Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

System Reliability Analysis Method Based on T-S FTA and HE-BN

For high-reliability systems in military,aerospace,and railway fields,the challenges of reliability analysis lie in dealing with unclear failure mechanisms,complex fault relationships,lack of fault data,and uncertainty of fault states.To overcome these problems,this paper proposes a reliability analysismethod based on T-S fault tree analysis(T-S FTA)and Hyper-ellipsoidal Bayesian network(HE-BN).The method describes the connection between the various systemfault events by T-S fuzzy gates and translates them into a Bayesian network(BN)model.Combining the advantages of T-S fault tree modeling with the advantages of Bayesian network computation,a reliability modeling method is proposed that can fully reflect the fault characteristics of complex systems.Experts describe the degree of failure of the event in the form of interval numbers.The knowledge and experience of experts are fused with the D-S evidence theory to obtain the initial failure probability interval of the BN root node.Then,the Hyper-ellipsoidal model(HM)constrains the initial failure probability interval and constructs a HE-BN for the system.A reliability analysismethod is proposed to solve the problem of insufficient failure data and uncertainty in the degree of failure.The failure probability of the system is further calculated and the key components that affect the system’s reliability are identified.The proposedmethod accounts for the uncertainty and incompleteness of the failure data in complex multi-state systems and establishes an easily computable reliability model that fully reflects the characteristics of complex faults and accurately identifies system weaknesses.The feasibility and accuracy of the method are further verified by conducting case studies.

A phenology-based vegetation index for improving ratoon rice mapping using harmonized Landsat and Sentinel-2 data

Ratoon rice,which refers to a second harvest of rice obtained from the regenerated tillers originating from the stubble of the first harvested crop,plays an important role in both food security and agroecology while requiring minimal agricultural inputs.However,accurately identifying ratoon rice crops is challenging due to the similarity of its spectral features with other rice cropping systems(e.g.,double rice).Moreover,images with a high spatiotemporal resolution are essential since ratoon rice is generally cultivated in fragmented croplands within regions that frequently exhibit cloudy and rainy weather.In this study,taking Qichun County in Hubei Province,China as an example,we developed a new phenology-based ratoon rice vegetation index(PRVI)for the purpose of ratoon rice mapping at a 30 m spatial resolution using a robust time series generated from Harmonized Landsat and Sentinel-2(HLS)images.The PRVI that incorporated the red,near-infrared,and shortwave infrared 1 bands was developed based on the analysis of spectro-phenological separability and feature selection.Based on actual field samples,the performance of the PRVI for ratoon rice mapping was carefully evaluated by comparing it to several vegetation indices,including normalized difference vegetation index(NDVI),enhanced vegetation index(EVI)and land surface water index(LSWI).The results suggested that the PRVI could sufficiently capture the specific characteristics of ratoon rice,leading to a favorable separability between ratoon rice and other land cover types.Furthermore,the PRVI showed the best performance for identifying ratoon rice in the phenological phases characterized by grain filling and harvesting to tillering of the ratoon crop(GHS-TS2),indicating that only several images are required to obtain an accurate ratoon rice map.Finally,the PRVI performed better than NDVI,EVI,LSWI and their combination at the GHS-TS2 stages,with producer's accuracy and user's accuracy of 92.22 and 89.30%,respectively.These results demonstrate that the proposed PRVI based on HLS data can effectively identify ratoon rice in fragmented croplands at crucial phenological stages,which is promising for identifying the earliest timing of ratoon rice planting and can provide a fundamental dataset for crop management activities.

Method for evaluation of geological strength index of carbonate cliff rocks:Coupled hyperspectral-digital borehole image technique

The deterioration of unstable rock mass raised interest in evaluating rock mass quality.However,the traditional evaluation method for the geological strength index(GSI)primarily emphasizes the rock structure and characteristics of discontinuities.It ignores the influence of mineral composition and shows a deficiency in assessing the integrity coefficient.In this context,hyperspectral imaging and digital panoramic borehole camera technologies are applied to analyze the mineral content and integrity of rock mass.Based on the carbonate mineral content and fissure area ratio,the strength reduction factor and integrity coefficient are calculated to improve the GSI evaluation method.According to the results of mineral classification and fissure identification,the strength reduction factor and integrity coefficient increase with the depth of rock mass.The rock mass GSI calculated by the improved method is mainly concentrated between 40 and 60,which is close to the calculation results of the traditional method.The GSI error rates obtained by the two methods are mostly less than 10%,indicating the rationality of the hyperspectral-digital borehole image coupled evaluation method.Moreover,the sensitivity of the fissure area ratio(Sr)to GSI is greater than that of the strength reduction factor(a),which means the proposed GSI is suitable for rocks with significant fissure development.The improved method reduces the influence of subjective factors and provides a reliable index for the deterioration evaluation of rock mass.

Spectral purification improves monitoring accuracy of the comprehensive growth evaluation index for film-mulched winter wheat

In order to further improve the utility of unmanned aerial vehicle(UAV)remote-sensing for quickly and accurately monitoring the growth of winter wheat under film mulching, this study examined the treatments of ridge mulching,ridge–furrow full mulching, and flat cropping full mulching in winter wheat.Based on the fuzzy comprehensive evaluation (FCE) method, four agronomic parameters (leaf area index, above-ground biomass, plant height, and leaf chlorophyll content) were used to calculate the comprehensive growth evaluation index (CGEI) of the winter wheat, and 14 visible and near-infrared spectral indices were calculated using spectral purification technology to process the remote-sensing image data of winter wheat obtained by multispectral UAV.Four machine learning algorithms, partial least squares, support vector machines, random forests, and artificial neural network networks(ANN), were used to build the winter wheat growth monitoring model under film mulching, and accuracy evaluation and mapping of the spatial and temporal distribution of winter wheat growth status were carried out.The results showed that the CGEI of winter wheat under film mulching constructed using the FCE method could objectively and comprehensively evaluate the crop growth status.The accuracy of remote-sensing inversion of the CGEI based on the ANN model was higher than for the individual agronomic parameters, with a coefficient of determination of 0.75,a root mean square error of 8.40, and a mean absolute value error of 6.53.Spectral purification could eliminate the interference of background effects caused by mulching and soil, effectively improving the accuracy of the remotesensing inversion of winter wheat under film mulching, with the best inversion effect achieved on the ridge–furrow full mulching area after spectral purification.The results of this study provide a theoretical reference for the use of UAV remote-sensing to monitor the growth status of winter wheat with film mulching.

Association between triglyceride-glucose index and colorectal polyps:A retrospective cross-sectional study

BACKGROUND Colorectal polyps(CPs)are frequently occurring abnormal growths in the colorectum,and are a primary precursor of colorectal cancer(CRC).The triglyceride-glucose(TyG)index is a novel marker that assesses metabolic health and insulin resistance,and has been linked to gastrointestinal cancers.AIM To investigate the potential association between the TyG index and CPs,as the relation between them has not been documented.METHODS A total of 2537 persons undergoing a routine health physical examination and colonoscopy at The First People's Hospital of Kunshan,Jiangsu Province,China,between January 2020 and December 2022 were included in this retrospective cross-sectional study.After excluding individuals who did not meet the eligibility criteria,descriptive statistics were used to compare characteristics between patients with and without CPs.Logistic regression analyses were conducted to determine the associations between the TyG index and the prevalence of CPs.The TyG index was calculated using the following formula:Ln[triglyceride(mg/dL)×glucose(mg/dL)/2].The presence and types of CPs was determined based on data from colonoscopy reports and pathology reports.RESULTS A nonlinear relation between the TyG index and the prevalence of CPs was identified,and exhibited a curvilinear pattern with a cut-off point of 2.31.A significant association was observed before the turning point,with an odds ratio(95% confidence interval)of 1.70(1.40,2.06),P<0.0001.However,the association between the TyG index and CPs was not significant after the cut-off point,with an odds ratio(95% confidence interval)of 0.57(0.27,1.23),P=0.1521.CONCLUSION Our study revealed a curvilinear association between the TyG index and CPs in Chinese individuals,suggesting its potential utility in developing colonoscopy screening strategies for preventing CRC.

Renal resistive index measurements by ultrasound in patients with liver cirrhosis:Magnitude and associations with renal dysfunction

BACKGROUND The hemodynamic alterations seen in liver cirrhosis lead to renal vasoconstriction,ultimately causing acute kidney injury(AKI).The renal resistive index(RRI)is the most common Doppler ultrasound variable for measuring intrarenal vascular resistance.AIM To evaluate the association of the RRI with AKI in patients with liver cirrhosis and to identify risk factors for high RRI.METHODS This was a prospective observational study,where RRI was measured using Doppler ultrasound in 200 consecutive hospitalized patients with cirrhosis.The association of RRI with AKI was studied.The receiver operating characteristic(ROC)curve analysis was utilized to determine discriminatory cut-offs of RRI for various AKI phenotypes.Multivariate analysis was conducted to determine the predictors of high RRI.RESULTS The mean patient age was 49.08±11.68 years,with the majority(79.5%)being male;the predominant etiology of cirrhosis was alcohol(39%).The mean RRI for the study cohort was 0.68±0.09,showing a progressive increase with higher Child-Pugh class of cirrhosis.Overall,AKI was present in 129(64.5%)patients.The mean RRI was significantly higher in patients with AKI compared to those without it(0.72±0.06 vs 0.60±0.08;P<0.001).A total of 82 patients(41%)had hepatorenal syndrome(HRS)-AKI,29(22.4%)had prerenal AKI(PRA),and 18(13.9%)had acute tubular necrosis(ATN)-AKI.The mean RRI was significantly higher in the ATN-AKI(0.80±0.02)and HRS-AKI(0.73±0.03)groups than in the PRA(0.63±0.07)and non-AKI(0.60±0.07)groups.RRI demonstrated excellent discriminatory ability in distinguishing ATN-AKI from non-ATN-AKI(area under ROC curve:93.9%).AKI emerged as an independent predictor of high RRI(adjusted odds ratio[OR]:11.52),and high RRI independently predicted mortality among AKI patients(adjusted OR:3.18).CONCLUSION In cirrhosis patients,RRI exhibited a significant association with AKI,effectively differentiated between AKI phenotypes,and predicted AKI mortality.

Three-dimensional choroidal vascularity index and choroidal thickness in fellow eyes of acute and chronic primary angle-closure using swept-source optical coherence tomography

AIM:To compare the three-dimensional choroidal vascularity index(CVI)and choroidal thickness between fellow eyes of acute primary angle-closure(F-APAC)and chronic primary angle-closure glaucoma(F-CPACG)and the eyes of normal controls.METHODS:This study included 37 patients with unilateral APAC,37 with asymmetric CPACG without prior treatment,and 36 healthy participants.Using swept-source optical coherence tomography(SS-OCT),the macular and peripapillary choroidal thickness and three-dimensional CVI were measured and compared globally and sectorally.Pearson’s correlation analysis and multivariate regression models were used to evaluate choroidal thickness or CVI with related factors.RESULTS:The mean subfoveal CVIs were 0.35±0.10,0.33±0.09,and 0.29±0.04,and the mean subfoveal choroidal thickness were 315.62±52.92,306.22±59.29,and 262.69±45.55μm in the F-APAC,F-CPACG,and normal groups,respectively.All macular sectors showed significantly higher CVIs and choroidal thickness in the F-APAC and F-CPACG eyes than in the normal eyes(P<0.05),while there were no significant differences between the F-APAC and F-CPACG eyes.In the peripapillary region,the mean overall CVIs were 0.21±0.08,0.20±0.08,and 0.19±0.05,and the mean overall choroidal thickness were 180.45±54.18,174.82±50.67,and 176.18±37.94μm in the F-APAC,F-CPACG,and normal groups,respectively.There were no significant differences between any of the two groups in all peripapillary sectors.Younger age,shorter axial length,and the F-APAC or F-CPACG diagnosis were significantly associated with higher subfoveal CVI and thicker subfoveal choroidal thickness(P<0.05).CONCLUSION:The fellow eyes of unilateral APAC or asymmetric CPACG have higher macular CVI and choroidal thickness than those of the normal controls.Neither CVI nor choroidal thickness can distinguish between eyes predisposed to APAC or CPACG.A thicker choroid with a higher vascular volume may play a role in the pathogenesis of primary angle-closure glaucoma.

Belief reliability:a scientific exploration of reliability engineering

This paper systematically introduces and reviews a scientific exploration of reliability called the belief reliability.Beginning with the origin of reliability engineering,the problems of present theories for reliability engineering are summarized as a query,a dilemma,and a puzzle.Then,through philosophical reflection,we introduce the theoretical solutions given by belief reliability theory,including scientific principles,basic equations,reliability science experiments,and mathematical measures.The basic methods and technologies of belief reliability,namely,belief reliability analysis,function-oriented belief reliability design,belief reliability evaluation,and several newly developed methods and technologies are sequentially elaborated and overviewed.Based on the above investigations,we summarize the significance of belief reliability theory and make some prospects about future research,aiming to promote the development of reliability science and engineering.

On the relationship between imprint and reliability in Hf_(0.5)Zr_(0.5)O_(2) based ferroelectric random access memory

The detrimental effect of imprint,which can cause misreading problem,has hindered the application of ferroelectric HfO_(2).In this work,we present results of a comprehensive reliability evaluation of Hf_(0.5)Zr_(0.5)O_(2)-based ferroelectric random access memory.The influence of imprint on the retention and endurance is demonstrated.Furthermore,a solution in circuity is pro-posed to effectively solve the misreading problem caused by imprint.

Introduction to the Special Issue on Computer-Aided Uncertainty Modeling and Reliability Evaluation for Complex Engineering Structures

1 Summary With the advancement of science and technology,complex engineering structures are widely used in extreme environments[1].In equipment service,many uncertainty factors significantly affect safety and reliability[2–5].Therefore,ensuring high reliability of structures has become an important research direction in engineering design.At the same time,the importance of equipment health management of complex engineering structures is becoming increasingly prominent[6–8].Computer-aided uncertainty modeling and reliability assessment have become key tools,and finite element simulation and algorithmic innovation play a key role in the reliability analysis of complex equipment[9,10].These techniques can accurately simulate stress and damage accumulation under various operating environments,providing engineers with important decision support and optimization solutions.

Interrater Reliability Estimation via Maximum Likelihood for Gwet’s Chance Agreement Model

Interrater reliability (IRR) statistics, like Cohen’s kappa, measure agreement between raters beyond what is expected by chance when classifying items into categories. While Cohen’s kappa has been widely used, it has several limitations, prompting development of Gwet’s agreement statistic, an alternative “kappa”statistic which models chance agreement via an “occasional guessing” model. However, we show that Gwet’s formula for estimating the proportion of agreement due to chance is itself biased for intermediate levels of agreement, despite overcoming limitations of Cohen’s kappa at high and low agreement levels. We derive a maximum likelihood estimator for the occasional guessing model that yields an unbiased estimator of the IRR, which we call the maximum likelihood kappa (κML). The key result is that the chance agreement probability under the occasional guessing model is simply equal to the observed rate of disagreement between raters. The κMLstatistic provides a theoretically principled approach to quantifying IRR that addresses limitations of previous κcoefficients. Given the widespread use of IRR measures, having an unbiased estimator is important for reliable inference across domains where rater judgments are analyzed.

On traceable iterated line graph and hamiltonian path index

Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.

Ultra Reliable Load-Aware Connection Management(LACM)Algorithm in WIA-FA Systems

The increasing demand for industrial automation and intelligence has put forward higher requirements for the reliability of industrial wireless communication technology.As an international standard based on 802.11,Wireless networks for Industrial Automation-Factory Automation(WIA-FA)greatly improves the reliability in factory automation scenarios by Time Division Multiple Access(TDMA).However,in ultra-dense WIA-FA networks with mobile users,the basic connection management mechanism is inefficient.Most of the handover and resource management algorithms are all based on frequency division multiplexing,not suitable for the TDMA in the WIA-FA network.Therefore,we propose Load-aware Connection Management(LACM)algorithm to adjust the linkage and balance the load of access devices to avoid blocking and improve the reliability of the system.And then we simulate the algorithm to find the optimal settings of the parameters.After comparing with other existing algorithms,the result of the simulation proves that LACM is more efficient in reliability and maintains high reliability of more than 99.8%even in the ultra-dense moving scenario with 1500 field devices.Besides,this algorithm ensures that only a few signaling exchanges are required to ensure load bal-ancing,which is no more than 5 times,and less than half of the best state-of-the-art algorithm.

Association between the cumulative triglyceride-glucose index and the recurrence of atrial fibrillation after radiofrequency catheter ablation

BACKGROUND Triglyceride-glucose(TyG)index values are a new surrogate marker for insulin resistance.This study aimed to explore the relationship between cumulative TyG index values and atrial fibrillation(AF)recurrence after radiofrequency catheter ablation(RFCA).METHODS A total of 576 patients with AF who underwent RFCA at the Second Affiliated Hospital of Xi'an Jiaotong University were included in this study.The participants were grouped based on cumulative TyG index values tertiles within 3 months after ablation.Cox regression and restricted cubic spline analyses were used to determine the relationship between cumulative TyG index values and AF recurrence.The predictive value of all risk factors was assessed by receiver operating curve analysis.RESULTS There were 375 patients completed the study(age:63.23±10.73 years,64.27%male).The risk of AF recurrence increased with increasing cumulative TyG index values tertiles.After adjusting for potential confounders,patients in the medium cumulative TyG index group[hazard ratio(HR)=4.949,95%CI:1.778–13.778,P=0.002]and the high cumulative TyG index group(HR=8.716,95%CI:3.371–22.536,P<0.001)had a higher risk of AF recurrence than those in the low cumulative TyG index group.The restricted cubic spline regression model also showed an increased risk of AF recurrence with increasing cumulative TyG index values.When considering cumulative TyG index values,left atrial diameter,and lactate dehydrogenase levels as a comprehensive factor,the model could effectively predict AF recurrence after RFCA[area under the curve(AUC)=0.847,95%CI:0.797–0.897,P<0.001].CONCLUSIONS Cumulative TyG index values were a risk factor for AF recurrence after RFCA.Monitoring longitudinal TyG index values may assist with optimized for risk stratification and outcome prediction for AF recurrence.

An evaluation of ureteral diameter ratio and vesicoureteral reflux index in the treatment of primary vesicoureteral reflux

Objective:Vesicoureteral reflux(VUR)index is a simple,validated tool that reliably predicts significant improvement and spontaneous resolution of primary reflux in children.The aim of this study was to evaluate and compare the ureter diameter ratio(UDR)and VUR index(VURx)of patients treated with endoscopic injection(EI)and ureteroneocystostomy(UNC)methods in the pediatric age group due to primary VUR.Methods:Patients under the age of 18 years old who underwent EI and UNC with the diagnosis of primary VUR between January 2011 and September 2021 were determined as the participants.The UDR was assessed using voiding cystourethrography,and the VURx score was determined prior to treatment based on hospital records included in the study.Results:A total of 255 patients,60(23.5%)boys and 195(76.5%)girls,with a mean age of 76.5(range 13.0e204.0)months,were included in the study.EI was applied to 130(51.0%)patients and UNC was applied to 125(49.0%)patients due to primary VUR.The optimum cut-off for the distal UDR was obtained as 0.17 with sensitivity and specificity of 73.0%and 63.0%,respectively.The positive and negative predictive values were 66.0%and 70.0%,respectively.Conclusion:When the UDR and VURx score are evaluated together for the surgical treatment of primary VUR in the pediatric age group,it is thought that it may be useful in predicting the clinical course of the disease and evaluating surgical treatment options.

Assessment on eco-environmental quality of the Yellow River Basin by considering desertification index

Desertification has had a significant impact on the ecological environment of the Yellow River Basin(YRB)in China.However,previous studies on the evaluation of the ecological environment quality(EEQ)in the YRB have paid limited attention to the indicator of desertification.It is of great significance to incorporate the desertification index into the spatiotemporal assessment of the EEQ in the YRB in order to protect the ecological environment in the region.In this study,based on multi-source remote sensing data from 91 cities in the YRB,this article proposes a desertification remote sensing ecological index(DRSEI)model,which builds upon the traditional Remote Sensing Ecological Index(RSEI)model,to analyze the spatiotemporal changes in the EEQ in the YRB from 2001 to 2021.Furthermore,using the geographic detector(GD),and geographically and temporally weighted regression(GTWR)model,the study assesses the impact of human and natural factors on the EEQ in the YRB.The research findings indicate that:(1)Compared to the traditional RSEI,the improved DRSEI shows a decreasing trend in the evaluation results of the EEQ.Among the 24 cities,the change in DRSEI exceeds 0.05 compared to RSEI,accounting for 26.37%of the YRB.The remaining 67 cities have changes within a range of less than 0.05,accounting for 73.63%of the YRB.(2)The results of the GD for individual and interactive effects reveal that rainfall and elevation have significant individual and interactive effects on the EEQ.Furthermore,after the interaction with natural factors,the explanatory power of human factors gradually increases over time.The spatial heterogeneity results of GTWR demonstrate that rainfall has a strong direct positive impact on the EEQ,accounting for 98.90%of the influence,while temperature exhibits a more pronounced direct inhibitory effect,accounting for 76.92%of the influence.Human activities have a strong negative impact on the EEQ and a weak positive impact.

Reliability Assessment of a New General Matching Composed Network

The reliability of a network is an important indicator for maintaining communication and ensuring its stable operation. Therefore, the assessment of reliability in underlying interconnection networks has become an increasingly important research issue. However, at present, the reliability assessment of many interconnected networks is not yet accurate,which inevitably weakens their fault tolerance and diagnostic capabilities. To improve network reliability,researchers have proposed various methods and strategies for precise assessment. This paper introduces a novel family of interconnection networks called general matching composed networks(gMCNs), which is based on the common characteristics of network topology structure. After analyzing the topological properties of gMCNs, we establish a relationship between super connectivity and conditional diagnosability of gMCNs. Furthermore, we assess the reliability of g MCNs, and determine the conditional diagnosability of many interconnection networks.

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Hybrid response surface method for system reliability analysis of pilereinforced slopes

To consider the complex soil-structure interaction in a pile-slope system,it is necessary to analyze the performance of pile-slope systems based on a three-dimensional(3D)numerical model.Reliability analysis of a pile-slope system based on 3D numerical modeling is very challenging because it is computationally expensive and the performance function of the pile failure mode is only defined in the safe domain of soil stability.In this paper,an efficient hybrid response surface method is suggested to study the system reliability of pile-reinforced slopes,where the support vector machine and the Kriging model are used to approximate performance functions of soil failure and pile failure,respectively.The versatility of the suggested method is illustrated in detail with an example.For the example examined in this paper,it is found that the pile failure can significantly contribute to system failure,and the reinforcement ratio can effectively reduce the probability of pile failure.There exists a critical reinforcement ratio beyond which the system failure probability is not sensitive to the reinforcement ratio.The pile spacing affects both the probabilities of soil failure and pile failure of the pile-reinforced slope.There exists an optimal location and an optimal length for the stabilizing piles.