•A nonstationary copula model for assessing the temporal variation of flood joint distribution is developed.•Conditional most-likely and conditional expectation combination strategies for ...nonstationary bivariate design flood estimation are proposed.•The nonstationary design flood estimation is influenced by the design lifespan length.
In this study, a framework is proposed to estimate the nonstationary bivariate design flood, which includes three key steps. First, a nonstationary copula model was constructed to analyze the temporal variation in the bivariate joint distribution. Second, the equivalent reliability method was used to calculate the design value of the dominant variable for a return period and the design lifespan length under non-stationarity. Third, the design value of the secondary variable that was conditioned on the design value of the dominant variable, was calculated using the conditional most likely combination and conditional expectation combination strategies. Through the above three steps, the typical design value combination of the nonstationary bivariate was obtained for a specific design standard. A case study, based on the nonstationary annual maximum 1-day (AM1) and 15-day (AM15) flood volume at the Yichang station, was conducted to illustrate the framework. The results indicate that the joint distribution of the AM1 and AM15 flood volumes varied over time. For a specific design standard, the design values of the AM15 and AM1 flood volumes decreased with an increase in the design lifespan length. Moreover, the conditional most likely estimation of the design value for the AM1 flood volume that was conditioned on the design value for the AM15 flood volume was greater than its conditional expectation estimation.
Anthropogenic alterations have resulted in widespread degradation of stream conditions. To aid in stream restoration and management, baseline estimates of conditions and improved explanation of ...factors driving their degradation are needed. We used random forests to model biological conditions using a benthic macroinvertebrate index of biotic integrity for small, non-tidal streams (upstream area ≤200 km2) in the Chesapeake Bay watershed (CBW) of the mid-Atlantic coast of North America. We utilized several global and local model interpretation tools to improve average and site-specific model inferences, respectively. The model was used to predict condition for 95,867 individual catchments for eight periods (2001, 2004, 2006, 2008, 2011, 2013, 2016, 2019). Predicted conditions were classified as Poor, FairGood, or Uncertain to align with management needs and individual reach lengths and catchment areas were summed by condition class for the CBW for each period. Global permutation and local Shapley importance values indicated percent of forest, development, and agriculture in upstream catchments had strong impacts on predictions. Development and agriculture negatively influenced stream condition for model average (partial dependence PD and accumulated local effect ALE plots) and local (individual condition expectation and Shapley value plots) levels. Friedman's H-statistic indicated large overall interactions for these three land covers, and bivariate global plots (PD and ALE) supported interactions among agriculture and development. Total stream length and catchment area predicted in FairGood conditions decreased then increased over the 19-years (length/area: 66.6/65.4% in 2001, 66.3/65.2% in 2011, and 66.6/65.4% in 2019). Examination of individual catchment predictions between 2001 and 2019 showed those predicted to have the largest decreases in condition had large increases in development; whereas catchments predicted to exhibit the largest increases in condition showed moderate increases in forest cover. Use of global and local interpretative methods together with watershed-wide and individual catchment predictions support conservation practitioners that need to identify widespread and localized patterns, especially acknowledging that management actions typically take place at individual-reach scales.
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•Restoration and management of streams need improved models and interpretability.•Random forests were used to predict stream condition for multiple time periods.•Multiple global and local methods were used to improve interpretability.•Global and local methods supported each other but gave different insight.•Extent matters: little predicted change watershed-wide, but large in some catchments.
Advanced computing performance and machine learning accuracy have pushed engineers and researchers to consider more and more complex mathematical models. Methods such as Deep Neural Networks have ...become increasingly ubiquitous. However, the problem of the interpretability of machine learning predictions in a decision process has been identified as a hot topic in several engineering fields, leading to confusion in various communities. This paper discusses a methodological framework of hybrid interpretability tools in neural network prediction for an engineering application. These tools analyze a decision’s consequences under different circumstances and situations. The aim is to reconcile the ML prediction accuracy and the interpretability for a global approach to making systems more flexible. In this study, the methods used to deal with the interpretability of neural network predictions have been treated from two perspectives: (i) model-specific as partial derivatives and (ii) model-agnostic methods. The latter tools could be used for any ML model prediction. In order to visualize and explain the inputs’ impacts on prediction results, Partial Dependence Plots (PDP), Individual Conditional Expectation (ICE), and Accumulated Local Effects (ALE) are used and compared. The prediction of the electrical power (PE) output of a combined cycle power plant has been chosen to demonstrate the feasibility of these methods under real operating conditions. The results show that the most influential input parameter among ambient temperature (AT), atmospheric pressure (AP)), vacuum (V), and relative humidity (RH) is AT. The visualization outputs allow us to identify the direction (positive or negative) and the form (linear, nonlinear, random, stepwise) of the relationship between the input variables and the model’s output. The results of the interpretation are coherent with the literature studies.
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•Hybridizing model-specific and model-agnostic to enhance interpretability.•Reconciling the prediction accuracy and interpretability for a flexibility approach.•Explaining the functionality of the proposed framework for interpretability purposes.•Detecting how input changes (quantitatively and qualitatively) affect predictions.
In this research, machine learning (ML) based frameworks are developed to predict the in-plane mixed-mode fracture load of asphalt mixtures. In an initial stage, the RReliefF technique guides the ...selection of four parameters out of eight, namely fracture toughness, T-stress term, and modes I and II stress intensity factors (SIFs), to serve as inputs for predictive models. Subsequently, three ML models, namely support vector machine regressor (SVR), extra tree regressor (ETR), and gradient boosting regressor (GBR), are trained and tested using 675 experimental data points. Optimal hyper-parameter values for each model are determined through the particle swarm optimization (PSO) technique. To leverage the strengths of each individual model, two techniques, ensemble voting and stacking, are employed to combine the individual models. The performance of the presented models is assessed using 88 previously unseen datasets. The results underscore the significant promise of ML approaches for predicting the fracture load of asphalt mixture components, achieving accuracies of 90.48%, 91.11%, and 90.38% for SVR, ETR, and GBR, respectively. Notably, ensemble voting and stacking techniques further enhance predictive accuracy, achieving impressive accuracies of 91.25% and 91.57% respectively. Ultimately, model interpretation is accomplished via individual conditional expectation (ICE) plots, and the correlation of each predictor with the output is determined, which closely aligned with previous research findings and experimental observations. Our findings underscore the substantial potential of ML approaches in studying the fracture behavior of asphalt mixture components, with implications for enhancing infrastructure durability and safety. Compared to traditional analytical methods, ML-based frameworks offer improved accuracy and robustness in modeling the complex behavior of asphalt mixtures under varying conditions, thereby facilitating more precise assessments of infrastructure performance and durability.
•Three ML models were built to predict the fracture load of asphalt mixtures.•Models were trained using 675 empirical data and assessed using 88 unseen data.•Using PSO enabled accurate choice of optimal hyper-parameters for each ML model.•Using RReliefF, fracture toughness emerged as the key feature for failure load.•ML models were interpreted to identify the correlation between predictors and target.
Mixing inequalities in Riesz spaces Kuo, Wen-Chi; Rogans, Michael J.; Watson, Bruce A.
Journal of mathematical analysis and applications,
12/2017, Letnik:
456, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Various topics in stochastic processes have been considered in the abstract setting of Riesz spaces, for example martingales, martingale convergence, ergodic theory, AMARTS, Markov processes and ...mixingales. Here we continue the relaxation of conditional independence begun in the study of mixingales and study mixing processes. The two mixing coefficients which will be considered are the α (strong) and φ (uniform) mixing coefficients. We conclude with mixing inequalities for these types of processes. In order to facilitate this development, the study of generalized L1 and L∞ spaces begun by Kuo, Labuschagne and Watson will be extended.
A known property of conditional expectation is extended to the framework of Markov kernels. Its meaning in terms of densities is provided. Some examples located in the field of clinical diagnosis are ...presented to delimit the main result of the paper.
This paper mainly focuses on distributed filtering for a discrete time-varying system observed by a sensor network, where each sensor can measure some partial state information of the system and ...communicate with its neighbours. A novel distributed event-triggered communication mechanism is designed to reduce the communication rate among the sensors and guarantee the performance of the filter. With a data scheduler, the sensor is able to decide whether to transmit data to its neighbours. By applying Gaussian approximation, an evaluation of the effect caused by the non-transmission event is derived, which characterizes the tradeoff between communication rate and state estimation performance. Subsequently, a corresponding sub-optimal filtering gain design protocol is proposed. Compared with the literature, the filtering algorithm proposed in this paper is less conservative. Finally, numerical simulation is provided to illustrate the improvement of performance and the robustness of the approximation.
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