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This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method.

An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers.

The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions.

A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

The uncertainty of the interval variable is represented by interval factor, and the interval variable is described as its mean value multiplied by its interval factor. Based on interval arithmetic rules, an analytical method of interval finite element for uncertain structures but not probabilistic structure or fuzzy structure is presented by combining the interval analysis with finite element method. The static analysis of truss with interval parameters under interval load is studied and the expressions of structural interval displacement response and stress response are deduced. The influences of uncertainty of one of structural parameters or load on the displacement and stress of the structure are examined through examples and some significant conclusions are obtained.

The purpose of this paper is to target on designing a short-term load prediction framework that can accurately predict the cooling load of office buildings.

A feature selection scheme and stacking ensemble model to fulfill cooling load prediction task was proposed. Firstly, the abnormal data were identified by the data density estimation algorithm. Secondly, the crucial input features were clarified from three aspects (i.e. historical load information, time information and meteorological information). Thirdly, the stacking ensemble model combined long short-term memory network and light gradient boosting machine was utilized to predict the cooling load. Finally, the proposed framework performances by predicting cooling load of office buildings were verified with indicators.

The identified input features can improve the prediction performance. The prediction accuracy of the proposed model is preferable to the existing ones. The stacking ensemble model is robust to weather forecasting errors.

The stacking ensemble model was used to fulfill cooling load prediction task which can overcome the shortcomings of deep learning models. The input features of the model, which are less focused on in most studies, are taken as an important step in this paper.

Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.

Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.

VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

The purpose of this paper is to focus on the influences of the uncertain dynamic responses on the reconstruction of loads.

Based on the assumption of unknown-but-bounded (UBB) noise, a time-domain approach to estimate the uncertain time-dependent external loads is presented by combining the inverse system method in modern control theory and interval analysis in interval mathematics. Inspired by the concept of set membership identification in control theory, an interval analysis model of external loads time history, which is indeed a region or feasible set containing all possible loads being consistent with the bounded structural acceleration responses is established and further solved by two interval algorithms.

Unlike traditional loads identification methods which only give a point estimation, an interval estimation of external loads time history, which is a region containing all the possible loads being consistent with the uncertain structural responses, is determined. The correlation characteristics among the responses of acceleration, velocity, and displacement are also discussed in consideration of the UBB uncertainty.

For one hand, the solution of the inverse problem in original system is transformed to the solution of the direct problem in inverse system; for another, the authors deal with the uncertainty by use of interval analysis method, and the identified interval process, which contains any possible external loads time history being consistent with the bounded structural responses can be approximately obtained.

This paper aims to develop a dynamic two-sided stable matching method based on preference information of the matching objects in uncertain environments, so as to solve the matching problem of cloud manufacturing tasks and services with load balancing.

For dynamic two-sided matching, due to the complexity of social environment and the limitation of human cognition, hesitation and fuzziness always exist in the process of multi-criteria assessment. First, in order to obtain the accurate preference information of each matching object, uncertain linguistic variables, uncertain preference ordinal and incomplete complementary matrices are used to evaluate multi-criteria preference information. This process is undertaken by considering the probability of each possible matching pair. Second, the preference information at different times is integrated by using the time-series weight to obtain the comprehensive satisfaction degree matrices of the matching objects. Further, the load adjustment parameter is used to increase the satisfaction degree of the matching objects. Afterward, a dynamic two-sided stable matching optimization model is constructed by considering stable matching conditions. The model aims to maximize the satisfaction degree and minimizes the difference in the satisfaction degree of matching objects. The optimal stable matching results can be obtained by solving the optimization model. Finally, a numerical example and comparative analysis are presented to demonstrate the characteristics of the proposed method.

Uncertain linguistic variables, uncertain preference orders and incomplete complementary matrices are used to describe multi-criteria preference information of the matching objects in uncertain environments. A dynamic two-sided stable matching method is proposed, based on which a DTSMDM (dynamic two-sided matching decision-making) model of cloud manufacturing with load balancing can be constructed. The study proved that the authors can use the proposed method to obtain stable matching pairs and higher matching objective value through comparative analysis and the sensitivity analysis.

A new method for the two-sided matching decision-making problem of cloud manufacturing with load balancing is proposed in this paper, which allows the matching objects to elicit language evaluation under uncertain environment more flexibly to implement dynamic two-sided matching based on preference information at different times. This method is suitable for dealing with a variety of TSMDM (two-sided matching decision-making) problems.

The purpose of this paper is to provide a new computational method based on the polynomial chaos (PC) expansion to identify the uncertain parameters of load sensing proportional valve (LSPV), which is commonly used to improve the efficiency of brake system in heavy truck.

For this investigation, the mathematic model of LSPV is constructed in the form of state space equation. Then the estimation process is implemented relying on the experimental measurements. With the coefficients of the PC expansion obtained by the numerical implementation, the output observation function can be transformed into a linear and time-invariant form. The uncertain parameter recursively update functions based on Newton method can therefore be derived fit for computer calculation. To improve the estimation accuracy and stability, the Newton method is modified by employing the acceptance probability to escape from the local minima during the estimation process.

The accuracy and effectiveness of the proposed parameter estimation method are confirmed by model validation compared with other estimation methods. Meanwhile, the influence of measurement noise on the robustness of the estimation methods is taken into consideration, and it is shown that the estimation approach developed in this paper could achieve impressive stability without compromising the convergence speed and accuracy too much.

The model of LSPV is originally developed in this paper, and then the authors propose a novel effective strategy for recursively estimating uncertain parameters of complicate pneumatic system based on the PC theory.

This paper aims to present an evaluation method for energy-absorption characteristics of thin-walled composite structures with random uncertain parameters.

The mechanical properties of T700/3234 are obtained by material performance tests and energy-absorption results are obtained by quasi-static crushing tests of thin-walled composite circular tubes. The indicators of triggering specific load (TSL) and specific energy absorption (SEA) are introduced and calculated to determine the energy-absorption characteristics and validate the probability finite element analysis model. The uncertainty in the parameters contain the machining tolerance for the thickness and inner diameter of composite circular tubes and are associated with the composite material system. The Plackett–Burman method is used to choose the measurement parameters. Then, the response surface method is used to build a second-order function of random uncertain parameters versus TSL/SEA, and the Monte Carlo method is finally used to obtain the probabilities of TSL and SEA.

The finite element models can accurately simulate the initial peak load, load-displacement curve and SEA value. The random uncertain parameter method can be used to evaluate the energy-absorption characteristics of thin-walled composite circular tubes.

The presented evaluation method for energy-absorption characteristics of thin-walled composite structures is an approach that considers uncertain parameters to increase the simulation accuracy and decrease the computational burden.

This methodology considers uncertain parameters in evaluating the energy-absorption characteristics of thin-walled composite structures, and this methodology can be applied to other thin-walled composite structures.

This paper aims on the trajectory tracking of the developed six wheel-legged robot with heavy load conditions under uncertain physical interaction. The accuracy of trajectory tracking and stable operation with heavy load are the main challenges of parallel mechanism for wheel-legged robots, especially in complex road conditions. To guarantee the tracking performance in an uncertain environment, the disturbances, including the internal friction, external environment interaction, should be considered in the practical robot system.

In this paper, a fuzzy approximation-based model predictive tracking scheme (FMPC) for reliable tracking control is developed to the six wheel-legged robot, in which the fuzzy logic approximation is applied to estimate the uncertain physical interaction and external dynamics of the robot system. Meanwhile, the advanced parallel mechanism of the electric six wheel-legged robot (BIT-NAZA) is presented.

Co-simulation and comparative experimental results using the BIT-NAZA robot derived from the developed hybrid control scheme indicate that the methodology can achieve satisfactory tracking performance in terms of accuracy and stability.

This research can provide theoretical and engineering guidance for lateral stability of intelligent robots under unknown disturbances and uncertain nonlinearities and facilitate the control performance of the mobile robots in a practical system.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.