Probability Density Function Curves Research Articles

Probabilistic assessment of existing shield tunnel longitudinal responses to tunnelling

AbstractThis paper proposes a probabilistic‐based framework to assess the failure probability of the existing shield tunnel owing to undercrossing tunnelling. A novel deterministic model using the two‐phase analysis method is presented to evaluate the longitudinal behaviours of the in‐service shield tunnel. First, the tunnelling‐induced settlement is estimated using the Loganathan and Poulos’ method; second, the longitudinal beam‐spring model (LBSM), which can explicitly consider the circumferential joints, is applied to reflect the performances of the existing shield tunnel. Two well‐documented case histories are selected to validate the effectiveness of the deterministic analysis model. The predictions are also compared with previous analytical methods. Afterward, to improve the computational efficiency, a surrogate model is then established to replace deterministic model and perform the global sensitivity analysis (GSA). A probabilistic analysis is further performed to explore the tunnelling‐induced deformation characteristics of the shield tunnel by means of Monte Carlo simulation (MCS) method. Parametric analyses are further performed to explore the influences of key variables on the failure probabilities of the existing shield tunnel. The results show the proposed deterministic model gives a satisfactory prediction in tunnelling‐induced responses of the existing shield tunnel. The LBSM can reflect the segmental ring and joint deformations more realistically. The uncertainties in the ground elastic modulus, joint rotation stiffness and the joint shearing stiffness dominate the tunnel settlement, joint opening and dislocation, respectively. The failure probability of tunnel settlement is more sensitive to volume loss than that of the joint opening and dislocation. The whole system failure probability is identical to that of the tunnel settlement failure mode. By increasing the coefficient of variation (COV) of random variables, probability density function (PDF) curves for neutral and pessimistic conditions become lower and wider, and the maximum joint opening and dislocation positions corresponding to the peaks of PDF apparently deviate from that of the determinate results. Increasing the two tunnel clearances, the allowable volume loss for opening and dislocation increase linearly, but it has insignificant influence on the tunnel failure mode. However, enlarge the new tunnel diameter leads to rapid decrease in the allowable volume loss for all failure modes.

Gas-liquid swirling flow behaviors and liquid-carrying mechanism inside a horizontal pipe

The behaviors of gas-liquid swirling flow under various swirler turns, neglected in previous studies, are essential for swirling flow applications. The role of swirler turns (1, 3, 5) in swirling flow characteristics was systematically investigated in a horizontal pipeline with an inner diameter of 32 mm. The temporal stability and circumferential symmetry of swirling liquid film become better with increasing swirler turns. The periodicity of the swirling liquid film interfacial wave induced by slug flow increases as the swirler turns decrease, while the main wave frequency decreases. Interestingly, for the original slug flow, the downstream void fraction probability density function curves are bimodal with 3 and 5 turns, while it is single-peaked at the swirler with 1 turn. The effectiveness of swirler with 1 turn, 3 turns, and 5 turns in promoting carrying liquid was 100 %, 82.08 %, and 89.22 %, respectively. The mechanism of liquid-carrying was explained in terms of perturbation waves and momentum transfer in the gas-liquid interface. Based on the homogeneous flow model and separated flow model, two predictive models for swirler pressure loss were proposed with maximum errors of 14.67 % and 17.86 %, respectively.

Flow pattern identification for internally threaded tubes based on pressure drop fluctuations

Internally threaded tubes, renowned for their exceptional heat transfer capabilities, are extensively used in heat exchangers. However, directly identifying two-phase flow patterns within internally threaded tubes poses a formidable challenge. To address this, this study conducted two-phase flow experiments with R600a within an internally threaded tube, encompassing a range of mass fluxes spanning from 40 t.369o 130 kg m−2 s−1. The experimental observations unveiled three distinct flow patterns: plug, slug, and annular flow. To validate the accuracy of these observed flow patterns, they were compared with an empirical flow pattern map. Meanwhile, pressure drop signals corresponding to various flow patterns were recorded under different experimental conditions using a high-frequency data acquisition card. The experimental findings indicated that the pressure drop signals fluctuate because of the difference in gas-liquid phase compressibility, while the fluctuation period and flow pattern change simultaneously with the flow rate. Specifically, plug flow exhibited the longest pressure drop fluctuation periods and the sharpest probability density function (PDF) curve. In contrast, annular flow exhibited the shortest fluctuation periods and the least sharp PDF curve. Based on the distinctive characteristics of the PDF curve, a novel parameter, K, was introduced primarily derived from the sharpness of the curve. This led to the formulation of innovative transition criteria, which achieved a prediction accuracy of 86.99% across all datasets in this study. This work furnishes a straightforward methodology for distinguishing flow patterns. The advantages of the proposed criteria include the requirement of measuring only pressure drop fluctuations to identify flow patterns without direct observation.

Probabilistic En Route Sector Traffic Demand Prediction Based on Quantile Regression Neural Network and Kernel Density Estimation

With the development of civil aviation in China, airspace congestion has become more and more serious and has gradually spread from airport terminal areas to en route networks. Traditionally, most prediction methods that obtain traffic flow data are based on the number of aircraft passing through an en route sector and require flight data to meet strict assumptions and conditions. While these methods are normally used in the actual operation of air traffic flow management departments in China, the results are not satisfactory due to the nonlinearity of traffic demand along en route sectors and the change in high-frequency noise. In order to refine aircraft control in airspace, it is necessary to predict traffic flow accurately. Thus, this paper proposes the quantile regression neural network and kernel density estimation method to obtain some quantiles of continuous traffic demand data in the future, which combines the strong nonlinear adaptive ability of neural networks with the ability of quantile regression to describe explanatory variables. By using these continuous conditional quantiles, we obtain the probability density function and probability density curve of the continuous traffic demand in the future using the kernel density estimation method. In this way, we can obtain not only a specific point prediction value and its change interval but also the probability of each value in the prediction change interval of traffic demand in the en route sector as well as a more accurate point prediction value for a specific day.

The Dynamics of Inequality and Poverty Among Children in Colombia During the COVID-19 Recession

This study examines the impact of the COVID-19 pandemic on the income, inequality, and poverty levels among Colombian children between 2019 and 2020, using data from the Luxembourg Income Study Database. The income distribution and changes among Colombian children are analyzed using the probability density function and growth incidence curve. The paper utilizes the Foster–Greer–Thorbecke methodology to measure child poverty in Colombia, decomposes the contributions of different subgroups to child poverty and its changes, and conducts a growth-distribution decomposition of changes in child poverty. The study also employs income-source decomposition to examine the contributions of different income sources to child inequality and its changes. The results show that Colombian children experienced a decline in income, an increase in inequality, and higher levels of poverty during the COVID-19 pandemic. Children from households with higher dependency ratios and those living in rural areas were more likely to experience poverty. The main driver of increased poverty among Colombian children was decreased income, and there was a significant worsening of inequality for ultra-poor children. Labor income emerged as the primary source of inequality and its changes, whereas capital income and private transfers played a role in reducing poverty. However, public social benefits slightly increased inequality levels. Overall, the recession caused by the COVID-19 pandemic is antipoor but pro-ultra-poor. To address similar recessions in the future, the government should expand public transfer payments especially programs targeting children to reduce income inequality and alleviate poverty among children, and bolster the provision of public services essential for children’s development.

Analysis on Probability Mass Function and Probability Density Function

Probability Mass Function (PMF) and Probability Density Function (PDF) are fundamental concepts in probability theory and statistics that play a crucial role in describing the probability distribution of random variables. This abstract provides a comprehensive overview of these concepts, highlighting their definitions, characteristics, and applications. The Probability Mass Function is a concept primarily associated with discrete random variables. It defines the probability of a specific outcome occurring. The PMF assigns probabilities to individual values in the sample space, providing a clear picture of the likelihood of each possible outcome. Commonly denoted as P(X=x), where X is the random variable and x is a specific value, the PMF must satisfy two essential properties: non-negativity and the sum of probabilities over all possible outcomes equals one. On the other hand, the Probability Density Function is a concept applied to continuous random variables. Unlike the PMF, which deals with specific values, the PDF deals with ranges of values. The PDF represents the probability that a continuous random variable falls within a given interval. Denoted as f(x), it is essential to note that the probability of any specific point is zero, and instead, probabilities are defined for intervals. The area under the PDF curve over a given interval corresponds to the probability of the random variable falling within that interval. Understanding the differences and similarities between PMF and PDF is crucial for statistical analysis. While PMF is discrete and deals with specific values, PDF is continuous and provides probabilities for intervals. Both functions are integral to the calculation of various statistical measures, including expected values, variance, and standard deviation. This abstract concludes with a discussion of practical applications in diverse fields, such as finance, engineering, and natural sciences, where a deep understanding of PMF and PDF is essential for making informed decisions and drawing meaningful conclusions from data. The integration of these concepts into statistical models and analyses enhances the accuracy and reliability of predictions, making PMF and PDF indispensable tools in the field of probability and statistics

Probabilistic analysis on the lateral capacity of suction caissons in spatially variable soils

This paper aims to investigate the ultimate lateral capacity of suction caissons embedded in clay with spatially varying undrained shear strength in the framework of probabilistic analysis for the first time. A non-stationary three-dimensional random field is used to represent the undrained shear strength with a linearly increasing trend with depths below the mudline. The stochastic finite difference method is employed to determine the probabilistic ultimate lateral capacity of suction caissons. The influences of the clay undrained strength heterogeneity κ, the coefficient of variation of undrained strength COVsu, and the autocorrelation distances on the probability density function (PDF) curves and cumulative distribution function (CDF) curves of the normalized ultimate lateral capacity N h are investigated . It is found that both the mean and standard deviation of normalized ultimate lateral capacity N h increase with the undrained strength heterogeneity κ, but the coefficient of variation of N h does not. Besides, the small autocorrelation distance of clay results in the low variability of normalized ultimate lateral capacity. This indicates the significance of probabilistic site characterization of the undrained strength of clay.

Impacts of Large-Scale Climate Oscillations on Fluvial Sediments in Central Poland: Evidence from Geochronological Analysis

Abstract The article presents the results of a collective analysis of 181 radiocarbon and 38 luminescence dating results from the time range 50–11.7 cal kBP for samples originating in fluvial sedimentary environment in Łódź region (central Poland), south of the last glacial maximum (LGM) line. Four sites were selected for a general of fluvial deposits and the obtained dating results Struga Żłobnicka, Parchliny, Warenka, and Swędów regions. Based on the summed probability density function (PDF) curves, the study demonstrates the response of the fluvial sedimentary environment to events of overregional scale. The collective analysis of the radiocarbon age determinations from the Łódź region allows for observing the correlation between local environmental changes and large-scale changes recorded in the NGRIP core. The warming periods Greenland interstadials (GI)-3, GI-4, and GI-5.1, the cooling event GI-1b within the warming GI-1, as well as the transition between GI-1a and Greenland stadials (GS)-1, were most prominently recorded in the PDF curves. The collective analysis of the luminescence age determinations reflects a change in the river valleys, expressed by a strong aggradation during the cold maximum of the studied period.

A New Framework for Employing Responsive End-Users Using FAHP and燩SO Algorithm

The capacitor bank and synchronous condenser have been the only available sources of reactive power. Nowadays, most of the appliances use a power electronic interface for their connection. Applying a power electronic interface adds many features to these appliances. One of the promising features is their capability to interact with Volt-VAR programs. In this paper was investigated the reactive power interaction of the end-user appliances. For this purpose, the distribution network buses are ranked based on their effectiveness, followed by studying their interaction in the Volt-VAR program. To be able to consider the uncertainties, Probability Density Function (PDF) curve was discretized to represent different scenarios, and the reduction method was utilized to reduce the situations.

STOCHASTIC STABILITY AND PARAMETRIC CONTROL IN A GENERALIZED AND TRI-STABLE VAN DER POL SYSTEM WITH FRACTIONAL ELEMENT DRIVEN BY MULTIPLICATIVE NOISE

The stochastic transition behavior of tri-stable states in a fractional-order generalized Van der Pol (VDP) system under multiplicative Gaussian white noise (GWN) excitation is investigated. First, according to the minimal mean square error (MMSE) concept, the fractional derivative can be equivalent to a linear combination of damping and restoring forces, and the original system can be simplified into an equivalent integer-order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and based on singularity theory, the critical parameters for stochastic [Formula: see text]-bifurcation of the system are found. Finally, the properties of stationary PDF curves of the system amplitude are qualitatively analyzed by choosing the corresponding parameters in each sub-region divided by the transition set curves. The consistency between numerical results obtained by Monte-Carlo simulation and analytical solutions verified the accuracy of the theoretical analysis process and the method used in this paper has a direct guidance in the design of fractional-order controller to adjust the system behavior.

FEATURES OF THE IMPLEMENTATION OF THE SPEAKER IDENTIFICATION SOFTWARE SYSTEM

The proposed architecture of the identification software system in the form of class and sequence diagrams. The main criteria for assessing the accuracy of speaker identification were studied and possible sources of loss of speaker identification accuracy were identified, which can be used when building a speaker identification system. A software system based on the proposed architecture and previously developed identification algorithms and methods was created.
 The following conclusions can be drawn on the basis of the performed research: approaches to the construction of existing announcer identification systems are considered; the main criteria for assessing the accuracy of announcer identification were investigated and the main sources of loss of accuracy during announcer identification were identified; the structural construction of the announcer identification system is considered, taking into account the identified sources of loss of accuracy during announcer identification; the proposed architecture of the speaker identification system in the UML language in the form of class and sequence diagrams; a software system was built that implements the functions of speech signal identification according to the methods and algorithm proposed in previous works.
 The software system uses a ranking method based on three different criteria. These include: calculation of the proximity of two-dimensional probability density function curves for the frequency of the main tone and the location in the spectrum of three frequency ranges that are extracted from the speech recorded in the speech signal; calculation of the proximity of the probability density function curves for each of these features separately; calculation of the degree of closeness of the absolute maxima of the formant spectra extracted from the speech recorded in the speech signal.

Structurally Nonlinear Fluttering of a Three-Degree-Freedom Wing with Random Disturbances

The differential equations of motion are established for a three-degree-freedom wing dynamic model subjected to unsteady aerodynamic loads and random perturbations. The system is dimensionally reduced by the improved average method to obtain the standard equations. Flutter problems of the deterministic wing system with high-order structural nonlinearity are studied using Hopf bifurcation theory and numerical simulation, the critical flutter speed is obtained and the effectiveness of the improved average method in the process of dimensionality reduction is verified. The stochastic P-bifurcation behaviors of the system are analyzed considering the effects of random perturbations of the longitudinal airflow by examining the qualitative variations of the probability density function curves. The results show that the deterministic wing system has a secondary bifurcation, a bistable phenomenon in which the equilibrium and the limit cycle oscillations coexist. The random disturbances significantly increases the critical flutter speed of the wing system, and the amplitude of limit cycle oscillations increases after including random perturbations for the same incoming flow speed.

Incorporation of a machine learning pathological diagnosis algorithm into the thyroid ultrasound imaging data improves the diagnosis risk of malignant thyroid nodules.

This study aimed at establishing a new model to predict malignant thyroid nodules using machine learning algorithms. A retrospective study was performed on 274 patients with thyroid nodules who underwent fine-needle aspiration (FNA) cytology or surgery from October 2018 to 2020 in Xianyang Central Hospital. The least absolute shrinkage and selection operator (lasso) regression analysis and logistic analysis were applied to screen and identified variables. Six machine learning algorithms, including Decision Tree (DT), Extreme Gradient Boosting (XGBoost), Gradient Boosting Machine (GBM), Naive Bayes Classifier (NBC), Random Forest (RF), and Logistic Regression (LR), were employed and compared in constructing the predictive model, coupled with preoperative clinical characteristics and ultrasound features. Internal validation was performed by using 10-fold cross-validation. The performance of the model was measured by the area under the receiver operating characteristic curve (AUC), accuracy, precision, recall, F1 score, Shapley additive explanations (SHAP) plot, feature importance, and correlation of features. The best cutoff value for risk stratification was identified by probability density function (PDF) and clinical utility curve (CUC). The malignant rate of thyroid nodules in the study cohort was 53.2%. The predictive models are constructed by age, margin, shape, echogenic foci, echogenicity, and lymph nodes. The XGBoost model was significantly superior to any one of the machine learning models, with an AUC value of 0.829. According to the PDF and CUC, we recommended that 51% probability be used as a threshold for determining the risk stratification of malignant nodules, where about 85.6% of patients with malignant nodules could be detected. Meanwhile, approximately 89.8% of unnecessary biopsy procedures would be saved. Finally, an online web risk calculator has been built to estimate the personal likelihood of malignant thyroid nodules based on the best-performing ML-ed model of XGBoost. Combining clinical characteristics and features of ultrasound images, ML algorithms can achieve reliable prediction of malignant thyroid nodules. The online web risk calculator based on the XGBoost model can easily identify in real-time the probability of malignant thyroid nodules, which can assist clinicians to formulate individualized management strategies for patients.

Measurability of neutron star tidal deformability from merging neutron star-black hole binaries

The neutron star-black hole binary (NSBH) system has been considered one of the promising detection candidates for ground-based gravitational-wave (GW) detectors such as LIGO and Virgo. The tidal effects of neutron stars (NSs) are imprinted on the GW signals emitted from NSBHs as well as binary neutron stars. In this work, we study how accurately the parameter $\lambda_{\rm NS}$ can be measured in GW parameter estimation for NSBH signals. We set the parameter range for the NSBH sources to $[4M_{\odot}, 10M_{\odot}]$ for the black hole mass, $[1M_{\odot}, 2M_{\odot}]$ for the NS mass, and $[-0.9, 0.9]$ for the dimensionless black hole spin. For realistic populations of sources distributed in different parameter spaces, we calculate the measurement errors of $\lambda_{\rm NS}$ ($\sigma_{\lambda_{\rm NS}}$) using the Fisher matrix method. In particular, we perform a single-detector analysis using the advanced LIGO and the Cosmic Explorer detectors and a multi-detector analysis using the 2G (advanced LIGO-Hanford, advanced LIGO-Livingstone, advanced Virgo, and KAGRA) and the 3G (Einstein Telescope and Cosmic Explorer) networks. We show the distribution of $\sigma_{\lambda_{\rm NS}}$ for the population of sources as a one-dimensional probability density function. Our result shows that the probability density function curves are similar in shape between advanced LIGO and Cosmic Explorer, but Cosmic Explorer can achieve $\sim 15$ times better accuracy overall in the measurement of $\lambda_{\rm NS}$. In the case of the network detectors, the probability density functions are maximum at $\sigma_{\lambda_{\rm NS}} \sim 130$ and $\sim 4$ for the 2G and the 3G networks, respectively, and the 3G network can achieve $\sim 10$ times better accuracy overall.

Effect of expansion on the wall heat flux in a supersonic turbulent boundary layer

Direct numerical simulation of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.25 and a friction Reynolds number of Reτ = 769 subjected to an expansion corner with a deflection angle of 12° is performed to investigate the effect of expansion on the characteristics of the wall heat flux (WHF). The effect of expansion on the statistical and structural properties of the fluctuating WHF is analyzed systematically in terms of probability density function, frequency spectra, and space-time correlations. Normalization using the local root mean square value yields good collapse of the probability density function curves. Unlike with wall pressure frequency spectra, it is found that expansion has little influence on the low-frequency components of the WHF spectrum. The correlation results show that the main effect of expansion is to increase the characteristic length scales and convection velocity of the WHF fluctuation in the post-expansion region. Furthermore, a direct comparison between the conditionally averaged flow fields and those presented in the authors' previous work [Tong et al., Phys. Fluids 34, 015127 (2022)] is performed to uncover the effect of expansion on the flow structures associated with extreme positive and negative WHF fluctuation events. We highlight that the extreme positive event emerges below a small hot spot under the action of a strong Q4 event, whereas the extreme negative event is relatively insensitive to expansion and still occurs between a pair of strong oblique vortices. In addition, we decompose the mean WHF into seven physics-informed contributions and quantify the effect of expansion on the dominating components with the aid of the bidimensional empirical mode decomposition method. The scale-decomposed results demonstrate quantitatively that expansion decreases the contribution of the large-scale structures in the outer region but the small-scale structures in the near-wall region contribute heavily to the mean WHF generation in the downstream region.

Characterization of aging mechanisms and state of health for second-life 21700 ternary lithium-ion battery

This paper focuses on the identification of aging mechanisms and the estimation of the state of health (SOH) for second-life 21700 nickel–cobalt–aluminum (NCA) lithium-ion batteries. NCA battery is aged at 1/2 C-rate in the laboratory until its SOH value reaches about 60%. Incremental capacity (IC) and different voltage (DV) and probability density function (PDF) analyses are used to explore the aging mechanisms of NCA battery and build SOH estimation models with and without multicollinearity. The results show that the capacity decays almost linearly throughout the aging cycle and the loss of lithium inventory (LLI) and the loss of active material (LAM) on anode are the main aging mechanisms. The equivalence between PDF and IC/DV analyses is proved by NCA battery. Peak (valley) features from IC, DV and PDF curves are extracted as health factors (HFs), which have good correlation with battery SOH. Principal component analysis (PCA) is employed to reduce the multicollinearity and more accurate SOH evaluation models are built based on principal component regression (PCR). The verification results show that the ICA-PCR, DVA-PCR and PDF-PCR models all have good evaluation accuracy.

Assessment of Destructive and Nondestructive Analysis for GGBS Based Geopolymer Concrete and Its Statistical Analysis.

Geopolymer is the alternative to current construction material trends. In this paper, an attempt is made to produce a sustainable construction composite material using geopolymer. Ground granulated blast furnace slag (GGBS)-based geopolymer concrete was prepared and tested for different alkaline to binder ratios (A/B). The effect of various temperatures on compressive strength properties was assessed. The cubes were exposed to temperature ranging from 50 to 70 °C for a duration ranging from 2 to 10 h, and the compressive strength of the specimens was analyzed for destructive and non-destructive analysis and tested for 7, 28, and 90 days. The obtained compressive strength (CS) results were analyzed employing the probability plot (PP) curve, distribution overview curve (DOC), probability density function (PDF), Weibull, survival, and hazard function curve. Maximum compressive strength was achieved for the temperature of 70 °C and an A/B of 0.45 for destructive tests and non-destructive tests with 44.6 MPa and 43.56 MPa, respectively, on 90 days of testing. The survival and hazard function curves showed incremental distribution characteristics for 28 and 90 days of testing results with a probability factor ranging from 0.8 to 1.0.

Evaluation of the raindrop size distribution representation of microphysics schemes in typhoon lekima using disdrometer network observations

Raindrop size distribution (RSD) is a crucial linkage between the precipitation characteristics and related microphysical processes. However, its representation in the numerical weather model still has significant uncertainties. In this study, by using the Weather Research and Forecasting (WRF) model with three widely-used bulk microphysics schemes: The Morrison, Thompson, and WRF double-moment 6-class (WDM6) microphysics schemes, the simulated RSD characteristics in the eyewall and spiral rainbands of Typhoon Lekima (2019) are evaluated against a dense disdrometer network observation. Verifications generally show the overestimated mass-weight mean diameter (Dm) but the underestimated normalized number concentration (Nw) by three microphysics schemes. In comparison with the other two schemes, the RSD characteristics simulated by the Thompson scheme are more consistent with the observation. Furthermore, simulations produced less and somewhat different RSD variability among the eyewall and rainbands than observations. From the outer rainband to the eyewall, the probability density function (PDF) curve of observed Dm shows a left-skewed distribution with a flatter shape and decreasing peakedness, whereas the simulations show a narrower and right-skewed PDF of Dm. The discrepancy between the model and observations is primarily attributed to more intense tendencies of Dm growth and Nw reduction in simulations during raindrops descend to the ground. Examinations of vertical profiles for rain-related microphysical processes indicate that this discrepancy likely originates with the over-predicted collision-coalescence process.

Assessment of the Flood and Drought Occurrence Using Statistically Downscaled Local Climate Models: A Case Study in Langat River Basin, Malaysia

Abstract Climate change is a complex and multi-layer issue with global and local entanglement. In this study, Langat River Basin is chosen. Secondary data was used including the historical flood and drought event reports, Standardized Precipitation Index-1 data and Canadian Earth System Model (CanESM2) along with Australian Community Climate and Earth System Simulator Coupled Model (ACCESS CM-2). These data were used to determine the monthly flood and drought precipitation risk based on five regions of Langat River Basin. The CanESM2 and ACCESS CM-2 based on RCP 4.5 and RCP 8.5 scenarios were downscaled and bias corrected for this study. The reliability of these models was then analyzed with Pearson correlation and probability density function (PDF). The future flood and drought risks from year 2020 to 2100 were predicted using the most reliable local climate model local climate hazard thresholds. The CanESM2 RCP 4.5 scenario was identified to have moderate relationship with the historical precipitation trend in Langat River Basin. The Pearson correlation outcomes were then verified by analyzing the PDF curve between models and historical precipitation. The result shows that the downscaled CanESM2 RCP 4.5 was determined to have moderate correlation r = 0.30, whereas highest similarity with the historical precipitation trend 98.63 % based on 2006 to 2018 period. The scenario is consistent with medium emission coupled with increasing mitigation efforts in Malaysia. Furthermore, the flood and drought risk assessment outcomes show that the occurrence rate for Central, Northern, Southern, Western, and Eastern region in Langat River Basin were determined as 41.97 %, 60.19 %, 40.23 %, 20.16 %, and 34.98% respectively. The Central region was predicted having two drought incidences (February 2069 and February 2099) due to extreme dry season predicted based on 2020 to 2100 period.

Interval forecasting for urban water demand using PSO optimized KDE distribution and LSTM neural networks

The current literature on water demand forecasting mostly focuses on giving accurate point predictions of water demand. However, the water demand point forecasting will encounter uninformative and unreliable problems when the uncertainty level of data increases. To solve the above problem, a hybrid model (KDE-PSO-LSTM), which combines long short-term memory networks (LSTM) to kernel density estimation (KDE) optimized by using the particle swarm optimization (PSO) algorithm, is proposed to acquire the water demand prediction interval (PI) to quantify the likely uncertainties in the predictions. At first, the prediction errors are obtained by the difference between the real values of water demand and the predictive values based on the LSTM model. Then, a novel splitting strategy is proposed to divided point predictions into different levels to deal with the problem that it is difficult to fit the prediction errors of the whole water demand using a single probability density function (PDF). Next, the PSO is used to optimize the hyper-parameter of the KDE method for fitting the PDF curves of different levels prediction errors. Moreover, due to the irregular distribution of prediction errors, a search method called confidence-window shifting is presented to determine the optimal prediction error interval from the fitted PDF curves. After that, the upper bounds and the lower bounds of the best intervals of prediction errors are added to the point predictions to attain the final PI of urban water demand. Finally, to demonstrate the superiorities of the proposed model, the proposed KDE-PSO distribution is compared to other well-known distributions, i.e, the KDE distribution, the Beta-PSO distribution and the normal distribution. The experimental results show that the comprehensive performances of the PIs generated from the proposed KDE-PSO-LSTM model are better than that of KDE-PSO-BP, KDE-PSO-RNN, ND-LSTM, KDE-LSTM, Beta-PSO-LSTM and KDE-GA-LSTM. Therefore, it can be demonstrated that the KDE-PSO-LSTM model can provide reliable decision support to policy-makers for making the optimal water supplying management.