Reliability-based Optimization Research Articles

An Analysis and Reliability-based Optimization Design Method of Trajectory Accuracy for Industrial Robots Considering Parametric Uncertainties

To address the challenges of poor trajectory accuracy in industrial robots, which has emerged as a technological bottleneck hindering further robots’ applications in high-precision manufacturing industries, this paper proposes a method for the analysis and reliability-based optimization design for industrial robots’ trajectory accuracy considering parametric uncertainties. Firstly, the dynamic equation of an articulated industrial robot with six degrees of freedom is derived, incorporating the Stribeck joint friction model, followed by the uncertain parameter identification of this dynamic model. Subsequently, an uncertainty simulation system for the robot is established based on the constructed dynamic model and the sensitivity of system uncertain parameters to the robot trajectory accuracy is analyzed, where 10 key parameters are obtained among 54 uncertain parameters. Finally, a reliability-based multi-objective optimization design methodology is proposed synthesizing the robot trajectory accuracy, manufacturing cost, and quality loss, to achieve tolerance design of the robot's parameters, and enables minimizing costs and quality losses while ensuring the robot's trajectory accuracy reliability. The performance and practicality of the proposed method were validated using a six-degree-of-freedom rotary joint serial industrial robot as an example.

Dynamic Optimization of Exclusive Bus Lane Location Considering Reliability: A Case Study of Beijing

For metropolises like Beijing, heavy congestions cause transit passengers’ unreliable travel time, including in vehicle time and waiting time. Comparing with other managerial measures, designing a lane for bus use only is an effective method to improve travel reliability, for it can eliminate the influence on bus-driving conditions. This paper proposes a reliable and practical method to determine exclusive bus lanes (EBL). A reliability-based optimization model is established, in which the tradeoff among bus and private car passengers’ travel time, reliability, and EBL construction cost are considered. Based on the actual network, a user equilibrium demand assignment model is applied to estimate the dynamic bus flow distribution. Since the model is nonlinear, a two-step method is proposed where tangent lines are introduced to constitute an envelope curve to linearize the model. This work conducts the statistical modeling and fitting analysis with actual bus trajectory data, collected on EBL in Beijing during peak hours. Passenger travel time distributions are fitted to estimate the statistical passenger travel time; Lognormal distribution and Gaussian distribution are the best fit. The optimization results indicate that the passenger travel time reliability can be improved by 5.5% by the optimized EBL location scheme. This study will provide a theoretical basis and methodological support for improving the service level of the public transportation system in large cities through the scientific planning of exclusive bus lanes.

Reliability-based optimization for concrete-filled steel tubular columns incorporating multi-advanced techniques and model constraints

This work presents an advanced structural reliability analysis of circular concrete-filled steel tubular (CFST) members through machine learning and global optimization, together with numerical Monte Carlo simulations (MCS). The artificial neural network (ANN) model is developed and validated against available experimental data. On the basis of monetary cost of materials, the optimal design of CFST members with reliability constraint is formulated and solved by balancing composite motion optimization (BCMO) algorithm. Based on the MCS, reliability analysis is then carried out to calculate the coefficient of variation of optimal design under different loads. Subsequently, a comprehensive prediction simulation, taking account of the uncertainty of experimental data and potential errors from models (ANN, MCS, and BCMO), is performed to generate the statistics on the axial capacity of CFST members. The critical value for the optimal solution is also investigated as a function of the input variables. The results of this study can be applied to achieve a better reliability-based design optimization with minimum cost for the circular CFST columns.

Reliability based optimisation of composite plates under aeroelastic constraints via adapted surrogate modelling and genetic algorithms

Composite materials are vital in aerospace for their exceptional strength-to-weight ratio. This study delves into reliability-based optimisation of composite plates within aeroelastic constraints, employing an efficient global optimisation method and genetic algorithms. Initial analysis focuses on aeroelastic responses such as limit flutter speed, gust response, and static loads, emphasising maximum strain assessment. To tackle optimisation challenges of composite stacking sequences, a homogenisation technique with lamination parameters is applied. We then formulate a constrained optimisation problem to minimise gust response while meeting flutter and maximum strain constraints. Surrogate models based on conditioned Gaussian Processes are developed for each aeroelastic response, facilitating optimisation within the composite design space. These models, with potential for local refinement, expedite optimal solution identification. Further, we integrate reliability-based optimisation into the framework to determine a robust stacking sequence using genetic algorithms, accounting for random fibre orientation variations. This holistic approach integrates aeroelastic analysis, constrained optimisation, surrogate modelling, and reliability-based optimisation, proving effective in designing reliable, efficient composite structures for aerospace, thus enhancing performance and safety.

Aero-Structural Comprehensive Nonprobabilistic Reliability-Based Optimization Method for High Aspect Ratio Wings

An aero-structural comprehensive reliability-based optimization method is proposed to construct the optimization framework of designing the high aspect ratio wing. There are three parts included in this method. 1) The ideal cruising shape is obtained by optimizing the geometrical parameters in the cruising conditions, where only the aerodynamic shape optimization is involved and the structural deformation is not considered. 2) The jig-shape optimization method is presented, where the aerodynamic performance of the wing structure with deformation is improved by adjusting the twist angle along the span direction to make sure that the shape with the aeroelastic deformation approaches the ideal cruising shape. 3) A nonprobabilistic reliability-based structural optimization is conducted by updating the thickness of composite layer, where the dispersion of mechanical properties of composite materials is considered and a nonprobabilistic reliability index according to strength and stiffness constraints is established. The global stiffness of the wing structure is changed after jig-shape optimization and structural optimization, and the jig-shape and structural scheme are modified alternately. The previously mentioned process needs to be repeated until the changes in the jig-shape and structural scheme in the iterations can be ignored. Finally, the effectiveness of this method has been verified through the numerical example followed by some conclusions.

Redefinition of failure envelope of composite materials considering uncertainty of test data

After conducting three World-Wide Failure Exercises (WWFEs), it has become apparent that existing strength theories or criteria have certain deficiencies, and no single theory can accurately match all experimental results. As a result, there is a growing focus on the uncertainties present in the macrocosm test data of composite materials. The paper introduces the concept of uncertainty into the collection of test data for the classical Tsai-Wu failure criterion and Hashin criterion. The method proposed involves fitting the coefficients of the failure criteria by treating experimental data as random variables, a technique that diverges significantly from the conventional method of using composite allowable values to define these coefficients. It also uses the probability of success as a constraint and defines the fitted error as an optimization objective. Monte Carlo sampling is employed to perform a reliability analysis, and six sigma is used for a reliability-based optimization of the failure criteria. The Multi-Island Genetic Algorithm is utilized to search for the optimal value. The approach presented in this study provides the ability to predict future failures in composite materials by considering the uncertainty of the test data. By incorporating uncertainties into the analysis and design process, a more accurate and reliable assessment of the performance of composite materials can be achieved. Moreover, there seems to be a significant difference in the fitting error between the mean data and the normal distribution data. Additionally, when Hashin criterion is modified, the test data matches the failure envelope more closely and the degree of fit between the experimental data and the failure envelope is higher.

Reliability-Based Design Optimization of the PEMFC Flow Field with Consideration of Statistical Uncertainty of Design Variables

Recently, with the fourth industrial revolution, the research cases that search for optimal design points based on neural networks or machine learning have rapidly increased. In addition, research on optimization is continuously reported in the field of fuel cell research using hydrogen as fuel. However, in the case of optimization research, it often requires a large amount of training data, which means that it is more suitable for numerical research such as CFD simulation rather than time-consuming research such as actual experiments. As is well known, the design range of fuel cell flow channels is extremely small, ranging from hundreds of microns to several millimeters, which means the small tolerance could cause fatal performance loss. In this study, the general optimization study was further improved in terms of reliability by considering stochastic tolerances that may occur in actual industry. The optimization problem was defined to maximize stack power, which is employed as objective function, under the constraints such as pressure drop and current density standard deviation; the performance of the optimal point through general optimization was about 3.252 kW/L. In the reliability-based optimization problem, the boundary condition for tolerance was set to 0.1 mm and tolerance was assumed to occur along a normal distribution. The optimal point to secure 99% reliability for the given constraints was 2.918 kW/L, showing significantly lower performance than the general optimal point.

Reliability-Based Design Optimization Applied to a Rotor Supported by Hydrodynamic Bearings

Rotating machines are an important part of industrial equipment. It is essential to improve their performance while reducing the manufacturing, operating, and maintenance costs. Ensuring their reliability is also crucial because a machine breakdown can result in significant costs and potential environmental and safety damage. Reliability-based optimization is an approach that aims to find an optimal and robust design that guarantees a machine’s reliability. In this study, we focused on optimizing the shaft diameter and oil temperature of a rotor supported by hydrodynamic bearings. We considered the materials’ elastic moduli, density, and bearing clearance as uncertain parameters. Our goal was to ensure 99% reliability regarding both the vibration amplitude and stability threshold. To model the machine, we used the finite element method and represented the bearings using stiffness and damping coefficients, considering the linear short bearing model. Due to the complexity of the model, we employed surrogate models to solve the reliability-based optimization problem. Our results showed that the optimization problem could be solved successfully using Kriging, polynomial chaos expansion, and polynomial chaos Kriging.

Augmented Space Integral Approach for Structural Reliability-Based Optimization

An efficient, fully decoupled approach is proposed to solve the structural reliability-based design optimization (RBDO) problem. The proposed approach utilizes augmented space integral and importance sampling (ASI-IS) to efficiently evaluate a functional relationship between the probability of failure and the design parameters, namely the so-called failure probability function. ASI-IS allows for the avoidance of both the intractable density fitting task associated with augmented space methods and the time-consuming repeated reliability evaluations associated with surrogate model approaches. The resulting functional relationship can be used to completely decouple the original RBDO problem into a deterministic one. Then, an iteration mechanism is constructed with gradually smaller design domains to enhance the efficiency of the optimization process. Furthermore, a sample reuse algorithm is proposed to improve the performance of the proposed approach by collecting the samples generated in previous iterations and reusing them in the current iteration in order to produce a better estimator of the failure probability function. Numerical and engineering examples, including a turbine blade and an aircraft inner flap, are given to demonstrate the efficiency and feasibility of the proposed approach.

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

Reliability-based design of high-performance hydrocyclones: Multi-objective optimization, fabrication using 3D-printing and experimental analysis

In the literature, several works aim to improve the performance of hydrocyclones using geometry optimization. However, these approaches do not consider the uncertainties in the models, design variables, and parameters, which can lead to solutions that do not correspond to the expected results when applied to real systems. Considering that, the present work proposed a reliability-based optimization of the hydrocyclone dimensions using the Advanced Mean Value (AMV) technique associated with the Multi-Objective Differential Evolution (MODE) algorithm. For that purpose, the maximization of total efficiency and minimization of underflow-to-throughput ratio and Euler number were taken as objectives and constraints were set to ensure an acceptable performance of the hydrocyclone in the main aspects of the process. Some of the obtained devices were selected to be fabricated through an additive manufacturing technique (3D printing) and, after that, be experimentally tested. The optimization results showed that the reliability-based optimization affected the Pareto curves in two different ways: a shortening or a displacement of the curve in relation to the nominal one, depending on which constraints are being activated. The experimental results demonstrated that the hydrocyclones obtained by the reliable approach had a greater tendency to meet the set constraints in practice. Finally, hydrocyclones with great experimental performance were obtained considering separation efficiency, concentration capacity, and energy consumption.

Concurrent Design Optimization of Tether-Net System and Actions for Reliable Space-Debris Capture

Tether-nets deployed from a chaser spacecraft are a promising solution to capturing space debris. The success of the one-shot capture process depends on the net’s structural dynamic properties, attributed to its physical design, and on the ability to perform an optimal launch and closure subject to sensing and actuation uncertainties. Hence, this paper presents a reliability-based optimization framework to simultaneously optimize the net design and its launch and closing actions to minimize the system mass (case 1) or closing time (case 2) while preserving a specified probability of capture success. Success is assessed in terms of a capture quality index and the number of locked node pairs. Gaussian noise is used to model the uncertainties in the dynamics, state estimation, and actuation of the tether-net, which is propagated via Monte Carlo sampling. To account for uncertainties and ensure computational efficiency, given the cost of simulating the tether-net dynamics, Bayesian optimization is used to solve this problem. Optimization results show that the mission success rate in the presence of uncertainties has increased from 75% to over 98%, while the capture completion time has almost halved.

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.

A Reliability-Based Optimization Framework for Planning Operational Profiles for Unmanned Systems

Abstract Unmanned engineering systems that execute various operations are becoming increasingly complex relying on a large number of components and their interactions. The reliability, maintainability, and performance optimization of these systems are critical due to their intricate nature and inaccessibility during operations. This paper introduces a new reliability-based optimization framework for planning operational profiles for unmanned systems. The proposed method employs deep learning techniques for subsystem health monitoring, dynamic Bayesian networks for system reliability analysis, and multi-objective optimization schemes for optimizing system performance. The proposed framework systematically integrates these schemes to enable their application to a wide range of tasks, including offline reliability-based optimization of system operational profiles. This framework is the first in the literature that incorporates health monitoring of multi-component systems with causal relationships. Using this hybrid scheme on unmanned systems can improve their reliability, extend their lifespan, and enable them to execute more challenging missions. The proposed framework is implemented and executed using a simulation model for the engine cooling and control system of an unmanned surface vessel.

Reliability-based design method for marine structures combining topology, shape, and size optimization

The uncertainty and extremity of ocean conditions make the design of marine structures a challenging process. Reliability-based optimization is a powerful approach to enhance material utilization and ensure system survivability. In this paper, a novel reliability-based design optimization (RBDO) method that combines topology, shape, and size optimization is proposed to achieve the design of marine structures. Within the framework of decoupled sequence optimization and reliability assessment, the developed method employs an innovative multi-technology combined optimization Scheme and a new reliability assessment algorithm. The combined optimization Scheme is established by simultaneously incorporating topology, shape, and size optimization technologies to further improve the lightweighting effect. The advanced arc interpolation algorithm is developed, which dynamically selects the advanced mean value method or arc interpolation method based on the trend judgment criterion to accelerate the calculation for the most probable point in reliability assessments. The RBDO examples of the wind turbine jacket and platform stiffened plate are utilized to verify the proposed method's applicability and validity, and the results are compared with those of other approaches. The findings prove that this RBDO method can effectively address reliability-based design problems of marine structures and is superior in providing lightweighting structures compared with others.

Intelligent co-design of material, process, and equipment for manufacturing high-quality traditional Chinese medicine preparations

In the context of Pharma 4.0, the design tools that support the pharmaceutical Quality by Design(QbD) are iterating fast toward intelligent or smart design. The conventional development methods for traditional Chinese medicine(TCM) preparations have the limitations such as over dependence on experience, low dimensions for the designed experiment parameters, poor compatibility between the process and equipment, and high trial-and-error cost during process scale-up. Therefore, this paper innovatively proposed the intelligent co-design involving material, process, and equipment for manufacturing high-quality TCM preparations, and introduced the design philosophy, targets, tools, and applications with TCM oral solid dosage(OSD) as an example. In terms of design philosophy, the pharmaceutical design tetrahedron composed of critical material attributes, critical process parameters, critical equipment attributes, and critical quality attributes was developed. The design targets were put forward based on the product performance classification system. The design tools involve a design platform that contains several modules, such a as the iTCM material database, the processing route classification system, the system modeling and simulation, and reliability-based optimization. The roles of different modules in obtaining essential and universal design knowledge of the key common manufacturing units were introduced. At last, the applications of the co-design methodology involving material, process, and equipment in the high shear wet granulation process development and the improvement of the dissolving or dispersion capability of TCM formula granules are illustrated. The research on advanced pharmaceutical design theory and methodology will help enhance the efficiency and reliability of drug development, improve the product quality, and promote the innovation of high-end TCM products across the industry.

S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method

S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method

Robust multidisciplinary analysis and optimization for conceptual design of flexible aircraft under dynamic aeroelastic constraints

We present a computational framework for robust multidisciplinary design and optimization of flexible aircraft, suited for the conceptual design exploration phase. Constraints are representative of some dynamic aeroelastic effects, including flutter and gust-induced structural stresses. Uncertainties on wing structural parameters are considered, and reliability-based optimization under dynamic aeroelastic constraints is addressed by a Bayesian approach. This work details the implementation aspects, covering disciplinary software tools and the overall aircraft design suite, the optimization algorithm and the approach to propagate uncertainty efficiently. Results are thoroughly discussed for a reference aircraft, which is optimized in the study with respect to a few wing parameters including aspect ratio. The proposed approach is compared to a conventional design methodology assuming a rigid airframe. We show that when applied to slender and flexible wings, the latter can produce dangerous non-conservative results, as its predictions are too optimistic both with respect to efficiency and to aeroelastic safety.

An efficient double-loop reliability-based optimization with metaheuristic algorithms to design soil nail walls under uncertain condition

An efficient double-loop reliability-based optimization with metaheuristic algorithms to design soil nail walls under uncertain condition