Gaussian Random Process Research Articles

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

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

Extending the Applicability of the Meyer–Peter and Müller Bed Load Transport Formula

The present paper deals with the applicability of the Meyer–Peter and Müller (MPM) bed load transport formula. The performance of the formula is examined on data collected in a particular location of Nestos River in Thrace, Greece, in comparison to a proposed Εnhanced MPM (EMPM) formula and to two typical machine learning methods, namely Random Forests (RF) and Gaussian Processes Regression (GPR). The EMPM contains new adjustment parameters allowing calibration. The EMPM clearly outperforms MPM and, also, it turns out to be quite competitive in comparison to the machine learning schemes. Calibrations are repeated with suitably smoothed measurement data and, in this case, EMPM outperforms MPM, RF and GPR. Data smoothing for the present problem is discussed in view of a special nearest neighbor smoothing process, which is introduced in combination with nonlinear regression.

Variance-based sensitivity analysis of dynamic systems with both input and model uncertainty

This paper develops a methodology to compute variance-based sensitivity indices for dynamic systems with time series inputs and outputs, while accounting for both aleatory and epistemic uncertainty sources, and both random process and random variable inputs. We present semi-analytical methods for computing sensitivity indices for linear systems with Gaussian random process inputs, and for the general case of nonlinear systems with non-Gaussian random process inputs. The novel elements in this approach are the treatment of model form error, quantifying the cumulative effects of uncertainty sources over time, and evaluating sensitivity indices for multi-physics models. Bayesian state and parameter estimation methods are incorporated to quantify the model uncertainty arising from unknown model parameters and model form errors, and sensitivity indices are computed before and after model updating. The proposed methods are illustrated for (a) a linear Timoshenko beam erroneously modeled as an Euler-Bernoulli beam, and (b) hypersonic flow behavior of a flexible panel represented by a coupled multi-physics nonlinear model.

On two approaches to the third-order solution of surface gravity waves

A third-order approximate solution for surface gravity waves in the finite water depth is studied in the context of potential flow theory. This solution corresponds to the steady-state part of a multidirectional irregular wave field and provides explicit expressions for the surface elevation, free-surface velocity potential, and velocity potential. The amplitude dispersion relation is also provided. Two approaches are used to derive the third-order analytical solution, resulting in two types of approximate solutions: the perturbation solution and the Hamiltonian solution. The perturbation solution is obtained by a classical perturbation technique in which the time variable is expanded in multiscale to eliminate secular terms. The Hamiltonian solution is derived from the canonical transformation in the Hamiltonian theory of water waves. By comparing the two types of solutions, it is found that they are completely equivalent for the first- and second-order solutions and the nonlinear dispersion, but for the third-order part only the sum–sum terms are the same. Due to the canonical transformation that could completely separate the dynamic and bound harmonics, the Hamiltonian solutions break through the difficulty that the perturbation theory breaks down due to singularities in the transfer functions when the quartet resonance criterion is satisfied. Furthermore, it is also found that some time-averaged quantities based on the Hamiltonian solution, such as mean potential energy and mean kinetic energy, are equal to those in the initial state in which the sea surface is assumed to be a Gaussian random process. This is because there are associated conserved quantities in the Hamiltonian form. All of these show that the Hamiltonian solution is more reasonable and accurate to describe the third-order steady-state wave field. Finally, based on the Hamiltonian solution, some statistics are given such as the volume flux, skewness, excess kurtosis, and non-uniqueness of the induced mean flow and mean surface.

The Thermal Error Estimation of the Machine Tool Spindle Based on Machine Learning

Thermal error is one of the main sources of machining error of machine tools. Being a key component of the machine tool, the spindle will generate a lot of heat in the machining process and thereby result in a thermal error of itself. Real-time measurement of thermal error will interrupt the machining process. Therefore, this paper presents a machine learning model to estimate the thermal error of the spindle from its feature temperature points. The authors adopt random forests and Gaussian process regression to model the thermal error of the spindle and Pearson correlation coefficients to select the feature temperature points. The result shows that random forests collocating with Pearson correlation coefficients is an efficient and accurate method for the thermal error modeling of the spindle. Its accuracy reaches to 90.49% based on only four feature temperature points—two points at the bearings and two points at the inner housing—and the spindle speed. If the accuracy requirement is not very onerous, one can select just the temperature points of the bearings, because the installation of temperature sensors at these positions is acceptable for the spindle or machine tool manufacture, while the other positions may interfere with the cooling pipeline of the spindle.

Machine learning calibration of low-cost NO<sub>2</sub> and PM<sub>10</sub> sensors: non-linear algorithms and their impact on site transferability

Abstract. Low-cost air pollution sensors often fail to attain sufficient performance compared with state-of-the-art measurement stations, and they typically require expensive laboratory-based calibration procedures. A repeatedly proposed strategy to overcome these limitations is calibration through co-location with public measurement stations. Here we test the idea of using machine learning algorithms for such calibration tasks using hourly-averaged co-location data for nitrogen dioxide (NO2) and particulate matter of particle sizes smaller than 10 µm (PM10) at three different locations in the urban area of London, UK. We compare the performance of ridge regression, a linear statistical learning algorithm, to two non-linear algorithms in the form of random forest regression (RFR) and Gaussian process regression (GPR). We further benchmark the performance of all three machine learning methods relative to the more common multiple linear regression (MLR). We obtain very good out-of-sample R2 scores (coefficient of determination) >0.7, frequently exceeding 0.8, for the machine learning calibrated low-cost sensors. In contrast, the performance of MLR is more dependent on random variations in the sensor hardware and co-located signals, and it is also more sensitive to the length of the co-location period. We find that, subject to certain conditions, GPR is typically the best-performing method in our calibration setting, followed by ridge regression and RFR. We also highlight several key limitations of the machine learning methods, which will be crucial to consider in any co-location calibration. In particular, all methods are fundamentally limited in how well they can reproduce pollution levels that lie outside those encountered at training stage. We find, however, that the linear ridge regression outperforms the non-linear methods in extrapolation settings. GPR can allow for a small degree of extrapolation, whereas RFR can only predict values within the training range. This algorithm-dependent ability to extrapolate is one of the key limiting factors when the calibrated sensors are deployed away from the co-location site itself. Consequently, we find that ridge regression is often performing as good as or even better than GPR after sensor relocation. Our results highlight the potential of co-location approaches paired with machine learning calibration techniques to reduce costs of air pollution measurements, subject to careful consideration of the co-location training conditions, the choice of calibration variables and the features of the calibration algorithm.

Efficient Propagation of Epistemic Uncertainty for Probabilistic Seismic Hazard Analyses (PSHAs) Including Partial Correlation of Magnitude–Distance Scaling

ABSTRACT Probabilistic seismic hazard analysis (PSHA) is moving from ergodic ground-motion models (GMMs) to nonergodic GMMs that account for site-source-specific source, path, and site effects and which require a much larger number of GMM branches on the logic tree to capture the full epistemic uncertainty. An efficient method for computing PSHA with a large number of GMM branches was developed by Lacour and Abrahamson (2019) using polynomial chaos (PC) expansion with the key assumption that the epistemic uncertainty in the median ground motion is fully correlated. In the current study, we remove the assumption of full correlation using a multivariate PC expansion. The correlation structure of the available median GMMs across scenarios is computed empirically. The median ground motion is modeled as a Gaussian random process with the correlation structure of the GMMs across the range of relevant earthquake scenarios. This Gaussian random process is discretized using the Karhunen–Loeve expansion, which leads to multivariate PC expansions of uncertain hazard curves. The hazard fractiles can be reconstructed during an efficient postprocessing phase that includes the effects of partial correlation between the GMMs. Multivariate PC expansions require significantly more terms than for the fully correlated case, which increases the calculation time by about a factor of 5, but it is still much more efficient than direct sampling of the branches of the GMM logic for a large number of branches. An example hazard calculation shows that the effect of using partial correlation in place of full correlation of the GMMs is small for the Next Generation Attenuation-West2 (NGA-West2) set of GMMs, indicating that the fully correlated assumption may be adequate for many applications. The multivariate PC method can be used to evaluate the effects of the partial correlation of the GMMs for sets of GMMs that are different from the NGA-West2 GMMs.

Crop Nitrogen Retrieval Methods for Simulated Sentinel-2 Data Using In-Field Spectrometer Data.

Nitrogen (N) is one of the key nutrients supplied in agricultural production worldwide. Over-fertilization can have negative influences on the field and the regional level (e.g., agro-ecosystems). Remote sensing of the plant N of field crops presents a valuable tool for the monitoring of N flows in agro-ecosystems. Available data for validation of satellite-based remote sensing of N is scarce. Therefore, in this study, field spectrometer measurements were used to simulate data of the Sentinel-2 (S2) satellites developed for vegetation monitoring by the ESA. The prediction performance of normalized ratio indices (NRIs), random forest regression (RFR) and Gaussian processes regression (GPR) for plant-N-related traits was assessed on a diverse real-world dataset including multiple crops, field sites and years. The plant N traits included the mass-based N measure, N concentration in the biomass (Nconc), and an area-based N measure approximating the plant N uptake (NUP). Spectral indices such as normalized ratio indices (NRIs) performed well, but the RFR and GPR methods outperformed the NRIs. Key spectral bands for each trait were identified using the RFR variable importance measure and the Gaussian processes regression band analysis tool (GPR-BAT), highlighting the importance of the short-wave infrared (SWIR) region for estimation of plant Nconc—and to a lesser extent the NUP. The red edge (RE) region was also important. The GPR-BAT showed that five bands were sufficient for plant N trait and leaf area index (LAI) estimation and that a surplus of bands effectively reduced prediction performance. A global sensitivity analysis (GSA) was performed on all traits simultaneously, showing the dominance of the LAI in the mixed remote sensing signal. To delineate the plant-N-related traits from this signal, regional and/or national data collection campaigns producing large crop spectral libraries (CSL) are needed. An improved database will likely enable the mapping of N at the agro-ecosystem level or for use in precision farming by farmers in the future.

Serviceability Assessment of Footbridges Via Improved Interval Analysis

Abstract This paper studies the propagation of uncertainties on serviceability assessment of footbridges in unrestricted traffic condition based on a nondeterministic approach. Multipedestrian loading is modeled as a stationary Gaussian random process through the equivalent spectral model which yields analytical expressions of the spectral moments of the footbridge dynamic response. The uncertain pedestrian-induced loading parameters and structural dynamic properties are modeled as interval variables. An approximate analytical procedure, based on the improved interval analysis, is introduced as an efficient alternative to classical optimization in order to propagate interval uncertainties. The presented procedure allows us to derive closed-form expressions of the bounds of the spectral moments of the response, as well as of the expected value and cumulative distribution function of the maximum footbridge acceleration. Two strategies are proposed to assess footbridges' serviceability. The first one leads to the definition of a range of comfort classes. The second strategy enables us to estimate an interval of probability of reaching at least a suitable comfort level.

Prediction of Oral Pharmacokinetics Using a Combination of In Silico Descriptors and In Vitro ADME Properties.

Accurate prediction of oral pharmacokinetics remains challenging. This study investigated quantitative approaches for the prediction of the area under the plasma concentration-time curve after oral administration (AUCp,oral) to rats using the in vitro-in vivo extrapolation (IVIVE), in silico model using machine learning approaches and the combination of the in silico model and in vitro data. A set of 595 structurally diverse compounds with determined AUCp,oral at 1 mg/kg, in vitro intrinsic clearance (CLint), an unbound fraction in plasma (fu,p) in rats, and kinetic solubility at pH 6.8 was used for this assessment. Prediction models developed by two different types of machine learning techniques (i.e., random forest regression and Gaussian processes) were evaluated using three validation methods implementing the time and cluster-split training and test set and fivefold cross-validation. The developed machine learning models have a square of correlation coefficient (R2) in the range of 0.381-0.685 with 33-45% of the compounds being predicted within 2-fold of the observed AUCp,oral value. The predictivity was improved by incorporating CLint, fu,p, and solubility as explanatory variables with R2 = 0.554-0.743. In cases where extraction by the liver is the main elimination pathway and intestinal extraction is negligible, AUCp,oral can be expressed by dose, CLint, and fu,p based on a well-stirred model. By using this conventional IVIVE approach, only 1.7-5.0% of compounds were predicted within the 2-fold error with R2 = 0.354-0.487. Two empirical scaling factors (ESFs) determined by linear regression analysis and machine learning approaches improved the predictivity of AUCp,oral with 33-44% predicted within twofold variability. The IVIVE using ESF predicted by random forest regression showed better predictivity of AUCp,oral with R2 = 0.471-0.618, while it still showed lower predictivity than machine learning approaches applied directly to AUCp,oral prediction. This study demonstrated that the combination of in silico and in vitro parameters is useful to improve the predictivity of the machine learning model for rat AUCp,oral and supports consideration for predicting AUCp,oral for human and other non-clinical species in a similar manner.

Quantitative Representation of Aleatoric Uncertainties in Network-Like Topological Structural Systems

Abstract The complex topological characteristics of network-like structural systems, such as lattice structures, cellular metamaterials, and mass transport networks, pose a great challenge for uncertainty qualification (UQ). Various UQ approaches have been developed to quantify parametric uncertainties or high dimensional random quantities distributed in a simply connected space (e.g., line section, rectangular area, etc.), but it is still challenging to consider the topological characteristics of the spatial domain for uncertainty representation and quantification. To resolve this issue, a network distance-based Gaussian random process uncertainty representation approach is proposed. By representing the topological input space as a node-edge network, the network distance is employed to replace the Euclidean distance in characterizing the spatial correlations. Furthermore, a conditional simulation-based sampling approach is proposed for generating realizations from the uncertainty representation model. Network node values are modeled by a multivariate Gaussian distribution, and the network edge values are simulated conditionally on the node values and the known network edge values. The effectiveness of the proposed approach is demonstrated on two engineering case studies: thermal conduction analysis of 3D lattice structures with stochastic properties and characterization of the distortion patterns of additively manufactured cellular structures.

Predicting Quality and Yield of Growing Alfalfa from a UAV

HighlightsThe canopy height distributions from photogrammetry were mostly Gaussian distributions.The mean canopy height and standard deviation from photogrammetry can be used to predict yield and nutritive values.Including average field maturity and pest pressures improves the models to R2 values of around 0.8.The best predictive model types were generally Gaussian random processes.Abstract. Alfalfa producers would be able to manage their crop production practices better if they knew the distribution of yield and nutritive values of the alfalfa growing throughout their fields. Unmanned aerial vehicles (UAVs) equipped with cameras and photogrammetry techniques provide methods to quickly capture the plant canopy structure at field scale. The goal of this study was to determine how to use the point clouds produced by the photogrammetry process to estimate the yield and nutritive value of alfalfa throughout its growth cycle. During the 2017 growing season, weekly measurements were taken of 1 m2 quadrats (~20 per week, 325 total) in a field of alfalfa managed for forage production. Measurements in each quadrat included manual measurements of maximum and average height, weed presence, disease damage, insect damage, maturity level, stand plant density, and many images of the quadrat from a UAV. After processing to remove outliers, the canopy heights from the photogrammetry point clouds were largely Gaussian distributions. Models were developed using supervised machine learning to estimate yield and nutritive values, including acid detergent fiber (ADF), neutral detergent fiber (NDF), and crude protein (CP), with different numbers of predictor (input) variables. Simple models with two predictor variables were only based on the mean and standard deviation of the heights of the photogrammetry point cloud. The models with three predictor variables added average field maturity level. Finally, the models with six predictor variables added weed presence, insect damage, and disease damage. A linear regression with all interaction terms was found to be the best type of model for predicting yield with six variables. For all other outputs and numbers of predictor variables, a Gaussian random process (GRP) model was best. The models improved with additional predictor variables, so the six-variable models were best able to predict yield and nutritive value. The R2 values for the six-variable models for predicting yield, ADF, NDF, and CP were 0.81, 0.81, 0.78, and 0.79, respectively. Keywords: Alfalfa, Machine learning, Nutritive value, Photogrammetry, Unmanned aerial vehicle, Yield.

Explicit solution of Rice/Lalanne peak probability distribution for statistical fatigue assessment in the frequency domain

A closed-form explicit solution for statistical fatigue life assessment under broad-band stochastic loading is proposed herein. Obtained solution is valid for stationary, random and ergodic zero mean Gaussian stress process. It is based on Rice/Lalanne peak stress probability distribution function. The solution is given in terms of special Gaussian HyperGeometric function which accurately describes the transcendent error weighting function between the Rayleigh (i.e. narrow-band) and Gaussian (i.e. broad-band) contribution of the random vibration fatigue model. HyperGeometric-based solution is more accurate compared to other approximate methods based on the peak distribution from literature. Fatigue benchmark test comparison is performed in time and frequency domains with very good match-up reported.

Granger Causality of Gaussian Signals from Binary or Non-uniformly Quantized Measurements

This paper studies the assessment of Granger causality between jointly Gaussian signals from binary/non-uniformly quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through non-uniformly quantized measurements. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations.

Detección óptica en 3D de un objeto flotante en una superficie marina agitada

In this paper we realize a comparison between two detectors: Matched Subspace Detector (MSD) and Modify Matched Subspace Detector (MMSD) when there is a images secuence (3D detection), where the parameters of sea surface and the parameters of floating object are priori unknown in computer simulation, with help of computer software MATLAB. Both detectors (MSD and MMSD) are based in the General Likelihood Ratio Test (GLRT); this method helps solve detection problems when the sea surface and floating object parameters are unknown. The sea surface is simulated as a Gaussian random process, and the floating object is simulated as a priori unknown deterministic process. The paper considers the dependence of the probability of detection with a fixed probability of false alarm on the difference between the average values of reflections from the sea surface and from a floating object with different ratios of the power of fluctuations of reflections from the object and from the sea Surface.

Reliability Analysis and Random Vibration of Nonlinear Systems Using the Adjoint Method and Projected Differentiation

Abstract This paper proposes a new methodology for time-dependent reliability and random vibrations of nonlinear vibratory systems using a combination of a time-dependent adjoint variable (AV) method and a projected differentiation (PD) method. The proposed approach is called AV-PD. The vibratory system is excited by stationary Gaussian or non-Gaussian input random processes. A Karhunen–Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. The nonlinear equations of motion (EOM) are linearized using a Taylor expansion using the first-order derivatives of the output with respect to the input KL random variables. An adjoint approach obtains the output derivatives accurately and efficiently requiring the solution of as many sets of EOM as the number of outputs of interest, independently of the number of KL random variables. The proposed PD method then computes the autocorrelation function of each output process at an additional cost of solving as many sets of EOM as the number of outputs of interest, independently of the time horizon (simulation time). A time-dependent reliability analysis is finally performed using a KL expansion of the output processes and Monte Carlo simulation (MCS). The number of solutions of the EOM scales only with the number of output random processes which is commonly much smaller than the number of input KL random variables. The efficiency and accuracy of the proposed approach is demonstrated using a four degree-of-freedom (DOF) half-car vibratory problem.

Fatigue life prediction of ship and offshore structures under wide-banded non-Gaussian random loadings: Part II: extension to wide-banded non-Gaussian random processes

Ships and offshore structures are exposed to various cyclic loads such as winds, waves and currents in their lifetime. These loads can result in fatigue failures at hot spots, and to prevent such failures, accurate estimates of the fatigue life of hot spots should be performed in the design stage. The cycle distribution indicative of the probability distribution of cycles is an important factor in estimation of fatigue damage to mechanical systems in frequency-domain methods. It depends on not only the counting method but also the statistical properties of random processes. Many studies deriving both theoretical and approximate models of rainflow-counted cycle distributions in wide-banded non-Gaussian processes have been conducted. However, some of the existing models require multi-dimensional integrations with much computational time or yield inaccurate representations of rainflow-cycle distributions. Therefore, a new model providing accurate cycle distributions is needed for fatigue analysis of offshore structures under wide-banded non-Gaussian random loadings.This paper consists of two parts: Part I is devoted to the development of a new approximation model for the joint probability distribution of mean and amplitude of rainflow-counted cycles in wide-band Gaussian random processes. This probabilistic model derived in Gaussian random processes could be transformed to the corresponding non-Gaussian processes through non-linear transformation technique. Part II discusses the detailed procedure and accuracy of the proposed model in fatigue damage assessment of offshore structures under non-Gaussian random loading. Rainflow cycle distribution in wide-band non-Gaussian processes is derived using the Hermite transformation function. The accuracy of the proposed model is verified through two numerical examples, and compared to other existing models.

Напрямки наукових дослiджень Ю.В. Козаченка: статистичне моделювання

В роботi висвiтлюються науковi здобутки доктора фiзико-математичних наук професора Юрiя Васильовича Козаченка в галузi статистичного моделювання. Козаченко Ю.В. працював на кафедрi теорiї ймовiрностей, статистики та актуарної математики КНУ iменi Тараса Шевченка. Професор Козаченко Ю.В. стояв бiля витокiв статистичного моделювання в Київському унiверситетi. Козаченко Ю.В. та його учнями розробленi науковi основи теорiї моделювання гауссових та близьких до них випадкових процесiв i полiв в рiзних функцiональних просторах iз заданими точнiстю i надiйнiстю. При розробцi методiв статистичного моделювання значна увага придiлялась дослiдженню збiжностi статистичних моделей випадкових процесiв та полiв в рiзних функцiональних просторах. До результатiв наукової школи Козаченка Ю.В. належить i розробка теорiї функцiональних просторiв випадкових величин. Значне мiсце в цих дослiдженнях займають простори Орлiча.

Inter-comparison of several soil moisture downscaling methods over the Qinghai-Tibet Plateau, China

Microwave remote sensing is able to retrieve soil moisture (SM) at an adequate level of accuracy. However, these microwave remotely sensed SM products usually have a spatial resolution of tens of kilometers which cannot satisfy the requirements of fine to medium scale applications such as agricultural irrigation and local water resource management. Several SM downscaling methods have been proposed to solve this mismatch by downscaling the coarse-scale SM to fine-scale (several kilometers or hundreds of meters). Although studies have been conducted over different climatic zones and from different data sets with good results, there is still a lack of a comprehensive comparison and evaluation between them to guide the production of high-resolution and high-accuracy SM data. Therefore, in this study we compared several SM downscaling methods (from 0.25° to 0.01°) based on polynormal fitting, physical model, machine learning and geostatistics over the Qinghai-Tibet plateau where there is a wide range of climate conditions from four aspects, that is, comparison with the original microwave product, comparison with in situ measurements, inter-comparison based on three-cornered hat (TCH) method, and a spatial feasibility analysis. The comparison results show that the method based on a physical model, in this case the Disaggregation based on Physical And Theoretical scale Change (DisPATCh) method, has the highest ability on preserving the coarse-scale feature of original microwave SM product, while to some extent, this ability could be a disadvantage for improving the accuracy of the downscaling results. In addition, soil evaporation efficiency (SEE) alone is not sufficient to represent SM spatial patterns over complex land surface. Geostatistics based area-to-area regression Kriging (ATARK) introduces the highest uncertainty caused by the overcorrection during the residual interpolation process while this process can also improve correlation (R) and correct the bias as well as provide more feasible spatial patterns and details. Two machine learning methods, the random forest (RF) and Gaussian process regression (GPR) show high stability on all comparison results but provide smoother spatial patterns. The multivariate statistical regression (MSR) method performs worst due to the fact that its simple linear regression model could not meet the requirement of SM fitting on complicated land surface. Moreover, all five downscaling methods show a declining accuracy after downscaling. This phenomenon may be caused by the spatial mismatch on fine-scale. In addition, this could also be caused by the tendency that downscaled results will usually provide more spatial details from downscaling predictors, while they cannot capture the temporal changes of the microwave SM product well. In general, this phenomenon tends to be more significant over heterogeneous land surface. All in all, five widely used soil moisture downscaling methods were compared based on a comprehensive comparison scheme to add to the body of knowledge in applicability of downcaling methods under different weather conditions.

Development of hybrid dimension adaptive sparse HDMR for stochastic finite element analysis of composite plate

A novel adaptive high dimensional model representation (HDMR) is developed for stochastic finite element analysis of composite plate. Uncertainty propagating through the physical system is quantified using this technique where only the significant dimensions are retained. Influence of these dimensions is modeled by different orders which are preferred to be low for computational tractability. These dimensions are identified by a sensitivity analysis using support points in the sparse grid which are generated using multiple levels of hierarchy, joint or marginal probability distributions and dimension adaptiveness. This multi level hierarchical generation of support points fill the domain of the input variables with major emphasis on the regions of interest which may be the entire space, limit state, maxima/minima or tail ends of the probability distribution function for rare events depending upon the nature of the problem. The hybrid characteristics of the proposed dimension decomposition is introduced in this paper where the component functions are expressed using orthogonal bases and the error term which is further modeled using Gaussian random process (i.e. Kriging). The performance of the proposed Hybrid dimension adaptive HDMR (hdA-HDMR) is illustrated using stochastic finite element analysis of laminated composite plate whose material properties are considered as homogeneous non-normal random fields.