Novel numerical methods for reliability analysis and optimization in engineering fuzzy heat conduction problem

To improve the performance and reliability of gas turbine like an aeroengine, the multi-object multi-discipline (MOMD) reliability optimization design of high press turbine (HPT) blade-tip radial running clearance (BTRRC) was first accomplished based on the mechanical dynamic assembly reliability (MDAR) theory and distributed collaborative response surface method (DCRSM). Four optimization models of MDAR were developed based on the features of assembly machinery and the thought of DCRSM, which are, respectively, called as the direct reliability optimization model (denoted by M1), the multilayer reliability optimization models (denoted by M2), the direct reliability optimization model-based probabilistic analysis (denoted by M3), and the multilayer reliability optimization model-based probabilistic analysis (denoted by M4). Through the MDAR optimization design of BTRRC by the four standard optimization models, some conclusions are drawn as follows: (1) the DCRSM is proved to be effective and feasible for MOMD MDAR optimization design with high computational efficiency and precision; (2) all the reliability optimization results of BTRRC and assembly objects satisfy the requirements of optimization design, and the optimized BTTRC variations are reduced by about 10% and obey the normal distribution, which are quite promising in improving the design and control of HPT BTRRC; (3) in computational efficiency, the computing time of M1 and M3 is far less than those of M2 and M4, meanwhile M3 and M4 are superior to M1 and M2; (4) in computational accuracy, M1 and M2 are better than M3 and M4, as well as M2 and M4 are higher than M1 and M3 theoretically. The presented study does not only fulfill the HPT BTRRC dynamic assembly design from a probabilistic optimization perspective and improve the performance and reliability of gas turbine engine, but also provides a promising approach and four valuable optimization models for MDAR optimization design. Besides, the present efforts are of great significance in enriching the theory and method of mechanical reliability design.

Machining center is a complex mechatronical product. Because of numerous influencing factors on its reliability, parts of their inaccurate description and the uncertainty of its failure behaviors, it is very difficult to analyze its reliability by traditional reliability model which is based on probability theory. To solve this problem, grey system theory combined with GO method reliability analysis was presented, and sequentially a practical reliability analysis model considering various operating conditions of the components of machining center was established. The method was used in reliability analysis of hydraulic system of Tray Automatic Exchange Device (TAED) of machining center. Firstly, through a systematical analysis of hydraulic system of tray automatic exchange device of machining center, its basic structure model was summarized, and the model of GO chart for the hydraulic system was established. Then, the gray dynamic analysis for the hydraulic system was derived, and a feasible method of dynamic analysis for the performance reliability of hydraulic system was provided. Finally, the availability and correctness of this method in the analysis and reliability evaluation of machining center was verified by comparing the calculated result of this method with that of the traditional static GO methodology and the FTA. This approach provided a theoretical basis for the prevention of failures of the hydraulic system of tray automatic exchange device, the improvement of the system reliability and security, and the development of security controls.

In industrial engineering, the reliability analysis, modeling and optimization for complex systems are very important. Although the works about reliability optimization with the traditional method are numerous, researchers still study more efficient and accurate methods to solve these reliability problems. The common cause failures are the multiple failures with a common cause, which is typical and serious in practical systems. Therefore, on the basis of normal optimization methods of system reliability, this paper proposes an optimization method of system with common cause failures based on importance measures. The optimization models of parallel system and the series-parallel system are built and are solved with hybrid genetic algorithm. By analyzing the system reliability and cost increasing, the proposed method gives the more accurate, valid and robust optimization results. Meanwhile, the method provides an idea for the reliability optimization of multistate systems.

An overview is presented of the methods available to quantify uncertainties and to combine them in a systems reliability analysis. The different sources of uncertainty are identified and a discussion is provided to illustrate their different nature. The methods of reliability analysis are then described showing how they can incorporate parameter and model uncertainty. Finally Bayesian methods are presented illustrating how to update probabilistic statements with new information and how to incorporate parameter and model uncertainty in the reliability predictions.

This paper researched on the static and fatigue strength of a 220-ton mining dump truck steering knuckle by the method of reliability analysis, Monte Carlo and response surface. The geometrical model of the steering knuckle was established in CATIA and this model was imported into HyperMesh to obtain the finite element model of steering knuckle. With this finite element model the static strength of the knuckle was checked in the case of uneven road condition in ANSYS in order to acquire the stress nephogram and deformation map. Taking the random influential factors of the reliability into account, the reliability analysis file was compiled by the language of APDL. Then the static and fatigue strength analysis was executed by the method of Monte Carlo and response surface in the PDS module to obtain the statistical results of residual strength and fatigue life, the failure probability and reliability. Finally the quantitative calculation of the failure probability was achieved. In order to realize lightweight design and improve the economy, the knuckle was optimized in ensuring the premise of safety and reliability.

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

In Reliability analysis, there are four main steps to perform. These steps are selection of the mathematical model that represents system states, selection of the mathematical representation that represents the operation of the system, quantitative and qualitative reliability analysis and to conclude the obtained results. In Faculty of Management Science and Informatics, there is a course called Reliability engineering in which reliability analysis is taught. During the course, the students are taught about the basic of the reliability engineering and reliability analysis. During this process, there are various topics that can be more challenging for a student, such as computation of the Importance measures. Thanks to this, we developed a software tool for such computation and this tool is also usable for the research activities in our faculty. By implementing this software tool in the teaching process in subject of the reliability engineering the students can better understand, how these measures can be computed and how can they be used for localizing weak spots in the system. Results from this tool can be then used in term projects and assignments by students of in research activities that uses these measures in reliability analysis.

This paper reviews three main methods in reliability analysis for power systems and applies them to a micro-grid with significant clean energy penetration. The approaches used are Reliability Block Diagrams (RBD), Fault Tree Analysis (FTA) and Markov Reliability Modeling (MRM). Each method is introduced and applied to a simple system to illustrate its application procedure. Reliability parameters such as the system's mean time to failure (MTTF), component structure importance, and reliability function are evaluated using simulation models. All three methods are then used to find the reliability measures of a real micro-grid which is characterized by significant clean energy penetration using solar photovoltaic panels and a fuel cell.

In this paper, the authors demonstrate how fault tree analysis could be used to perform reliability analysis of hardware-software systems. The functional dependency of the hardware components on the interfacing software components is appropriately modeled using fault trees. The MIT (Massachusetts Institute of Technology)-CSR's (Center for Space Research) ACIS (Advanced X-ray Astrophysics Facility Imaging Charge Couple Device Imaging Spectrometer) system is used to illustrate the fault tree analysis method in reliability analysis of complex hardware-software systems. The ACIS science instrument system is a space borne system to acquire and process X-ray images over the sky, and sends them to earth. It has hardware and software components with interfaces between them making it a very good example of a complex hardware software system. This approach could be used in analyzing other complex systems being designed today and in identifying the critical components to make the system safe and more reliable.

In order to ensure high reliability of complex engineered systems against deterioration or natural and man-made hazards, it is essential to have an efficient and accurate method for estimating the probability of system failure regardless of different system configurations (series, parallel, and mixed systems). Since system reliability prediction is of great importance in civil, aerospace, mechanical, and electrical engineering fields, its technical development will have an immediate and major impact on engineered system designs. To this end, this chapter presents a comprehensive review of advanced numerical methods for system reliability analysis under uncertainty. Offering excellent in-depth knowledge for readers, the chapter provides insights on the application of system reliability analysis methods to engineered systems and gives guidance on how we can predict system reliability for series, parallel, and mixed systems. Written for the professionals and researchers, the chapter is designed to awaken readers to the need and usefulness of advanced numerical methods for system reliability analysis.

Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems.

In this paper, a new method is developed that can be applied efficiently in reliability analysis and design verification of structures under random vibration. This method is based on singular value decomposition of modal coordinates cross covariance matrix. Computational algorithm and relative flow chart for this method is developed and compatible reliability criterion with this algorithm has been extracted. In order to results verification, we use Miles relation and Monte Carlo simulation -that are two well known methods in reliability analysis- and all of these methods are applied to a simple finite element model. Results show that new algorithm is more efficient for reliability analysis of structures under random vibration.

This paper proposes a new goal-oriented (GO) method for reliability analysis of repairable systems with multiple-input and multi-function component (MIMFC). First, a new GO operator combination, which is composed of a new function GO operator and a new auxiliary GO operator, is created to represent MIMFC. The new function GO operator named as Type 22 operator is created to represent MIMFC itself, and the auxiliary GO operator named as Type 15B operator is created to represent multi-condition control signals of MIMFC. Then, GO operation formulas of the new GO operator combination are deduced based on logical relationships among inputs, outputs, and the component itself. The reliability analysis process of the new GO method is formulated. Furthermore, this new GO method is applied for the first time in steady availability analysis and qualitative analysis of the fan drive system of a power-shift steering transmission. Finally, the results obtained by the new GO method are compared with the results of fault tree analysis (FTA) and Monte Carlo simulation (MCS), and the comparison results show that this new GO method is reasonable and advantageous in reliability analysis of repairable systems with MIMFC. Moreover, the analysis process shows that it is more advantageous in the aspect of building system models and conducting reliability analysis. Overall, this paper not only improves the basic theory of the GO method and expands the application of the GO method, but it also provides a new approach for reliability analysis of repairable systems with MIMFC.

Efficient system reliability analysis illustrated for a retaining wall and a soil slope

PurposeDegraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.Design/methodology/approachThe research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.FindingsThe proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.Research limitations/implicationsThe models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.Practical implicationsThese models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.Originality/valueA unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.