Deterministic Measures Research Articles

Interval state estimation method for distribution networks considering multi-attribute decision making and multi-source measurement data uncertainty

The operation of distribution networks faces significant challenges due to uncertainties and measurement errors. This paper presents an innovative interval state estimation method that leverages multisource measurement data and multi-attribute decision-making to enhance accuracy and reliability. We first extract deterministic uncertainty measures from heterogeneous measurement data. By analyzing the interplay between determinacy and uncertainty, we construct an interval representation space that enables precise extraction, integration, and analysis of multisource data. Subsequently, we develop an interval multi-attribute decision-making model that reflects the dynamic preferences of the distribution network, resulting in a robust interval state estimation model that incorporates uncertainty. An improved Krawczyk-Moore (KM) algorithm facilitates iterative solutions, while Monte Carlo simulations validate the model's effectiveness in handling multisource data fusion and uncertainty analysis. Simulation results demonstrate a 0.02 improvement in measurement error statistics, with estimation error statistics remaining stable and the estimated interval coverage probability decreasing by approximately 0.4. Overall, this method outperforms traditional approaches, particularly in scenarios characterized by data uncertainty and multisource data integration, thereby enhancing estimation accuracy.

Rigorous Assessment of Model Inference Accuracy using Language Cardinality

Models such as finite state automata are widely used to abstract the behavior of software systems by capturing the sequences of events observable during their execution. Nevertheless, models rarely exist in practice and, when they do, get easily outdated; moreover, manually building and maintaining models is costly and error-prone. As a result, a variety of model inference methods that automatically construct models from execution traces have been proposed to address these issues. However, performing a systematic and reliable accuracy assessment of inferred models remains an open problem. Even when a reference model is given, most existing model accuracy assessment methods may return misleading and biased results. This is mainly due to their reliance on statistical estimators over a finite number of randomly generated traces, introducing avoidable uncertainty about the estimation and being sensitive to the parameters of the random trace generative process. This paper addresses this problem by developing a systematic approach based on analytic combinatorics that minimizes bias and uncertainty in model accuracy assessment by replacing statistical estimation with deterministic accuracy measures. We experimentally demonstrate the consistency and applicability of our approach by assessing the accuracy of models inferred by state-of-the-art inference tools against reference models from established specification mining benchmarks.

Novel deterministic and probabilistic forecasting methods for crude oil price employing optimized deep learning, statistical and hybrid models

In this paper, individual and hybrid methods are proposed employing optimized statistical and deep learning (DL) models for deterministic (point) and probabilistic (interval) forecasting of crude oil price time series. The statistical models are optimized using the Forecast package of R. To enhance the performance of DL models, a novel pruning DE-DL method is proposed, which employs the differential evolution (DE) algorithm to optimize architecture and continuous and discrete-valued hyper-parameters. The proposed DE-DL method is so generic that it can be applied to optimize different DL models for any supervised learning problem. Five DL models (LSTM, BiLSTM, GRU, CNN, and ConvLSTM) are optimized for forecasting monthly crude oil prices and hybridized with an optimized ARIMA model for developing optimized additive and multiplicative hybrid forecasting models. The effectiveness of the proposed methods is evaluated through deterministic and probabilistic forecasting measures, comparing the results with six optimized statistical models, thirteen machine learning models, five optimized DL models, and ten optimized hybrid models. It is observed from the simulation results that the proposed optimized Additive-ARIMA-GRU hybrid model provides statistically superior forecasts, and the t Location Scale distribution is more suitable than the Gaussian distribution for computing reliable prediction intervals with different significance levels.

Centrality measures in fuzzy social networks

Centrality measures have been widely used to capture the properties of different nodes in a social network, particularly when the edges are fully deterministic. Various models have also been proposed to calculate nodes’ centrality in graphs where there might be some uncertainty in relation to the edges. Their common characteristic is that graph uncertainty is essentially embedded into the calculation of centrality to compute a single crisp value. However, as the degree of uncertainty may vary, centrality values may also vary. In this paper, making use of fuzzy set theory, we assume that a social network is modelled by a fuzzy graph and a fuzzy variable is used to describe the truth degree of an edge between two nodes. Based on this formulation, appropriate definitions are given to determine the truth degree of different centrality values for a node and thereby centrality as a fuzzy relation. Three well-known centrality measures, degree, h-index and k-shell, are extended to calculate the truth degree for the centrality of a node in a fuzzy graph. Experimental results demonstrate that the proposed centrality measures can determine the importance of nodes in a fuzzy graph more accurately than other fuzzy or deterministic centrality measures.

On the verification of ensemble precipitation forecasts over the Godavari River basin

The ensemble forecasts from Numerical Weather Prediction (NWP) models are considered as essential elements for operational hydrologic forecasting. However, these forecasts are burdened with significant inherent biases and cannot be used directly for hydrologic forecasting. Therefore, the present study examines the capability of ensemble precipitation forecasts obtained from two NWP models i.e., a 20-member ensemble from the National Center for Environmental Prediction (NCEP) and a 50-member ensemble from the European center for Medium-term Weather Forecasts (ECMWF). The skill of 70-member multi-model grand ensemble (MME) generated from the NCEP and ECMWF forecasts is also verified in this study. Furthermore, post-processing of the raw ensemble members was carried out using two methods (Quantile Mapping (QM) and Quantile Regression Forests (QRF)) in order to minimize the inherent biases. The analysis was performed over subbasins of an Indian river basin namely the Godavari River Basin. Here, a set of deterministic and probabilistic verification measures (forecast error box plots, correlation coefficient, Relative Mean Error, mean Continuous Ranked Probability Score, spread-skill relationship, rank histograms, reliability diagram, Area under Relative Operating Characteristic Curve) were employed to assess various quality attributes of the forecasts. The findings from the study suggests that QRF post-processed NCEP and MME forecasts are comparatively better than other forecasts in terms of all employed verification measures over all subbasins. The QRF post-processed forecasts were found to be superior than QM post-processed and raw forecasts over all subbasins. The adopted post-processing methods resulted in improved forecasts at shorter lead times. However, the skill of both raw and post-processed forecasts declines at higher lead times over all subbasins.

Deterministic and Probabilistic Measures of Liquefaction Susceptibility: A Comparison

Deterministic and Probabilistic Measures of Liquefaction Susceptibility: A Comparison

Novel deterministic and probabilistic resilience assessment measures for engineering and infrastructure systems based on the economic impacts

Engineering and infrastructure systems are commonly subjected to various types of destructive events that disrupt their functionalities and cause direct and indirect economic losses. The resilience assessment enables stakeholders and decision-makers to identify how a system copes with a disruptive event, how it adjusts to the new disrupted condition, and how it is capable of recovering its functionality swiftly and inexpensively. Although different indices have been proposed to quantify system resilience in recent years, developing a comprehensive and reliable index is an ongoing subject. By considering the importance of the economic aspects of engineering and infrastructure systems, the current research employs three variables of: functionality level, time, and cost, simultaneously, to define novel comprehensive, comparative, and comprehensible indices for resilience and its features. In this regard, the resilience curve of an engineering system is described in functionality-time-cost (FTC) coordinates, and deterministic indices are defined for absorptive capacity, adaptive capacity, recoverability, and resilience of a system. Additionally, the Bayesian Network approach is used to account for the inherent uncertainties in the resilience assessment process and to develop probabilistic indices for the mentioned features. Finally, a case study is presented to demonstrate how ignoring the economic impacts of disruptive events might be misleading when evaluating resilience.

Bias Correction of Mixed Distributions of Temperature with Strong Diurnal Signal

Abstract The performance of first-moment and full-distribution bias-correction methods of monthly temperature distributions for seasonal prediction is analyzed by comparing two approaches: the standard all-in-data procedure and the 6-hourly stratification of data. Five models are applied to remove the systematic errors of the CFSv2 forecasts of temperature for the rainy season in the Ethiopian Blue Nile River basin domain. Using deterministic evaluation measures, it is found that the stratification marginally increases the forecast skill especially in regions where the data distribution of temperature is prominently multimodal. The improvement may be attributed to a split of the mixed distribution into a set of unimodal distributions. A necessary condition for this splitting into unimodal distributions is that the amplitude of the diurnal cycle be larger than the interannual variability in the sample. The maximum improvement of stratification is achieved by the first-moment correction model. Significance Statement This paper evaluates bias-correction methods of monthly forecast distributions of temperature to improve seasonal forecast skill. It is found that marginal skill is gained when bias correction of the diurnal cycle is performed. This paper contributes to the discussion on the value of subdaily model output data.

Approximation rate in Wasserstein distance of probability measures on the real line by deterministic empirical measures

We are interested in the approximation in Wasserstein distance with index ρ≥1 of a probability measure μ on the real line with finite moment of order ρ by the empirical measure of N deterministic points. The minimal error converges to 0 as N→+∞ and we try to characterize the order associated with this convergence. In Xu and Berger (2019), Xu and Berger show that, apart when μ is a Dirac mass and the error vanishes, the order is not larger than 1 and give a sufficient condition for the order to be equal to this threshold 1 in terms of the density of the absolutely continuous with respect to the Lebesgue measure part of μ. They also prove that the order is not smaller than 1/ρ when the support of μ is bounded and not larger when the support is not an interval. We complement these results by checking that for the order to lie in the interval 1/ρ,1, the support has to be bounded and by stating a necessary and sufficient condition in terms of the tails of μ for the order to be equal to some given value in the interval 0,1/ρ, thus precising the sufficient condition in terms of moments given in Xu and Berger (2019). We also give a necessary condition for the order to be equal to the boundary value 1/ρ. In view of practical application, we emphasize that in the proof of each result about the order of convergence of the minimal error, we exhibit a choice of points explicit in terms of the quantile function of μ which exhibits the same order of convergence.

Minimum costs paths in intermodal transportation networks with stochastic travel times and overbookings

In intermodal transportation, it is essential to balance the trade-off between the cost and duration of a route. The duration of a path is inherently stochastic because of delays and the possibility of overbooking. We study a problem faced by a company that supports shippers with advice for the route selection. The challenge is to find Pareto-optimal solutions regarding the route’s costs and the probability of arriving before a specific deadline. We show how this probability can be calculated in a network with scheduled departure times and the possibility of overbookings. To solve this problem, we give an optimal algorithm, but as its running time becomes too long for larger networks, we also develop a heuristic. The idea of this heuristic is to replace the stochastic variables by deterministic risk measures and solve the resulting deterministic optimization problem. The heuristic produces, in a fraction of the optimal algorithm’s running time, solutions of which the costs are only a few percent higher than the optimal costs.

Experimental High-Resolution Winter Seasonal Climate Reforecasts for Florida

AbstractWe present here the analysis of 20 years of high-resolution experimental winter seasonal CLImate reForecasts for Florida (CLIFF). These winter seasonal reforecasts were dynamically downscaled by a regional atmospheric model at 10km grid spacing from a global model run at T62 spectral resolution (~210km grid spacing at the equator) forced with sea surface temperatures (SST) obtained from one of the global models in the North American Multimodel Ensemble (NMME). CLIFF was designed in consultation with water managers (in utilities and public water supply) in Florida targeting its five water management districts, including two smaller watersheds of two specific stakeholders in central Florida that manage public water supply. This enterprise was undertaken in an attempt to meet the climate forecast needs of water management in Florida.CLIFF has 30 ensemble members per season generated by changes to the physics and the lateral boundary conditions of the regional atmospheric model. Both deterministic and probabilistic skill measures of the seasonal precipitation at the zero-month lead for November-December-January (NDJ) and one-month lead for December-January-February (DJF) show that CLIFF has higher seasonal prediction skill than persistence. The results of the seasonal prediction skill of land surface temperature are more sobering than precipitation, although, in many instances, it is still better than the persistence skill.

Stability and accuracy of deterministic project duration forecasting methods in earned value management

PurposeEarned Value Management (EVM) is a project monitoring and control technique that enables the forecasting of a project's duration. Many EVM metrics and project duration forecasting methods have been proposed. However, very few studies have compared their accuracy and stability.Design/methodology/approachThis paper presents an exhaustive stability and accuracy analysis of 27 deterministic EVM project duration forecasting methods. Stability is measured via Pearson's, Spearman's and Kendall's correlation coefficients while accuracy is measured by Mean Squared and Mean Absolute Percentage Errors. These parameters are determined at ten percentile intervals to track a given project's progress across 4,100 artificial project networks with varied topologies.FindingsFindings support that stability and accuracy are inversely correlated for most forecasting methods, and also suggest that both significantly worsen as project networks become increasingly parallel. However, the AT + PD-ESmin forecasting method stands out as being the most accurate and reliable.Practical implicationsImplications of this study will allow construction project managers to resort to the simplest, most accurate and most stable EVM metrics when forecasting project duration. They will also be able to anticipate how the project topology (i.e., the network of activity predecessors) and the stage of project progress can condition their accuracy and stability.Originality/valueUnlike previous research comparing EVM forecasting methods, this one includes all deterministic methods (classical and recent alike) and measures their performance in accordance with several parameters. Activity durations and costs are also modelled akin to those of construction projects.

High-dimensional central limit theorems for a class of particle systems

We consider a class of particle systems that generalizes the eigenvalues of a class of matrix-valued processes, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems (CLTs) to characterize the fluctuations of the empirical measures around the limit measures by using stochastic calculus. As applications, CLTs for Dyson’s Brownian motion and the eigenvalues of Wishart process are recovered under slightly more general initial conditions, and a CLT for the eigenvalues of a symmetric matrix-valued Ornstein-Uhlenbeck process is obtained.

Saving for the future: Evaluating the sustainability and design of Pension Reserve Funds

In several countries public finances are under pressure by pension obligations rising due to downward trends in fertility, increased longevity and financial markets with low interest rates. For these reasons, the establishment of Pension Reserve Funds (PRF) has flourished. Regardless of the specific objectives that these PRFs may have, a critical issue is to assess their sustainability over the long-run. Moreover, this sustainability analysis is particularly complex, due to the interaction between the macroeconomic environment, financial performance and the labor market.In this article, we use a projection model aimed to evaluate the sustainability of the PRF in a small open economy such as Chile. The case of Chile is interesting because it shares common features with economies open to international markets that have either defined benefits pension schemes and/or defined contribution schemes with minimum pension guarantees. Moreover, since the Chilean PRF features relatively well defined contribution and withdrawal rules, we have a framework against which our methodology can be used to explore the effects on PRF's sustainability of altering these rules.Our methodology takes into consideration the stochastic nature of macroeconomic, financial and labor market variables in order to evaluate the sustainability of the PRF. In contrast to deterministic measures such as funding ratios, our methodology is more appropriate to assess the role of the contribution and withdrawal rules for PRFs in evaluating the key underlying risks and their consequences for the sustainability of PRFs.

Proactive and reactive scheduling of the steelmaking and continuous casting process through adaptive robust optimization

The schedule of a steelmaking and continuous casting (SCC) process defines the unit assignments of casts and ladles, and the processing sequence and timing in each unit. These decisions have to meet strict production requirements such as limited storage duration and continuous operation under various disruptions. Uncertain processing time is a common factor that may invalidate the initial schedule. Traditional deterministic reactive scheduling implements corrective measures for every disruption event by either repairing the deterministic schedule or rescheduling from scratch. In this work, we present a novel adaptive robust optimization method for SCC scheduling under uncertainty. Compared to the deterministic scheduling method, adaptive robust proactive scheduling generates an initial schedule immune to most major disruptions eliminating the need for most changes. Adaptive robust hybrid scheduling presents an attractive trade-off between solution conservatism and excessive scheduling modifications.

Multifractal formalism for the inverse of random weak Gibbs measures

Any Borel probability measure supported on a Cantor set included in [Formula: see text] and of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs measures. The study requires, in particular, to develop in this context of random dynamics a suitable version of the results known for heterogeneous ubiquity associated with deterministic Gibbs measures.

The relationship among probabilistic, deterministic and potential skills in predicting the ENSO for the past 161\xa0years

Here, we explored in depth the relationship among the deterministic prediction skill, the probabilistic prediction skill and the potential predictability. This was achieved by theoretical analyses and, in particular, by an analysis of long-term ensemble ENSO hindcast over 161 years from 1856 to 2016. First, a nonlinear monotonic relationship between the deterministic prediction skill and the probabilistic prediction skill, derived by theoretical analysis, was examined and validated using the ensemble hindcast. Further, the co-variability between the potential predictability and the deterministic prediction skill was explored in both perfect model assumption and actual model scenario. On these bases, we investigated the relationship between the potential predictability and probabilistic prediction skill from both the practice of ENSO forecast and theoretical perspective. The results of the study indicate that there are nonlinear monotonic relationships among these three kinds of measures. The potential predictability is considered to be a good indicator for the actual prediction skill in terms of both the deterministic measures and the probabilistic framework. The relationships identified here exhibit considerable significant practical sense to conduct predictability researches, which provide an inexpensive and moderate approach for inquiring prediction uncertainties without the requirement of costly ensemble experiments.

Improving the Accuracy of Hydrodynamic Simulations in Data Scarce Environments Using Bayesian Model Averaging: A Case Study of the Inner Niger Delta, Mali, West Africa

In this paper, the study area was the Inner Niger Delta (IND) in Mali, West Africa. The IND is threatened by climate change, increasing irrigation, and dam operations. 2D hydrodynamic modelling was used to simulate water levels, discharge, and inundation extent in the IND. Three different digital elevation models (DEM) (SRTM, MERIT, and a DEM derived from satellite images were used as a source of elevation data. Six different models were created, with different sources of elevation data and different downstream boundary conditions. Given that the performance of the models varies according to the location in the IND, the variable under consideration and the performance criteria, Bayesian Model Averaging (BMA) was used to assess the relative performance of each of the six models. The BMA weights, along with deterministic performance measures, such as the Nash Sutcliffe coefficient (NS) and the Pearson’s correlation coefficient (r), provide quantitative evidence as to which model is the best when simulating a particular hydraulic variable at a particular location. After the models were combined with BMA, both discharge and water levels could be simulated with reasonable precision (NS > 0.8). The results of this work can contribute to the more efficient management of water resources in the IND.

On the Outlying Eigenvalues of a Polynomial in Large Independent Random Matrices

Abstract Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A_N,B_N)$, where $A_N$ and $B_N$ are independent Hermitian random matrices and the distribution of $B_N$ is invariant under conjugation by unitary operators. We assume that the empirical eigenvalue distributions of $A_N$ and $B_N$ converge almost surely to deterministic probability measures $\mu$ and $\nu$, respectively. In addition, the eigenvalues of $A_N$ and $B_N$ are assumed to converge uniformly almost surely to the support of $\mu$ and $\nu ,$ respectively, except for a fixed finite number of fixed eigenvalues (spikes) of $A_N$. It is known that almost surely the empirical distribution of the eigenvalues of $P(A_N,B_N)$ converges to a certain deterministic probability measure $\eta \ (\textrm{sometimes denoted}\ P^\square(\mu,\nu))$ and, when there are no spikes, the eigenvalues of $P(A_N,B_N)$ converge uniformly almost surely to the support of $\eta$. When spikes are present, we show that the eigenvalues of $P(A_N,B_N)$ still converge uniformly to the support of $\eta$, with the possible exception of certain isolated outliers whose location can be determined in terms of $\mu ,\nu ,P$, and the spikes of $A_N$. We establish a similar result when $B_N$ is replaced by a Wigner matrix. The relation between outliers and spikes is described using the operator-valued subordination functions of free probability theory. These results extend known facts from the special case in which $P(X,Y)=X+Y$.

A fuzzy robustness measure for the scheduling of commissioned product development projects

Due to a considerable degree of uncertainty, the generation of robust schedules for the execution of product development projects is a crucial planning task. In the area of robust project scheduling, one basic option is to apply surrogate robustness measures as estimates of schedule robustness. Although project managers typically possess vague information about activity variations, most surrogate measures neglect this knowledge and are entirely based on deterministic data. In this contribution, we therefore present the “fuzzy overlap”, that is, to the best of our knowledge, the first surrogate robustness measure for schedule stability which accounts for fuzzy activity duration. We provide a mathematical formulation and embed the fuzzy overlap in a two-stage planning approach for the scheduling of product development projects, which aims at balancing the minimization of project costs as the basic scheduling objective with the maximization of schedule robustness. In a numerical study, we compare the performance of our proposed approach with comparable deterministic surrogate robustness measures. The results indicate that the consideration of fuzzy information enhances schedule robustness compared to the application of traditional deterministic surrogate robustness measures.