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Variable-fidelity optimization (VFO) frameworks generally aim at taking full advantage of high-fidelity (HF) and low-fidelity (LF) models to solve computationally expensive problems. The purpose of this paper is to develop a novel modified trust-region assisted variable-fidelity optimization (MTR-VFO) framework that can improve the optimization efficiency for computationally expensive engineering design problems.

Though the LF model is rough and inaccurate, it probably contains the gradient information and trend of the computationally expensive HF model. In the proposed framework, the extreme locations of the LF kriging model are firstly utilized to enhance the HF kriging model, and then a modified trust-region (MTR) method is presented for efficient local search. The proposed MTR-VFO framework is verified through comparison with three typical methods on some benchmark problems, and it is also applied to optimize the configuration of underwater tandem wings.

The results indicate that the proposed MTR-VFO framework is more effective than some existing typical methods and it has the potential of solving computationally expensive problems more efficiently.

The extreme locations of LF models are utilized to improve the accuracy of HF models and a MTR method is first proposed for local search without utilizing HF gradient. Besides, a novel MTR-VFO framework is presented which is verified to be more effective than some existing typical methods and shows great potential of solving computationally expensive problems effectively.

As the infrastructure of the railway, the rail could sink or deform to different degrees due to the impact of train operation or the geological changing force for years, which will lead to the possibility that the facilities on both sides of the rail invade the rail clearance and bring hidden dangers to the safe operation of the train. The purpose of this paper is to design the gauge to measure the clearance parameters of rail.

Aiming at the problem, the gauge for clearance measurement was designed based on a combination measurement method in this paper. It consists of the measurement box and the rail measurement vehicle, which integrates a laser displacement sensor, inclination sensor, gauge sensor and mileage sensor. The measurement box was placed outside the rail vehicle. Through the design of a hardware circuit and software system, the movement measurement of the clearance parameters was realized.

In this paper, the measurement equations of horizontal distance and vertical height were established, the optimal solutions of the structural parameters in the equations were obtained by Levenberg–Marquardt method, then the parameter calibration problem was also solved.

The gauge has high precision; its measurement uncertainty reaches 1.27 mm. The gauge has manual and automatic working modes, which are convenient to operate and have practical popularization value.

This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source.

The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method.

The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted.

The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

To reduce the computational complexity per step from O(n²) to O(n) for optimization based on quadratic surrogates, where n is the number of design variables.

Applying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitively expensive when the complexity of the simulation codes is large. Increasingly, response surface approximations (RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimizers in order to reduce the CPU time required for the optimization of complex multidisciplinary systems. For evaluation by the optimizer, RSAs provide a computationally inexpensive lower fidelity representation of the system performance. The curse of dimensionality is a major drawback in the implementation of these approximations as the amount of required data grows quadratically with the number n of design variables in the problem. In this paper a novel technique to reduce the magnitude of the sampling from O(n²) to O(n) is presented.

The technique uses prior information to approximate the eigenvectors of the Hessian matrix of the RSA and only requires the eigenvalues to be computed by response surface techniques. The technique is implemented in a sequential approximate optimization algorithm and applied to engineering problems of variable size and characteristics. Results demonstrate that a reduction in the data required per step from O(n²) to O(n) points can be accomplished without significantly compromising the performance of the optimization algorithm.

A reduction in the time (number of system analyses) required per step from O(n²) to O(n) is significant, even more so as n increases. The novelty lies in how only O(n) system analyses can be used to approximate a Hessian matrix whose estimation normally requires O(n²) system analyses.

To propose a new method for solving constrained global optimization problems using a method that consists of transforming a constrained global optimization problem into an unconstrained one without using any penalty coefficients.

Use of an unconstrained global optimization method such as the Alienor method which has been adapted for several variables.

Use of the adapted Alienor method allowed the solution of the transformed problem with little difficulty.

Transforms the original objective function into a new one involves the introduction of some extra parameters. Cannot guarantee the convergence to a global solution of the original problem. The simple described approach, provides new possibilities.

No further parameters introduced in this new approach, and no conditions or hypotheses are imposed on the objective function or on the constraints.

New method of transforming a constrained problem into an unconstrained one, with use of proven Alienor method adapted to several variables.

This paper aims to introduce the usage of sensitivity analysis (SA) for the problem of faults identification in three-phase induction motors (IMs). These motors are susceptible to different kinds of faults that should be detected in a proper time to keep the systems working in a safety environment.

One of the effective approaches for faults identifications, which is presented in the literature, is a model-based strategy. This strategy mainly depends on using a software model to make an identification decision. Therefore, this work intends to examine the model sensitivity towards variables’ variation. The SA toolbox of Matlab R2017b package is used for this purpose since the Matlab software is a well-known environment, and it is easy for a nonstatistical person to deal with it. As a study case, open-circuit and stator inter-turn faults in the stator windings of a three-phase IM have been chosen.

The results show that the model-based strategy is considerably speed up by up to 30% when neglecting the trivial model’s parameters with the same accurate identification decision as compared with the results of this strategy without using the SA.

The novelty of this work is summarized in devoting the usage of SA in the field of faults identification to enhance the speed of final decision.

To investigate the feasibility of using single/multi variable optimisation techniques with vibration measurements in solving the inverse crack identification problem.

The finite element method is used to solve the forward crack problem with a special nodal crack force approach. The multi‐variable optimisation approach is reduced to a much more efficient single‐variable one by decoupling the physical variables in the problem.

It is shown that, for the crack identification problem, global optimisation algorithms perform much better than other algorithms relying heavily on objective function gradients. Simultaneous identification of crack size and location proved to be difficult. Decoupling of the physical variable is introduced and proved to provide efficient results with single‐variable optimisation algorithms.

Need for improving the reliability and accuracy of the procedure for smaller crack sizes. Need for developing and investigation more rigorous and robust multi‐variable optimisation algorithm.

Any information about approximate crack size and location provides significant aid in the maintenance and online monitoring of rotating equipment.

The paper offers practical approach and procedure for online monitoring and crack identification of slow rotating equipment.

The purpose of this paper is to review the progress made in arc welding automation using trajectory planning, seam tracking and control methodologies.

This paper discusses key issues in trajectory planning towards achieving full automation of arc welding robots. The identified issues in trajectory planning are real-time control, optimization methods, seam tracking and control methodologies. Recent research is considered and brief conclusions are drawn.

The major difficulty towards realizing a fully intelligent robotic arc welding system remains an optimal blend and good understanding of trajectory planning, seam tracking and advanced control methodologies. An intelligent trajectory tracking ability is strongly required in robotic arc welding, due to the positional errors caused by several disturbances that prevent the development of quality welds. An exciting prospect will be the creation of an effective hybrid optimization technique which is expected to lead to new scientific knowledge by combining robotic systems with artificial intelligence.

This paper illustrates the vital role played by optimization methods for trajectory design in arc robotic welding automation, especially the non-gradient approaches (those based on certain characteristics and behaviour of biological, molecular, swarm of insects and neurobiological systems). Effective trajectory planning techniques leading to real-time control and sensing systems leading to seam tracking have also been studied.

In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).

In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.

The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.

The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

The paper proposed a fast procedure for solving the reliability-based robust design optimization (RBRDO) by modifying the RBRDO formulation and transforming it into a series of RBRDO subproblems. Then for each subproblem, the objective function, constraint function and reliability index are approximated using Taylor series expansion, and their approximate forms depend on the deterministic design vector rather than the random vector and the uncertain estimation in the inner loop of RBRDO can be avoided. In this way, it can greatly reduce the evaluation number of performance function. Lastly, the trust region method is used to manage the above sequential RBRDO subproblems for convergence.

As is known, RBRDO is nested optimization, where the outer loop updates the design vector and the inner loop estimate the uncertainties. When solving the RBRDO, a large evaluation number of performance functions are needed. Aiming at this issue, the paper proposed a fast integrated procedure for solving the RBRDO by reducing the evaluation number for the performance functions. First, it transforms the original RBRDO problem into a series of RBRDO subproblems. In each subproblem, the objective function, constraint function and reliability index caused are approximated using simple explicit functions that solely depend on the deterministic design vector rather than the random vector. In this way, the need for extensive sampling simulation in the inner loop is greatly reduced. As a result, the evaluation number for performance functions is significantly reduced, leading to a substantial reduction in computation cost. The trust region method is then employed to handle the sequential RBRDO subproblems, ensuring convergence to the optimal solutions. Finally, the engineering test and the application are presented to illustrate the effectiveness and efficiency of the proposed methods.

The paper proposes a fast procedure of solving the RBRDO can greatly reduce the evaluation number of performance function within the RBRDO and the computation cost can be saved greatly, which makes it suitable for engineering applications.

The standard deviation of the original objective function of the RBRDO is replaced by the mean and the reliability index of the original objective function, which are further approximated by using Taylor series expansion and their approximate forms depend on the deterministic design vector rather than the random vector. Moreover, the constraint functions are also approximated by using Taylor series expansion. In this way, the uncertainty estimation of the performance functions (i.e. the mean of the objective function, the constraint functions) and the reliability index of the objective function are avoided within the inner loop of the RBRDO.