Reliability Optimization Design Research Articles

Optimizing MEP Design in Pharmaceutical Cleanroom with the Integration of 2D To 7D in BIM

Abstract: This paper examines the optimization of pharmaceutical cleanroom design using 2D to 7D Modelling in Building Information Modelling (BIM). The goal is to enhance the reliability, different methods, statistical data, and performance of pharmaceutical production plants by effectively allocating components within design constraints. Mathematical optimization techniques improve facility design, ensuring robustness and operational efficiency. The study proposes a reliable optimal design for air-conditioning systems in pharmaceutical cleanrooms, considering uncertainties in design parameters and operational strategies. Resilient cleanroom systems are developed, and adaptable to various conditions while maintaining high performance standards. Additionally, the research explores the application of experimental design methodologies in optimizing drug delivery systems, such as factorial and etc, to enhance the quality and efficiency of pharmaceutical products and processes.

Research on optimal design method of dynamic stress parameters of helical gear based on orthogonal experimental design

Aiming at the reliability optimization design problem of two-grade helical cylindrical gear transmission system, the UG parameterized model based on expression and ADAMS dynamic simulation model under real working conditions are integrated in ISIGHT platform, and the distribution law of peak contact force on the tooth surface of helical gear pair in the transmission system at different meshing times is obtained. Considering the uncertainty of material properties, load conditions and geometric parameters, the sample set was generated according to the orthogonal experimental design method, and the Kriging approximation model was established. On this basis, the contact strength reliability of helical gear was analyzed. The mathematical model of meshing efficiency reliability optimization of helical gear pair was established and solved by Hooke-Jeeves Direct Search method. The results show that the meshing efficiency and reliability of the optimized helical gear pair are improved, and the peak value of the contact force is obviously reduced.

Time-dependent reliability assessment and optimal design of corroded reinforced concrete beams

It remains a significant challenge to quantitatively describe the corrosion of reinforced concrete (RC) structures under chloride penetration. Moreover, when considering uncertainties throughout the life cycle of corroded RC structures for assessing their safety, reliability, and optimal design, the complexity of the problem intensifies. To address these issues, this paper studies the time-dependent reliability analysis and optimal design of corroded RC beams. At first, the time-dependent reliability of beams is investigated by considering both the serviceability limit state (SLS), which corresponds to the corrosion initiation of the reinforced steel, and the ultimate limit state (ULS), associated with the bending failure of the beam. This analysis takes into account the time-dependent chloride diffusion coefficient and incorporates a stochastic process. The reliability is evaluated using the Monte Carlo Simulation (MCS) method and the cumulative distribution function (CDF) method. Subsequently, a time-dependent reliability-based design optimization (TRBDO) problem is formulated, and the PSO-MCS, a methodology incorporating a particle swarm optimization (PSO) algorithm and MCS is adopted to solve it. After optimization, the initial cost of the specific RC beam is reduced from 1351.879€ to 1247.075€, while the time-dependent reliability within [0, 100] years is improved from 0.6057 to 0.6508. The effectiveness of the CDF, MCS and PSO-MCS methods are demonstrated through reliability analysis and design examples of corroded RC beams.

Reliability analysis and optimization design of magnetic fluid dynamic seal shell structure under thermal/mechanical load

In order to study the reliability of Magnetic fluid dynamic seal shell structure under thermal/mechanical load, the improving cooling structure, calculating fuzzy fatigue reliability, and collaborative optimization design of fatigue reliability and lightweight are studied in this paper. The temperature model of the shell structure under four temperature conditions is established to analyze the influence of the thermal deformation caused by excessive local temperature. The cooling structure is improved, and the maximum temperature under the maximum temperature condition is reduced by 40.154 °C. For the sake of calculating the reliability of the new shell structure, a strength analysis model under thermal/mechanical load is built, and the fuzzy fatigue reliability function is obtained based on Latin hypercube sampling and the second-order response surface method. Four kinds of reliability are acquired by coding the functional functions and four kinds of membership functions with MATLAB, but all of them are lower than 90 % of the industrial requirements. To improve the reliability of the new shell structure and carry out the anti-fatigue lightweight design at the same time, an approximate model was constructed based on the interval analysis method and second-order response surface method for analysis. The accuracy of the approximate model was verified by re-sampling and finite element analysis. Based on the non-dominated sorting genetic algorithm, the optimal solution is determined. The optimization results show that the stress target value is reduced by 19.3 %, the weight target value is reduced by 3 %, and the fuzzy fatigue reliability reaches 94.65 %, 94.58 %, 93.89 %, and 96.31 % respectively. A new cooling structure of the Magnetic fluid dynamic seal is obtained and the maximum temperature is reduced. Moreover, the reliability of the new shell structure under thermal/mechanical load coupling is improved.

Performance analysis of electrical signal output of multi-state flexoelectric structures with parameter uncertainties through quasi-Monte Carlo method

Flexoelectric effect is a more universal electromechanical coupling effect than piezoelectric effect. Flexoelectric beams as the main structural component of flexoelectric power signal output have broad application prospects in the next generation of micro–nano electromechanical systems. However, the electrical signal output of flexoelectric structures in macro-scale is far less than the output of the piezoelectric signal. Therefore, it is urgent to explore the influence of the parameter uncertainties on the electrical signal output of the flexoelectric structures, in order to improve the electrical signal output of flexoelectric materials with excellent design performance. Based on the quasi-static theory, the output voltage model and the output charge model of flexoelectric structures as well as the effective piezoelectric coefficient model are constructed. Then the influences of the flexoelectric parameters on the output voltage and the output charge are researched as well as the influence of the effective piezoelectric coefficient. Finally, the influences of uncertain parameters under different electrical states (e.g. the electrical open circuit and short circuit states) on the output performance of flexoelectric signal are studied by the quasi-Monte Carlo method, in order to further provide a reference for the reliability analysis and optimization design of the flexoelectric structures.

Multi-Task Learning for Design Under Uncertainty With Multi-Fidelity Partially Observed Information

Abstract The assessment of system performance and identification of failure mechanisms in complex engineering systems often requires the use of computation-intensive finite element software or physical experiments, which are both costly and time-consuming. Moreover, when accounting for uncertainties in the manufacturing process, material properties, and loading conditions, the process of reliability-based design optimization (RBDO) for complex engineering systems necessitates the repeated execution of expensive tasks throughout the optimization process. To address this problem, this paper proposes a novel methodology for RBDO. First, a multi-fidelity surrogate modeling strategy is presented, leveraging partially observed information (POI) from diverse sources with varying fidelity and dimensionality to reduce computational cost associated with evaluating expensive high-dimensional complex systems. Second, a multi-task surrogate modeling framework is proposed to address the concurrent evaluation of multiple constraints for each design point. The multi-task framework aids in the development of surrogate models and enhances the effectiveness of reliability analysis and design optimization. The proposed multi-fidelity multi-task machine learning model utilizes a Bayesian framework, which significantly improves the performance of the predictive model and provides uncertainty quantification of the prediction. Additionally, the model provides a highly accurate and efficient framework for reliability-based design optimization through knowledge sharing. The proposed method was applied to two design case studies. By incorporating POI from various sources, the proposed approach improves the accuracy and efficiency of system performance prediction, while simultaneously addressing the cost and complexity associated with the design of complex systems.

Time-dependent fatigue reliability estimation and optimal design of scraper chains under corrosive wear effect

Fatigue damage is one of the main failures of the scraper chain. Moreover, corrosive wear has a detrimental effect on fatigue crack propagation. It is so essential to study the fatigue reliability of the scraper chain considering the interaction of corrosive wear and fatigue. This paper is intended to propose a reliability-based estimation and optimal design of the scraper chain considering the performance degradation of the scraper chain under the interaction of corrosive wear and fatigue. First, the dynamic model of the scraper conveyor is established based on the finite element method. Second, Paris Low is used to empirically describe the occurrence of cracking with corrosion effects. Furthermore, the time-dependent reliability of scraper chains under the interaction of the corrosive wear and fatigue crack propagation is addressed by the fourth-moment saddlepoint approximation (FMSA) method, and the reliability-based design optimization (RBDO) of the scraper chain is then carried out. Finally, the applicability of the proposed method is verified by the SGZ1000/1400 scraper conveyor.

Fatigue life and fatigue reliability mechanism of ball bearings

Abstract As the main supporting parts of rotating machinery, the fatigue life and fatigue reliability of ball bearings directly affect the accuracy, stability and reliability of equipment. Based on the quasi-static model of bearing and the fatigue life theory, this paper analyzes the effect of the external loads on the mechanical properties and fatigue life of bearing, and studies the action mechanism of bearing working conditions and other parameters. In addition, based on the stress–strength model and the fatigue life model of bearing, the fatigue reliability and sensitivity of bearings are analyzed by means of perturbation method, Edgeworth series and fourth moment technique, and the correctness is verified by the Monte Carlo simulation. Results have important theoretical and practical value, and can provide theoretical support for the research of reliability optimization design, fault mechanism and fault diagnosis method of ball bearings.

Predicting steel column stability with uncertain initial defects using bayesian deep learning

The stability of steel columns is difficult to predict accurately due to uncertain initial defects such as geometric imperfections and residual stress. To address this issue, we propose a probabilistic model that uses variational autoencoder (VAE) and transfer learning to estimate the loading capacities of steel columns. Our model can predict the confidence intervals of buckling loads without knowing the exact distribution of initial defects, providing more comprehensive information for engineering applications than traditional deterministic strength index. We establish a dataset of 1500 load-displacement curves of steel columns using four data augmentation approaches, and analyze the data distribution to validate the model's assumptions. Various criterions, including the mean squared error (MSE), the prediction interval coverage probability (PICP), and the prediction interval normalized average width (PINAW), are adopted to comprehensively measure the performance of confidence interval prediction. The numerical experiment validates that the trained model accurately predicts the confidence intervals for load-displacement responses, which perfectly cover the true curves with reasonable PINAW. Finally, we conduct a case study with a practical experiment to illustrate the model's potential application in failure probability calculation and reliability design. Our proposed model provides a promising probabilistic solution for quantifying the impact of uncertain parameters on structural analysis and significantly simplifies probability-based reliability design and optimal design processes.

Reliability analysis and optimization design of hydrogen storage composite pressure vessel with hybrid random-fuzzy uncertainties

In this study, a progressive failure model for hydrogen storage composite pressure vessel (CPV) burst is established. The burst pressure and progressive damage behavior of the CPV are analyzed. Besides, kriging and response surface (RS) surrogate models for CPV burst are established. The verification and the comparative analysis of the surrogate models are carried out. Then, the reliability of the CPV is analyzed with hybrid random-fuzzy uncertainties, and the influence of longitudinal tensile strength, hoop layer thickness, and helical layer thickness on the hybrid reliability is explored. Finally, a unified reliability index is established with hybrid random-fuzzy uncertainties, and the modified particle swarm optimization (PSO) algorithm is applied to carry out reliability-based optimization design. The minimum weight of the composite shell is set as the objective, and the reliability of the CPV with hybrid random-fuzzy uncertainties is set as the constraint. The results show that the hoop layer of the CPV is the main load-bearing structure. The kriging and RS surrogate models are effectiveness to surrogate the burst pressure of the CPV, and the RS model is simpler and more computationally efficient than kriging model, which is more suitable for reliability analysis and optimization design. Under the condition of hybrid random-fuzzy uncertainties, the reliability of the hydrogen storage CPV exhibits fuzzy uncertainty, and there is a possibility of reliability equal to 0 under the low λ-cut level, making it difficult to meet reliability requirements. Increasing the longitudinal tensile strength, the hoop layer thickness and the helical layer thickness can improve the reliability of the hydrogen storage CPV. Furthermore, the optimization method proposed in this study improves its reliability from 0.7043 to 1. This study establishes reliability analysis and optimization design methods for hydrogen storage CPV with hybrid random-fuzzy uncertainties, which contributes to further improvement on the safety of CPV.

Reliability evaluation and optimization design method of piezoelectric actuator vibration suppression system

As an effective means of structural vibration suppression, piezoelectric actuator vibration suppression system(PAVSS) has been gradually applied in structural vibration control. However, the performance degradation or failure of piezoelectric actuator under long service life will lead to the degradation of service reliability of PAVSS, so the scheme obtained by deterministic optimization method is difficult to ensure the service reliability. Aiming at the reliability evaluation and optimal design of PAVSS in service, the failure mechanism considering of the performance degradation or failure of piezoelectric actuator is analyzed, and the reliability evaluation method based on nested sampling and weighted statistics is constructed, which solves the reliability evaluation problem of PAVSS with the characteristics of load-sharing and redundancy. A reliability-based optimization method based on master-slave parallel genetic algorithm is proposed to optimize the position and angle of the actuators. At last, the feasibility and effectiveness of the proposed method are proved by an example, which not only provides a theoretical basis for the high reliability design of PAVSS in service, but also provides a new solution for the engineering problem of structural vibration control.

Analysis of Blocking Capability Failure Mechanism in IGBT Module Under High Salt Spray Environment

High salt spray environment is a threat to the long-term stability and the robustness of an insulated gate bipolar transistor (IGBT) module. Failure mechanisms of IGBTs have been discussed in normal and high humidity environment, which in high salt spray environment is unclear and seldom reported. In this paper, experiments in high salt spray environment are conducted on wire-bonding IGBT modules to reveal failure mechanism. Different degradations of the blocking capability are observed for the same packaged IGBTs in the salt spray environment. Based on experiment results, degradation substances in the internal package are analyzed by means of scanning electron microscope (SEM) and X-ray diffraction (XRD) to reveal the key composition affecting the blocking capability of IGBT switches. Finally, a failure model is used to reveal the mechanism that the insulation strength of the terminal area in the chip edge is reduced by substances, resulting in the blocking failure of IGBT switches. The analysis of IGBT module failure mechanism is of great significance to reliability evaluation and optimal design for package structures of power modules applied in harsh environments.

Reliability-based design optimization for seismic structures considering randomness associated with ground motions

When addressing the dynamic reliability analysis of structures, it becomes necessary to account for multiple limit state functions or their combinations. In scenarios where structures are subjected to random excitation, this can lead to intricate inter-dependencies among different limit states, and the computational workload can pose a substantial challenge in ensuring sufficient precision. Code-based design primarily ensures safety at the member level, while deterministic optimization fails to accommodate the inherent uncertainties associated with external excitation or the system as a whole. Therefore, in such cases, to address both the uncertainties in excitations and the presence of multiple limit states while mitigating computational challenges, equivalent extreme-value criteria are employed within the framework of the probability density evolution method to calculate the global reliability of the structure subjected to stochastic ground motions generated from the physically motivated stochastic ground motion model. Numerical optimization is subsequently conducted using genetic algorithms, aiming to minimize the cost of the superstructure while adhering to the design performance criteria related to the inter-story drift ratio and considering global reliability. Additionally, multi-objective optimization is carried out using NSGA-II, permitting the generation of multiple solutions, from which one can select the most suitable solution as needed. The numerical results illustrate the effectiveness of this technique in achieving an optimal balance between the cost of the structure and the consideration of global reliability, providing a comprehensive solution for dynamic reliability analysis and design optimization of structures under random excitations.

A new solution framework for time-dependent reliability-based design optimization

Time-dependent reliability-based design optimization (TRBDO) has attracted intensive research attentions in recent years by virtue of its unique ability to allow consideration of dynamic uncertainties caused by stochastic processes and material property degradation. However, existing TRBDO methods are generally too intricate to be practically applicable for practical engineering application. On top of that, extremely high computational cost for complex TRBDO problems further hinders its practicability. To facilitate smooth implementation via enhancing computational efficiency in solving TRBDO problems, this study proposes an innovative and efficient solution framework. The strategy is that time-dependent performance function in each probabilistic constraint is discretized into a series of instantaneous performance functions to transform the original TRBDO problem into a RBDO problem. The reliability of each probabilistic constraint in the transformed RBDO problem is then considered under extreme value condition. With engagement of the first-order reliability method, the RBDO problem is transformed into two different triple-loop timeindependent RBDO problem. However, the issue of expensive computational cost still persists due to the triple-loop structure and identification of temporal variables under extreme value condition. To this gap, a decoupled strategy is adopted to resolve the triple-loop structure into a series of cycles of double-loop reliability analyses and deterministic optimization. Two numerical examples and three engineering applications are employed to demonstrate the supreme computational performance of the currently proposed solution framework. Results show that the proposed framework is capable of achieving a reliable optimal design at a fast convergence speed.

Direct probability integral method for reliability sensitivity analysis and optimal design of structures

Direct probability integral method for reliability sensitivity analysis and optimal design of structures

Novel bootstrap-based ellipsoidal convex model for non-probabilistic reliability-based design optimization with insufficient input data

Performing reliability-based design optimization with insufficient input data is a significant and challenging issue as accurately quantifying epistemic uncertainty can be difficult in such scenarios. Non-probabilistic models can marginally alleviate the need for a large sample size by constructing the boundaries of uncertainty parameters. However, most of the existing non-probabilistic models account for only the available or known samples. For cases with insufficient data, the compact uncertainty domain may result in considerably hazardous results, particularly for the problems that require high reliability. Therefore, a novel bootstrap-based ellipsoidal convex model (BECM) is proposed herein to account for both known and unknown data. Herein, the bootstrap method is introduced to non-probabilistic convex models for the first time to quantify the ellipsoidal shape uncertainty caused by insufficient input data. Further, the proposed BECM is also integrated into non-probabilistic reliability-based design optimization. The entire framework of uncertainty quantification and reliability optimization design for insufficient input data is established. Marginally conservative results can finally be achieved in a rational and objective manner by partially sacrificing the ellipsoid volume. Comprehensive comparisons and detailed discussions on aspects, including the problem complexity, initial sample size, and distribution type, are also conducted. The numerical results show that the BECM displays the best performance in terms of accuracy and robustness. It can achieve an approximate balance between being conservative and taking risks. The significant advantages are also illustrated by an engineering example of linear buckling analysis of stiffened cylindrical shells.

A global strategy based on deep learning for time‐dependent optimal reliability design

AbstractTime‐dependent reliability‐based design optimization (RBDO) is a computationally tough problem that needs to be addressed urgently. The difficulty of solving the time‐dependent RBDO mainly comes from the time‐dependent reliability analysis involved in probabilistic constraints, which itself is one of the thorny problems in the reliability community and makes the computational cost become much more onerous. In this paper, a deep‐learning‐assisted approach is proposed to solve the time‐dependent RBDO. The proposed approach leverages the classification capability of the deep learning, and constructs the alternative model for the actual probabilistic constraint function in the so‐called augmented reliability space, so as to make the trained alternative model accurate wherever it will be invoked. Moreover, a sequential sampling technique utilizing the classification probability provided by the deep learning is proposed to further reduce the computational cost. Then, the time‐dependent reliability analysis involved in the time‐dependent RBDO is conducted by the cheaper alternative model instead of the original computing‐intensive probabilistic constraint function, which evidently reduces the computational burden. The presented examples showcase the performance of the proposed approach. Especially, for the complicated engineering application, the proposed approach saves about 10% of the computational cost compared with the existing methods.

Reliability analysis and optimization design of a repairable k-out-of-n retrial system with two failure modes and preventive maintenance

This article deals with a repairable k-out-of-n: G system with retrial feature and two maintenance policies. All components in the system have two failure modes, mode a failure and mode b failure. When a component fails, the failed component will be repaired instantly if the repair equipment is idle. Otherwise, it enters into a retrial orbit and tries again after some time until it is repaired. The single repair equipment may be subject to breakdown in a busy period, and in order to improve system reliability, the idle repair equipment will be performed preventive maintenance. The Markov process theory and Laplace transform method are adopted to compute the reliability indexes of the system. Also, four optimization design models are constructed to determine the optimal repair rates of the components with two failure modes, and the minimization problems of the total expected cost function per unit time and the cost-effectiveness ratio are solved. To verify the correctness of the model, numerical analysis is executed to demonstrate the impact of each parameter on system reliability indexes, the optimal solutions of different optimization design models are obtained by using differential evolution algorithm and genetic algorithm.

Uncertain ballistic effects and reliability optimization design of ceramics composite armors

The uncertain ballistic effects and reliability optimization design of the ceramics composite armors are investigated. Considering the material uncertainty, the ballistic penetration process is analyzed through simulation model. The effects interlayer SiC mass fraction and the matrix thickness gradient ratio are discussed. The optimal parameters of both material and structure are obtained through reliability design methods and verified through ballistic experiments. The results show that the standard deviation can be reduced when interlayer SiC mass fraction increases. The ballistic depth can be reduced by increasing the gradient ratio. Through optimization, the ballistic reliability of the ceramic composite armor is improved.

High-Precision Isogeometric Static Bending Analysis of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

A new quasi-three-dimensional (3D) shear deformation theory, called the spectral displacement formulation (SDF), is proposed for high-precision static bending analyses of functionally graded plates. The main idea is to expand unknown displacement fields into Chebyshev series of a unique form in the thickness direction; the truncation numbers are set to be adjustable to meet various application requirements. Specifically, 3D elasticity solutions and traction-free boundary conditions can be approached by increasing the number of Chebyshev bases. The SDF is also an extension of the classical plate theory and naturally avoids the shear locking problem, making it versatile for functionally graded material (FGM) plates of arbitrary thicknesses. The C1 continuity requirement for the discretization of the generalized displacements is conveniently fulfilled by the nonuniform rational B-splines (NURBS)-based isogeometric method. Numerical examples demonstrate the excellent performance of the proposed method for the displacement and stress analyses of functionally graded plates. The high precision and versatility of the present method have manifested its great potential applications in strain-based or stress-based reliability analysis, optimization design, fatigue analysis, and fracture analysis of FGM plates, and other related fields.