Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming

Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

The prediction of projectile-target intersection for moving tank based on adaptive robust constraint-following control and interval uncertainty analysis

To improve the hit probability of tank at high speed,a prediction method of projectile-target intersection based on adaptive robust constraint-following control and interval uncertainty analysis is proposed.The method proposed provides a novel way to predict the impact point of projectile for moving tank.First,bidirectional stability constraints and stability constraint-following error are constructed using the Udwadia-Kalaba theory,and an adaptive robust constraint-following controller is designed considering uncertainties.Second,the exterior ballistic ordinary differential equation with uncertainties is integrated into the controller,and the pointing control of stability system is extended to the impact-point control of projectile.Third,based on the interval uncertainty analysis method combining Chebyshev polynomial expansion and affine arithmetic,a prediction method of projectile-target intersection is proposed.Finally,the co-simulation experiment is performed by establishing the multi-body system dynamic model of tank and mathematical model of control system.The results demonstrate that the prediction method of projectile-target intersection based on uncertainty analysis can effectively decrease the uncertainties of system,improve the prediction accuracy,and increase the hit probability.The adaptive robust constraint-following control can effectively restrain the uncertainties caused by road excitation and model error.

Generalized nth-Order Perturbation Method Based on Loop Subdivision Surface Boundary Element Method for Three-Dimensional Broadband Structural Acoustic Uncertainty Analysis

In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.

Uncertainty and sensitivity analysis of in-vessel phenomena under severe accident mitigation strategy based on ISAA-SAUP program

The phenomenology involved in severe accidents in nuclear reactors is highly complex.Currently,integrated analysis programs used for severe accident analysis heavily rely on custom empirical parameters,which introduce considerable uncertainty.Therefore,in recent years,the field of severe accidents has shifted its focus toward applying uncertainty analysis methods to quantify uncertainty in safety assessment programs,known as“best estimate plus uncertainty(BEPU).”This approach aids in enhancing our comprehension of these programs and their further development and improvement.This study concentrates on a third-generation pressurized water reactor equipped with advanced active and passive mitigation strategies.Through an Integrated Severe Accident Analysis Program(ISAA),numerical modeling and uncertainty analysis were conducted on severe accidents resulting from large break loss of coolant accidents.Seventeen uncertainty parameters of the ISAA program were meticulously screened.Using Wilks'formula,the developed uncertainty program code,SAUP,was employed to carry out Latin hypercube sampling,while ISAA was employed to execute batch calculations.Statistical analysis was then conducted on two figures of merit,namely hydrogen generation and the release of fission products within the pressure vessel.Uncertainty calculations revealed that hydrogen production and the fraction of fission product released exhibited a normal distribution,ranging from 182.784 to 330.664 kg and from 15.6 to 84.3%,respectively.The ratio of hydrogen production to reactor thermal power fell within the range of 0.0578–0.105.A sensitivity analysis was performed for uncertain input parameters,revealing significant correlations between the failure temperature of the cladding oxide layer,maximum melt flow rate,size of the particulate debris,and porosity of the debris with both hydrogen generation and the release of fission products.

Review on uncertainty analysis and information fusion diagnosis of aircraft control system

In the aircraft control system,sensor networks are used to sample the attitude and environmental data.As a result of the external and internal factors(e.g.,environmental and task complexity,inaccurate sensing and complex structure),the aircraft control system contains several uncertainties,such as imprecision,incompleteness,redundancy and randomness.The information fusion technology is usually used to solve the uncertainty issue,thus improving the sampled data reliability,which can further effectively increase the performance of the fault diagnosis decision-making in the aircraft control system.In this work,we first analyze the uncertainties in the aircraft control system,and also compare different uncertainty quantitative methods.Since the information fusion can eliminate the effects of the uncertainties,it is widely used in the fault diagnosis.Thus,this paper summarizes the recent work in this aera.Furthermore,we analyze the application of information fusion methods in the fault diagnosis of the aircraft control system.Finally,this work identifies existing problems in the use of information fusion for diagnosis and outlines future trends.

Analysis of sleep quality,disease uncertainty,and psychological tolerance in patients undergoing chemotherapy for digestive tract malignancies

BACKGROUND Colorectal cancer is the second leading cause of cancer-related deaths among digestive tract malignancies,following gastric cancer.Sleep is of great significance for maintaining human health.The incidence of sleep disorders in patients with cancer is approximately twice that observed in the general population.Lack of sleep can prolong hospital stays,increase the likelihood of infection,and increase mortality rates.Therefore,studying the factors related to sleep quality is significant for improving the quality of life of patients with malignant tumors of the digestive tract.AIM To investigate the relationships among sleep quality,disease uncertainty,and psychological resilience in patients undergoing chemotherapy for digestive tract malignancies.METHODS A total of 131 patients with malignant digestive tract tumors who were treated at Hefei BOE Hospital between April 2021 and September 2022 were selected as research participants.Based on their Pittsburgh Sleep Quality Index(PSQI)scores,participants were divided into either the sleep disorder group(PSQI score>7)or the normal sleep group(PSQI score≤7).The clinical data—together with the Mishel Uncertainty in Illness Scale for Adults(MUIS-A)and Connor-Davidson Resilience Scale(CD-RISC)scores—were compared.RESULTS In this study,78(59.54%)patients with digestive tract malignancies developed sleep disorders after chemotherapy.Sleep disorder incidence was higher in patients with colorectal cancer than in those with gastric and esophageal cancers(P<0.05).The total MUIS-A score and those for each item in the sleep disorder group were higher than those in the normal sleep group.The total CD-RISC score and those for each item in the sleep disorder group were lower than those in the normal sleep group(P<0.05).The PSQI scores of patients with malignant digestive tract tumors were positively correlated with the scores for lack of disease information,disease uncertainty,and unpredictability in the MUIS-A and negatively correlated with the scores for tenacity,self-improvement,and optimism in the CD-RISC(P<0.05).CONCLUSION Patients undergoing chemotherapy for digestive tract malignancies are prone to sleep problems related to disease uncertainty and psychological resilience.Therefore,interventions can be implemented to improve their sleep quality.

Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of Wave Mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum Mechanics, when Schrödinger proved that the Matrix Mechanics independently developed by Werner Heisenberg was equivalent to Wave Mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

Measurement Uncertainty Analysis of the Rotary-scan Method for the Measurable Dimension of Cylindrical Workpieces

The measurement uncertainty analysis is carried out to investigate the measurable dimensions of cylindrical workpieces by the rotary-scan method in this paper.Due to the difficult alignment of the workpiece with a diameter of less than 3 mm by the rotary scan method,the measurement uncertainty of the cylindrical workpiece with a diameter of 3 mm and length of 50 mm which is measured by a roundness measuring machine,is evaluated according to GUM(Guide to the Expression of Uncertainty in Measurement)as an example.Since the uncertainty caused by the eccentricity of the measured workpiece is different with the dimension changing,the measurement uncertainty of cylindrical workpieces with other dimensions can be evaluated the same as the diameter of 3 mm but with different eccentricity.Measurement uncertainty caused by different eccentricities concerning the dimension of the measured cylindrical workpiece is set to simulate the evaluations.Compared to the target value of the measurement uncertainty of 0.1μm,the measurable dimensions of the cylindrical workpiece can be obtained.Experiments and analysis are presented to quantitatively evaluate the reliability of the rotary-scan method for the roundness measurement of cylindrical workpieces.

Research status and prospects of the fractal analysis of metal material surfaces and interfaces

As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.

Multilevel analysis of the central-peripheral-target organ pathway:contributing to recovery after peripheral nerve injury

Peripheral nerve injury is a common neurological condition that often leads to severe functional limitations and disabilities.Research on the pathogenesis of peripheral nerve injury has focused on pathological changes at individual injury sites,neglecting multilevel pathological analysis of the overall nervous system and target organs.This has led to restrictions on current therapeutic approaches.In this paper,we first summarize the potential mechanisms of peripheral nerve injury from a holistic perspective,covering the central nervous system,peripheral nervous system,and target organs.After peripheral nerve injury,the cortical plasticity of the brain is altered due to damage to and regeneration of peripheral nerves;changes such as neuronal apoptosis and axonal demyelination occur in the spinal cord.The nerve will undergo axonal regeneration,activation of Schwann cells,inflammatory response,and vascular system regeneration at the injury site.Corresponding damage to target organs can occur,including skeletal muscle atrophy and sensory receptor disruption.We then provide a brief review of the research advances in therapeutic approaches to peripheral nerve injury.The main current treatments are conducted passively and include physical factor rehabilitation,pharmacological treatments,cell-based therapies,and physical exercise.However,most treatments only partially address the problem and cannot complete the systematic recovery of the entire central nervous system-peripheral nervous system-target organ pathway.Therefore,we should further explore multilevel treatment options that produce effective,long-lasting results,perhaps requiring a combination of passive(traditional)and active(novel)treatment methods to stimulate rehabilitation at the central-peripheral-target organ levels to achieve better functional recovery.

Mixed uncertainty analysis of polycyclic aromatic hydrocarbon inhalation and risk assessment in ambient air of Beijing

This article presents the application of an integrated method that estimates the dispersion of polycyclic aromatic hydrocarbons （PAHs） in air, and assesses the human health risk associated with PAHs inhalation. An uncertainty analysis method consisting of three components were applied in this study, where the three components include a bootstrapping method for analyzing the whole process associated uncertainty, an inhalation rate （IR） representation for evaluating the total PAH inhalation risk for human health, and a normally distributed absorption fraction （AF） ranging from 0% to 100% to represent the absorption capability of PAHs in human body. Using this method, an integrated process was employed to assess the health risk of the residents in Beijing, China, from inhaling PAHs in the air. The results indicate that the ambient air PAHs in Beijing is an important contributor to human health impairment, although over 68% of residents seem to be safe from daily PAH carcinogenic inhalation. In general, the accumulated daily inhalation amount is relatively higher for male and children at 10 years old of age than for female and children at 6 years old. In 1997, about 1.73% cancer sufferers in Beijing were more or less related to ambient air PAHs inhalation. At 95% confidence interval, approximately 272-309 individual cancer incidences can be attributed to PAHs pollution in the air. The probability of greater than 500 cancer occurrence is 15.3%. While the inhalation of ambient air PAHs was shown to be an important factor responsible for higher cancer occurrence in Beijing, while the contribution might not be the most significant one.

Multi-parameters uncertainty analysis of logistic support process based on GERT

The uncertainty analysis is an effective sensitivity analysis method for system model analysis and optimization. However,the existing single-factor uncertainty analysis methods are not well used in the logistic support systems with multiple decision-making factors. The multiple transfer parameters graphical evaluation and review technique（MTP-GERT） is used to model the logistic support process in consideration of two important factors, support activity time and support activity resources, which are two primary causes for the logistic support process uncertainty. On this basis,a global sensitivity analysis（GSA） method based on covariance is designed to analyze the logistic support process uncertainty. The aircraft support process is selected as a case application which illustrates the validity of the proposed method to analyze the support process uncertainty, and some feasible recommendations are proposed for aircraft support decision making on carrier.

Sensitivity and Uncertainty Analysis of Regional Marine Ecosystem Services Value

Marine ecosystem services are the benefits which people obtain from the marine ecosystem,including provisioning services,regulating services,cultural services and supporting services. The human species,while buffered against environmental changes by culture and technology,is fundamentally dependent on the flow of ecosystem services. Marine ecosystem services become increasingly valuable as the terrestrial resources become scarce. The value of marine ecosystem services is the monetary flow of ecosystem services on specific temporal and spatial scales,which often changes due to the variation of the goods prices,yields and the status of marine exploitation. Sensitivity analysis is to study the relationship between the value of marine ecosystem services and the main factors which affect it. Uncertainty analysis based on varying prices,yields and status of marine exploitation was carried out. Through uncertainty analysis,a more credible value range instead of a fixed value of marine ecosystem services was obtained in this study. Moreover,sensitivity analysis of the marine ecosystem services value revealed the relative importance of different factors.

Uncertainty Analysis and Optimization of Quasi-Zero Stifness Air Suspension Based on Polynomial Chaos Method

To improve the vibration isolation performance of suspensions,various new structural forms of suspensions have been proposed.However,there is uncertainty in these new structure suspensions,so the deterministic research cannot refect the performance of the suspension under actual operating conditions.In this paper,a quasi-zero stifness isolator is used in automotive suspensions to form a new suspension−quasi-zero stifness air suspension(QZSAS).Due to the strong nonlinearity and structural complexity of quasi-zero stifness suspensions,changes in structural parameters may cause dramatic changes in suspension performance,so it is of practical importance to study the efect of structural parameter uncertainty on the suspension performance.In order to solve this problem,three suspension structural parameters d_(0),L_(0) and Pc_(0) are selected as random variables,and the polynomial chaos expansion(PCE)theory is used to solve the suspension performance parameters.The sensitivity of the performance parameters to diferent structural parameters was discussed and analyzed in the frequency domain.Furthermore,a multi-objective optimization of the structural parameters d_(0),L_(0) and Pc_(0) of QZSAS was performed with the mean and variance of the root-mean-square(RMS)acceleration values as the optimization objectives.The optimization results show that there is an improvement of about 8%−1_(0)%in the mean value and about 4_(0)%−55%in the standard deviation of acceleration(RMS)values.This paper verifes the feasibility of the PCE method for solving the uncertainty problem of complex nonlinear systems,which provide a reference for the future structural design and optimization of such suspension systems.

Uncertainty Analysis for Ship-Bank Interaction Tests in A Circulating Water Channel

This paper presents a systematic model test program to assess the uncertainty of the ship-bank interaction forces,using the planar motion mechanism(PMM)system in a circulating water channel(CWC).Therefore,the uncertainties due to ship-bank distance and water depth are considered,and they are calculated via the partial differentials of the regression formulae based on the test data.The general part of the uncertainty analysis(UA)is performed according to the ITTC recommended procedure 7.5-02-06.04,while the uncertainty of speed is identified as the bias limit due to the flow velocity maldistribution in the CWC.In each example test for the UA of ship-bank interaction forces,12 repeated measurements were conducted.Results from the UA show that the contribution of water depth error and flow velocity maldistribution to the total uncertainty is noticeable,and the paper explains how they increase with the change of the test conditions.The present study will be useful in understanding the uncertainty regarding the ship-bank interaction force measurement in a CWC.

Uncertainty analysis of runoff and sedimentation in a forested watershed using sequential uncertainty fitting method

The Soil and Water Assessment Tool （SWAT） was implemented in a small forested watershed of the Soan River Basin innorthern Pakistan through application of the sequential uncertainty fitting （SUFI-2） method to investigate the associateduncertainty in runoff and sediment load estimation. The model was calibrated for a 10-year period （1991–2000） with aninitial 4-year warm-up period （1987–1990）, and was validated for the subsequent 10-year period （2001–2010）. Themodel evaluation indices R2 （the coefficient of determination）, NS （the Nash-Sutcliffe efficiency）, and PBIAS （percentbias） for stream flows simulation indicated that there was a good agreement between the measured and simulated flows.To assess the uncertainty in the model outputs, p-factor （a 95% prediction uncertainty, 95PPU） and r-factors （averagewideness width of the 95PPU band divided by the standard deviation of the observed values） were taken into account.The 95PPU band bracketed 72% of the observed data during the calibration and 67% during the validation. The r-factorwas 0.81 during the calibration and 0.68 during the validation. For monthly sediment yield, the model evaluation coefficients（R2 and NS） for the calibration were computed as 0.81 and 0.79, respectively; for validation, they were 0.78and 0.74, respectively. Meanwhile, the 95PPU covered more than 60% of the observed sediment data during calibrationand validation. Moreover, improved model prediction and parameter estimation were observed with the increasednumber of iterations. However, the model performance became worse after the fourth iterations due to an unreasonableparameter estimation. Overall results indicated the applicability of the SWAT model with moderate levels of uncertaintyduring the calibration and high levels during the validation. Thus, this calibrated SWAT model can be used for assessmentof water balance components, climate change studies, and land use management practices.

Bayesian data analysis to quantify the uncertainty of intact rock strength

One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks.First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σand mused in the Hoek-Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares(NLLS) method. The paper discusses the use of a Student’s t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek-Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.

Uncertainty analysis of flow rate measurement for multiphase flow using CFD

The venturi meter has an advantage in its use,because it can measure flow without being much affected by the type of the measured fluid or flow conditions.Hence,it has excellent versatility and is being widely applied in many industries.The flow of a liquid containing air is a representative example of a multiphase flow and exhibits complex flow characteristics.In particular,the greater the gas volume fraction（GVF）,the more inhomogeneous the flow becomes.As a result,using a venturi meter to measure the rate of a flow that has a high GVF generates an error.In this study,the cause of the error occurred in measuring the flow rate for the multiphase flow when using the venturi meter for analysis by CFD.To ensure the reliability of this study,the accuracy of the multiphase flow models for numerical analysis was verified through comparison between the calculated results of numerical analysis and the experimental data.As a result,the Grace model,which is a multiphase flow model established by an experiment with water and air,was confirmed to have the highest reliability.Finally,the characteristics of the internal flow Held about the multiphase flow analysis result generated by applying the Grace model were analyzed to find the cause of the uncertainty occurring when measuring the flow rate of the multiphase flow using the venturi meter.A phase separation phenomenon occurred due to a density difference of water and air inside the venturi,and flow inhomogeneity happened according to the flow velocity difference of each phase.It was confirmed that this flow inhomogeneity increased as the GVF increased due to the uncertainty of the flow measurement.

Application of SWAT Model to the Olifants Basin: Calibration, Validation and Uncertainty Analysis

The application of the Soil and Water Assessment Tool (SWAT) to the Olifants Basin in South Africa was the focus of our study with emphasis on calibration, validation and uncertainty analysis. The Basin was discretized into 23 sub-basins and 226 Hydrologic Response Units (HRUs) using 3 arc second (90 m × 90 m) pixel resolution SRTM DEM with stream gauge B7H015 as the Basin outlet. Observed stream flow data at B7H015 were used for model calibration (1988-2001) and validation (2002-2013) using the split sample approach. Relative global sensitivity analysis using SUFI-2 algorithm was used to determine sensitive parameters to stream flow for calibration of the model. Performance efficiency of the Olifants SWAT model was assessed using Nash-Sutcliffe (NSE), coefficient of determination (R2), Percent Bias (PBIAS) and Root Mean Square Error-Observation Standard deviation Ratio (RSR). Sensitivity analysis revealed in decreasing order of significance, runoff curve number (CN2), alpha bank factor (ALPHA_BNK), soil evaporation compensation factor (ESCO), soil available water capacity (SOIL_AWC, mm H2O/mm soil), groundwater delay (GW_ DELAY, days) and groundwater “revap” coefficient (GW_REVAP) to be the most sensitive parameters to stream flow. Analysis of the model during the calibration period gave the following statistics;NSE = 0.88;R2 = 0.89;PBIAS = -11.49%;RSR = 0.34. On the other hand, statistics during the validation period were NSE = 0.67;R2 = 0.79;PBIAS = -20.69%;RSR = 0.57. The observed statistics indicate the applicability of the SWAT model in simulating the hydrology of the Olifants Basin and therefore can be used as a Decision Support Tool (DST) by water managers and other relevant decisions making bodies to influence policy directions on the management of watershed processes especially water resources.

Uncertainty analysis of seawater intrusion forecasting

In order to describe the importance of uncertainty analysis in seawater intrusion forecasting and identify the main factors that might cause great differences in prediction results, we analyzed the influence of sea level rise, tidal effect, the seasonal variance of influx, and the annual variance of the pumping rate, as well as combinations of different parameters. The results show that the most important factors that might cause great differences in seawater intrusion distance are the variance of pumping rate and combinations of different parameters. The influence of sea level rise can be neglected in a short-time simulation （ten years, for instance）. Retardation of seawater intrusion caused by tidal effects is obviously important in aquifers near the coastline, but the influence decreases with distance away from the coastline and depth away from the seabed. The intrusion distance can reach a dynamic equilibrium with the application of the sine function for seasonal effects of influx. As a conclusion, we suggest that uncertainty analysis should be considered in seawater intrusion forecasting, if possible.