Stochastic Sensitivities Research Articles

Optimal location of UPFC based on sensitivity of CDF with power system’s stochasticity

In this paper, a stochastic sensitivity algorithm is introduced to optimize the location of unified power flow controller (UPFC) in large scale power grid. The stochastic sensitivities are defined as the total operation cost of power system to control parameters of UPFC. Firstly, probability optimal power flow (POPF) model with power system’s randomness is established. Then point estimate method (PEM) is utilized to solve the above problem, so that the stochastic sensitivities of UPFC in all possible transmission lines could be obtained. Finally, by sorting the influence degree of UPFC at different locations to cumulative distribution function (CDF) of operation cost, the optimal location for UPFC could be selected correspondingly. To this end, IEEE-5 and IEEE-14 systems are employed to verify our proposed approach. The results show that installing UPFC by the method in this paper could significantly reduce the probability distribution of operation cost in higher region.

A polynomial dimensional decomposition framework based on topology derivatives for stochastic topology sensitivity analysis of high-dimensional complex systems and a type of benchmark problems

In this paper, a new computational framework based on the topology derivative concept is presented for evaluating stochastic topological sensitivities of complex systems. The proposed framework, designed for dealing with high dimensional random inputs, dovetails a polynomial dimensional decomposition (PDD) of multivariate stochastic response functions and deterministic topology derivatives. On one hand, it provides analytical expressions to calculate topology sensitivities of the first three stochastic moments which are often required in robust topology optimization (RTO). On another hand, it offers embedded Monte Carlo Simulation (MCS) and finite difference formulations to estimate topology sensitivities of failure probability for reliability-based topology optimization (RBTO). For both cases, the quantification of uncertainties and their topology sensitivities are determined concurrently from a single stochastic analysis. Moreover, an original example of two random variables is developed for the first time to obtain analytical solutions for topology sensitivity of moments and failure probability. Another 53-dimension example is constructed for analytical solutions of topology sensitivity of moments and semi-analytical solutions of topology sensitivity of failure probabilities in order to verify the accuracy and efficiency of the proposed method for high-dimensional scenarios. Those examples are new and make it possible for researchers to benchmark stochastic topology sensitivities of existing or new algorithms. In addition, it is unveiled that under certain conditions the proposed method achieves better accuracies for stochastic topology sensitivities than for the stochastic quantities themselves.

Cost-Sensitive Weighting and Imbalance-Reversed Bagging for Streaming Imbalanced and Concept Drifting in Electricity Pricing Classification

In data streaming environments such as a smart grid, it is impossible to restrict each data chunk to have the same number of samples in each class. Hence, in addition to the concept drift, classification problems in streaming data environments are inherently imbalanced. However, streaming imbalanced and concept drifting problems in the power system and smart grid have rarely been studied. Incremental learning aims to learn the correct classification for the future unseen samples from the given streaming data. In this paper, we propose a new incremental ensemble learning method to handle both concept drift and class imbalance issues. The class imbalance issue is tackled by an imbalance-reversed bagging method that improves the true positive rate while maintains a low false positive rate. The adaptation to concept drift is achieved by a dynamic cost-sensitive weighting scheme for component classifiers according to their classification performances and stochastic sensitivities. The proposed method is applied to a case study for the electricity pricing in Australia to predict whether the price of New South Wales will be higher or lower than that of Victorias in a 24-h period. Experimental results show the effectiveness of the proposed algorithm with statistical significance in comparison to the state-of-the-art incremental learning methods.

Fast stochastic forward sensitivities in Monte Carlo simulations using stochastic automatic differentiation (with applications to initial margin valuation adjustments)

Fast stochastic forward sensitivities in Monte Carlo simulations using stochastic automatic differentiation (with applications to initial margin valuation adjustments)

Fast Stochastic Forward Sensitivities in Monte-Carlo Simulations Using Stochastic Automatic Differentiation (with Applications to Initial Margin Valuation Adjustments (MVA))

In this note we apply the stochastic (backward) automatic differentiation to calculate stochastic forward sensitivities. A forward sensitivity is a sensitivity at a future point in time, conditional to the future states (i.e., it is a random variable). A typical application of stochastic forward sensitivities is the exact calculation of an initial margin valuation adjustment (MVA), assuming that the initial margin is determined from a sensitivity based risk model. The ISDA SIMM model is an example of such a model. We demonstrate that these forward sensitivities can be obtained in a single stochastic (backward) automatic differentiation sweep with an additional conditional expectation step. Although the additional conditional expectation step represents a burden, it enables us to utilize the expected stochastic (backward) automatic differentiation - a modified version of the stochastic (backward) automatic differentiation. As a test case we consider a hedge simulation requiring the numerical calculation of 5 million sensitivities. This calculation, showing the accuracy of the sensitivities, requires approximately 10 seconds on a 2014 laptop. However, in real application the performance may even be more impressive since 90% of the computation time is consumed by the conditional expectation regression, which does not scale with the number of products.

Thermochemical behaviorsof textile dying sludge, paper mill sludge, and their blends during (co-)combustion

This study aimed at the quantification of thermochemical behaviors of textile dye sludge (TDS), paper mill sludge (PMS), and their various blend ratios during (co-)combustion. Changes in mass loss percentage (MLP) and rate (MLR) were estimated as a function of temperature, heating rate, and blend ratio. Our results pointed to a direct influence of blend ratios on mass loss percentage. Stochastic uncertainties and sensitivities associated with best-fit predictions of MLP and MLR responses were detected using all-at-once versus one-at-a-time Monte Carlo simulations. Co-combustion of TDS and PMS provided more flame stability owing to their volatile matter contents than did the combustion of pure TDS or PMS. The high C and H contents of TDS relative to those of PMS led to high lower heating value (higher energy). Effect of increased temperature on the co-combustion manifested itself in the breakdown of (hemi-)cellulose initially and lignin progressively in TDS and PMS. The increasing TDS of the blend ratio increased both MLP and MLR. Stochastic uncertainty analysis of the deterministic empirical models pinpointed overestimation by 15.6% in mean MLP and by 50% in mean MLR. Sensitivity analysis pointed to blend ratio as the most influential predictor on both MLP and MLR.

Stochastic uncertainty and sensitivities of nitrogen flows on dairy farms in The Netherlands

Nutrient management decisions and environmental policy making must be based on sound data and proper analysis. Annual data collection and monitoring of farm and nutrient performance are wrought with uncertainties. Such uncertainties need to be addressed as it may lead to ambiguities and wrong conclusions. We developed an input-output N balance model to describe and quantify N flows in dairy farming systems. Input for this model was based on monitored data for one year (2005) from one experimental (detailed monitoring) and 14 pilot commercial dairy farms (less detailed monitoring). A Monte Carlo approach was used to quantify effects of uncertainty of input data on annual farm N surplus, soil surface N surplus and N intake during grazing, followed by a sensitivity analysis to apportion the different sources of uncertainty. Uncertainties in data input were described with probability density functions. Farm N surplus of the 14 pilot farms ranged between 81 and 294 kg ha−1, soil surface N surplus between 35 and 256 kg ha−1, and N intake during grazing between 27 and 108 kg ha−1. The uncertainties of N flows – both relative and absolute – increased from farm N surplus (CV = 8%; SD = 15 kg N ha−1) to soil surface N surplus (CV = 12%; SD = 16 kg N ha−1) to N intake during grazing (CV = 49%; SD = 28 kg N ha−1). Variation in uncertainty among farms in farm and soil surface N surplus and N intake during grazing was substantial and was related to the farm structure and farm characteristics such as production intensity, N fixation by clover and annual changes in stocks of roughage and manure. We found that a monitoring program based on more measurements instead of estimates and/or fixed rate values from literature will not always result in a better quantification of farm and soil surface N surplus on clover-based dairy farms. However, on farms with no N fixation, an intensive monitoring program reduced the uncertainty in farm and soil surface N surplus by 23% and the uncertainty of N intake during grazing was reduced by more than 30%. Knowledge about uncertainties of N flows is necessary to correctly interpret the N performance on dairy farms and its evolution through time. A first step is to get insights into the most uncertain N flows on a dairy farm. The next step, where possible, is to improve the estimation of the most uncertain N flows. Based on the insights from this study, these steps will underpin the validation of trends in N performance and justify decisions in environmental policy making and/or decisions for making on-farm improvements.

A new sampling-based RBDO method via score function with reweighting scheme and application to vehicle designs

Sampling-based methods are general but time consuming for solving a reliability-based design optimization (RBDO) problem. However, one of the major drawbacks of using Monte Carlo simulation (MCS) to compute the sensitivities of reliability functions is computation intensive. In order to alleviate the computation burden, score function together with the MCS method is exploited to compute the stochastic sensitivities of reliability functions. Furthermore by reweighting an initial set of samples, the objective and constraint functions become smooth functions of changes of the parameters of probability distribution, rather than the stochastic functions obtained using MCS. A new sampling-based RBDO method by using score function with reweighting scheme is proposed to perform sensitivities analysis of reliability functions to improve the computational efficiency and accuracy. Several numerical examples are used to show the advantages of the proposed method. Comparisons to the conventional methods are made and discussed. Two large-scale industrial vehicle design problems are solved to demonstrate the feasibility of the proposed method.

SPSens: a software package for stochastic parameter sensitivity analysis of biochemical reaction networks

SPSens is a software package for the efficient computation of stochastic parameter sensitivities of biochemical reaction networks. Parameter sensitivity analysis is a valuable tool that can be used to study robustness properties, for drug targeting, and many other purposes. However its application to stochastic models has been limited when Monte Carlo methods are required due to extremely high computational costs. SPSens provides efficient, state of the art sensitivity analysis algorithms in a single software package so that sensitivity analysis can be easily performed on stochastic models of biochemical reaction networks. SPSens implements the algorithms in C and estimates sensitivities with respect to both infinitesimal and finite perturbations to system parameters, in many cases reducing variance by orders of magnitude compared to basic methods. Included among the features of SPSens are serial and parallel command line versions, an interface with Matlab, and several example problems. SPSens is distributed freely under GPL version 3 and can be downloaded from http://sourceforge.net/projects/spsens/. The software can be run on Linux, Mac OS X and Windows platforms.

Stochastic and scaling climate sensitivities: Solar, volcanic and orbital forcings

Climate sensitivity (λ) is usually defined as a deterministic quantity relating climate forcings and responses. While this may be appropriate for evaluating the outputs of (deterministic) GCM's it is problematic for estimating sensitivities from empirical data. We introduce a stochastic definition where it is only a statistical link between the forcing and response, an upper bound on the deterministic sensitivities. Over the range ≈30 yrs to 100 kyrs we estimate this λusing temperature data from instruments, reanalyses, multiproxies and paleo spources; the forcings include several solar, volcanic and orbital series. With the exception of the latter ‐ we find thatλ is roughly a scaling function of resolution Δt: λ ≈ with exponent 0 ≈ < Hλ ≈ < 0.7. Since most have Hλ > 0, the implied feedbacks must generally increase with scale and this may be difficult to achieve with existing GCM's.

Stochastic shape sensitivity in powder metallurgy processing

Stochastic shape sensitivity in forming process of powder metallurgy materials is analyzed. For this purpose the rigid-poroplastic material model has been assumed. The theoretical formulation for stochastic shape sensitivity is described which presents probabilistic distributions taking into account random initial and boundary conditions. The control volume approach is discussed. Stochastic finite element equations for rigid – poroplastic materials are solved for the first two probabilistic moments. Numerical simulations were performed to illustrate shape sensitivity problems in the process of compression of rigid-poroplastic cylinder. The differences in deterministic and stochastic sensitivities are presented. The results derived can be used for the subsequent quantitative stochastic shape design as well as stochastic shape optimization.

Stochastic sensitivity in metal forming of rigid-poroplastic materials

Stochastic sensitivity in metal forming process of rigid-poroplastic material is analyzed. The theoretical formulation for stochastic sensitivity is described which presents probabilistic distributions taking into account random initial and boundary conditions. The stochastic equations for metal forming process as well as for stochastic sensitivities are presented. Stochastic finite element equations for rigid-poroplastic materials are solved for the first two probabilistic moments. As the examples the sensitivity problems in the process of compression of rigid-poroplastic ring with random material parameters are discussed. The differences in deterministic and stochastic sensitivities are presented. The results derived can be used for the subsequent quantitative stochastic design as well as stochastic optimization.

Sampling-based RBDO using the stochastic sensitivity analysis and Dynamic Kriging method

This paper presents a sampling-based RBDO method using surrogate models. The Dynamic Kriging (D-Kriging) method is used for surrogate models, and a stochastic sensitivity analysis is introduced to compute the sensitivities of probabilistic constraints with respect to independent or correlated random variables. For the sampling-based RBDO, which requires Monte Carlo simulation (MCS) to evaluate the probabilistic constraints and stochastic sensitivities, this paper proposes new efficiency and accuracy strategies such as a hyper-spherical local window for surrogate model generation, sample reuse, local window enlargement, filtering of constraints, and an adaptive initial point for the pattern search. To further improve computational efficiency of the sampling-based RBDO method for large-scale engineering problems, parallel computing is proposed as well. Once the D-Kriging accurately approximates the responses, there is no further approximation in the estimation of the probabilistic constraints and stochastic sensitivities, and thus the sampling-based RBDO can yield very accurate optimum design. In addition, newly proposed efficiency strategies as well as parallel computing help find the optimum design very efficiently. Numerical examples verify that the proposed sampling-based RBDO can find the optimum design more accurately than some existing methods. Also, the proposed method can find the optimum design more efficiently than some existing methods for low dimensional problems, and as efficient as some existing methods for high dimensional problems when the parallel computing is utilized.

Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems With Correlated Random Variables

This study presents a methodology for computing stochastic sensitivities with respect to the design variables, which are the mean values of the input correlated random variables. Assuming that an accurate surrogate model is available, the proposed method calculates the component reliability, system reliability, or statistical moments and their sensitivities by applying Monte Carlo simulation to the accurate surrogate model. Since the surrogate model is used, the computational cost for the stochastic sensitivity analysis is affordable compared with the use of actual models. The copula is used to model the joint distribution of the correlated input random variables, and the score function is used to derive the stochastic sensitivities of reliability or statistical moments for the correlated random variables. An important merit of the proposed method is that it does not require the gradients of performance functions, which are known to be erroneous when obtained from the surrogate model, or the transformation from X-space to U-space for reliability analysis. Since no transformation is required and the reliability or statistical moment is calculated in X-space, there is no approximation or restriction in calculating the sensitivities of the reliability or statistical moment. Numerical results indicate that the proposed method can estimate the sensitivities of the reliability or statistical moments very accurately, even when the input random variables are correlated.

Sensitivity summation theorems for stochastic biochemical reaction systems

We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances is shown to depend on the size of the measurement time window ( ϵ) within which reaction events are counted for measuring a single flux. It is found that the degree of the ϵ-dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time-scale separation. This ϵ-dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks.

Stochastic sensitivity analysis using HDMR and score function

Probabilistic sensitivities provide an important insight in reliability analysis and often crucial towards understanding the physical behaviour underlying failure and modifying the design to mitigate and manage risk. This article presents a new computational approach for calculating stochastic sensitivities of mechanical systems with respect to distribution parameters of random variables. The method involves high dimensional model representation and score functions associated with probability distribution of a random input. The proposed approach facilitates first-and second-order approximation of stochastic sensitivity measures and statistical simulation. The formulation is general such that any simulation method can be used for the computation such as Monte Carlo, importance sampling, Latin hypercube, etc. Both the probabilistic response and its sensitivities can be estimated from a single probabilistic analysis, without requiring gradients of performance function. Numerical results indicate that the proposed method provides accurate and computationally efficient estimates of sensitivities of statistical moments or reliability of structural system.

Stochastic uncertainties and sensitivities of a regional-scale transport model of nitrate in groundwater

Groundwater quality management relies more and more on models in recent years. These models are used to predict the risk of groundwater contamination for various land uses. This paper presents an assessment of uncertainties and sensitivities to input parameters for a regional model. The model had been set up to improve and facilitate the decision-making process between stakeholders and in a groundwater quality conflict. The stochastic uncertainty and sensitivity analysis comprised a Monte Carlo simulation technique in combination with a Latin hypercube sampling procedure. The uncertainty of the calculated concentrations of nitrate leached into groundwater was assessed for the various combinations of land use, soil type, and depth of the groundwater table in a vulnerable, sandy region in The Netherlands. The uncertainties in the shallow groundwater were used to assess the uncertainty of the nitrate concentration in the abstracted groundwater. The confidence intervals of the calculated nitrate concentrations in shallow groundwater for agricultural land use functions did not overlap with those of non-agricultural land use such as nature, indicating significantly different nitrate leaching in these areas. The model results were sensitive for almost all input parameters analyzed. However, the NSS is considered pretty robust because no shifts in uncertainty between factors occurred between factors towards systematic changes in fertilizer and manure inputs of the scenarios. In view of these results, there is no need to collect more data to allow science based decision-making in this planning process. © 2008 Elsevier B.V. All rights reserved.

Stochastic sensitivity analysis by dimensional decomposition and score functions

This article presents a new class of computational methods, known as dimensional decomposition methods, for calculating stochastic sensitivities of mechanical systems with respect to probability distribution parameters. These methods involve a hierarchical decomposition of a multivariate response function in terms of variables with increasing dimensions and score functions associated with probability distribution of a random input. The proposed decomposition facilitates univariate and bivariate approximations of stochastic sensitivity measures, lower-dimensional numerical integrations or Lagrange interpolations, and Monte Carlo simulation. Both the probabilistic response and its sensitivities can be estimated from a single stochastic analysis, without requiring performance function gradients. Numerical results indicate that the decomposition methods developed provide accurate and computationally efficient estimates of sensitivities of statistical moments or reliability, including stochastic design of mechanical systems. Future effort includes extending these decomposition methods to account for the performance function parameters in sensitivity analysis.

Age‐Specific Fitness Components and Their Temporal Variation in the Barn Owl

Theory predicts that temporal variability plays an important role in the evolution of life histories, but empirical studies evaluating this prediction are rare. In constant environments, fitness can be measured by the population growth rate lambda, and the sensitivity of lambda to changes in fitness components estimates selection on these traits. In variable environments, fitness is measured by the stochastic growth rate lambda(S), and stochastic sensitivities estimate selection pressure. Here we examine age-specific schedules for reproduction and survival in a barn owl population (Tyto alba). We estimated how temporal variability affected fitness and selection, accounting for sampling variance. Despite large sample sizes of old individuals, we found no strong evidence for senescence. The most variable fitness components were associated with reproduction. Survival was less variable. Stochastic simulations showed that the observed variation decreased fitness by about 30%, but the sensitivities of lambda and lambda(S) to changes in all fitness components were almost equal, suggesting that temporal variation had negligible effects on selection. We obtained these results despite high observed variability in the fitness components and relatively short generation time of the study organism, a situation in which temporal variability should be particularly important for natural selection and early senescence is expected.

HOW GENERAL ARE THE DETERMINANTS OF THE STOCHASTIC POPULATION GROWTH RATE ACROSS NEARBY SITES?

A key question in both life history evolution and conservation biology is how much the contributions of different demographic processes to the rate of population growth vary from place to place. Using data from a six-year demographic study of five nearby populations, we asked, for the first time, how well the sensitivities and elasticities of the stochastic population growth rate (λs) to the means and standard deviations of underlying vital rates (survival, growth, reversion, and reproduction) can be generalized among populations. Relying on Tuljapurkar's approximation for λs, we used standard mathematical formulas for the sensitivities and elasticities of λs to the vital rate means, and we derived approximations for the sensitivities and elasticities of λs to the vital rate standard deviations. No single vital rate mean or standard deviation had the highest stochastic sensitivity or elasticity across all five populations. However, the summed sensitivities and elasticities of different types of vital rates were much more consistent: the mean survival rates had the highest summed sensitivity and elasticity, and the standard deviations of growth or reversion rates had the highest summed sensitivity or elasticity in all populations. The rank order of the individual sensitivities and elasticities of the vital rate means were, in general, also highly correlated among populations, with the exception of one population that showed a distinctive sensitivity/elasticity pattern, but the sensitivities and elasticities of the vital rate standard deviations were less correlated among populations. Environmental variables (geographical location, elevation, and geological parent material) did not predict the degree of similarity in sensitivity/elasticity patterns between population pairs. Our results show that overall patterns in the stochastic sensitivities and elasticities of mean vital rates can be extrapolated accurately across closely adjacent populations, but that caution is needed when extrapolating sensitivities/elasticities of vital rate standard deviations or when applying the single most important vital rate from one population to others.