Stochastic Quantification Research Articles

Data-driven and knowledge-guided denoising diffusion probabilistic model for runoff uncertainty prediction

The existing medium and long-term runoff prediction methods, which are based on data-driven and knowledge-guided methods, are associated with inherent limitations, and chaotic phenomena in runoff prediction models often leads to oscillation in the prediction error, affecting the robustness of the prediction. A knowledge-guided denoising diffusion probabilistic model (DK-RDDPM) that introduces physical theory to guide constraint quantification and obtain effective runoff uncertainty prediction results is therefore proposed in this study. The main advantage of this model is that the physical randomness in the runoff prediction process can be captured and combined with the Saint-Venant process to guide model optimization and realize more accurate medium- and long-term runoff prediction. The main contributions of this study are the establishment of a dynamic runoff probabilistic prediction model with stochastic quantification characteristics that includes the prediction uncertainty over time, and modelling of the physical constraint boundary of runoff prediction from the perspective of partial differentiation. The effectiveness of the DK-RDDPM was verified by predicting runoff in the Qijiang and Tunxi Basins in China. The results show that: 1) Encoding the physical random uncertainty operator in runoff prediction into the network of the denoising diffusion probabilistic model (DDPM) effectively captures the physically complex implicit randomness of the process, thus reducing the error that results from randomness in runoff prediction. 2) The constraint matrix that is formed using the Saint-Venant equation and the prediction matrix are layered and projected, with the fluctuation range of the constraints in each step adjusted in the optimization direction within a certain random threshold range. 3) The DK-RDDPM shows superior performance to the benchmark models, even under the influence of different noise interference factors.

Stochastic Quantification of Spatial Variability of Flow Fields in Heterogeneous, Non-uniform, Confined Aquifers

Stochastic Quantification of Spatial Variability of Flow Fields in Heterogeneous, Non-uniform, Confined Aquifers

The role of different sources of uncertainty on the stochastic quantification of subsurface discharges in heterogeneous aquifers

The quantification of subsurface discharges may significantly be affected by multiple sources of uncertainty, especially in highly heterogeneous aquifers. In this work, subsurface discharges within alluvial aquifers located in the province of Lecco (Lombardy, Northern Italy) are quantified relying upon a Monte Carlo (MC) framework under geological and conditioning data uncertainty sources. These are respectively employed through different geological conceptual models, whose facies spatial distributions are simulated through Sequential Indicator Simulations methodology (SISIM), and by conditioning stochastic facies simulations with different data constraints. Stochastic porosity fields are then achieved upon facies simulated fields by associating average porosity values to each local simulated facies. Then, stochastic subsurface discharge fluxes are quantified under steady hydraulic conditions upon saturated hydraulic fields, inferred from porosity ones. Then, the study of subsurface discharges is pursued via the Generalized Extreme Values (GEV) approach. This method enables both to interpret peak-over-thresholds (POTs) discharges spatial distribution, and to study the role geological and data uncertainty sources on their quantification, for example studying discharges conveyed towards a lake through the surrounding aquifer. These uncertainty-based analyses show that subsurface discharges clearly convey in correspondence of main alluvial aquifers, as well as the tendency to be collected along preferential pathways. Furthermore, the inspection of POTs empirical probability spatial distributions highlights that the geological uncertainty plays as a primary uncertainty source rather than the conditioning data. The latter plays a minor role, e.g. between different employed models, only in presence of a relevant geological difference between analyzed ones. These results are consistent with other kinds of information, such as hydrogeological sections and available piezometric maps, providing novel contributions to understanding how to quantify subsurface discharges in poorly monitored aquifers or how to treat various sources of uncertainty.

Stochastic Quantification of Array Antennas With Random Feeding Errors Using an Improved Polynomial Chaos Expansion Method

Electromagnetic properties of an array antenna are inevitably affected by random magnitude and phase errors in the feeding network. Polynomial chaos expansion (PCE) method can analyze such problems, but the number of numerical quadrature grows rapidly with stochastic dimensionality for solving the PCE coefficients. An improved PCE algorithm is proposed to improve the computational efficiency. A large array is decomposed into several small groups those can be efficiently treated by the PCE method. Stochastic quantification of the whole array is achieved by the superposition of grouped results. In addition, the proposed method can integrate with the method of moments to treat real-world arrays. The results computed by this method agree with those of Monte Carlo, and the computational time is reduced by two orders of magnitude for a dipole array with 64 elements.

Stochastic quantification of CO2 fault sealing capacity in sand-shale sequences

Structural fault trapping of buoyant fluids, such as hydrocarbons and CO2, relies on fault sealing capacity. The traditional approach to quantifying the sealing capacity of fault zone materials is Shale Gouge Ratio (SGR), which implicitly homogenizes fault properties. However, a large range of fault throw and the presence of fault heterogeneity can lead to different trapping capacities for the same structure. This paper presents a stochastic study to statistically determine the possible range of CO2 column height at a normal fault in sand-shale sequences. We present the procedures of two stochastic models including the continuous shale gouge model (CSGM) and the discrete smear model (DSM). The models are applied in an example case for the High Island field in the Gulf of Mexico (GOM) basin combining borehole geophysical data and measurements from laboratory experiments. Both one-dimensional and two-dimensional cases are discussed. The results show that more than 50% of the realizations predict negligible fault sealing capacity. The CSGM method shows that CO2 column height is overall proportional to SGR and breakthrough pressure. The DSM model suggests that clay smear continuity may significantly affect fault sealing capacity. Large fault throws (>100 m) result in smear breaches and therefore in highly variable maximum CO2 column heights, varying from 0 m to a maximum of ∼95 m. Both the DSM method and the CSGM method proposed in this paper permit explaining geologic uncertainties and the resulting variability of column heights observed in the field. Our results together with the field data from the literature demonstrate the utility of combining both methods to help improve column height prediction. Uncertainty quantification of clay ductility, smear location, and fault heterogeneity is important for determining fault sealing capacity and improving reservoir risk management associated with carbon dioxide geological storage.

Stochastic scheduling of ground movement problem integrated with taxiway routing and gate/stand allocation

The authors propose a new scheduling model and solution method for Ground Movement Problem (GMP) which is designed to manage the movements of flights on the surface of airport air-side in an effective manner. Since the arrival time for arrival flights and off-block time for departure flights are usually uncertain parameters for GMP, the proposed scheduling model is stochastic and integrates the three-dimensional (3-D) taxiway routes’ assignment (with variable taxiing speed for flights) and the gates/stands allocation for the flights, with fully capturing multiple constraints related to taxiways, gates/stands and aircraft performance limits. The solution method also provides a stochastic quantification scheme concerning both uncertainties by the arrival time and off-block time information. The schedule results can realize the immunity of the above time uncertainties within a tolerable risk probability. We finally provide numerical analysis to verify the stochastic scheduling model with mixed integer and linear programming (MILP) basics and illustrate the effectiveness of proposed solution method by a test case on Hangzhou international airport in China.

Temporal Variability in the Response of a Linear Time-Invariant Catchment System to a Non-Stationary Inflow Concentration Field

Predicting the effects of changes in dissolved input concentration on the variability of discharge concentration at the outlet of the catchment is essential to improve our ability to address the problem of surface water quality. The goal of this study is therefore dedicated to the stochastic quantification of temporal variability of concentration fields in outflow from a catchment system that exhibits linearity and time invariance. A convolution integral is used to determine the output of a linear time-invariant system from knowledge of the input and the transfer function. This work considers that the nonstationary input concentration time series of an inert solute to the catchment system can be characterized completely by the Langevin equation. The closed-form expressions for the variances of inflow and outflow concentrations at the catchment scale are derived using the Fourier–Stieltjes representation approach. The variance is viewed as an index of temporal variability. The closed-form expressions therefore allow to evaluate the impacts of the controlling parameters on the temporal variability of outflow concentration.

A semi-analytical stochastic buckling quantification of porous functionally graded plates

This paper introduces a semi-analytical approach integrated with Monte Carlo simulation for stochastic buckling analyses of porous functionally graded plates arising due to the inevitable source-uncertainties of geometrical configurations and material properties. Analytical derivations based on the classical plate theory in conjunction with three-variable refined shear deformation theory are carried out first leading to closed-form solutions for buckling loads and thereby, the closed-form equations are exploited to conduct the comprehensive stochastic quantification of buckling loads in a non-intrusive framework based on Monte Carlo simulation. The deterministic framework is validated with a separate finite element analysis before implementing it for stochastic analysis. The first-order and second-order perturbation theory integrated with the Taylor series expansion are utilized to derive closed-form expressions for the mean and variance of stochastic buckling loads which are compared with Monte Carlo simulation results. Sensitivity of stochastic buckling loads on individual and compound uncertainties are investigated to determine the relative importance of different uncertainty sources. Effects of plate thickness, volume fraction index, and degree of stochasticity variations on the probability distributions of the first three stochastic buckling loads are investigated for both uniaxial and biaxial load cases. The complete probabilistic descriptions presented in this paper assert that the overlapping areas in probability distribution plots corresponding to the consecutive buckling modes lead to the existence of non-unique critical buckling modes, which could potentially be crucial for analyses and designs of structural systems under an inevitable stochastic environment. This article convincingly demonstrates the importance of considering source-uncertainties in porous functionally graded structures including the critical loopholes for a buckling analysis in the presence of such uncertainties.

Geostatistical independent simulation of spatially correlated soil variables

The selection of best management practices to reduce soil and water pollution often requires estimation of soil properties. It is important to find an efficient and robust technique to simulate spatially correlated soils parameters. Co-kriging and co-simulation are techniques that can be used. These methods are limited in terms of computer simulation due to the problem of solving large co-kriging systems and difficulties in fitting a valid model of coregionalization. The order of complexity increases as the number of covariables increases. This paper presents a technique for the conditional simulation of a non-Gaussian vector random field on point support scale. The technique is termed Independent Component Analysis (ICA). The basic principle underlining ICA is the determination of a linear representation of non-Gaussian data so that the components are considered statistically independent. With such representation, it would be easy and more computationally efficient to develop direct variograms for the components. The process is presented in two stages. The first stage involves the ICA decomposition. The second stage involves sequential Gaussian simulation of the generated components (which are derived from the first stage). This technique was applied for spatially correlated extractable cations such as magnesium (Mg) and iron (Fe) in a Canadian watershed. This paper has a strong application in stochastic quantification of uncertainties of soil attributes in soil remediation and soil rehabilitation.

Stochastic quantification of the electric power generated by a piezoelectric energy harvester using a time–frequency analysis under non-stationary random vibrations

Vibration energy, which is widely available, can be converted into electric energy using a piezoelectric energy harvester that generates alternating current in response to applied mechanical strain. For the last decade, there has been a strong surge of interest in developing an electromechanically-coupled analytical model of a piezoelectric energy harvester. Such a model is of great importance to enable understanding of the first principle of the piezoelectric transduction and to quantify harvestable electric power under a given vibration condition. However, existing analytical models that operate under an assumption of deterministic excitations cannot deal with the random nature present in realistic vibrations, even though this randomness considerably affects the variation in harvestable electric power. Furthermore, even when random vibrations are taken into account, existing stochastic analytical models can only be applied to stationary excitations, such as in the case of white Gaussian noise. This paper thus proposes a three-step framework for stochastic quantification of the electric power generated by a piezoelectric energy harvester under non-stationary random vibrations. First, we propose estimation of the time-varying power spectral density (PSD) of the input non-stationary random vibration using a statistical time–frequency analysis. The second step is to employ an existing electromechanical model as the linear operator for calculating the output voltage response. The final step is to estimate the time-varying PSD of the output voltage response. Following this three-step process, the expected electric power can be estimated from the autocorrelation function which is the inverse Fourier transform of the time-varying PSD of the output voltage response. The merits of the proposed framework are two-fold in that it enables: (i) quantification of the time-varying electric power generated under non-stationary random vibrations and (ii) consideration of the randomness in the design process of the energy harvester. Four case studies are used to demonstrate the effectiveness of the proposed framework.

Stochastic model for the process of Wine Award: Visualization and quantification

Sensory analysis is an important part of the process of evaluation of the quality of wines. Nowadays, one of the most used methods for describing this evaluation is the concept of awards. In the process of granting the award for a wine, each specialist assigns a score for the quality according to the tasting score sheet proposed by the Organisation Internationale de la Vigne et du Vin (OIV). After this, on the basis of the average of the scores assigned by each specialist, the award of the wine is determined. The present proposal seeks to refine the concept of award on the basis of the scores assigned to each item on the tasting score sheet, as well as giving theoretical support to the refinement of the award concept, identified as consistency. The defined technical support uses statistical tools for the modeling and structuring of the methodology. Finally, a method of visualizing the dynamic of the scores assigned by each specialist is presented. It is concluded that the stochastic quantification and the theory of graphs allowed the visualization and definition of a theoretical support that refines the process of the determination of wine quality.