds of categorical and continuous training images were selected to verify the network simulation performances. Results show that reconstruction accuracy for facies types of conditioning data is almost consistent with those of the references, keeping similarities in terms of spatial variability, connectivity, structural similarity, and facies type reproductions. Meanwhile, for the saved BicycleGAN, inputting different kinds of conditioning data once only, and a variety of simulations can be obtained rapidly, thereby realizing conditioning reconstruction of geological reservoir models.