Uncertainty Analysis Method Research Articles

A multi-scale uncertainty analysis method based on the Hermite–Chebyshev polynomials for dynamic responses of FRP composite structures with hybrid uncertainties

Multi-scale hybrid uncertainties in material properties of FRP composites stemming from their manufacturing processes present significant challenges for dynamic analysis and reliability assessment. This paper proposes a multi-scale uncertainty surrogate model based on Hermite–Chebyshev polynomials. The relationship between micro- and macro-scale material properties is established using the Mori–Tanaka method. To demonstrate the efficacy of the proposed method, case studies are conducted on both a FRP wide-flange I-beam structure and a FRP truss bridge. Results indicate that this method accurately determines the probability density functions and cumulative distribution functions of natural frequencies and mode shapes. Notably, the method efficiently computes the upper and lower bounds of dynamic failure probability of FRP truss bridge with high numerical efficiency.

Probabilistic seismic performance assessment of aqueduct structures considering different sources of uncertainty

This investigation aims to propose the compound intensity measure and establish the seismic performance assessment framework considering multiple uncertainties for aqueduct structures. For this purpose, taking the typical three-span aqueduct structure as an engineering case, the uncertainty sample pairs are generated by Latin Hypercube Sampling. The seismic response under different ground motion intensities is obtained by incremental dynamic analysis (IDA), and the mapping relationship between structural damage characteristics and limit states is clarified. According to statistical analysis, quantitative recommendation values for the record-to-record, design parameters, performance index values, limit states and finite element model fidelity uncertainties are determined. Then, the multivariate compound intensity measure IMC is developed by taking into account the correlation between single intensity measure. Furthermore, the seismic performance assessment framework of aqueduct structures is established by the single and compound intensity measures. The total dispersion by multiple uncertainty factors is determined by the square-root-sum-of-squares (SRSS) method and the effects of uncertainty factors on the seismic fragility analysis results of aqueduct structures is explored. Subsequently, based on the seismic fragility function and the seismic hazard function, the seismic risk assessment method considering multiple uncertainties is proposed. The analysis results show that with the increase of uncertainty factors, the seismic fragility curves of the aqueduct structure under different limit states rotate clockwise along the IMR. The 50-year exceedance probabilities considering multiple uncertainties is 2.57∼3.14 (PGV) and 1.92∼2.28 (IMC) times that of considering only record-to-record and structural design parameters, further revealing the traditional method can overestimate the potential seismic risk of aqueduct structures. On the other hand, compared with the IMC, the effect of uncertainty factors on the 50-year exceedance probabilities obtained by PGV is more significant. In a word, the compound intensity measure and the multiple uncertainty analysis method proposed in this investigation can be utilized for the seismic performance assessment system of aqueduct structures.

Uncertainty analysis method for diagnosing multi-point defects in urban drainage systems

Urban drainage system (UDS) plays a key role in city urbanization, where defective pipes can lead to seepage. Previous studies have identified the locations of defects in UDS using inverse optimization models. However, the unique optimal solution neglects uncertainty analysis, which may lead to misdiagnosis. In addition, the multi-point defect diagnosis has heavy computational burden due to high dimensional parameters space. To address these issues, this paper proposes a hybrid method that leverages the genetic algorithm (GA) to identify probable space, and then utilizes the adaptive Metropolis (AM) to provide an estimation of the posterior probability distribution (PPD). Firstly, a multi-population GA is employed for the maximum exploration within the model space. Then, AM algorithm is used to explore the final PPD of each pipe defect parameter. The metrics accuracy (ACC), Matthews correlation coefficient (MCC) and mean absolute error (MAE) are used to evaluate the diagnosis performance. A synthetic UDS case with randomized multi-point seepage scenarios is used to validate the method. Results indicate that the proposed hybrid method is effective in diagnosing multi-point defect, with 0.91, 0.78 of the hybrid method and 0.87, 0.69 of the DiffeRential Evolution Adaptive Metropolis method for the ACC and MCC, respectively. Meanwhile, the diagnosis speed has increased by 32%. The result PPD passes the 90% confidence interval validation. The proposed method can provide effective uncertainty analysis to reduce misdiagnosis of the traditional method.

A data-driven maximum entropy method for probability uncertainty analysis based on the B-spline theory

The probability density function (PDF) is quite important for structural reliability analysis; thus, accurate PDF modeling methods draw increasing attention. This paper proposes a novel metaheuristic data-driven paradigm of the maximum entropy method (MEM) based on the B-spline function theory. Firstly, a B-spline proxy of the MEM PDF is proposed for probability uncertainty analysis. We derive the parameter calculation formulation and calculate the undetermined parameters via the raw data of structural responses. Then, to determine the knots of the B-spline functions, we propose a novel data-driven approach with the aid of a powerful metaheuristic algorithm and the response data information. Different from the traditional MEM, the proposed method is a complete data-driven solution approach and does not involve the statistical moment calculation and the nonlinear equations composed of statistical moments. Combining the advantages of the B-spline theory and the MEM, the proposed method can reconstruct the response PDF with a complex shape, such as the PDF with multiple peaks or heavy tails. For verification, two numerical examples and one engineering example are analyzed, and compared with some classical PDF modeling methods. The results show that the proposed method is superior to the compared methods in terms of computational accuracy, when the same sample data is used.

A new polynomial chaos expansion method for uncertainty analysis with aleatory and epistemic uncertainties

A new polynomial chaos expansion method for uncertainty analysis with aleatory and epistemic uncertainties

Advances in InSAR Analysis of Permafrost Terrain

ABSTRACTDifferential interferometric synthetic aperture radar (InSAR) is a remote sensing technique for measuring surface displacements with precision down to millimeters, most commonly from satellites. In permafrost landscapes, InSAR measurements can provide valuable information on geomorphic processes and hazards, including thaw subsidence and frost heave, thermokarst, and permafrost creep. We first review recent progress in InSAR data availability, InSAR processing and uncertainty analysis methods relevant to permafrost studies. These technical advances have contributed to our understanding of surface deformation in flat and sloping terrain in polar and mountainous regions. We emphasize two emerging trends. First, InSAR increasingly enables insight into the mechanisms, controls, and drivers of permafrost landscape dynamics on subseasonal to decadal time scales. Second, InSAR observations in conjunction with models enable novel ways to infer subsurface parameters, such as near‐surface ground ice content and active layer thickness. We anticipate that in the coming decade, InSAR will mature into a widely used operational tool for monitoring, modeling, and planning across rapidly changing permafrost landscapes.

Uncertainty analysis method of high-speed wind tunnel standard model test results based on GUM and MCM

Abstract The standard model is a standard calibration model that has a well-known geometric shape and can represent the aerodynamic layout characteristics of a certain type of aircraft. It has many functions, including evaluating the accuracy of wind tunnel test data, verifying the integrity of the wind tunnel flow field and measurement system, and developing and verifying wind tunnel test technology. Conducting wind tunnel tests using standard models is a key step in realizing the functions of standard models. However, all existing literature on standard model tests has not effectively evaluated the uncertainty of the test results, which makes it impossible to evaluate the reliability of the test results. Based on the GUM and MCM uncertainty analysis methods, this paper establishes a method for quantitatively evaluating the uncertainty of the test results of high-speed wind tunnel standard model tests through rigorous mathematical derivation, providing technical support for precisely quantifying the uncertainty of standard model test results.

Building reliability of risk assessment of domino effects in chemical tank farm through an improved uncertainty analysis method

The severity and complexity of fire-induced domino effects have received widespread attention. The spatial and temporal evolution process modeling of domino accidents is still stuck in single crisp value, in which the uncertainty will affect the reliability of the results. In this paper, we propose a computational method for uncertainty propagation of the evolution process modeling of the domino effect called Uncertainty Propagation of Domino Evolution Model (UPDEM), aiming to increase the reliability of risk assessment results. The method is capable of obtaining ranges and corresponding probability envelopes for tiame to failure and escalation probabilities, and quantifying uncertainty for all computational models that require input parameters. The uncertainty is quantified based on the evidence theory and a parameter cropping method based on the stress-strength interference model is proposed to optimize the evidence theory. The proposed method is applied to a case study and compared with previous studies. The comparison confirms that the results are more reliable after considering uncertainty and can produce the worst possible scenario consequence. Conducting the sensitivity analysis to prioritize the treatment of parameters and identify effective measures in risk control. The methodology can provide an important reference for decision-makers to prevent and control domino effects.

Leakage diagnostic method for water supply pipeline based on ground penetrating radar and image correlation algorithm

In this paper, a new leakage diagnostic method for water supply pipeline based on ground penetrating radar(GPR), image correlation algorithm and uncertainty analysis method is proposed. The presented leakage diagnosis based on GPR can identify the leakage by using the change of hyperbolic echo in the radar echo map before and after leakage. However, the determination of leakage regions needs to be done manually and the accuracy of leakage diagnostic results are affected by subjectivity and experience of technicians. Additionally, the adverse effects of testing errors and calculation errors on identification results are not being considered in the presented leakage diagnostic method. In this paper, the change of hyperbolic echo in radar echo map caused by leakage is explained firstly based on the experimental results. And then, the image correlation algorithm is introduced to calculate the correlation coefficients of radar echo maps before and after leakage, which can be used as the leakage diagnostic indicator. Finally, the uncertainty analysis method is used to consider the influence of testing errors and calculation errors on the leakage diagnostic indicator and the new leakage diagnostic method for water supply pipeline is proposed. The proposed leakage diagnostic method is the novelty of this paper and its workability is verified in the laboratory and the field tests. The results show that the proposed method can effectively identify the leakage region in water supply pipeline.

Efficient Electromagnetic Compatibility Optimization Design Based on the Stochastic Collocation Method

Nowadays, in the field of electromagnetic compatibility (EMC), numerical methods such as finite element analysis are often used for simulation analysis. These numerical methods take a long time to solve some complex simulation problems, which is not conducive to the optimal design of EMC. In particular, the intelligent optimization algorithm that needs continuous iterative calculation will not be realized because of the long optimization time. This paper realizes the innovative application of the uncertainty analysis method (Stochastic Collocation Method) in EMC optimization design. Two typical EMC optimization design problems, namely, the prediction of cable crosstalk and the design of shielding performance of metal boxes, are proposed to verify the effectiveness of the optimization algorithm. Meanwhile, its performance is compared with the classical intelligent optimization algorithms such as genetic algorithms and immune algorithms.

Quantifying ‘realistic’ uncertainty bounds as a part of sound hydrological modelling practice in data scarce regions of southern Africa

This study was based on two premises; the ultimate objective of hydrological modelling is a contribution to sustainable water resources management, and the inherent uncertainties in model results should be realistically quantified. The study uses methods of uncertainty analysis that have been previously applied in the southern Africa region which are based on constraining model outputs using the likely ranges of a set of hydrological indices. One objective was to offer suggestions for sound modelling practice and highlight potential problems. The approach is applied to two case studies where there are very limited streamflow observations. The uncertainty ensemble outputs from the hydrological model are input into a water supply allocation model to assess system performance under different abstraction scenarios. The results are compared with the limited available evidence of system performance and the conclusion is that the uncertainty bands are generally acceptable for future decision making.

Experimental analysis of self-propelled characteristics with uncertainty analysis of ONR tumblehome hull

In this paper, the self-propelled characteristics of the benchmark ONRT hull were studied experimentally at both Froude numbers, Fr = 0.20 and Fr = 0.30. The assessments were conducted under free-running conditions using a fully appended Office of Naval Research Tumblehome (ONRT), model 5613, scaled at 48.9, a customary proportion in academic research. To demonstrate the reliability of self-propulsion experiments conducted at the Istanbul Technical University, Ata Nutku Ship Model Testing Laboratory (ITU-AN), an uncertainty analysis method was applied to the ONRT results. The self-propulsion points from the studies in literature at both Fr = 0.20 and Fr = 0.30, were compared with the present test results. Based on the analysis results at self-propulsion points, it was noted that there was a high level of both intra-laboratory repeatability and inter-laboratory reproducibility characteristics. Through repeated tests, it was discerned that the uncertainties impacting essential parameters were, in descending magnitude, thrust, torque, and rotational rate. Consequently, this investigation enhances the precision and reliability of results by presenting the thrust and torque characteristics of the ONRT hull form, along with associated uncertainties for these Fr numbers.

Multi-Regional Integrated Energy Economic Dispatch Considering Renewable Energy Uncertainty and Electric Vehicle Charging Demand Based on Dynamic Robust Optimization

Aiming at the problem of source-load uncertainty caused by the increasing penetration of renewable energy and the large-scale integration of electric vehicles (EVs) into modern power system, a robust optimal operation scheduling algorithm for regional integrated energy systems (RIESs) with such uncertain situations is urgently needed. Based on this background, aiming at the problem of the irregular charging demand of EV, this paper first proposes an EV charging demand model based on the trip chain theory. Secondly, a multi-RIES optimization operation model including a shared energy storage station (SESS) and integrated demand response (IDR) is established. Aiming at the uncertainty problem of renewable energy, this paper transforms this kind of problem into a dynamic robust optimization with time-varying parameters and proposes an improved robust optimization over time (ROOT) algorithm based on the scenario method and establishes an optimal scheduling mode with the minimum daily operation cost of a multi-regional integrated energy system. Finally, the proposed uncertainty analysis method is verified by an example of multi-RIES. The simulation results show that in the case of the improved ROOT proposed in this paper to solve the robust solution of renewable energy, compared with the traditional charging load demand that regards the EVs as a whole, the EV charging load demand based on the trip chain can reduce the cost of EV charging by 3.5% and the operating cost of the multi-RIES by 11.7%. With the increasing number of EVs, the choice of the starting point of the future EV trip chain is more variable, and the choice of charging methods is more abundant. Therefore, modeling the charging demand of EVs under more complex trip chains is the work that needs to be studied in the future.

SpyderZ: An Efficient Support Vector Machine Library for Photometric Redshift Estimation and Redshift Probability Information

We present SpyderZ, a Python-based library for photometric redshift estimation using support vector machines (implemented with scikit-learn). Our approach discretizes redshift values into uniformly-sized bins and uses one-vs-one support vector classifiers with voting strategies to produce effective probability density functions (ePDFs) over redshift for each galaxy. These ePDFs, which are not constrained to be Gaussian or any other shape, allow for our model's predictions to be used quantitatively with uncertainty analysis methods, and have been shown to enable reliable catastrophic outlier detection. Adapted from the previous IDL package SpiderZ, SpyderZ offers training and evaluation speed optimizations on the order of 102, along with support for parallelization across CPU cores. Our library also offers in-built data sanity checks, result visualizations, metric calculations, cross validation, batch evaluations, and parallelized hyperparameter search (grid search and random search).

Relevant interval perturbation method for uncertainty analysis of structural–acoustic coupling model

The parameters in structural–acoustic coupling models are often coupled with each other, and the independence of the uncertain parameters is a necessary condition for using the traditional interval perturbation method. This article proposes a relevant interval perturbation method for the uncertainty analysis of a structural–acoustic coupling model with uncertain-but-bounded parameters. Aiming at the linear inequality constraint relationship in the uncertain parameters, this method introduces a sensitivity ranking mechanism for the uncertainty parameters, which overcomes the limitation of uncertain parameter independence in the traditional interval model, and effectively restrains the interval expansion phenomenon of the system response in the uncertainty analysis. Through numerical examples, it is demonstrated that the relevant interval perturbation analysis method can effectively solve a constrained problem when there are uncertain parameters, and the obtained response interval radius is smaller than that of the traditional method under constraint conditions.

Uncertainty analysis and economic value prediction of water environmental capacity based on Copula and Bayesian model: A case study of Yitong River, China

Water environmental capacity (WEC) is an indicator of environment management. The uncertainty analysis of WEC is more closely aligned with the actual conditions of the water body. It is crucial for accurately formulating pollution total emissions control schemes. However, the current WEC uncertainty analysis method ignored the connection between water quality and discharge, and required a large amount of monitoring data. This study analyzed the uncertainty of the WEC and predicted its economic value based on Copula and Bayesian model for the Yitong River in China. The Copula model was employed to calculate joint probabilities of water quality and discharge. And the posterior distribution of WEC with limited data was obtained by the Bayesian formula. The results showed that the WEC-COD in the Yitong River was 9009.67 t/a, while NH3–N had no residual WEC. Wanjinta Highway Bridge-Kaoshan Town reach had the most serious pollution. In order to make it have WEC, the reduction of COD and NH3–N was 5330.47 t and 3017.87 t. The economic value of WEC-COD was 5.97 × 107 CNY, and the treatment cost was 2.04 × 108 CNY to make NH3–N have residual WEC. The economic value distribution of WEC was extremely uneven, which could be utilized by adjusting the sewage outlet. In addition, since the treated water was discharged into the Sihua Bridge-Wanjinta Highway Bridge reach, the WEC-COD and the economic value were 19,488.51 t/a and 8.24 × 107 CNY. Increasing the flow of rivers could effectively improve WEC and economic value. This study provided an evaluation tool for guiding river water environment management.

An integrated uncertainty analysis method for the risk assessment of hydrogen refueling stations

In order to assess more rigorously the risks of hydrogen refueling stations (HRSs) with consideration of uncertainties, an uncertainty analysis method integrating the Hydrogen Plus Other Alternative Fuels Risk Assessment Models (HyRAM+), Monte Carlo simulation, and Latin Hypercube Sampling (LHS) method is proposed in this paper. In order to discuss and demonstrate the potential ability of the proposed method, the leak risk of a 35 MPa dispenser at a HRS is assessed. The results indicate that the proposed method can effectively quantify the leak risk uncertainty of the dispenser at a HRS. These uncertainties considered have significant effects on the leak risks of the dispenser, and the risk contribution of jet fire is much larger than that from explosion. Moreover, the leak risk of the dispenser is underestimated by the HyRAM+, so it should be used by combining a reliable safety factor. Current work can provide a more accurate method for the risk assessment and performance-based design of HRSs.

ACE surrogate Model–Based uncertainty and sensitivity analysis methods for severe accident codes

This paper explores the alternating conditional expectation (ACE) algorithm-based surrogate model to advance the state-of-practice in uncertainty and sensitivity analysis methodologies for severe accident codes. For engineering purposes, the ACE algorithm has been used as an alternative means to find the optimal functional forms of the multiple input variables and response variables of interest. Analysis results here demonstrate that compared with the reference cases the proposed surrogate model provides much higher performance in terms of the coefficient of determination (R2) and normalized root mean square error (NRMSE), thus giving more robust insights into the relationship and correlation between the input parameters and figures of merit (FOMs) of interest. Relevant results and insights are summarized in terms of points of interest.

Realistic estimation framework of radioactive release distributions into the environment during nuclear power plant accidents

Since the level 2 PSA of OPR-1000 was the requirement for regulatory purposes, Cs-137 release estimation was contained as the Nuclear Safety Act of ROK in which the Cs-137 release frequency exceeding 100 TBq was determined to happen less than 1.0E-6 per year after the Fukushima Daiichi Accident. However, Cs-137 release estimation from the conventional level 2 PSA of OPR-1000 provided uncertainty due to dominant accident sequence consideration. Thus, this study aimed to develop systematic methods through the overall framework to quantify realistic uncertainty concerns of radioactive material release using sensitivity and uncertainty analysis methods and apply them to OPR-1000. This framework helped to quantify confidential value for the Cs-137 release under the BEPU approach using both parametric and non-parametric methods to cover both realistic and conservative points. Uncertainty propagation analysis showed the unexpected uncertainty increase of Cs-137 release exceeding 100 TBq. The non-parametric uncertainty analysis provided higher conservative concerns for safety than the realistic concerns in terms of economics when compared with the parametric uncertainty analysis. Wilks’ uncertainty analysis showed the importance to consider conservative Cs-137 release in order to reach the higher safety need. Sensitivity analysis showed reasonable relationships between engineering safety parameters with the Cs-137 release.

Application of the Uncertainty Analysis Method to Evaluating the Mechanical Strength of Steam Generator Metal at PWR-based NPPs During Hydraulic Tests and Seismic Loads

Application of the Uncertainty Analysis Method to Evaluating the Mechanical Strength of Steam Generator Metal at PWR-based NPPs During Hydraulic Tests and Seismic Loads