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Active-learning surrogate model–based reliability analysis is widely employed in engineering structural reliability analysis to alleviate the computational burden of the Monte Carlo method. To date, most of these methods are built based on the single-fidelity surrogate model, such as the Kriging model. However, the computational burden of constructing a fine Kriging model may be still expensive if the high-fidelity (HF) simulation is extremely time-consuming. To solve this problem, an active-learning method based on the multi-fidelity (MF) Kriging model for structural reliability analysis (abbreviated as AMK-MCS+AEFF), which is an online data-driven method fusing information from different fidelities, is proposed in this paper. First, an augmented expected feasibility function (AEFF) is defined by considering the cross-correlation, the sampling density, and the cost query between HF and low-fidelity (LF) models. During the active-learning process of AMK-MCS+AEFF, both the location and fidelity level of the updated sample can be determined objectively and adaptively by maximizing the AEFF. Second, a new stopping criterion that associates with the estimated relative error is proposed to ensure that the iterative process terminates in a proper iteration. The proposed method is compared with several state-of-the-art methods through three numerical examples and an engineering case. Results show that the proposed method can provide an accurate failure probability estimation with a less computational cost.

The Kriging-based reliability analysis is extensively adopted in engineering structural reliability analysis for its capacity to achieve accurate failure probability estimation with high efficiency. Generally, the Kriging-based reliability analysis is an active-learning process that mainly includes three aspects: (1) the determination of the design space; (2) the rule of choosing new samples, i.e., the learning function; and (3) the stopping criterion of the active-learning process. In this work, a new learning function and an error-based stopping criterion are proposed to enhance the efficiency of the active-learning Kriging-based reliability analysis. First, the reliability-based lower confidence bounding (RLCB) function is proposed to select the update points, which can balance the exploration and exploitation through the probability density-based weight. Second, an improved stopping criterion based on the relative error estimation of the failure probability is developed to avoid the pre-mature and late-mature of the active-learning Kriging-based reliability analysis method. Specifically, the samples that have large probabilities to change their safety statuses are identified. The estimated relative error caused by these samples is derived as the stopping criterion. To verify the performance of the proposed RLCB function and the error-based stopping criterion, four examples with different complexities are tested. Results show that the RLCB function is competitive compared with state-of-the-art learning functions, especially for highly non-linear problems. Meanwhile, the new stopping criterion reduces the computational resource of the active-learning process compared with the state-of-the-art stopping criteria.

Kriging surrogate model has been widely used in engineering design optimization problems to replace computational cost simulations. To facilitate the usage of the Kriging surrogate model-assisted engineering optimization design, there are still challenging issues on the updating of Kriging surrogate model for the constraints, since there exists prediction error between the Kriging surrogate model and the real constraints. Ignoring the interpolation uncertainties from the Kriging surrogate model of constraints may lead to infeasible optimal solutions. In this paper, general sequential constraints updating approach based on the confidence intervals from the Kriging surrogate model (SCU-CI) are proposed. In the proposed SCU-CI approach, an objective switching and sequential updating strategy is introduced based on whether the feasibility status of the design alternatives would be changed because of the interpolation uncertainty from the Kriging surrogate model or not. To demonstrate the effectiveness of the proposed SCU-CI approach, nine numerical examples and two practical engineering cases are used. The comparisons between the proposed approach and five existing approaches considering the quality of the obtained optimum and computational efficiency are made. Results illustrate that the proposed SCU-CI approach can generally ensure the feasibility of the optimal solution under a reasonable computational cost.

The hexagonal periodic structure of the honeycomb is a magic product of nature and shows great mechanical potential. In this work, a type of metamaterial vibration isolator with a honeycomb structure is proposed. The strain, deformation, and natural frequency of the vibration isolator are calculated by the two-dimensional plane finite element model and the simulation accuracies are validated by the experiments. As the design of the metamaterial vibration isolator involves time-consuming finite-element simulation, a multi-fidelity sequential optimization approach based on feasible region analysis (MF-FA) is proposed. In the proposed method, the refined and coarse mesh models are developed as the high- and low-fidelity models, and a two-phase multi-fidelity updating strategy is carried out. In the first phase, sample points are added to the constraint boundary to find the feasible solution quickly, in the second phase, the quality of the feasible optimization solution is gradually improved in the feasible region until it converges to the global optimal solution. Finally, the optimized metamaterial vibration isolator is manufactured and its superiority is validated. Results illustrate that the proposed approach can obtain a desirable optimum, whose natural frequency error between the experimental and the expected value is improved by 12.67% compared with the initial design.

The influence of inner fillet radius, as part of the shear deformation zone, on effective strain homogeneity in equal channel angular pressing (ECAP) of AZ91 magnesium alloy was analyzed in this paper. The uniaxial compression and ring upsetting were carried out to obtain the true stress-strain curve of AZ91 billet and friction factor between billet and die, respectively. The flow net experiment and hardness testing experiment were used to verify the simulation results. The results show the inner fillet radius, as the secondary factor (as we all known, the outer corner angle was the most important factor), had an influence on both the quantity and distribution of effective strain. With the increment of inner fillet radius, the effective strain value decreased in both the inner and outer regions. This mainly attributed to the alleviating effect of compression stress of extruded billet in ECAP.

In this paper, SBSC+SRU: an error-guided adaptive Kriging modeling method is proposed for the system reliability analysis with multiple failure modes. Therein, the accuracies of Kriging models will be improved by a novel learning function, in which the magnitude of Component Limit State Functions (CLSFs), uncertainties of Kriging models, and the coupling relationships among CLSFs are considered to identify the location and component index of the new sample. Then, the maximum estimated relative error of predicted failure probability is derivated by quantifying the probability of wrong sign prediction of samples. To be specific, the highly uncertain samples are first defined, after that the probability of wrong sign prediction of each highly uncertain sample is deduced combining the predictions of Kriging models and coupling relationship among all CLSFs. Therefore, the proposed approach knows the real-time estimated error and could terminate the adaptive updating process under the accuracy requirement. Three numerical examples including parallel and series system problems and an engineering case concerning the system reliability analysis of a stiffened cylindrical shell are studied to validate the performance of the proposed method. Results demonstrate that the proposed method converges to the required estimated accuracy while saving considerable computational burdens compared with state-of-the-art approaches.

The problem of locating a contour widely exists in the engineering product design, such as the constrained optimization problem, reliability analysis, and so on. The surrogate model-assisted contour prediction methods have gained more attention lately because they can alleviate the computational burden significantly compared with the traditional simulation-based approaches. Representatively, the method built on the expected improvement (EI) infill criterion can allocate a contour from expensive simulations by refining the Kriging model with high-fidelity (HF) samples sequentially. Recently, the multi-fidelity (MF) Kriging model has gained remarkable attention because it integrates the accurate but costly HF model and cheap but biased low-fidelity (LF) model to provide an accurate prediction of the original black-box system. To facilitate the usage of the MF Kriging model in the contour prediction, a novel sequential multi-fidelity surrogate model-assisted contour prediction method is developed in this work. First, an extended expected improvement (EEI) infill criterion is developed to overcome the shortcoming of the original EI criterion on determining the locations and fidelity level of new samples. The developed EEI criterion can quantify the improvement of a sample from different fidelities over the contour of interest by considering the relative correlation between different fidelities. Second, considering the significant effect of the high-to-low simulation cost ratio on the MF Kriging model, the proposed approach selects an HF sample or several LF samples with equivalent computational resources to refine the MF Kriging model in each cycle according to their total improvements to the contour of interest. To this end, the EEI criterion is further revised combining a parallel strategy to generate the LF samples. The performance of the proposed approach is tested on three numerical examples with different complexities and an engineering case. The results show that the proposed approach has better efficiency, prediction accuracy, and robust performance compared with several state-of-the-art methods.

To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian (CEL) method in predicting close-range air blast loads of cylindrical charges, a neural network-based simulation (NNS) method with higher accuracy and better efficiency was proposed. The NNS method consisted of three main steps. First, the parameters of blast loads, including the peak pressures and impulses of cylindrical charges with different aspect ratios (L/D) at different stand-off distances and incident angles were obtained by two-dimensional numerical simulations. Subsequently, incident shape factors of cylindrical charges with arbitrary aspect ratios were predicted by a neural network. Finally, reflected shape factors were derived and implemented into the subroutine of the ABAQUS code to modify the CONWEP model, including modifications of impulse and overpressure. The reliability of the proposed NNS method was verified by related experimental results. Remarkable accuracy improvement was acquired by the proposed NNS method compared with the unmodified CONWEP model. Moreover, huge efficiency superiority was obtained by the proposed NNS method compared with the CEL method. The proposed NNS method showed good accuracy when the scaled distance was greater than 0.2 m/kg1/3. It should be noted that there is no need to generate a new dataset again since the blast loads satisfy the similarity law, and the proposed NNS method can be directly used to simulate the blast loads generated by different cylindrical charges. The proposed NNS method with high efficiency and accuracy can be used as an effective method to analyze the dynamic response of structures under blast loads, and it has significant application prospects in designing protective structures. •A neural network-based simulation method (NNS) for air-blast loads was proposed.•The effect of aspect ratio of cylindrical charge on air-blast loads was considered.•Remarkable accuracy improvement was acquired by NNS compared with CONWEP model.•Huge efficiency superiority was obtained by NNS compared with CEL method.

Vessel-mounted cranes operate in complex marine environments, where precise measurement of cargo positions and attitudes is a key technological challenge to ensure operational stability and safety. This study introduces an integrated measurement system that combines vision and inertial sensing technologies, utilizing a stereo camera and two inertial measurement units (IMUs) to capture cargo motion in five degrees of freedom (DOF). By merging data from the stereo camera and IMUs, the system accurately determines the cargo’s position and attitude relative to the camera. The specific methodology is introduced as follows: First, the YOLO model is adopted to identify targets in the image and generate bounding boxes. Then, using the principle of binocular disparity, the depth within the bounding box is calculated to determine the target’s three-dimensional position in the camera coordinate system. Simultaneously, the IMU measures the attitude of the cargo, and a Kalman filter is applied to fuse the data from the two sensors. Experimental results indicate that the system’s measurement errors in the x, y, and z directions are less than 2.58%, 3.35%, and 3.37%, respectively, while errors in the roll and pitch directions are 3.87% and 5.02%. These results demonstrate that the designed measurement system effectively provides the necessary motion information in 5-DOF for vessel-mounted crane control, offering new approaches for pose detection of marine cranes and cargoes.

When agricultural vehicles operate in the field, the soft road excitation makes it difficult to measure the vehicle vibration. A camera-accelerator system can solve this issue by utilizing computer vision information; however, the relationship between the field road surface and the vehicle vibration response remains an unsolved problem. This study aims to investigate the correlation of the soft road excitation of different long-wave surfaces with the vehicle vibration response. Vibration equation between the vehicle and soft road surface system was established to produce an effective roughness model of the field soft road surface. In order to simulate the vehicle vibration state under different long-wave road surfaces, the soil rectangular pits with 21 kinds of different spans and depths were applied to the road surfaces, and a tractor vibration test system was built for vibration test. The frequency spectrum analysis was performed for the vibration response and the roughness signals of the road surfaces. The results showed that coefficient (R2) of frequency correlation between the roughness excitation and the original unevenness at the excitation point at the rear end of the rectangular soil pit fell within 0.9641∼0.9969. The main frequency band of the vibration response fell within 0∼3 Hz, and the phenomenon of quadruple frequency existed. The correlation of roughness excitation with quadruple frequency fell within 0.992165∼1. The primary excitation points were located at the rear end of the rectangular soil pit. In addition, it also indicated that when the vehicle was driven without autonomous power, the vehicle vibration frequency mainly depended on the excitation frequency of the field road surface and the frequency at the maximum vehicle vibration intensity was 2 or 3 times of that at the maximum field soft road excitation. These findings may provide a reference for optimal design of vibration reduction and control for agricultural vehicles.