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This paper aims to develop a method for evaluating the failure probability and global sensitivity of multiple failure modes based on convex-probability hybrid uncertainty.

The uncertainty information of the input variable is considered as convex-probability hybrid uncertainty. Moment-independent variable global sensitivity index based on the system failure probability is proposed to quantify the effect of the input variable on the system failure probability. Two-mode sensitivity indices are adopted to characterize the effect of each failure mode on the system failure probability. The method based on active learning Kriging (ALK) model with a truncated candidate regions (TCR) is adopted to evaluate the systems failure probability, as well as sensitivity index and this method is termed as ALK-TCR.

The results of five examples demonstrate the effectiveness of the sensitivity index and the efficiency of the ALK-TCR method in solving the problem of multiple failure modes based on the convex-probability hybrid uncertainty.

Convex-probability hybrid uncertainty is considered on system reliability analysis. Moment-independent variable sensitivity index based on the system failure probability is proposed. Mode sensitivity indices are extended to hybrid uncertain reliability model. An effective global sensitivity analysis approach is developed for the multiple failure modes based on convex-probability hybrid uncertainty.

Ensuring the safety of structures is important. However, when a structure possesses both an implicit performance function and an extremely small failure probability, traditional methods struggle to conduct a reliability analysis. Therefore, this paper proposes a reliability analysis method aimed at enhancing the efficiency of rare event analysis, using the widely recognized Relevant Vector Machine (RVM).

Drawing from the principles of importance sampling (IS), this paper employs Harris Hawks Optimization (HHO) to ascertain the optimal design point. This approach not only guarantees precision but also facilitates the RVM in approximating the limit state surface. When the U learning function, designed for Kriging, is applied to RVM, it results in sample clustering in the design of experiment (DoE). Therefore, this paper proposes a FU learning function, which is more suitable for RVM.

Three numerical examples and two engineering problem demonstrate the effectiveness of the proposed method.

By employing the HHO algorithm, this paper innovatively applies RVM in IS reliability analysis, proposing a novel method termed RVM-HIS. The RVM-HIS demonstrates exceptional computational efficiency, making it eminently suitable for rare events reliability analysis with implicit performance function. Moreover, the computational efficiency of RVM-HIS has been significantly enhanced through the improvement of the U learning function.

This paper aims to solve the problem that pipes conveying fluid are faced with severe reliability failures under the complicated working environment.

This paper proposes a dynamic reliability and variance-based global sensitivity analysis (GSA) strategy with non-probabilistic convex model for pipes conveying fluid based on the first passage principle failure mechanism. To illustrate the influence of input uncertainty on output uncertainty of non-probability, the main index and the total index of variance-based GSA analysis are used. Furthermore, considering the efficiency of traditional simulation method, an active learning Kriging surrogate model is introduced to estimate the dynamic reliability and GSA indices of the structure system under random vibration.

The variance-based GSA analysis can measure the effect of input variables of convex model on the dynamic reliability, which provides useful reference and guidance for the design and optimization of pipes conveying fluid. For designers, the rankings and values of main and total indices have essential guiding role in engineering practice.

The effectiveness of the proposed method to calculate the dynamic reliability and sensitivity of pipes conveying fluid while ensuring the calculation accuracy and efficiency in the meantime.

Pressure pulsations and vibration working condition lead to dynamic troubles in hydraulic devices. It is highly desirable to be able to estimate the durability at the design stage so that appropriate maintenance period can be determined for safety and reliability. The purpose of this paper is to propose a quantitative evaluation method for pulsation and vibration based on reliability.

Pressure pulsations are approximately treaded as a stationary random process. The principle of transform function and fluid network chain rules are used to disassemble the hydraulic power unit into the series‐system. Mean square deviation of dynamic stress under the pumping source white noise exciting was calculated based on frequency responses. Statistical regularity of displacement and stress responses of pipelines under external random vibration are obtained by the spectrum analysis. Both the first‐passage failure criterion and fatigue damage accumulation failure criterion are adopted to analyze the dynamic pressure reliability of hydraulic pipelines.

The terminal joint, bellow pipe and pipe clamps are verified as the weak location of the pipelines. The mean square deviations of pulsations and vibration response influence the pipelines reliability. The results indicated that the preventative design method of controlling the pressure below 10 per cent of rated pressure does not meet the security specification of the hydraulic power unit.

The paper proposes a quantitative evaluation method for random pressure pulsation and external vibration based on reliability, which provides a new approach for the safety assessment and design of hydraulic pipelines.

The theory and method of the gray model control with removed residuals is used first for the study of active vibration control of a rotor system. For the symmetric rotor bearing system having a single disk, a scheme of gray model control with removed residuals about the rotor vibration is designed in this paper. The results of simulated calculation showed that this control scheme not only has good effectiveness, but also can be realized easily.

The purpose of this paper is to study the resonance failure sensitivity analysis of straight-tapered assembled pipe conveying nonuniform axial fluid by an active learning Kriging (ALK) method.

In this study, first, the motion equation of straight-tapered assembled pipe conveying nonuniform fluid is built. Second, the Galerkin method is used for calculating the natural frequency of assembled pipe conveying nonuniform fluid. Third, the ALK method based on expected risk function (ERF) is used to calculate the resonance failure probability and moment independent global sensitivity analysis.

The findings of this paper highlight that the eigenfrequency and critical velocity of uniform fluid-conveying pipe are less than the reality and the error is biggest in first-order natural frequency. The importance ranking of input variables affecting the resonance failure can be obtained. The importance ranking is different for a different velocity and mode number. By reducing the uncertainty of variables with a high index, the resonance failure probability can be reduced maximally.

There are no experiments on the eigenfrequency and critical velocity. There is no experiments about natural frequency and critical velocity of straight tapered assembled pipe to verify the theory in this paper.

The originality of this paper lies as follows: the motion equation of straight-tapered pipe conveying nonuniform fluid is first obtained. The eigenfrequency of nonuniform fluid and uniform fluid inside the assembled pipe are compared. The resonance reliability analysis of straight-tapered assembled pipe is first proposed. From the results, it is observed that the resonance failure probability can be reduced efficiently.