MODIFIED SCHEME BASED ON SEMI-ANALYTIC APPROACH FOR COMPUTING NON-PROBABILISTIC RELIABILITY INDEX

A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.

A Bayesian Updating Method for Non-Probabilistic Reliability Assessment of Structures with Performance Test Data

For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.

A Comprehensive Model for Structural Non-Probabilistic Reliability and the Key Algorithms

It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was proposed on the basis of the fuzzy convex set(FCS)model.This new reliability model can account for different relations between the structural failure region and variable domain.Key computational algorithms were studied in detail.First,the optimization strategy for robust reliability is improved.Second,Monte Carlo algorithms(i.e.,uniform sampling method)for hyper-ellipsoidal convex sets were studied in detail,and errors in previous reports were corrected.Finally,the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index.Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms.

Non-probabilistic fuzzy reliability analysis of pile foundation stability by interval theory

Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was introduced to determine the probability-distributed function of mechanical parameters. Then the functional function of reliability analysis was constructed based on the study of bearing mechanism of pile foundation, and the way to calculate interval values of the functional function was developed by using improved interval-truncation approach and operation rules of interval numbers. Afterwards, the non-probabilistic fuzzy reliability analysis method was applied to assessing the pile foundation, from which a method was presented for non- probabilistic fuzzy reliability analysis of pile foundation stability by interval theory. Finally, the probability distribution curve of non- probabilistic fuzzy reliability indexes of practical pile foundation was concluded. Its failure possibility is 0.91%, which shows that the pile foundation is stable and reliable.

Application of non-probabilistic reliability on aerostat capsule

Aerostat capsule is small sample data,so designing reliability is very difficult to be obtained accurately by conventional probabilistic reliability method. Based on the interval non-probabilistic reliability theory,an instability mathematics model of envelope structure is studied,and the calculation formula of interval reliability index is put forward. Through the mechanical experiments of three capsule structures,the experimental results of the interval reliability are obtained. By comparing the theoretical and measured values,it is found that the theoretical reliability index is more conservative. Non-probabilistic reliability method can reflect the reliability degree of the capsule body under different loading conditions,which can provide some guidance for engineering application.

Comparison of Structural Probabilistic and Non-Probabilistic Reliability Computational Methods under Big Data Condition

In this article,structural probabilistic and non-probabilistic reliability have been evaluated and compared under big data condition.Firstly,the big data is collected via structural monitoring and analysis.Big data is classified into different types according to the regularities of the distribution of data.The different stresses which have been subjected by the structure are used in this paper.Secondly,the structural interval reliability and probabilistic pre-diction models are established by using the stress-strength interference theory under big data of random loads after the stresses and structural strength are comprehensively considered.Structural reliability is computed by using various stress types,and the minimum reliability is determined as structural reliability.Finally,the advan-tage and disadvantage of the interval reliability method and probability reliability method are shown by using three examples.It has been shown that the proposed methods are feasible and effective.

Reliability and Validity of Addiction Severity Index in Drug Users with Methadone Maintenance Treatment in Guizhou Province, China

Objective To evaluate the reliability and validity of the Chinese version of addiction severity index （ASI）-5th version （ASI-C-5）, in illegal drug users receiving methadone maintenance treatment （MMT） in China. Methods One hundred and eighty-six heroin addicts （144 men and 42 women） receivihg MMT at three clinics in Guizhou province, southwest China, were recmited. They were all interviewed with a questionnaire of ASI-C-5 and 35 were re-interviewed at an interval of seven days to assess its test-retest reliability. Results Cronbach＇s alpha for internal consistency of CSs varied from 0.60 to 0.81 in all domains. Test-retest reliability of composite scores （CSs） of ASI-C-5 were satisfactory （r=0.38-0.97）. Based on item analysis and expert＇s suggestions, five items were deleted and one item was modified in ASI-C-5. Criterion validity of ASI-C-5 was found acceptable, as compared to addicts＇ self-rating anxiety scale （SAS） and self-rating depression scale （SDS） （r=0.59 and 0.45） except for social support rating scale （SSRS）. Conclusions ASI-C-5 can be used for heroin addicts receiving MMT with acceptable reliability and validity.

A modified method to calculate reliability index using maximum entropy principle

Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.

Reliability-Based Load and Resistance Factors Design for Offshore Jacket Platforms in the Bohai Bay:Calibration on Target Reliability Index

The target reliability index has been effectively used as the best solution to deal with the relationship between the structural safety and the optimal economy in any structural design. However, the target reliability index for offshore jacket platforms based on different sea areas in China has never been calibrated. This paper presents an approach for its calibration, and suggests many kinds of associated load cases. The uncertainties of loads and structural resistance are mainly in- vestigated. The target reliability index for structural components, tubular joints and piles of offshore jacket plaffortns are discussed respectively in detail. Finally, through the calibrated results from the offshore jacket platforms of QK18-1, JZ20-2, SZ36-1 and BZ28-1 in the Bohai Bay, it is proposed to adopt 2.8 as the target reliability index of offshore jacket platforms in the Bohai Bay for a 25-year design period. The results provide significant reference for the design of offshore jacket platforms.

Reliability of Chinese web-based ocular surface disease index questionnaire in dry eye patients:a randomized,crossover study

AIM:To assess the reliability of web-based version of ocular surface disease index in Chinese(C-OSDI)on clinically diagnosed dry eye disease(DE)patients.METHODS:A total of 254 Chinese participants(51%male,129/254;mean age:27.90±9.06 y)with DED completed paper-and web-based versions of C-OSDI questionnaires in a randomized crossover design.Ophthalmology examination and DED diagnosis were performed prior to the participants being invited to join the study.Participants were randomly designated to either group A(paper-based first and webbased second)or group B(web-based first and paper-based second).Final data analysis included participants that had successfully completed both versions of the C-OSDI.Demographic characteristics,test-retest reliability,and agreement of individual items,subscales,and total score were evaluated with intraclass correlation coefficients(ICC),Spearman rank correlation,Wilcoxon test and Rasch analysis.RESULTS:Reliability indexes were adequate,Pearson correlation was greater than 0.8 and ICCs range was 0.827 to 0.982;total C-OSDI score was not statistically different between the two versions.The values of mean-squares fit statistics were very low compared to 1,indicating that the responses to the items by the model had a high degree of predictability.While comparing the favorability 72%(182/254)of the participants preferred web-based assessment.CONCLUSION:Web-based C-OSDI is reliable in assessing DED and correlation with the paper-based version is significant in all subscales and overall total score.Webbased C-OSDI can be administered to assess individuals with DED as participants predominantly favored online assessment.

The stability safety factor calibration based on the reliability index

When the bridge structure stability safety factor of the first type is 4, the research that whether the structure reliability index will reach target reliability index under the more-likely-to-happen collapse situation of the second type is necessary. The stability calculations of the first and the second type are made respectively for single layer and single span rigid frame bridge. Based on the critical load obtained from the stability calculation of the first type, the stability safety factor of the first type is taken as 4, and the first order reliability method is used to program and calculate the reliability index. Then, the load effect under the stability reliability index cal- culation of the first type and the critical load of the second type are employed to calculate the reliability index of the second type. The evaluation of structure stability safety factor is discussed according to reliability index. Based on the discussion above, parameter analysis of the stable critical loads of two types is made, and the in- fluence of critical load change on reliability index is researched. The result shows that stability analysis should identify collapse state; when the stability safety factor of the first type is 4, but the structure has the collapse of the second type, the reliability index cannot be ensured to reach the target reliability index under certain condi- tions.

Target reliability index for serviceability limit state of single piles

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

A Method for Determining the Reliability Index of a Materiel Subsystem

This paper presents a method for determining the reliability index of a subsystem in the materiel demonstration phase-AHP Failure Rate Method. It fully considers the various factors which influence a subsystem reliability index and solves a difficult problem that puzzles the demonstration personnel.

Reliability and Validity of Chinese Version of the Addiction Severity Index among Drug Users in the Community

Objective To assess the reliability and validity of a new Chinese version of the Addiction Severity Index （ASI-C） in drug users in the community. Methods Three hundred and eighty-one drug users in the community in Chengdu, Sichuan province were recruited. They were interviewed with a questionnaire consisting of the ASI-C revised on the basis of the previous Chinese version and 38 were interviewed for the second time at an interval of 7 days to evaluate test-retest reliability. Results Cronbach＇s c~ coefficients for the internal consistency of the scale varied from 0.49 to 0.86. Test-retest correlation coefficients ranged from 0.50 to 0.93. Criterion validity was found acceptable, as compared with the Symptom Checklist 90 （SCL-90）. Conclusion The ASI-C presented acceptable reliability and validity in a sample of drug users in the community.

Genetic Algorithms of Structural Fuzzy Reliability Index

In this paper the simple generation algorithms are improved. According to the geometric meaning of the structural reliability index, a method is proposed to deal with the variables in the standard normal space. With consideration of variable distribution, the correlation coefficient of the variables and its fuzzy reliability index, the feasibility and the reliability of the algorithms are proved with an example of structural reliability analysis and optimization.

Derivation of Reliability Index Vector Formula for Series System and Its Application

In this study, a reliability index vector formula is proposed for series system with two failure modes in term of the concept of reliability index vector and equivalent failure modes. Firstly, the reliability index vector is introduced to determine the correlation coefficient between two failure modes, and then, the reliability index vector of a series system can be obtained. Several numerical cases and an analysis on offshore platform are performed, and the results show that this scheme provided here has better computational accuracy, and its calculation process is simpler for the series systems reliability calculations compared with the other methods. Also this scheme is more convenient for the engineering applications.

Instantaneous Reliability Index of a Typical Repairable System

A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of reliability.The paper first described the system as an abstract Cauchy problem by choosing suitable operators and state spaces.Then,with the TrotterKato theorem and strong continuous semi-group theorem,the method of solving the instantaneous reliability index of the repairable system was constructed.The convergence of the method was also proved in theory in this paper.To show the effectiveness of this method,some numerical examples were given at the end of the paper.

The solution of minimum reliability index for modified weak point of arbitrary curved beam under pure bending

This paper is based on the fundamental loading model of pure bending and the analytical model of a circular beam element with arbitrary initial deflection. The L.W. Guo solution is modified and generalized according to the elastic theory, and the analytical solution for the stress of the beam element with arbitrary initial deflection under pure bending is derived. Using yield theory of edge strength, an expression for the safety margin of one point in the arbitrary curved beam under pure bending （ACPB） is built. This paper modifies the model for weak points of service structures and establishes a foundation for safe design and inspection of imperfect structures. Also, according to the theory of the method of advanced first-order second-moment（AFOSM） , this paper derives an expression for the reliability index of one point in ACPB. Lastly, it modifies the solution for weak points by solving the minimal reliability index.

Reliability Index of Tall Buildings in Earthquake Zones

The paper develops a reliability index approach to assess the reliability of tall buildings subjected to earthquake loading. The reliability index β model measures the level of reliability of tall buildings in earthquake zones based on their response to earthquake loading and according to their design code. The reliability index model is flexible and can be used for: 1) all types of concrete and steel buildings and 2) all local and international codes of design. Each design code has its unique reliability index β as a magnitude and the interaction chart corresponding to it. The interaction chart is a very useful tool in determining the building drift for the desired level of reliability during the preliminary design of the building members. The assessments obtained using the reliability index approach of simulated, tested, and actual buildings in earthquake zones were acceptable as indicators of the buildings reliability.