Nonstationary Field Research Articles

Magnetic Field Feature Fusion of Underwater Vehicle Model Based on Principal Component Analysis

Aiming at the model of underwater vehicle, a magnetic field feature fusion method based on principal component analysis (PCA) is proposed, focusing on: Non-stationary, nonlinear and non-Gaussian magnetic field time domain of underwater vehicle model based on genetic algorithm optimization neural network Feature extraction technology, underwater vehicle model fusion technology based on principal component analysis of magnetic field time-domain features, constructs effective PCA fusion features with low dimension, and finally uses the model sample recording data to conduct experiments on the main methods of this paper Verification and experimental simulation results show that PCA fusion features can reduce the feature dimension on the basis of maintaining a sufficient amount of effective information, and improve the target recognition efficiency. The results confirm the effectiveness of the related algorithms.

Optimization and Uncertain Nonlinear Vibration of Pre/post-buckled In-Plane Functionally Graded Metal Nanocomposite Plates

PurposeThis paper studies the nonlinear free and forced vibration of in-plane bi-directional functionally graded (FG) metal nanocomposite plates considering uncertain material elastic properties in the pre/post buckling states. Initially, the distribution of the nano-reinforcement volume fraction is designed through an optimization process to minimize the amount of the reinforcement in case of simply supported and clamped plates.MethodsThe elastic modulus of the nanocomposite is modeled as a non-stationary random field using the Karhunen–Loève expansion (KLE) technique while the uncertain output variables are modeled using the polynomial chaos expansion (PCE). The considered plates are thin, so the classical plate theory with the von Kármán nonlinear strain field is used for the analysis. The harmonic balance method and the fourth-order Runge Kutta method are used to estimate the vibration responses.ResultsThe in-plane optimization process of the nonreinforcement volume fraction distribution yielded a 14% and 70% saving in the reinforcement amount in the case of the simply supported plate and the clamped plate respectively. The uncertainty in the vibration amplitude in the pre-buckled state can be multiples of the uncertainty in the elastic modulus and follows near normal distributions. In the post-buckled state, the nature of the probability distribution depends on the excitation force and frequency. In general, the FG plates can have similar or more uncertainty levels compared to the equivalent homogenous plates.ConclusionThe uncertainty in the nonlinear vibration of in-plane functionally graded plates depends on the boundary conditions, modeling definition of the input uncertainty, the excitation force and frequency.

Spatially varying anisotropy for Gaussian random fields in three-dimensional space

Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces. In the ocean, the variability of a response may vary with depth, and ocean currents may lead to spatially varying anisotropy. We construct a class of non-stationary anisotropic Gaussian random fields (GRFs) in three dimensions through stochastic partial differential equations (SPDEs), where computations are done efficiently using Gaussian Markov random field approximations. A key novelty is the parametrization of the spatially varying anisotropy through vector fields.In a simulation study, we find that simple stationary models obtain reasonable parameter estimates with a moderate number of observations and a single realization, whereas the most complex non-stationary anisotropic model requires dense observations and multiple realizations. Further, we construct a stationary and a non-stationary GRF prior for salinity in an ocean mass outside Trondheim, Norway, based on simulations from the complex numerical ocean model SINMOD. These GRF priors are then evaluated using in-situ measurements collected with an autonomous underwater vehicle. We find that the new model outperforms the stationary anisotropic GRF prior for real-time prediction of unobserved locations both in terms of root mean square error and continuous rank probability score.

Scalable Bayesian Transport Maps for High-Dimensional Non-Gaussian Spatial Fields

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and uncertainty quantification of the map estimation, while resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional distributions due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for flexible marginals. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output. Supplementary materials for this article are available online.

An innovative integrated path planning and trajectory tracking framework for a quadrotor slung load system in an urban environment

In this paper, a hybrid path planning and trajectory tracking controller for a quadrotor slung load system is presented. This controller has benefited from the fuzzy inference system in its tracking and swing stabilization tasks. This system also plays an important role in creating a grid-based obstacle avoidance method that works based on the concept of generating Non-stationary Artificial Potential Field (NAPF) in the proximity of the objects tracking a virtual target on the path computed by A* algorithm. The weakness of the conventional artificial potential field method, that is to stuck in local minima, is now resolved by this so-called hybrid A*-NAPF method in which the potential field is non-stationary. The A* algorithm as a fast optimal path determination method computes the discrete initial path using a network of grids already generated through transferring the environment to a binary occupancy map. The performance of the whole integrated system is investigated through various simulation scenarios including those with moving obstacles. The results indicate a very good performance with high adaptability characteristic.

Efficient simulation of non-stationary non-homogeneous wind field: Fusion of multi-dimensional interpolation and NUFFT

The stochastic wave approach is a new realization of the spectral representation method and has been widely used for the simulation of stationary non-homogeneous or non-stationary homogeneous wind fields. However, it inevitably creates many unnecessary simulation points due to the invoking of the Fast Fourier Transform (FFT) and suffers from low efficiency in non-stationary non-homogeneous scenarios due to the incapability to accelerate the summation of trigonometric functions. In this study, an efficient approach is developed for the simulation of non-stationary non-homogeneous wind field. Central to this approach is a multi-dimensional interpolation used to decouple the evolutionary spectra accompanied by the application of non-uniform FFT (NUFFT) to expedite the simulation. A surrogate model that accurately approximates the 3D evolutionary spectrum related to height, frequency, and time is established by the 3D reduced Hermite interpolation, which enables a successful separation of the frequency components. Then, the NUFFT is applied to speed up the summation of trigonometric functions over wavenumbers with a well-designed non-uniformly distributed sampling points, which effectively reduces the segments used in the Fourier transform. Since there is no required mapping between the wavenumbers and the locations of simulation points in NUFFT, a significant number of unnecessary simulation points in the FFT scenario is avoided. Moreover, the wind samples at different locations can be obtained by directly altering the query points of NUFFT, thus the efficiency of the enhanced approach is almost independent of the number of simulation points. The numerical example in simulating the non-stationary non-homogeneous wind field of a long-span cable-stayed bridge demonstrates the efficiency of the developed approach and validates the effectiveness of the simulated wind samples in view of evolutionary spectrum and coherence function.

A Fourier series non-stationary coherency model with respect to site conditions for the horizontal component of ground motion

A Fourier series non-stationary coherency model with respect to the site conditions for the horizontal component was developed. The evolution of the model was achieved using parameters related to the site, inter-station distance, and time. First, based on the simulation of a non-stationary ground-motion field considering the wave-passage effect and site-response effect, the approach used for the estimation of coherency using wavelet transform is presented. Subsequently, the Fourier series non-stationary coherency model is formulated. The parameters are considered piecewise constant variables to represent the non-stationarity of the estimated coherency. The effects of the site and inter-station distance on the proposed model are presented. Parameters related to the site and inter-station distance were obtained. Finally, the proposed model is compared with the ground motion records at the SMART-1 array during Event 45, the stationary model, and the data from the Argostoli rock-site dense array. This indicates that the Fourier series non-stationary coherency model with respect to site conditions for the horizontal component can well match the correlation of the realistic spatially variable seismic ground motion, which is related to the site, time, and inter-station distance.

Analytical Models of Time-Dependent Physical Fields of the Earth: Local Version

A new method for analytical description of time-dependent signals of different nature based on local and regional versions of the method of linear integral representations in spaces of different dimensions is proposed. The inverse problem of finding the field sources is reduced to solving ill-conditioned systems of linear algebraic equations with an approximate right-hand side. The results of a mathematical experiment on finding elements of nonstationary gravity and magnetic fields of the Earth are presented.

Self-focusing and self-splitting properties of partially coherent temporal pulses propagating in dispersive media.

Based on the coherence theory for non-stationary optical fields, we introduce a new class of partially coherent pulse sources with multi-cosine-Gaussian correlated Schell-model (MCGCSM) and derive the analytic expression for the temporally mutual coherence function (TMCF) of an MCGCSM pulse beam when it propagates through dispersive media. The temporally average intensity (TAI) and the temporal degree of coherence (TDOC) of the MCGCSM pulse beams spreading in dispersive media are investigated numerically, respectively. Our results show that over propagation distance, the evolution of pulse beams is from the primary single beam into multiple subpulses or form flat-topped TAI distributions by controlling source parameters. Moreover, when the chirp coefficient s < 0, the MCGCSM pulse beams through dispersive media will show the characteristics of two self-focusing processes. The reason why there are two self-focusing processes is explained from the perspective of physical meaning. The results in this paper can open the applications of pulse beams in multiple pulse shaping and laser micromachining and material processing.

ИНТЕЛЛЕКТУАЛЬНОЕ ПЛАНИРОВАНИЕ СТРАТЕГИЙ И УПРАВЛЕНИЕ ГРУППОЙ МОБИЛЬНЫХ РОБОТОВ В УСЛОВИЯХ НЕПОЛНОТЫ ИНФОРМАЦИИ

Different problems of strategy planning and control of a mobile robot group under complex dynamicconditions with incomplete information about the external environment are considered. Approachesto solving problems of effective work scheduling under conditions of inconstant active groupcomposition, searching for the source of a nonstationary concentration field, supervisory control ofdiscrete-event systems are presented. An original mathematical model formulated in terms of work-shiftscheduling problems and a problem-oriented modification of evolutionary algorithms with a specializedset of heuristics for its efficient solution are developed for the problem of scheduling top-level groupwork. Searching and monitoring the source of the nonstationary concentration field is carried out usinga decentralized multi-agent control strategy that combines elements of bionic and gradient approaches,as well as a method for generating artificial potential fields. The considered control strategy has lowcomputational complexity, high variability with respect to the types of fields surveyed, and is easily scalableto control any available number of mobile robots. The latter is of special importance, in particularwhen considering the problem of parallel and independent monitoring of multiple sources. It is proposedto use the means of logical inference, namely automatic theorem proving in the calculus of positivelyconstructed formulas, to solve various problems of the supervised control theory of discrete-eventsystems used at different levels of the robotic complex hierarchical control system. Features of the calculusallows solving complex problems of dynamic systems control, as well as processing and controllingevents based on environmental data in real time in the process of logical inference efficiently. Theapproach based on positively constructed formulas allows studying the properties of automata-baseddiscrete-event systems, as well as to synthesize and model finite automata for the construction and realizationof monolithic and modular supervisors. A general scheme combining the considered approachesfor controlling a group of mobile robots at different levels and time scales within a single hierarchicalcontrol system is proposed.

Random pulse source with the temporal multi-complex degree of coherence

Based on the coherence theory, the non-stationary optical fields with the complex degree of coherence (CDOC) are expanded from stationary fields, and random pulse sources with temporal multi-complex degree of coherence (TMCDOC) is introduced. Theoretical model for the random pulse sources with TMCDOC is established. The analytical transmission formulas for the temporally spectral density and TMCDOC of the pulse beam spreading through dispersive media are derived and its propagation properties in dispersive media are explored. One can find from the numerical results that the TMCDOC pulse beam will evolve from a single pulse at the source plane into N subpulses in the far field or produce far field spectral density with flat-topped profiles. The variation of the non-trivial phase of the CDOC can regulate the propagation angle of the TMCDOC pulse beam. Moreover, in case of the propagation in dispersive media with chirp coefficient s < 0, the TMCDOC pulse beam will exhibit self-focusing process, and its coherence curves will be reversed from the clockwise rotation in the near field to anticlockwise rotation in the far field.

Two dimension-reduction probabilistic models for simulating nonstationary turbulent wind fields

The reasonable modeling of a nonstationary stochastic turbulent wind field is an important basis and premise for the analysis of the wind-induced response and reliability of engineering structures. In the present study, two dimension-reduction probabilistic models are established for simulating the multi-dimensional and multi-variable nonstationary turbulent wind fields based on the double proper orthogonal decomposition (DPOD) and the double spectral representation method (DSRM). Among them, the DPOD, originally used to simulate a stationary turbulent wind field, is extended to a nonstationary one, and the DSRM is a newly proposed method for a nonstationary turbulent wind field with a large number of simulation points. In essence, the DPOD is a discrete method with explicit physical significance and flexible spatial location of simulation points, while the DSRM is a continuous method, of which the simulation efficiency is theoretically independent of the number of simulation points. Furthermore, by introducing the dimension-reduction methods based on random function and POD-FFT (Fast Fourier transform) technique into the DPOD and the DSRM, the nonstationary stochastic turbulent wind field can be effectively described with merely three elementary random variables. Numerical examples of the nonstationary stochastic turbulent wind fields acting on a long-span bridge and a communication tower fully verify the effectiveness and superiority of the proposed methods.

Probabilistic analysis of skirted foundations under combined loading in soils modelled by non-stationary random fields

Skirted foundations are widely used in offshore engineering. The soils that skirted foundations are sited in commonly exhibit inherent spatial variability due to complex formation processes and stress history. In this study, probabilistic undrained capacities are investigated for skirted foundations with varying embedment ratios in spatially variable soils characterised by both stationary and non-stationary random fields using lower bound random finite element limit analysis combined with Monte Carlo simulation. Results show that the spatial variability of soil tends to decrease the uniaxial capacities. The coefficient of variation of soil strength, among the investigated parameters, could significantly affect stochastic uniaxial bearing capacities. Both embedment ratio and soil heterogeneity index affect the size and the shape of probabilistic failure envelopes, while statistical characteristics of soil strength including coefficient of variation and autocorrelation distance affect the size of probabilistic failure envelopes but have a minor influence on the shape. A larger embedment ratio is recommended to be adopted for skirted foundations sited in spatially variable soils from the perspective of load-carrying capacity. A series of expressions are proposed to describe the deterministic and probabilistic normalised failure envelopes for skirted foundations under combined vertical, horizontal and moment loadings.

High-efficiency simulation of nonstationary wind velocity using diagonal POD of decomposed time-frequency interpolation node spectrum matrices

The classical spectral representation method (SRM) used extensively to simulate nonstationary wind fields suffers from lower efficiency. Although some tries can already accelerate SRM, the efficiency improvement is restricted when the number of simulation points is large. For this reason, this paper proposed a high-efficiency interpolation scheme to boost the efficiency of SRM. Firstly, the decomposed time-frequency interpolation node spectrum matrices can be approximately decouple into the products of time and frequency functions using diagonal proper orthogonal decomposition (POD). Specifically, the POD operation is just for the diagonal elements, which are low-dimensional matrices. Since Cholesky decomposition is merely needed in the time-frequency interpolation point, the time consumed by spectral decomposition will be significantly reduced. Then, one-dimensional (1D) interpolation is implemented for these decoupling terms in the time and frequency directions, respectively. The decoupling results only contains a few time terms, so the number of 1D interpolation operations can be considerably decreased. Moreover, by exchanging the summation order, very few fast Fourier transform operations are required to accelerate harmonic superposition. Therefore, the proposed method may further enhance the simulation efficiency. Finally, through numerical examples, the accuracy and superiority of the proposed method are demonstrated.

The behavior of partially coherent twisted space-time beams in atmospheric turbulence

We study how atmospheric turbulence affects twisted space-time beams, which are non-stationary random optical fields whose space and time dimensions are coupled with a stochastic twist. Applying the extended Huygens–Fresnel principle, we derive the mutual coherence function of a twisted space-time beam after propagating a distance z through atmospheric turbulence of arbitrary strength. We specialize the result to derive the ensemble-averaged irradiance and discuss how turbulence affects the beam’s spatial size, pulse width, and space-time twist. Lastly, we generate, in simulation, twisted space-time beam field realizations and propagate them through atmospheric phase screens to validate our analysis.

Design and Analysis of an Effective Multi-Barriers Model Based on Non-Stationary Gaussian Random Fields

In this paper, we propose an extension to the barrier model, i.e., the Multi-Barriers Model, which could characterize an area of interest with different types of obstacles. In the proposed model, the area of interest is divided into two or more areas, which include a general area of interest with sampling points and the rest of the area with different types of obstacles. Firstly, the correlation between the points in space is characterized by the obstruction degree of the obstacle. Secondly, multiple Gaussian random fields are constructed. Then, continuous Gaussian fields are expressed by using stochastic partial differential equations (SPDEs). Finally, the integrated nested Laplace approximation (INLA) method is employed to calculate the posterior mean of parameters and the posterior parameters to establish a spatial regression model. In this paper, the Multi-Barriers Model is also verified by using the geostatistical model and log-Gaussian Cox model. Furthermore, the stationary Gaussian model, the barrier model and the Multi-Barriers Model are investigated in the geostatistical data, respectively. Real data sets of burglaries in a certain area are used to compare the performance of the stationary Gaussian model, barrier model and Multi-Barriers Model. The comparison results suggest that the three models achieve similar performance in the posterior mean and posterior distribution of the parameters, as well as the deviance information criteria (DIC) value. However, the Multi-Barriers Model can better interpret the spatial model established based on the spatial data of the research areas with multiple types of obstacles, and it is closer to reality.

Modulation effect on rotor-stator interaction subjected to fluctuating rotation speed in a centrifugal pump

In the paper, the modulation effect of rotor-stator interaction subjected to fluctuating rotation speed is investigated numerically. A quasi-bivariate variable mode decomposition method for analyzing non-stationary flow fields is proposed for the first time. Different from the previous studies, this paper emphasizes the local features of the transient flow field at fluctuating rotation speed. The results show that the impact of fluctuating rotation speed on the impeller force is limited, but it significantly impacts the pressure pulsation at fluctuating frequency. The correlation between amplitude and fluctuation ratio is positive. Meanwhile, the fluctuating rotation speed also induces sidebands centered on the blade passing frequency and its harmonics. The periodic changes in rotational speed lead to frequency and amplitude modulation of pressure pulsations. The magnitude of the instantaneous frequency and amplitude increases as the fluctuation ratio grows. The change in pressure field is well synchronized with the rotational speed, while the change in velocity field lags behind the rotational speed. The variation of pressure field with rotational speed is mainly attributed to two aspects. One is the flow structure at the fluctuating frequency, and the other is the instantaneous component of the flow structure at blade passing frequency.

Transient Electromagnetic Flaw Detection and Casing Wall Thickness Measurements in Multi-String Wells

The transient electromagnetic method is the most effective in the studying of multi-string wells. First, the nonstationary field is measured after the current is turned off (without the primary field) that reduces the coil spacing to zero, i.e. combine the generator and receiver coils. This significantly improves the vertical characteristic of the probe, allows the probe to register small defects. Second, the non-stationary mode allows separating signals from the first, second, third, etc. strings much easier than the harmonic mode. It improves the accuracy of thickness estimation and defect detection. The paper proposes an algorithm for interpreting the measurement results.

A Spatial Invariance Principle for Non-stationary Random Fields

A Spatial Invariance Principle for Non-stationary Random Fields

Визуализация эволюции тепловых полей при отражении ударной волны от торца канала ударной трубы

Panoramic thermographic visualization of a non-stationary thermal fields on the rectangular shock tube end wall was carried out. Thermal fields evolution of outer (end wall) surface during shock wave reflection is studied. Heat fluxes distribution data were obtained at various times within 4 seconds after reflection. The influence of the boundary layer on heat transfer behind the reflected shock wave is analyzed.