Nonstationary Model Research Articles

Ice ridge evolution: Investigation in-situ and computer simulations

The article presents a two-dimensional three-layer non-stationary thermodynamic model allowing to calculate the annual variation (thermodynamic evolution) of the ice ridge using external meteorological and hydrological parameters as well as the information on the initial ice ridge porosity. For the test model simulation, the results of the study of morphometric characteristics of the ice ridge carried out in May-June 2011 and in April 2012 at « North Pole −38» and «North Pole −39» drifting stations were used. These studies were conducted using electric thermal drilling with computer recording of the penetration rate. Boreholes were drilled along the cross-section of the ridge crest at 0.5 m intervals. Cross-sectional profiles of ice ridge are illustrated. Applying the proposed model, it was possible to adequately reproduce the observed evolutionary changes in the main morphometric parameters (sail height, keel depth, thickness of the consolidated layer) of the investigated ice ridge.

A Non-Stationary Multi-UAV Cooperative Channel Model for 6G Massive MIMO mmWave Communications

A Non-Stationary Multi-UAV Cooperative Channel Model for 6G Massive MIMO mmWave Communications

Probabilistic stationary subspace regression model for soft sensing of nonstationary industrial processes

AbstractBenefitting from the development of industrial intelligence, data‐driven soft sensors have been widely applied in industrial processes in recent years. Driven by fluctuations in raw material quality, varying loads, and uncertain disturbances, industrial processes are often characterized by nonstationary properties. However, the nonstationary characteristics of the process are not considered in traditional data‐driven methods, leading to the poor prediction performance of soft sensors. Meanwhile, numerous nonstationary modelling methods have been proposed for process monitoring, with probabilistic stationary subspace analysis (PSSA) showing significant application potential. Unfortunately, PSSA has not yet been used to develop effective soft sensors for nonstationary processes. Therefore, the PSSA model is extended to the regression form (PSSR), and a corresponding soft sensing model is developed in this paper. Unlike previous approaches, the proposed PSSR can offer a suitable description of nonstationary processes and fully capture the mathematical correlation between input and output variables. Finally, the prediction performance of PSSR is verified through case studies on a numerical example and penicillin fermentation process. The experimental results indicate that PSSR can provide a superior solution for soft sensing modelling of nonstationary industrial processes.

Mitigating infectious disease risks through non-stationary flood frequency analysis: a case study in Malaysia based on natural disaster reduction strategy.

The occurrence of floods has the potential to escalate the transmission of infectious diseases. To enhance our comprehension of the health impacts of flooding and facilitate effective planning for mitigation strategies, it is necessary to explore the flood risk management. The variability present in hydrological records is an important and neglecting non-stationary patterns in flood data can lead to significant biases in estimating flood quantiles. Consequently, adopting a non-stationary flood frequency analysis appears to be a suitable approach to challenge the assumption of independent and identically distributed observations in the sample. This research employed the generalized extreme value (GEV) distribution to examine annual maximum flood series. To estimate non-stationary models in the flood data, several statistical tests, including the TL-moment method was utilized on the data from ten stream-flow stations in Johor, Malaysia, which revealed that two stations, namely Kahang and Lenggor, exhibited non-stationary behaviour in their annual maximum streamflow. Two non-stationary models efficiently described the data series from these two specific stations, the control of which could reduce outbreak of infectious diseases when used for controlling the development measures of the hydraulic structures. Thus, the application of these models may help prevent biased prediction of flood occurrences leading to lower number of cases infected by disease.

Projection of snowfall extremes in the French Alps as a function of elevation and global warming level

Abstract. Following the projected increase in extreme precipitation, an increase in extreme snowfall may be expected in cold regions, e.g., for high latitudes or at high elevations. By contrast, in low- to medium-elevation areas, the probability of experiencing rainfall instead of snowfall is generally projected to increase due to warming conditions. Yet, in mountainous areas, despite the likely existence of these contrasted trends according to elevation, changes in extreme snowfall with warming remain poorly quantified. This paper assesses projected changes in heavy and extreme snowfall, i.e., in mean annual maxima and 100-year return levels, in the French Alps as a function of elevation and global warming level. We apply a recent methodology, based on the analysis of annual maxima with non-stationary extreme value models, to an ensemble of 20 adjusted general circulation model–regional climate model (GCM–RCM) pairs from the EURO-CORDEX experiment under the Representative Concentration Pathway 8.5 (RCP8.5) scenario. For each of the 23 massifs of the French Alps, maxima in the hydrological sense (1 August to 31 July) are provided from 1951 to 2100 and every 300 m of elevations between 900 and 3600 m. Results rely on relative or absolute changes computed with respect to current climate conditions (corresponding here to +1 ∘C global warming level) at the massif scale and averaged over all massifs. Overall, daily mean annual maxima of snowfall are projected to decrease below 3000 m and increase above 3600 m, while 100-year return levels are projected to decrease below 2400 m and increase above 3300 m. At elevations in between, values are on average projected to increase until +3 ∘C of global warming and then decrease. At +4 ∘C, average relative changes in mean annual maxima and 100-year return levels, respectively, vary from −26 % and −15 % at 900 m to +3 % and +8 % at 3600 m. Finally, for each global warming level between +1.5 and +4 ∘C, we compute the elevation threshold that separates contrasted trends, i.e., where the average relative change equals zero. This elevation threshold is shown to be lower for higher return periods, and it is projected to rise from 3000 m at +1.5 ∘C to 3350 m at +4 ∘C for mean annual maxima and from 2600 to 3000 m for 100-year return levels. These results have implications for the management of risks related to extreme snowfall.

Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions

We consider an observation-driven location model where the unobserved location variable is modeled as a random walk process and where the error variable is from a mixture of normal distributions. The time-varying location can be extended with a stationary process to account for cyclical and/or higher order autocorrelation. The mixed normal distribution can accurately approximate many continuous error distributions. We obtain a flexible modeling framework for the robust filtering and forecasting based on time-series models with non-stationary and nonlinear features. We provide sufficient conditions for strong consistency and asymptotic normality of the maximum likelihood estimator of the parameter vector in the specified model. The asymptotic properties are valid under correct model specification and can be generalized to allow for potential misspecification of the model. A simulation study is carried out to monitor the forecast accuracy improvements when extra mixture components are added to the model. In an empirical study we show that our approach is able to outperform alternative observation-driven location models in forecast accuracy for a time-series of electricity spot prices.

A time-varying Copula-based approach to quantify the effects of antecedent drought on hot extremes

Hot extremes may adversely impact human health and agricultural production. Owing to anthropogenic and climate changes, the close and dynamic interaction between drought and hot extremes in most areas of China need to be revisited from the perspective of nonstationarity. This study therefore proposes a time-varying Copula-based model to describe the nonstationary dependence structure of summer extreme temperature (SET) and antecedent soil moisture condition to quantify the dynamic risk of hot extremes conditioned on dry/wet condition. A general statistical inspection procedure which was composed of maximum likelihood (ML)-based estimation, nonstationary Goodness-of-fit (GOF) tests, the log likelihood ratio (LR) tests and minimum corrected Akaike information criterion-based selection was promoted to select the best-fitted nonstationary models efficiently. This study proposed a new approach to identify the soil moisture driving law over extreme temperature from the point view of tail monotonicity and nonstationary risk assessment. Owing to the LTI-RTD (left tail increasing and right tail decreasing) tail monotonicity for dependence structure of these two extremes derived from most areas, two kinds of the driving laws of soil moisture over SET were detected. Because of the spatiotemporal divergence of sensitivity index derived from tail monotonicity (SITM), we can conclude that the spatial and temporal heterogeneity of response degree of ET over the variations of antecedent dry/wet conditions is evident. Incorporation of nonstationarity and tail monotonicity helps identify the changes of driving mechanism (laws) between soil moisture and hot extremes.

Likelihood-free inference in state-space models with unknown dynamics

Likelihood-free inference (LFI) has been successfully applied to state-space models, where the likelihood of observations is not available but synthetic observations generated by a black-box simulator can be used for inference instead. However, much of the research up to now has been restricted to cases in which a model of state transition dynamics can be formulated in advance and the simulation budget is unrestricted. These methods fail to address the problem of state inference when simulations are computationally expensive and the Markovian state transition dynamics are undefined. The approach proposed in this manuscript enables LFI of states with a limited number of simulations by estimating the transition dynamics and using state predictions as proposals for simulations. In the experiments with non-stationary user models, the proposed method demonstrates significant improvement in accuracy for both state inference and prediction, where a multi-output Gaussian process is used for LFI of states and a Bayesian neural network as a surrogate model of transition dynamics.

An approach for computing the thermal balance and energy consumption of concrete pits during boiling of frozed logs for veneer production

ABSTRACT An approach for computing the thermal balance and energy consumption of pits during boiling of frozed logs intended for veneer production has been presented. With the help of our own non-stationary model, the boiling times of beech logs with a diameter of 0.4 m, initial temperature of −10°C, and moisture content of 0.6 kg·kg−1 were determined at water temperatures in the pit equal to 70°C, 80°C and 90°C. Using the determined logs’ boiling durations and the mentioned approach, the change in energy required for the entire boiling process and that for each of the components of the thermal balance was calculated. Computer simulations were performed for concrete pit with a volume of 20 m3 and a degree of filling with logs 45%, 60%, and 75%. It was found that the total energy consumption of the pit increases from 169 to 205 kWh·m−3 when the temperature of the boiling water increases from 70°C to 90°C at a pit filling level of 75%. The approach can be applied to compute thermal balances of concrete pits during boiling of frozed and non-frozed logs to any desired final average mass temperature required for the mechanical processing of the plasticized logs.

Multi-taper S-transform method for estimating Wigner-Ville and Loève spectra of quasi-stationary harmonizable processes

Current non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to overestimation and ambiguity of structural responses. The quasi-stationary harmonizable process with its Wigner-Ville spectrum (WVS) and Loève spectrum, which do not suffer from the deficiencies of EPSD, is suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, the multi-taper S-transform (MTST) method for estimating WVS and Loève spectrum of multi-variate quasi-stationary harmonizable processes is presented. The analytical biases and variances of the WVS, Loève spectrum, and time-invariant and time-varying coherence estimators from the MTST method are provided under the assumption that the target multi-variate harmonizable process is Gaussian. Using a numerical case of a bivariate harmonizable wind speed process, the superiority and reliability of the MTST method are demonstrated through comparisons with several existing methods for the WVS and Loève spectrum estimations. Finally, the MTST method is applied to two pieces of ground motion acceleration records measured during the Turkey earthquake in 2023.

Identification of dynamic drought propagation from a nonstationary perspective and its application to drought warnings

Accurate drought warnings in changing environments remain challenging since the nonstationary behaviors of drought propagation. The novelty of this study is the presentation of a nonstationary framework for drought propagation analysis and the objective determination of drought propagation thresholds. The calculated propagation probabilities and thresholds are responsive to changing environments. The Generalized Addictive Models in Location, Scale and Shape (GAMLSS) and time-varying Clayton copula function were adopted to establish the nonstationary joint distribution between meteorological and hydrological drought indices. Several indices reflecting the climatic and anthropic impacts on hydrological process were selected as covariates. Combined with the conditional probability distribution function, the time-varying drought propagation probabilities can be estimated to describe the watershed drought tolerance variations. The receiver operator characteristic (ROC) curves were utilized to determine the propagation thresholds for drought warnings. The upper Yellow River Basin (UYRB) was selected as the study area. Results indicate that the nonstationary models show better fitting performance for two drought indices series. The Clayton copula function with dynamic parameters offers a more accurate description of the linkages between two types of drought. The analysis of watershed drought tolerance reveals a declining trend from June to October, contrasting with an increasing trend during other months. In comparison to the stationary approach, the hit rates of the proposed method improve by 0.18, reaching 0.88, while the false alarm rates decrease by 0.11, reaching 0.24. The criteria for propagation threshold determination in the UYRB is established as a conditional probability of 20%. These findings can provide a foundation for drought warning management in a changing environment.

A KDE-based non-parametric cloud approach for efficient seismic fragility estimation of structures under non-stationary excitation

With the development of performance-based earthquake engineering, the risk-informed assessment framework has received broad recognition over the world, of which the probability seismic fragility analysis is an important step. The classic seismic fragility adopts the lognormal assumption and forms a parametric derivation. With the development of fragility theory, researchers are hoping to seek out non-parametric approaches to express the intrinsic fragility in a pure analytical form without any distribution assumptions. Besides, how to keep the calculation efficiency (e.g., combining with cloud approach) and how to consider the non-stationary stochastic responses (e.g., combining with non-stationary stochastic excitation model) are critical aspects in fragility that deserve further attention of researchers. In this paper, a kernel density estimation (KDE) based non-parametric cloud approach is proposed for efficient seismic fragility estimation of structures under non-stationary excitation. First, the methodology framework of the efficient approach is illustrated. Then, the procedures of non-stationary stochastic seismic response of structures and KDE-based non-parametric cloud approach for efficient seismic fragility are demonstrated. After that, an application example via a three-span-six-story reinforced concrete frame is given for implementation, followed with a parametric analysis of critical factors. During the process, the classic parametric linear-regression based cloud approach (cloud-LR) and benchmark Monte-Carlo-simulation based cloud approach (cloud-MCS) are also incorporated for validation. In general, the analysis verifies the effectiveness of the non-parametric cloud-KDE approach without requiring more computation work (i.e., same as the parametric cloud-LR approach and much less than the benchmark cloud-MCS approach). Meanwhile, the non-parametric cloud-KDE approach indicates a comparable accuracy with the classic fragility approaches (i.e., less deviation than the parametric cloud-LR approach and much closer to the benchmark cloud-MCS approach), and with the increase of stochastic cloud-point number, the corresponding fitting degree of cloud-KDE approach is growing better. The research provides a new sight for the development of non-parametric seismic fragility approach, and the corresponding findings can be further combined with the probabilistic hazard and risk analysis for a non-parametric assessment procedure in performance-based earthquake engineering.

Simulation of non-stationary ground motions and its applications in high concrete faced rockfill dams via direct probability integral method

Many high concrete face rockfill dams (CFRDs) have been constructed in earthquake-prone areas in recent years, and it is essential to evaluate the seismic safety performance of these dams considering the randomness of seismic excitation. In this paper, the relationship between the stochastic ground motion generation method and the direct probability integral method (DPIM) is established by using the number theory point selection method as the bridge. The DPIM is introduced into the field of stochastic dynamic analysis and multi-index reliability evaluation of high CFRD for the first time. First, a non-stationary stochastic excitation model at five sites is established based on the latest standard for the seismic design of hydraulic structures. Then, taking a practical project as an example, stochastic dynamic response analysis and reliability assessment based on dam crest settlement deformation and dam slope cumulative slippage are conducted by using DIPM. Finally, the influence of these two indexes on reliability is explored by drawing the equal failure probability curve. The results show that the stochastic dynamic analysis and reliability assessment framework established in this paper can provide probabilistic seismic safety assessments for high CFRDs. Sliding damage of the dam slope is more likely than the deformation damage of the rockfill from the perspective of probability.

A Non-Stationary Cluster-Based Channel Model for Low-Altitude Unmanned-Aerial-Vehicle-to-Vehicle Communications

Under the framework of sixth-generation (6G) wireless communications, the unmanned aerial vehicle (UAV) plays an irreplaceable role in a number of communication systems. In this paper, a novel cluster-based low-altitude UAV-to-vehicle (U2V) non-stationary channel model with uniform planar antenna arrays (UPAs) is proposed. In order to comprehensively model the scattering environment, both single and twin clusters are taken into account. A novel continuous cluster evolution algorithm that integrates time evolution and array evolution is developed to capture channel non-stationarity. In the proposed algorithm, the link between the time evolution of twin clusters and that of single clusters is established to regulate the temporal evolution trend. Moreover, an improved observable radius method is applied to UPAs for the first time to describe array evolution. Based on the combination of cluster evolution and time-variant channel parameters, some vital statistical properties are derived and analyzed, including space–time correlation function (ST-CF), angular power spectrum density (PSD), Doppler PSD, Doppler spread (DS), frequency correlation function (FCF), and delay spread (RS). The non-stationarity in the time, space, and frequency domain is captured. It demonstrates that the airspeed, density of scatterers within clusters, and carrier frequency have an impact on statistical properties. Furthermore, twin clusters have more flexible spatial characteristics with lower power than single clusters. These conclusions can provide assistance and reference for the design and deployment of 6G UAV communication systems.

Effects of non-stationary wind velocity models on buffeting performance of closed-box girder suspension bridges

Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges. The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of a super long-span suspension bridge was investigated in this paper. Firstly, four non-stationary wind velocity models are established by combing the time-varying average wind velocity with an exponential function and the fluctuating wind velocity with four modulation functions, respectively. These non-stationary wind velocity models have obvious non-stationary characteristics and then are validated by the classical power spectrum densities. Finally, three displacement responses of the bridge deck under four different independent variables of β in the exponential function and four modulation functions were compared, respectively. Results show that the turbulence intensities using two non-uniform modulation functions (NMF) are larger than those using uniform modulation functions (uMF). Moreover, the root mean square (RMS) values of three displacement responses increase with the decrease of β. Besides, the RMS values of three displacement under two NMFs are larger than those under two uMFs, and their RMS values under the second uMF are the smallest.

A Kriging Method for the Estimation of ALS Point-Cloud Accuracy without Ground Truth

Airborne LiDAR scanning is a promising approach to providing high-resolution products that are appropriate for different applications, such as flood management. However, the vertical accuracy of airborne LiDAR point clouds is not constant and varies in space. Having a better knowledge of their accuracy will assist decision makers in more accurately estimating the damage caused by flood. Data producers often report the total estimation of errors by means of comparison with a ground truth. However, the reliability of such an approach depends on various factors including the sample size, accessibility to ground truth, distribution, and a large enough diversity of ground truth, which comes at a cost and is somewhat unfeasible in the larger scale. Therefore, the main objective of this article is to propose a method that could provide a local estimation of error without any third-party datasets. In this regard, we take advantage of geostatistical ordinary kriging as an alternative accuracy estimator. The challenge of considering constant variation across the space leads us to propose a non-stationary ordinary kriging model that results in the local estimation of elevation accuracy. The proposed method is compared with global ordinary kriging and a ground truth, and the results indicate that our method provides more reliable error values. These errors are lower in urban and semi-urban areas, especially in farmland and residential areas, but larger in forests, due to the lower density of points and the larger terrain variations.

Learning and Optimization with Seasonal Patterns

Decision Making in a Nonstationary Environment with Periodic Rewards Multiarmed bandit (MAB) is a powerful tool in sequential decision making. Traditional MAB models assume constant mean rewards over time, an assumption often too restrictive for real-world applications in which rewards can vary seasonally. In “Learning and Optimization with Seasonal Patterns,” Chen, Wang, and Wang challenge the standard assumption and study a nonstationary MAB model with periodic rewards. They introduce a two-stage policy that combines Fourier analysis with a confidence bound–based learning procedure. This innovative approach allows the algorithm to adapt to time-varying mean rewards that follow a periodic pattern. The first stage estimates the periods of all decision-making arms, whereas the second stage exploits this information to optimize long-term rewards. The study proves that the learning policy is near optimal, achieving a regret upper bound that scales with the square root of the time horizon and the periods of the arms. This work opens new avenues for more adaptive and efficient decision making in many applications that face seasonality, such as the fashion industry and service systems.

Research on the influence of the non-stationary effect of the magnetorheological finishing removal function on mid-frequency errors of optical component surfaces.

With the continuous development of modern optical systems, the demand for full spatial frequency errors of optical components in the system is increasing. Although computer-controlled sub-aperture polishing technology can quickly correct low-frequency errors, this technology significantly worsens the mid-frequency errors on the surface of the component, which greatly inhibits the improvement of optical system performance. Therefore, we conducted in-depth research on the non-stationary effect of the removal function caused by the fluctuation in magnetorheological polishing and their influence on the mid-frequency errors of the component surface. We established a non-stationary profile model of the removal function and applied this model to simulate the distribution of mid-frequency errors on the surface of the processed component, considering the non-stationary effect. The simulation results showed that the non-stationary effect of the removal function weaken the mid-frequency ripple errors but increase other mid-frequency errors. Therefore, we first proposed the optimal single-material removal thickness corresponding to the non-stationary effect and experimentally verified the effectiveness of the optimal material removal thickness in suppressing mid-frequency errors. The experimental results showed that when the magnetorheological finishing single-material removal thickness is set to the optimal value, both the mid-frequency ripple errors and the mid-frequency RMS on the surface significantly decrease. Therefore, this work provides a basis for improving the existing magnetorheological finishing process and effectively suppressing the mid-frequency errors on the surface of processed components. It also provides theoretical and technical support for the magnetorheological processing and manufacturing of high-precision optical components. At the same time, the non-stationary effect and the corresponding analytical models has the potential to be extended to other polishing tools.

A New Method of Building Envelope Thermal Performance Evaluation Considering Window–Wall Correlation

This study proposes a new method to accurately evaluate the overall building envelope thermal performance considering the window–wall correlation, providing a new tool for building thermal design. Firstly, a non-stationary room heat transfer model is established based on the Resistance-Capacity Network method. The influence of solar heat gain through the windows on the heat transfer process of the walls in the actual environment is considered, and the room’s integrated thermal resistance and integrated heat capacity indexes describing the overall room thermal resilience performance are proposed. Then, a field research test is conducted around Lhasa to obtain the local dwelling information, climate conditions, and indoor thermal environment. Numerical simulations using EnergyPlus are made to verify the effectiveness of the indexes in describing the overall building (maximum difference within 3.67% MBE and 2.92% CVRMSE) based on the field test results. Finally, the proposed envelope thermal performance index is used to analyze the local residential buildings around Lhasa. The results show that the lack of consideration of window–wall correlation has led to the failure of a local newly built building’s actual envelope performance to meet the design requirements. These findings could help to develop the thermal design method of the building envelope.

Effect analysis of spatial discrepancy of secondary emission yield on multipactor formation

Spatial discrepancy of secondary emission yield (SEY) is probably exacerbated by unexpected surface contamination or imperfect surface treatments for SEY suppression, which accordingly provokes increased multipactor risk in microwave devices. In this paper, an improved 2D2V nonstationary statistical modeling for multipactor of parallel plates capable of regarding all electron impacts and electron exchange at the periodic boundaries is developed to investigate the effect of this spatial SEY discrepancy on multipactor formation in microwave devices. The comparison with the 1D2V statistical modeling results, which is valid for the parallel-plate multipactor, proves the accuracy of this improved 2D2V statistical modeling and the necessity of appropriate boundary setting in multipactor analysis with spatial SEY variation. The modeling results also reveal that the multipactor establishment is dominated by the electron multiplication and the electron overflow in the high-SEY region, thus making the multipactor threshold strongly dependent on both the SEY property and the dimension of the region. Electron multiplication can be fully sustained in the high-SEY region when its size exceeds a critical dimension, which satisfies a scaling law (the sustaining dimension is proportional to the gap with the product of the RF frequency and the gap kept constant) and varies with the involved multipactor mode. This research will help in evaluating accidental multipactor risk caused by the surface contamination and the efficiency of multipactor prevention via applying surface treatments for SEY suppression to accessible regions.