Analytical Probabilistic Model Research Articles

Design and hydrologic performance estimation of highway filter drains using a novel analytical probabilistic model

Sustainable drainage systems (SuDS) are nature-based methods of managing urban stormwater runoff. Although they are widely used, some SuDS, such as highway filter drains (HFDs), are understudied with respect to sizing and performance. For the first time, we developed an analytical probabilistic model (APM) that can be used to design and estimate the hydrologic performance of HFDs. Unlike the conventionally used design-storm based or continuous simulation approaches, our APM can directly calculate the runoff capture ratios of HFDs using closed-form analytical equations. Validation of the APM presented here shows that it is robust and reliable. The relative differences between the APM-estimated and continuous simulation-determined runoff capture ratios for all the simulated design cases are less than 8.5%.

Dynamic probabilistic analytical modeling for estimating rainfall–runoff transformation rates in drylands

Abstract Precipitation-runoff changes used in the development of precipitation-runoff models depict general runoff mechanisms in physical precipitation-runoff processes. For this purpose, it must be able to adequately express the characteristics of the physical system. Similar to other water resources management models, analytical-probabilistic models may be developed with different levels of complexity according to different types of rainfall–runoff developments. In this research, a log-normal probabilistic model was used to estimate the return period of rainfall and Soil and Water Assessment Tool (SWAT) software was used to convert rainfall values into discharge and runoff height in agricultural lands. The slope and the level of plant shade cover were considered the two basic factors in the estimation of the subsurface flow used in agriculture. Slopes of less than 0.015 and land cover level of more than 70% of extreme points were obtained to ensure subsurface water sources and prevent erosion.

Permeable pavement hydraulic optimization by using an analytical-probabilistic model

Abstract On-source storage controls are a sustainable solution for stormwater management in a scenario of continuous urban area growth. Structures that manage storage volumes through infiltration include extra environmental benefits, such as groundwater recharge, evapotranspiration, and pollutant load removal. Permeable pavement systems are among these controls and can easily integrate into dense urban areas, resulting in paved surfaces contributing to stormwater management. The shift toward on-source strategies is encouraged through regulations, policies, incentives, and awareness campaigns, which are substantially increasing their dissemination. Optimizing the design of on-source storage controls with infiltration, such as permeable pavement systems, through robust methodologies can reduce reservoir depth, reducing environmental impact and costs without impact on reliability. The analytical-probabilistic (AP) method using derived probability distribution theory from rainfall event characteristics and the mathematical description of hydrologic processes within the permeable pavement systems provides an analytical equation that can be used as a design tool, proving robustness analogous with continuous simulations. Results obtained with the AP method were compared with traditional event-based methodologies and continuous simulation, assessing the reliability of the proposed method in optimizing permeable pavement systems' reservoir depth.

Analytical probabilistic progressive damage modeling of single composite filaments of material extrusion

This research focuses on investigating the elastic and damage characteristics of individual composite beads utilized in additively manufactured (3D printed) composites. A novel analytical probabilistic progressive damage model (PPDM) is introduced to comprehensively capture the elastic and damage attributes of these single 3D printed beads, which constitute the foundational elements of 3D printed composites. The PPDM is formulated based on assumptions of a perfectly elastic, perfectly plastic, and elasto-plastic matrix. For the elasto-plastic matrix, a novel formulation of the damage is developed to offer a more realistic view of the internal mechanics. Furthermore, a novel method of measuring the Young’s modulus of 3D printed composites is assessed. To this end, the Sentmanat extensional rheometer (SER) fixture is used to conduct a series of tensile tests on Kevlar and glass fiber-reinforced nylon beads. The experimental data of the SER are compared with those from an Instron tensile machine. Finally, the results of the PPDM and the experiments are compared and reveal a strong agreement in both the elastic region and the ultimate strength and strain.

New Online DV-Hop Algorithm via Mobile Anchor for Wireless Sensor Network Localization

In many applications of Wireless Sensor Networks (WSNs), event detection is the main purpose of users. Moreover, determining where and when that event occurs is crucial; thus, the positions of nodes must be identified. Subsequently, in a range-free case, the Distance Vector-Hop (DV-Hop) heuristic is the commonly used localization algorithm because of its simplicity and low cost. The DV-Hop algorithm consists of a set of reference nodes, namely, anchors, to periodically broadcast their current positions and assist nearby unknown nodes during localization. Another potential solution includes the use of only one mobile anchor instead of these sets of anchors. This solution presents a new challenge in the localization of rang-free WSNs because of its favorable results and reduced cost. In this paper, we propose an analytical probabilistic model for multi-hop distance estimation between mobile anchor nodes and unknown nodes. We derive a non-linear analytic function that provides the relation between the hop counts and distance estimation. Moreover, based on the recursive least square algorithm, we present a new formulation of the original DV-Hop localization algorithm, namely, online DV-Hop localization, in WSNs. Finally, different scenarios of path planning and simulation results are conducted.

An Upscaled Model of Fill‐And‐Spill Hydrological Response

AbstractThe hydrology of wetland‐dominated landscapes is often controlled by a fill‐and‐spill mechanism, whereby surface depressions retain water and release it once a deficit is filled. The response of these systems to precipitation/snowmelt events is influenced by the local storage deficit and connectivity between storage features. To estimate runoff generated from a heterogeneous wetland complex, a closed‐form analytical upscaled probabilistic model is developed. The mathematical solution requires information on the distribution of initial deficits and wetland local contributing areas, which may be estimated via a combination of spatial analysis and field observation. The model is used to explore the influence of spatial heterogeneity of wetland properties including deficit depth, local contributing area, and cascade depth (the number of wetlands in‐series within a cascade) on runoff response. It is also used to clarify “gatekeeper” storage features role at large scales and for systems with shallow wetland cascade depths. The proposed solution is shown to be a generalization of the well‐known Probability Distributed Model and Xinanjiang runoff models, augmented to include information about local contributing areas and wetlands connectivity. The closed form probabilistic mathematical solution is verified by comparing results with Monte Carlo simulations. The proposed runoff model has been implemented in Raven, a hydrologic model, to test the method performance in lumped runoff simulation of wetland‐dominated basins influenced by fill‐and‐spill hydrology. This study can contribute to our understanding of wetland characteristics distribution on landscape hydrology, and compensate for insufficiently resolved elevation data in flat terrains where threshold criteria are hard to estimate.

Development of an analytical permeable pavement model for vehicular access areas

Permeable pavements (PPs) are widely used for stormwater control in urbanized areas as they provide absorption and retention of surface runoff. Previous studies on PP systems mainly focus on non-vehicular access areas with light traffic loads where the base usually connects to native soils which allow exfiltration from the bottom. The runoff reduction performance of the PPs in vehicular access areas (PPs-VAA) featured by more complex structure with underdrain outflow control still needs in-depth investigation. In this study, an analytical probabilistic model was developed to quantify the runoff control performance of PPs-VAA taking into account the effects of climate conditions, layer configurations and varying underdrain outflows. The calibration and verification of the proposed analytical permeable pavement model for vehicular access areas (APPM-VAA) were performed by comparing the analytical results with SWMM simulation results. The model was tested in case studies in Guangzhou and Jinan, China, with humid and semi-humid climate conditions, respectively. Close agreement between the results obtained from the proposed analytical model and those from continuous simulation outputs was observed. The proposed analytical model is proved to be capable of rapidly assessing the runoff control performance of PPs-VAA; it can thus be used in the hydrologic design and analysis of permeable pavement systems in engineering practices.

Application of Analytical Probabilistic Models in Urban Runoff Control Systems’ Planning and Design: A Review

Urban stormwater is known to cause a myriad of problems, ranging from flooding to water quality degradations. This paper provides an extensive review of analytical probabilistic model (APMs) used in the design of urban runoff control systems. APMs are closed-form mathematical expressions representing a long-term system’s output performance derived from the probability distribution of the system’s input variables. Once derived, the APMs are easy to handle, allow for sensitive analysis, and can be co-opted into optimization frameworks. The implementation of APM in the planning and design of runoff control systems will not only help address the runoff quantity and quality problems of urban stormwater, but will also go a long way in optimizing the benefits derived from the systems. This paper reviews studies that document the negative impacts of urbanization on runoff quantity and quality, and the best management practices (BMPs) used to mitigate the impacts. Three design methodologies used in urban stormwater control systems were reviewed. A detailed review of research on the development and use of APMs in urban stormwater management in various runoff control systems is presented, and recommendations are proffered.

KDE-Based Rainfall Event Separation and Characterization

Rainfall event separation is mainly based on the selection of the minimum inter-event time (MIET). The traditional approach to determining a suitable MIET for estimating the probability density functions is often using the frequency histograms. However, this approach cannot avoid arbitrariness and subjectivity in selecting the histogram parameters. To overcome the above limitations, this study proposes a kernel density estimation (KDE) approach for rainfall event separation and characterization at any specific site where the exponential distributions are suitable for characterizing the rainfall event statistics. Using the standardized procedure provided taking into account the Poisson and Kolmogorov–Smirnov (K-S) statistical tests, the optimal pair of the MIET and rainfall event volume threshold can be determined. Two climatically different cities, Hangzhou and Jinan of China, applying the proposed approach are selected for demonstration purposes. The results show that the optimal MIETs determined are 12 h for Hangzhou and 10 h for Jinan while the optimal event volume threshold values are 3 mm for both Hangzhou and Jinan. The KDE-based approach can facilitate the rainfall statistical representation of the analytical probabilistic models of urban drainage/stormwater control facilities.

Influence of climatic parameters on the probabilistic design of green roofs

Green roofs are effective tools for stormwater control in highly urbanized areas since they allow the reduction of peak runoffs and volumes discharged in sewer systems. Their design is quite standardized, except for the thickness of the growing medium layer, which is strictly related to vegetation type and rainfall regime. The paper proposes an analytical probabilistic approach that relates the climatic variables, the growing medium thickness, and the water content in the condition of fulfilled field capacity to the probability that runoff from green roofs exceeds a fixed threshold. The developed equations also consider the possibility of a reduced retention capacity due to previous rainfall events, that strongly influence the performance of these green infrastructures, especially when short dry periods and/or low evapotranspiration rates occur. This feature, neglected by the traditional design storm approach, and only partially considered by previous analytical probabilistic models, represent a great potentiality of the proposed equations that are also more user-friendly and less time-consuming than continuous simulation analysis. The focus of the paper is on the influence of climatic parameters on runoff probability. To this aim to perform the monthly analysis is fundamental, especially when there is a strong variability of the climatic parameters throughout the year.The model was tested in a case study in Milano, Italy. The application presented a good agreement between the results obtained from the proposed equations and those obtained from the continuous simulation of recorded data. The results also highlighted the importance of performing analysis on a monthly scale.

Development of an analytical probabilistic model to estimate runoff event volumes in South Korea

• A lognormal distribution best represents the rainfall characteristics of South Korea. • An analytical probabilistic model (APM) for lognormal distribution is developed. • The return period of APM is overestimated due to the seasonal rainfall distribution. • The APM adjustment magnitudes and the seasonal rainfall distributions are correlated. This study showed that the complex rainfall characteristics of South Korea, where rainfall is concentrated during a specific period, are poorly represented with a simple single parameter distribution. Thus, a two-parameter lognormal distribution that best represents the rainfall characteristics of South Korea was proposed by comparing four different distributions. Using this distribution, this study developed a suitable analytical probabilistic model (APM) to simulate runoff event volumes in South Korea and suggested an APM parameter-adjustment method based on rainfall characteristics. Thirty-year rainfall data recorded at ten stations were grouped based on the interevent time definition (IETD) of each station. With the grouped rainfall events, the probability density function (PDF) of the lognormal distribution was confirmed to best fit the rainfall event characteristic histograms in South Korea, including those of the rainfall event volume, duration, and interevent time. The APM was developed by deriving the PDF of the runoff event volume with a lognormal distribution, and a frequency analysis was performed based on the runoff event volume obtained by the APM and the Storm Water Management Model (SWMM) to verify the suitability of the derived model. The runoff event volumes output by the APM were compared with the runoff event volumes simulated by the SWMM. The exceedance probabilities and return periods output by the developed APM with a lognormal distribution were very close to the SWMM results. However, the return periods output by the APM were overestimated, and adjustment parameters were needed to match the outputs to the SWMM results. This study found a strong correlation between the adjustment parameters and the coefficients of variation in the average monthly rainfall. This result suggested that model parameter adjustments are necessary before applying an APM to rainfall datasets with large coefficients of variation in average monthly rainfall data.

Wavelength Selective Switch-Based Clos Network: Blocking Theory and Performance Analyses

A Clos network is a classical switching network often used in conventional electrical switches. In a Wavelength Selective Switch (WSS) based Clos all-optical switching network, the wavelength dimension needs to be additionally considered. However, the conventional blocking theory of the Clos network may not be valid in this scenario and it may be necessary to conduct a theoretical study specifically for the WSS-based Clos all-optical switching network. In this paper, we derive the strictly non-blocking conditions for the WSS-based Clos network for the cases where there is no wavelength conversion, partial wavelength conversion, and full wavelength conversion. For the situation where there is service blocking, we also formulate probabilistic analytical models to estimate the blocking performance for the three types of WSS-based Clos networks. The gain of transceiver utilization achieved by the WSS-based Clos network with wavelength conversion is evaluated and compared with that of one without wavelength conversion. We also evaluate the impact of partial wavelength conversion capability on the blocking performance of a WSS-based Clos network.

PLANNING OF GROUP ACTIONS OF UNMANNED AERIAL VEHICLES IN A DISTRIBUTED INTELLIGENT CONTROL SYSTEM

The actual progress achieved in the field of unmanned flying vehicles makes it possible to use Unmanned Aerial Vehicles (UAVs) to solve various tasks in the civil and defense areas. As a result, UAV groups require scheduling of their actions at various stages of their mission. In their previous publications the authors suggested the architecture of a distributed intellectual control system for the implementation of UAVs collective actions. It was demonstrated, that one of the most important functions of such an intellectual control system is the so called pre-flight scheduling of UAVs actions within a group. The article discusses the approaches to the implementation of algorithms that ensure the pre-flight scheduling of UAVs actions in the frames of a distributed intellectual control system, summarizing the current state of research in this area as well as the authors’ own results. The most important task to be solved at the stage of a UAV group’s actions pre-flight scheduling is to determine the types of UAVs involved in the implementation of the target task. An approximate solution to this problem is proposed, basing on the use of analytical probabilistic models to evaluate the group actions efficiency. The use of such models makes it possible to determine the optimal number of UAVs in the group, to justify the requirements for their survivability, the characteristics of both on-board optoelectronic means and weapons. Algorithms for scheduling the UAV group actions are described, which are based on both mathematical models and formalized criteria for evaluation of the collective actions efficiency. In this case, the planning task, as a rule, can be reduced to the problem of integer linear or nonlinear programming. The possibility of using artificial intelligence technologies for the purposes of the UAV group actions scheduling is discussed. Special attention is paid to the problem of planning the UAV group actions within the framework of a decentralized strategy of flock management.

Figure-of-Merit for a Long-Term Survivorship of a Species Determined from the Short-Term Mortality Rate of Its Individual Organisms

The two analytical (“mathematical”) probabilistic predictive models considered in this analysis suggest that (1) the nonrandom time-derivative of the long-term mortality rate at a rather arbitrary initial moment of time for a particular type of species of interest can be viewed as a suitable physical or biological criterion, a sort of a figure of merit (FoM), of its long-term viability/survivorship and that (2) this derivative can be determined as the variance of the random mortality rate for the significantly shorter, of course, lifespan of the individual organisms that the type of species as a whole, addressed by the first model, is comprised of. This suggestion is obtained as a modification and extension of and as an “analogy” to a concept that the author developed earlier in application to microelectronics products. So, it is assumed in our approach that the long-term survivorship of a species comprised of numerous individual organisms is analogous to the long-term performance of an electronic product comprised of numerous mass-produced components. In the original research, it was shown that the time-derivative at the initial moment of time of the nonrandom infant mortality portion (IMP) of the bathtub curve (BTC) for an electronic product is, in effect, the variance of the random failure rate (RFR) of the mass-produced components that this product is comprised of, and it is assumed that such an analogy is applicable also to the long-term survivorship of a species comprised of numerous individual organisms. The larger this variance, the shorter is the expected long-term lifetime (survivorship) of the species as a whole. Future work should be focused, first of all, on the verification of the trustworthiness of our basic assumption for different species, including humans, and on the accumulation of statistical data for long-term survivorship of various species and their existing or future habitats, with consideration of the roles of gravity, temperature, level of radiation, attributes of the atmosphere, if any, etc., as well as on calculating lifespan variances for the organisms that the species of interest are comprised of.

Rainfall-induced landslides assessment in the Fengjie County, Three-Gorge reservoir area, China

It is critical to accurately assess the location and evolution of impending landslide hazards, especially when influenced by the effects of climate change. However, most existing landslide models only analyze the stability of individual grid cells without considering soil interaction between adjacent cells. This means that the stability of individual grid cells is not necessarily representative of actual slope stability at a given location, in turn affecting the accuracy of landslide stability assessments. In this paper, slope units are defined using the morphological image analysis and homogeneous slope unit method to represent the actual slope conditions and to extract the profile of each slope unit. The critical slip surface of the soil mass is investigated to account for the interaction between adjacent grid cells within the slope unit. A probabilistic analytical landslide model is established and the response mechanism of the hydrological processes is proposed. This model is applied to landslide hazard assessment in the Three-Gorges Reservoir Area, Fengjie County, China. Using historical rainfall data, the distribution of landslide hazards is analyzed for different antecedent precipitation levels and rainfall return periods. The results show that the amount of antecedent precipitation, and rainfall return period, have different effects on landslide triggering in the area. Importantly, the model reveals that extreme rainfall events induced by climate change will lead to a large number of new landslides in areas where they are not anticipated. Further investigation and monitoring (e.g., early-warning systems, long-term assessment) of rainfall-induced landslides in the Three-Gorges Reservoir Area is recommended.

Runoff recession features in an analytical probabilistic streamflow model

The development of run-of-river hydropower requires the flow duration curve (FDC) to estimate the electricity production. As obtaining an FDC based on gauging station streamflow requires significant cost and time (i.e., more than several years), it is important to predict the FDC in the absence of streamflow data. An analytical probabilistic model of streamflow dynamics (p(Q) model) can calculate the FDC, which requires several rainfall and runoff recession parameters. To estimate the recession parameters in the absence of discharge data, we selected two approaches: the geomorphic recession flow model (GRFM) and geological recession approach (GRA). The GRFM and GRA associate the river network and geology, respectively, with runoff recession features. This study aims to comprehend the characteristics of the GRFM and GRA employed in the p(Q) model by targeting 57 basins throughout Japan. We found different performance trends between the GRFM and GRA that corresponded to specific basin characteristics. While the GRFM performed well in high precipitation basins, the GRA performed well in basins with abundant unconfined groundwater contributions. These results agree with the features in the derivations of the GRFM and GRA. In addition, we found a complementary relationship between the GRFM and GRA based on the baseflow index (BFI), which suggests that the complementary relationship is one method to improve the performance of the p(Q) model in the absence of streamflow data.

Analytical derivation of urban flood frequency models accounting saturation-excess runoff generation

Derived flood frequency models developed specifically for urban stormwater management purposes are referred to as analytical probabilistic stormwater models. These models use closed-form analytical equations to estimate flood frequencies under various land use conditions which facilitate quick analysis of different design alternatives. In this paper, in order to further improve the capability of the analytical probabilistic models, additional analytical expressions relating a catchment’s peak discharge rate to its physical characteristics and the local rainfall statistics are derived considering saturation-excess in addition to infiltration-excess runoff generation and various possible hydrograph shapes. These analytical expressions along with the frequency distributions of the input rainfall event volume and duration are used to develop a new derived flood frequency model suitable for catchments where saturation-excess runoff generation is possible. An example application of the new model to a test catchment in Hamilton, Ontario, Canada is illustrated to verify the accuracy of the new model. Assuming hypothetically that the same catchment is instead located at several other places in the United States, the reliability of the analytical probabilistic models under different climatic conditions is verified as well.

Probabilistic assessment of the buildings and structures construction duration

One of the main conditions for achieving the set value of the buildings and structures construction duration is the construction production planning. Due to the fact that the construction process has an uncertain dynamic nature, it is recommended to use probabilistic analytical models to determine such a calculated parameter as the duration. The article proposes a probabilistic model for estimating the duration of construction of buildings and structures on the basis of the normalized Erlang's law of the n-th order. This model allows, by changing the number and duration of work lying on the critical path, to assess the construction project completion probability within the prescribed period.

Bayesian inference for damage identification based on analytical probabilistic model of scattering coefficient estimators and ultrafast wave scattering simulation scheme

Ultrasonic Guided Waves (GW) actuated by piezoelectric transducers installed on structures have proven to be sensitive to small structural defects, with acquired scattering signatures being dependent on the damage type. This study presents a generic framework for probabilistic damage characterization within complex structures, based on physics-rich information on ultrasound wave interaction with existent damage. To this end, the probabilistic model of wave scattering properties estimated from measured GWs is inferred based on absolute complex-valued ratio statistics. Based on the probabilistic model, the likelihood function connecting the scattering properties predicted by a computational model containing the damage parametric description and the scattering estimates is formulated within a Bayesian system identification framework to account for measurement noise and modelling errors. The Transitional Monte Carlo Markov Chain (TMCMC) is finally employed to sample the posterior probability density function of the updated parameters. However, the solution of a Bayesian inference problem often requires repeated runs of “expensive-to-evaluate” Finite Element (FE) simulations, making the inversion procedure firmly demanding in terms of runtime and computational resources. To overcome the computational challenges of repeated likelihood evaluations, a cheap and fast Kriging surrogate model built and based on a set of training points generated with an experiment design strategy in tandem with a hybrid Wave and Finite Element (WFE) computational scheme is proposed in this study. In each “numerical experiment”, the training outputs (i.e. ultrasound scattering properties) are efficiently computed using the hybrid WFE scheme which combines conventional FE analysis with periodic structure theory. By establishing the relationship between the training outputs and damage characterization parameters statistically, the surrogate model further enhances the computational efficiency of the exhibited scheme. Two case studies including one numerical example and an experimental one are presented to verify the accuracy and efficiency of the proposed algorithm.

A Note for Probabilistic Model of Polymer Crystallization in Temperature Gradients

A polymer crystallization kinetics model is the most important way to characterize the crystallization rate of polymers. Because polymers are poor heat conductors, the cooling of thick-walled shapes results in temperature gradients. Piorkowska (Piorkowska, E. J. Appl. Polym. Sci., 2002, 86: 1351–1362.) derived the probabilistic analytical model of polymer crystallization in temperature gradients based on the Avrami equation. However, there are some misunderstandings when using this model. Here, isotactic polypropylene (iPP) is chosen as a model polymer and its crystallization is studied in a temperature gradient field. Based on the results of the Monte Carlo method, the probabilistic model methodology is discussed. The results show that when the product has a large temperature gradient and a large temperature difference, the probabilistic model cannot be used directly; instead, it is necessary to use the average probabilistic model. This means that the sample should be divided into several smaller parts and the probabilistic model used separately for each small part. The values are then averaged to obtain the mean conversion degree of the melt into spherulites for the whole product. The effects of the division number are also discussed. The goal of the present paper is to better understand the polymer crystallization kinetics model in terms of temperature gradients.