Dynamic Probabilistic Analysis Research Articles

A dynamic probabilistic analysis method for wind turbine rotor based on the surrogate model

Due to the long and flexible characteristics of the wind turbine blade, the influence of the fluid–structure interaction (FSI) on the dynamic response results cannot be ignored. The dynamic analysis of the wind turbine rotor based on the fluid–structure interaction is very computationally expensive, and the dynamic reliability analysis considering the influence of randomness usually requires a large number of computational samples. In this study, a surrogate model-based dynamic probabilistic analysis method for the characteristics of the wind turbine rotor was established, combining numerical simulation, intelligent algorithms, and data mining methods for wind turbines. This method allows for fast and inexpensive reliability and sensitivity analysis by building accurate surrogate models with a limited number of expensive fluid–structure interaction (FSI) samples. In the case of a 5 MW wind turbine rotor, the average relative error of the test was 0.093%, the reliability was 0.9515, and two variables insensitive variables were found. The results showed that this method could effectively analyze the reliability and sensitivity of the wind turbine rotor, adapted well to the nonlinear and high dimensional characteristics of the wind turbine rotor, and reduced the cost of wind turbine research by controlling the number of expensive samples. In addition, this research provided a reference for using intelligent algorithms and data mining methods in wind turbine design.

A high-resolution dynamic probabilistic material flow analysis of seven plastic polymers; A case study of Norway

Plastic pollution has long been identified as one of the biggest challenges of the 21st century. To tackle this problem, governments are setting stringent recycling targets to keep plastics in a closed loop. Yet, knowledge of the stocks and flows of plastic has not been well integrated into policies. This study presents a dynamic probabilistic economy-wide material flow analysis (MFA) of seven plastic polymers (HDPE, LDPE, PP, PS, PVC, EPS, and PET) in Norway from 2000 to 2050. A total of 40 individual product categories aggregated into nine industrial sectors were examined. An estimated 620 ± 23 kt or 114 kg/capita of these seven plastic polymers was put on the Norwegian market in 2020. Packaging products contributed to the largest share of plastic put on the market (∼40%). The accumulated in-use stock in 2020 was about 3400 ± 56 kt with ∼60% remaining in buildings and construction sector. In 2020, about 460 ± 22 kt of plastic waste was generated in Norway, with half originating from packaging. Although ∼50% of all plastic waste is collected separately from the waste stream, only around 25% is sorted for recycling. Overall, ∼50% of plastic waste is incinerated, ∼15% exported, and ∼10% landfilled. Under a business-as-usual scenario, the plastic put on the market, in-use stock, and waste generation will increase by 65%, 140%, and 90%, respectively by 2050. The outcomes of this work can be used as a guideline for other countries to establish the stocks and flows of plastic polymers from various industrial sectors which is needed for the implementation of necessary regulatory actions and circular strategies. The systematic classification of products suitable for recycling or be made of recyclate will facilitate the safe and sustainable recycling of plastic waste into new products, cap production, lower consumption, and prevent waste generation.

Bond-slip model uncertainty quantification and effect on nonlinear behavior simulations of reinforced concrete columns

In advanced finite element (FE) modeling of reinforced concrete (RC) structures, realistic bond-slip behavior, i.e., imperfect bonding, at the steel–concrete interface needs to be considered with caution. This paper compiles an experimental database on bond-slip behavior from the literature, evaluates a variety of existing models for predicting bonding properties, and develops a new model to better characterize the bond-slip behavior using the experimental database. Recognizing variations in bonding properties, the authors also quantify the prevailing uncertainties as indicated by experimental data in the new model by Bayesian linear regression. To study the effect of bond-slip model uncertainties on the nonlinear behavior simulations of RC columns under static and dynamic loadings, the recently developed geometrically nonlinear fiber-based frame element capable of capturing bond-slip is used in this study together with a commonly-used bonding stress-slip pattern. To this end, three RC columns are firstly modeled with bonding properties determined from eight existing models and the newly developed one, showing that the simulated behaviors using different models can be different to various degrees. Next, the relative importance of the uncertainty in bonding properties is evaluated with comparison to that of the uncertainties in concrete/steel properties. The results indicate uncertainties associated with bonding properties can significantly alter the nonlinear behavior predictions of RC columns, and thus not negligible, particularly for probabilistic dynamic analysis of RC columns under large intensity excitation levels.

Intelligent Extremum Surrogate Modeling Framework for Dynamic Probabilistic Analysis of Complex Mechanism

The reliability analysis of complex mechanisms involves time-varying, high-nonlinearity, and multiparameters. The traditional way is to employ Monte Carlo (MC) simulation to achieve the reliability level, but this method consumes too much computing resources and is even computationally intractable. To improve the efficiency and accuracy of dynamic probabilistic analysis of complex mechanisms, an intelligent extremum surrogate modeling framework (IESMF, short for) is proposed based on extremum response surface method (ERSM), combined with artificial neural network (ANN) method and an improved optimize particle swarm optimization (PSO) method. Hereinto, the ERSM is used to simplify the dynamic process of output response to the extremum value of transient analysis; ANN is applied to establish a mathematical model between input variables and response, and the improved PSO method is utilized in search of initial weights and thresholds of the model. The effectiveness of the IESMF is demonstrated to perform the Rack-and-pinion steering mechanism (RPSM) reliability analysis. The results show that when the allowable value of gear root stress is equal to 850 MPa, the RPSM has a reliability degree of 0.9971. Through the validation process, it is illustrated that IESMF is accurate and efficient in dynamic probabilistic analysis of complex mechanisms, and its comprehensive performance is better than the MC method and ERSM. The research effort offers new ideas for the reliability estimation of a complex mechanism, thus enriching the method and theory of mechanical reliability design.

Dynamic probabilistic analysis of non-homogeneous slopes based on a simplified deterministic model

This article proposes an efficient procedure for the probabilistic seismic analysis of slopes and applies it to two slope examples including a real engineering project. The proposed procedure evaluates the stability condition of a non-homogeneous slope by using a discretization kinematic approach (DKA), and accounts for the time and space variations of a seismic loading by employing pseudo-dynamic method (PDM). Three uncertainty quantification techniques (Subset Simulation, Global Sensitivity Analysis and First Order Reliability Method), are implemented into the procedure in order to provide multiple probabilistic results (e.g. failure probability, reliability index, design point and sensitivity index) for slope seismic reliability problems. The introduced DKA is validated by comparing with two previous studies. Additionally, a variety of hypothetical cases were analyzed in order to provide some insights into the following two issues about slope seismic analyses: 1) the comparison of two seismic methods (PDM and pseudo-static method) in a probabilistic framework; 2) the accuracy of FORM for estimating failure probability. By benefiting from the high computational efficiency of the introduced DKA, two further studies related to sensitivity analysis and fragility curves are also carried out. The obtained results show that the proposed procedure is effective for slope probabilistic seismic analyses and is able to efficiently provide a variety of useful results.

Structural dynamic probabilistic evaluation using a surrogate model and genetic algorithm

To improve the computational accuracy and efficiency of dynamic probabilistic analysis of complex structures, an extremum Kriging method (EKM) with multi-population genetic algorithm (MPGA) is proposed fusing extremum response surface method (ERSM), Kriging model and MPGA. Particularly, the EKM is developed by combining the Kriging model and ERSM to handle dynamic processes of related variables and to reduce computational burden by regarding the extreme value of response process in each dynamic analysis within the time domain. The MPGA is used to replace gradient decent to find the hyperparameter θ in the Kriging model by solving the maximum-likelihood equation. The effectiveness of the proposed method was validated by performing the dynamic probabilistic analysis of an aeroengine high-pressure compressor blisk radial running deformation with fluid-thermal-structural interaction. The analytical results illustrate that the reliability degree of the blisk is 0·9956 under the allowable value uallow = 1·75 × 10−3 m, and gas temperature is the leading factor against output response, followed by rotational speed, inlet velocity, material density and outlet pressure. Moreover, the developed MPGA-EKM is superior to other methods in computational accuracy and efficiency. The efforts of this study provide a useful insight to design complex structures and enrich mechanical reliability theory.

Dynamic probabilistic analysis of accidents in construction projects by combining precursor data and expert judgments

Construction accident occurrences are essentially rare, stochastic, and dynamic. This study proposes a method for accident prediction that fully captures these natures based on historical data and prior knowledge. The method utilizes the relatively high occurrence frequency of precursor events and the dependency between precursors and accidents. The modeling approach consists of three steps: (1) characterize the stochastic occurrences of precursor events over time based on precursor data; (2) estimate the failure rate of the Poisson model which is assumed to be a prior distribution of accident occurrences; and (3) elicit the expert knowledge about the stochastic dependency between near miss occurrences and accident occurrences. A copula-based Markov model is used to develop the time series model of precursors while a copula-based protocol is proposed to aid expert judgment elicitation and quantification. The probability of accident occurrence is then dynamically updated according to the observed historical near miss numbers. The proposed method is applied to a metro construction project. A five-year long near miss data were collected and used as accident precursor data, while three experts were invited to provide relevant information. The developed accident model is used to predict the accident-prone periods, which are consistent with the months that the observed near miss occurrence frequency deviates significantly from normality. Thus, the model can be used to support the planning of necessary safety improvement programs before the accident risk increased.

Application of extremum response surface method-based improved substructure component modal synthesis in mistuned turbine bladed disk

To improve the computational efficiency of vibration characteristics and reliability analysis for a detailed numerical model of the mistuned turbine bladed disk, a new methodology called extremum response surface method-based improved substructural component modal synthesis (ERSM-ISCMS) is proposed by combining the ISCMS and ERSM. First, the degrees of freedom of the detailed finite element model for the numerical mistuned turbine bladed disk are decreased by ISCMS, which is called as reduced-order model. Compared with high fidelity finite element model, the time saving ratio and the computational accuracy of the first 40 order frequencies are, respectively, 36.37% and 99.99%~99.86% obtained by ISCMS under the same working environment, which can satisfy the engineering requirements. Then, the ERSM is applied to analyze the dynamic probability of the maximum vibration response for the numerical mistuned turbine bladed disk. The investigation indicates that the computational efficiency of ERSM is higher 38.92% than that of traditional RSM in the same computer and the same reduced-order model. Thus, the ERSM-ISCMS is a more effective method to investigate dynamic probabilistic analysis of the mistuned turbine bladed disk, it benefits for the complex structures and develops the theory method for the mechanical reliability design.

Improved Decomposed-Coordinated Kriging Modeling Strategy for Dynamic Probabilistic Analysis of Multicomponent Structures

The probabilistic design of complex structure usually involves the features of numerous components, multiple disciplines, nonlinearity, and transients and, thus, requires lots of simulations as well. To enhance the modeling efficiency and simulation performance for the dynamic probabilistic analysis of the multicomponent structure, we propose an improved decomposed-coordinated Kriging modeling strategy (IDCKMS), by integrating decomposed-coordinated (DC) strategy, extremum response surface method (ERSM), genetic algorithm (GA), and Kriging surrogate model. The GA is used to resolve the maximum-likelihood equation and achieve the optimal values of the Kriging hyperparameter θ . The ERSM is utilized to resolve the response process of outputs in surrogate modeling by extracting the extremum values. The DC strategy is used to coordinate the output responses of analytical objectives. The probabilistic analysis of an aeroengine high-pressure turbine blisk with blade and disk is conducted to validate the effectiveness and feasibility of this developed method, by considering the fluid–thermal–structural interaction. In respect of this investigation, we see that the reliability of turbine blisk is 0.9976 as the allowable value of radial deformation is 2.319 × 10−3 m. In terms of the sensitivity analysis, the highest impact on turbine blisk radial deformation is of gas temperature, followed by angular speed, inlet velocity, material density, outlet pressure, and inlet pressure. By the comparison of methods, including the DC surrogate modeling method (DCSMM) with quadratic polynomial, the DCSMM with Kriging, and the direct simulation with finite-element model, from the model-fitting features and simulation performance perspectives, we discover that the developed IDCKMS is superior to the other three methods in the precision and efficiency of modeling and simulation. The efforts of this article provide a highly efficient and highly accurate technique for the dynamic probabilistic analysis of complex structure and enrich reliability theory.

Probabilistic dynamic analysis of composite plates due to low velocity impact

The low velocity impact (LVI) analysis of fiber-reinforced plastic (FRP) plates is a significant study to evaluate the reliability of lightweight structures. This study has wide applications in offshore and naval industries. Safety and reliability assessment as per the international standards is one of the basic objectives of the study. LVI on FRP plates are studied taking the material parameters and loading as random variables. FRP plates are subjected to failure under impact by in-plane loading. To evaluate the safe load carrying capacity and the reliability under impact, dynamic analysis of composite plate subjected to LVI is carried out. Reliability analysis is performed to calculate the stochastic behavior of FRP plates. During impact, the in-plane damage modes such as matrix cracking, fiber failure, and shear cracking are modeled using a failure criterion. The out of plane delamination is modeled using cohesive surfaces. The variability related with the system properties due to the inherent scatter in the geometric and material properties and input loads are modeled in a stochastic fashion. The stochastic finite element analysis (SFEA) is performed to determine the stochastic response of system using Gaussian process response surface method (GPRSM). The safety level qualification is achieved in terms of reliability level targeted.

Multi-unit dynamic PRA

Dynamic Probabilistic Risk Analysis (PRA) methods couple stochastic methods (e.g., RAVEN) with safety analysis codes (e.g., RELAP5-3D) to determine risk associated to complex systems such as nuclear plants. Compared to classical PRA methods, which are based on static logic structures (e.g., Event-Trees, Fault-Trees), they can evaluate with higher resolution the safety impact of timing and sequencing of events on the accident progression. Recently, special attention has been given to nuclear plant sites which consist of multiple units and, in particular, on the safety impact of system dependencies, shared systems and common resources on core damage frequencies. In the literature, classical PRA methods have been employed to model multi-unit sites in a limited number of cases while Dynamic PRA methods have never been applied to analyze a full multi-unit model. This paper presents a PRA analysis of a multi-unit plant using Dynamic PRA methods. We employ RAVEN as stochastic tool coupled with RELAP5-3D. The site under consideration consists of three units (each unit is composed by a reactor and its associated spent fuel pool) while the considered initiating event is a seismic induced station blackout event. This paper describes in detail how the multi-unit site has been constructed and, in particular, how unit dependencies and shared resources are modeled from both a deterministic and stochastic point of view.

Decomposed-Coordinated Framework With Enhanced Extremum Kriging for Multicomponent Dynamic Probabilistic Failure Analyses

For multicomponent structures enduring dynamic workloads coming from multi-physical fields, safety assessment is significant to guarantee the normal operation of entire structure system. In this paper, an enhanced extremum Kriging-based decomposed coordinated framework (E2K-DCF) is proposed to improve the dynamic probabilistic failure analyses of multicomponent structures. In this method, extremum Kriging model (EKM) is developed by introducing Kriging model into extremum response surface method (ERSM) to process the transient response problem and shorten computational burden in dynamic probabilistic failure analyses. Multiple population genetic algorithm (MPGA) is employed to solve maximum likelihood equation (MLE) and find the optimal hyperparameter $\boldsymbol \theta $ in the EKM, which is promising to enhance approximate accuracy; decomposed-coordinated (DC) strategy is used to handle the coordinated relationship of multiple analytical objectives. To validate the proposed E2K-DCF, the probabilistic failure analysis of turbine blisk radial deformation is conducted by comparing with different methods within time domain [0 s, 215 s], considering fluid-thermal-structural interaction. It is revealed that the failure probability of blisk radial deformation is only 0.0022 when the allowable value is $2.5702\times 10^{-3}$ m acquired from real world practice. Compared to the other approaches, this E2K-DCF has obvious advantages in fitting time and accuracy as well as simulation efficiency and accuracy. The results illustrate that the E2K-DCF is effective and applicable in dynamic probabilistic failure analysis. The efforts of this paper provide a novel viewpoint for the transient reliability evaluation of multicomponent structures, which is likely to enrich mechanical reliability theory.

Dynamic probabilistic design technique for multi-component system with multi-failure modes

For unacceptable computational efficiency and accuracy on the probabilistic analysis of multi-component system with multi-failure modes, this paper proposed multi-extremum response surface method (MERSM). MERSM model was established based on quadratic polynomial function by taking extremum response surface model as the sub-model of multi-response surface method. The dynamic probabilistic analysis of an aeroengine turbine blisk with two components, and their reliability of deformation and stress failures was obtained, based on thermal-structural coupling technique, by considering the nonlinearity of material parameters and the transients of gas flow, gas temperature and rotational speed. The results show that the comprehensive reliability of structure is 0.9904 when the allowable deformations and stresses of blade and disk are 4.78×10–3 m and 1.41×109 Pa, and 1.64×10–3 m and 1.04×109 Pa, respectively. Besides, gas temperature and rotating speed severely influence the comprehensive reliability of system. Through the comparison of methods, it is shown that the MERSM holds higher computational precision and speed in the probabilistic analysis of turbine blisk, and MERSM computational precision satisfies the requirement of engineering design. The efforts of this study address the difficulties on transients and multiple models coupling for the dynamic probabilistic analysis of multi-component system with multi-failure modes.

Improved Kriging with extremum response surface method for structural dynamic reliability and sensitivity analyses

The safety and reliability of any complex mechanical structures are critical to ensure that they can function properly. Therefore, we need to thoroughly evaluate their reliability by performing dynamic probabilistic analyses, including the reliability and sensitivity analyses, which take the variation in the input variables into consideration. The typical approach is by performing the Monte Carlo (MC) simulation, which requires thousands of runs and could be computationally intractable. An efficient and accurate surrogate model can help reduce the computational burden in these analyses. To further reduce the computational complexity, we model only the extremum values, instead of modeling all the output responses within the time domain of interest. The developed surrogate model is called the improved Kriging (IK) algorithm with extremum response surface method (ERSM), or the IK-ERSM model. Compared to the previously developed QP-ERSM, which uses the quadratic polynomial (QP) model, the improved Kriging can better model the nonlinearity within the system. To build the IK model, we employ the genetic algorithm (GA) method to find the Kriging hyperparameters θ, by solving the maximum likelihood equation (MLE). This model shows a good accuracy, with a testing error of less than 1%. The effectiveness of the developed IK-ERSM model is demonstrated to perform the reliability and sensitivity analyses of the compressor blisk radial deformation. For the direct simulation, we consider the fluid–structure coupling of the system, for a more realistic analysis. The results show that the compressor blisk has a reliability degree of 0.9984 when the allowable value of the compressor blisk radial deformation is 1.60×10−3 m. From the sensitivity analysis results, we identify that the angular speed has the highest impact on the output response, followed by the inlet velocity and material density. Through the validation process, we see that the developed IK-ERSM model has a better overall performance than the QP-ERSM and K-ERSM models, in terms of the fitting times and testing errors. With these results, the IK-ERSM is demonstrated to be efficient and accurate in structural dynamic probabilistic analysis. This study provide a useful insight for the dynamic probabilistic design of complex structure and enrich mechanical reliability theory.

Dynamic Reliability Design of Multicomponent Structure with Improved Weighted Regression Distributed Collaborative Surrogate Model Method

For dynamic reliability design of complex structures with multiple components, an improved weighted regression distributed collaborative surrogate model method (IWRDCSMM) is developed from the extremum response surface method (ERSM), decomposed‐coordinated thought, and improved weighted regression principle. The ERSM is used to address the dynamic reliability and sensitivity analyses of multicomponent structures and enhance the computing efficiency. The decomposed‐coordinated thought is applied to handle the relationship among multiple components. The improved weighted regression method is used to find the efficient samples with smaller errors to improve the modeling accuracy. The proposed method is first introduced for dynamic probabilistic analysis (including reliability analysis and sensitivity analysis) of multicomponent structures. The method is then mathematically modeled by adopting the efficient samples selected based on the improved weighted regression method. Finally, the radial deformation dynamic probabilistic analysis of an aeroengine turbine blisk assembled by blade and disk is accomplished, in respect of the IWRDCSMM, fluid‐thermal‐structure interaction, and the randomness of input parameters within the time domain [0, T]. The results illustrate that the reliability degree of turbine blisk radial deformation is 0.9951 when the allowable value uallow is 2.30 × 10−3 m, and all the input parameters affecting the turbine blisk radial deformation are gas temperature, angular speed, inlet velocity, outlet pressure, material density, and inlet pressure, successively. As revealed by the comparison of different methods, the IWRDCSMM has high fitting speed and simulation efficiency with the guarantee of accuracy. The efforts of this study provide a promising dynamic probabilistic analysis technique for complex structures with multiple components and enrich mechanical reliability theory.

Dynamic probabilistic design approach of high-pressure turbine blade-tip radial running clearance

To develop the high performance and high reliability of turbomachinery just like an aeroengine, distributed collaborative time-varying least squares support vector machine (LSSVM) (called as DC-T-LSSVM) method was proposed for the dynamic probabilistic analysis of high-pressure turbine blade-tip radial running clearance (BTRRC). For structural transient probabilistic analysis, time-varying LSSVM (called as T-LSSVM) method was developed by improving LSSVM, and the mathematical model of the T-LSSVM was established. The mathematical model of DC-T-LSSVM was built based on T-LSSVM and distributed collaborative strategy. Through the dynamic probabilistic analysis of BTRRC with respect to the nonlinearity of material property and the dynamics of thermal load and centrifugal force load, the probabilistic distributions and features of different influential parameters on BTRRC, such as rotational speed, the temperature of gas, expansion coefficients, the surface coefficients of heat transfer and the deformations of disk, blade and casing, are obtained. The deformations of turbine disk, blade and casing, the rotational speed and the temperature of gas significantly influence BTRRC. Turbine disk and blade perform the positive effects on the BTRRC, while turbine casing has the negative impact. The comparison of four methods (Monte Carlo method, T-LSSVM, DCERSM and DC-T-LSSVM) reveals that the DC-T-LSSVM reshapes the possibility of the probabilistic analysis of complex turbomachinery and improves the computational efficiency while preserving the accuracy. The efforts offer a useful insight for rapidly designing and optimizing the BTRRC dynamically from a probabilistic perspective.

Transient probabilistic analysis for turbine blade-tip radial clearance with multi-component and multi-physics fields based on DCERSM

Against the background of the probabilistic analysis for High Pressure Turbine (HPT) Blade-tip Radial Running Clearance (BRRC) to achieve the high-performance and high-reliability of aeroengine, Distributed Collaborative Extremum Response Surface Method (DCERSM) was proposed for the dynamic probabilistic analysis of complex turbomachinery on the foundation of quadratic polynomials response surface model. On the basis of deeply investigating Extremum Response Surface Method (ERSM), the mathematical model of DCERSM was established based on quadratic polynomial function. As illustrated in BRRC transient probabilistic analysis with multiple components and multi-physics fields based on DCERSM, blade-tip radial static clearance δ=1.82 mm is advisable synthetically considering the reliability and working efficiency of gas turbine. The reliability, distribution characteristics and failure probability of BRRC are obtained. Besides, rotational speed ω and gas temperature T are the most important factors and expansivity coefficients and surface coefficients of heat transfer show also important influence on BRRC variation. Through the comparison of three methods (DCERSM, ERSM, Monte Carlo method), it is demonstrated that DCERSM reshapes the possibility of complex turbomachinery probabilistic analysis and improves computing efficiency while preserving the accuracy. DCERSM offers a useful insight for BRRC dynamic reliability design and optimization with multi-object and multi-discipline. The efforts of this study also enrich the theory and method of mechanical reliability design.

Fatigue Reliability Assessment of Railway Bridges Based on Probabilistic Dynamic Analysis of a Coupled Train-Bridge System

This paper presents an approach to fatigue reliability assessment of railway bridges based on probabilistic dynamic analysis of a coupled train-bridge system. The fatigue loading from moving trains is investigated through a novel approach in which three-dimensional (3D) numerical models of both the train and the bridge are integrated with a wheel-rail interaction model to perform coupled dynamic analysis. The results of this analysis are used to estimate the long-term fatigue loading and the time-variant fatigue reliability of bridge details. Train speed and track irregularities are selected as random variables in the coupled train-bridge system model. Probabilistic dynamic stress analysis is conducted for each train passage to obtain samples of the stress range and its cycle count. This information is used to identify the probability distributions of the stress range. Fatigue reliability is evaluated by solving a fatigue limit-state function established through the S-N approach. Effects of train speed and track irregularities on the fatigue loading and fatigue reliability are analyzed and discussed. Additionally, the proposed approach is illustrated on an existing steel railway bridge.

Dynamic probabilistic analysis of stress and deformation for bladed disk assemblies of aeroengine

In order to describe and control the stress distribution and total deformation of bladed disk assemblies used in the aeroengine, a highly efficient and precise method of probabilistic analysis which is called extremum response surface method (ERSM) is produced based on the previous deterministic analysis results with the finite element model (FEM). In this work, many key nonlinear factors, such as the dynamic feature of the temperature load, the centrifugal force and the boundary conditions, are taken into consideration for the model. The changing patterns with time of bladed disk assemblies about stress distribution and total deformation are obtained during the deterministic analysis, and at the same time, the largest deformation and stress nodes of bladed disk assemblies are found and taken as input target of probabilistic analysis in a scientific and reasonable way. Not only their reliability, historical sample, extreme response surface (ERS) and the cumulative probability distribution function but also their sensitivity and effect probability are obtained. Main factors affecting stress distribution and total deformation of bladed disk assemblies are investigated through the sensitivity analysis of the model. Finally, compared with the response surface method (RSM) and the Monte Carlo simulation (MCS), the results show that this new approach is effective.

A dynamic probabilistic design method for blade-tip radial running clearance of aeroengine high-pressure turbine

Around the engineering background of the probabilistic design of high-pressure turbine (HPT) blade-tip radial running clearance (BTRRC) which conduces to the high-performance and high-reliability of aeroengine, a distributed collaborative extremum response surface method (DCERSM) was proposed for the dynamic probabilistic analysis of turbomachinery. On the basis of investigating extremum response surface method (ERSM), the mathematical model of DCERSM was established. The DCERSM was applied to the dynamic probabilistic analysis of BTRRC. The results show that the blade-tip radial static clearance δ = 1.82 mm is advisable synthetically considering the reliability and efficiency of gas turbine. As revealed by the comparison of three methods (DCERSM, ERSM, and Monte Carlo method), the DCERSM reshapes the possibility of the probabilistic analysis for turbomachinery and improves the computational efficiency while preserving computational accuracy. The DCERSM offers a useful insight for BTRRC dynamic probabilistic analysis and optimization. The present study enrichs mechanical reliability analysis and design theory.