Practical Engineering Example Research Articles

An active learning reliability method combining population Monte Carlo and Kriging model for small failure probability

This study investigates the analysis of small failure probability problems and proposes the AK-PMC method, which combines the Population Monte Carlo (PMC) method with an active learning Kriging model (AK). The PMC method, as a variant of importance sampling, iteratively improving the quality of particles by reweighting them and updating the proposal distributions. In AK-PMC, Kriging model and PMC collaborate with each other. In each iteration, PMC draws potential importance samples according to the prediction information of Kriging model and Kriging is updated by choosing an optimal training point among the importance samples of PMC. After several iterations, the importance samples of PMC will cover the important failure regions and the Kriging model will accurately predict the limit state surface. To avoid the waste of training points, the relative error of failure probability estimated by PMC is derived by considering the prediction information of Kriging model. Three numerical examples and one practical engineering example are investigated to verify the performance of the proposed method.

Theta-regularized Kriging: Modeling and algorithms

To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived the optimization problem for this model from a maximum likelihood perspective. Additionally, we presented specific implementation details for the iterative process, including the regularized optimization algorithm and the geometric search cross-validation tuning algorithm. Three distinct penalty methods, Lasso, Ridge, and Elastic-net regularization, were meticulously considered. Meanwhile, the proposed Theta-regularized Kriging models were tested on nine common numerical functions and two practical engineering examples. The results demonstrate that, compared with other penalized Kriging models, the proposed model performs better in terms of accuracy and stability.

Dynamic modeling of a sliding ring on an elastic rod with incremental potential formulation

Abstract Mechanical interactions between rigid rings and flexible cables find broad application in both daily life (hanging clothes) and engineering system (closing a tether-net). A reduced-order method for the dynamic analysis of sliding rings on a deformable one-dimensional (1D) rod-like object is proposed. In contrast to the conventional approach of discretising joint rings into multiple nodes and edges for contact detection and numerical simulation, a single point is used to reduce the order of the model. To ensure that the sliding ring and flexible rod do not deviate from their desired positions, a new barrier function is formulated using the incremental potential theory. Subsequently, the interaction between tangent frictional forces is obtained through a delayed dissipative approach. The proposed barrier functional and the associated frictional functional are C2 continuous, hence the nonlinear elastodynamic system can be solved variationally by an implicit time-stepping scheme. The numerical framework is initially applied to simple examples where the analytical solutions are available for validation. Then, multiple complex practical engineering examples are considered to showcase the effectiveness of the proposed method. The simplified ring-to-rod interaction model has the capacity to enhance the realism of visual effects in image animations, while simultaneously facilitating the optimisation of designs for space debris removal systems.

Calculation method and evaluation of surrounding rock pressure of vertical shaft

The surrounding rock pressure of vertical shafts is one of the basic parameters of shaft lining design. Investigating its calculation methods and applicable scopes has great engineering significance. The paper classifies and compares the calculation methods, discusses the application scopes of various calculation methods, and proposes that the axisymmetric layered method is highly consistent with the field monitoring data for the calculation of surrounding rock pressure of vertical shafts in bedrock sections on the basis of practical engineering examples. On the basis of Terzaghi theory, the calculation formula of surrounding rock pressure of vertical shaft in inclined rock strata with single group joints is derived. The formula can reflect the influence of rock strata dip angle and joints.

The Aerobic Granules Process for Wastewater Treatment: From Theory to Engineering

Aerobic granules are small, dense aggregates of microbial cells that form naturally in aerobic wastewater treatment systems. They are characterized by their spherical shape, strong structural integrity, and ability to rapidly settle. These granules are formed through a self-immobilization process where different microbial species coalesce to degrade organic and inorganic compounds in wastewater. This study summarizes the development of aerobic granulation technology in wastewater treatment and the mechanism of aerobic granules’ formation, analyzes the characteristics and the factors affecting the aerobic granules’ formation, and presents practical engineering examples of its application from pilot-scale to full-scale operation.

Urban distribution network planning and zoning design based on improved K-means clustering in low carbon background

Abstract Aiming at the problem that the traditional algorithm is difficult to adapt to the chaotic planning of urban distribution network and the uneven distribution of load points, an improved K-means clustering algorithm based zoning planning method of urban distribution network is proposed. Firstly, considering the effect of the capacity margin on the partition, the weighted factor is introduced to improve the Euclidean distance. Secondly, considering the selection of power supply units according to the distribution characteristics of the substation, the distance between the cluster center and the substation is calculated. Finally, a distribution network zoning planning model with the maximum number of inter-station power supply units and the minimum total Euclidean distance of power distribution as the objective function is constructed. Finally, taking the transformation of a distribution network in Fujian Province as a practical engineering example, the results show that the average difference of load partition obtained by the improved K-means clustering algorithm is reduced by 34.35% compared with the traditional method.

Structural damage identification under ambient temperature variations based on CNN and normalized modal flexibility-autoregressive coefficients hybrid index

This study proposes a novel method to identify structural damage considering ambient temperature variations. In this method, the normalized modal flexibility based index (nMFBI) and autoregressive (AR) coefficients are combined to form the nMFBI-AR hybrid index, and convolutional neural networks (CNN) are exploited to locate and quantify the damage. Moreover, the effects of ambient temperature variations and measurement noise are not considered in the training dataset, which is preferable in practical engineering. To verify the effectiveness of the proposed method, firstly, a numerical structure of a simply supported beam is investigated, and the performance of the nMFBI-AR index is evaluated by making a comparison with the nMFBI and AR indexes. Then, the proposed method is further verified by a test model of a three-story frame and a practical engineering example of a continuous rigid frame bridge. The results demonstrate that although the influence of ambient temperature variations and measurement noise are only considered in the test datasets, this approach has the best performance in locating and quantifying structural damage, and the errors are less than 16%, which is promising. In addition, this paper provides a guideline and a new idea for the study of damage index based on time-frequency hybrid information.

The Application of Membrane Separation Technology in the Pharmaceutical Industry.

With the advancement in membrane technology, membrane separation technology has been found increasingly widespread applications in the pharmaceutical industry. It is utilized in drug separation and purification, wastewater treatment, and the recycling of wastewater resources. This study summarizes the application history of membrane technology in the pharmaceutical industry, presents practical engineering examples of its applications, analyzes the various types of membrane technologies employed in the pharmaceutical sector, and finally, highlights the application cases of renowned international and Chinese membrane technology companies in the pharmaceutical field.

Interface reduction technique for Enhanced Craig-Bampton method

Substructure coupling and model order reduction using Component Mode Synthesis (CMS) have, over recent years, gained considerable attention in the vibroacoustic analysis of complex structures. In the CMS methodology, the interior dynamics of each subcomponent in a substructured system are represented by a truncated set of normal modes within the lower frequency range, while all physical degrees of freedom (DOFs) at the interface are retained. In cases where there are many interconnected subcomponents within a system, in particular when these components are finely discretised in the Finite Element (FE) domain, the reduced system matrices may still involve a significant number of equations. This, in turn, leads to a considerable computational workload. To address this issue, further reduction of the system matrices concerning the interface DOFs by using a set of truncated interface modes can be considered. However, the accuracy of the reduced matrices depends on the representation of the truncated dynamics in the reduction process. In this work, two interface reduction techniques are presented to truncate the interface dynamics of the Enhanced Craig-Bampton (ECB) equations of motion. The first technique is a classical interface reduction approach that assumes decoupled internal and interface dynamics. The second approach is an extension of the first one by incorporating an additional coupling term that accounts for interactions between the truncated internal and interface dynamics. The performance of each interface reduction technique is evaluated by applying them to three practical engineering examples. In these instances, resonance frequencies, associated errors, transfer functions, and normal modes are compared to those obtained using both the classical CB method and the full model.

A new adaptive multi-kernel relevance vector regression for structural reliability analysis

Surrogate models have been widely used in structural reliability analysis to improve the computational efficiency and the accuracy of failure probability. Recently, several multi-kernel relevance vector regression (MKRVR) models have been studied to evaluate the failure probability. However, existing multiple kernel functions for relevance vector regression models are fixed choices, which increases the number of calls to the limit state function (LSF) and leads to inaccurate results. To address the problem, this paper presents a new adaptive MKRVR model combined with Monte Carlo simulation (MCS). Firstly, a stepwise kernel selection strategy is developed to adaptively select better-performing kernel functions and eliminate redundant kernel functions for constructing the MKRVR model. Secondly, a new active learning function is proposed by considering the probability of mis-prediction and spatial locations of the existing sampling point to identify the new training sample points. Thirdly, a hybrid efficient stopping criterion is adopted to terminate the learning process automatically. Three benchmark examples and one practical engineering example are introduced to demonstrate the effectiveness of the proposed method. Results show that the proposed method can provide accurate failure probability by less number of calls to the LSF than existing fixed kernel-based methods.

Yard Space Allocation Algorithm for Unloading Containers at Marine Terminals

The issue of unloading efficiency for containers is the operational bottleneck for most traditional container terminals. In addressing the intricate challenges of space allocation in container yards during ship unloading, this study focuses on the real-time, dynamic decision-making needs that are currently unmet by existing planning methods. To tackle this, the article introduces a novel model for container space allocation that aims to maximize the “attractiveness” of yard spaces. This model factors in key considerations like the allocation of container handling equipment resources, the rate of container handling equipment traversing the yard, and container handling equipment operations across containers. A unique Monte Carlo tree search (MCTS)-based algorithm is developed to solve this multi-objective problem. The algorithm’s efficacy is rigorously tested via numerical experiments, where it outperforms existing approaches like UCT-MCTS, AMAF-MCTS, and manual scheduling plans using practical engineering examples. This research not only provides a more dynamic and efficient method for yard space allocation but also offers empirical evidence to support its practicality and effectiveness.

Harmonic Loss Calculation Method Based on Fourier Expansion for HVDC System Transformer

The harmonics generated by devices in HVDC (High Voltage Direct Current) system and the harmonics input at the grid side have a great impact on the loss assessment of the converter transformer. Therefore, this paper proposes a simplified and efficient harmonic loss algorithm based on the classical transformer harmonic model, and Fourier transform and generates the code in MATLAB software. Practical engineering examples have proved that the proposed algorithm can accurately calculate the load loss and harmonic loss of the rheology by filtering data in the HVDC system. Therefore, it can solve the problems such as unclear calculation of harmonic resistance in existing standard theoretical algorithms or difficulty in obtaining test data of stray loss and eddy current loss at the fundamental frequency.

Application of Adaptive Neuro-Fuzzy Inference Systems with Principal Component Analysis Model for the Forecasting of Carbonation Depth of Reinforced Concrete Structures

The carbonation of reinforced concrete is one of the intrinsic factors that cause a significant decrease in service performance in concrete structures. To decrease the effect of carbonation-induced corrosion during the lifetime of the concrete structure, a prediction of carbonation depth should be made. The carbonation of concrete is affected by many factors, such as the compressive strength of the concrete, service life, carbonation time, carbon dioxide concentration, working stress, temperature, and humidity. On the basis of these seven parameters, combined with the predictive power of the adaptive network-based fuzzy inference system (ANFIS) and principal component analysis (PCA), which can reduce data dimensions before modeling, we introduced a novel approach—the PCA–ANFIS model—that can predict the carbonation of reinforced concrete. Practical engineering examples were adopted to verify the superiority of the suggested PCA–ANFIS model, with 90% of the carbonation depth data used for training and 10% used for testing. The root mean square error (RMSE) values for the ANFIS, ANN, PCA–ANN, and PCA–ANFIS training were 12.23, 6.28, 5.42, and 1.38, respectively. The results showed that the PCA–ANFIS model is accurate and can be used as a fundamental tool for predicting the service life of concrete structures.

USE OF ORDINARY DIFFERENTIAL EQUATIONS APPLIED TO MECHANICAL AND ELECTRICAL PROBLEMS WITH FIRST ORDER LINEAR SYSTEMS

In recent years there has been an increased interest in the study of mathematics applied to engineering to study aspects of its teaching. In the present research work, a compilation of analytical concepts of differential equations applied to the solution of problems of electrical circuits, a branch of electrical engineering and mechanical engineering problems, specifical problems of spring-mass mechanical systems, through the description of the analytical solutions of direct current electrical circuits and spring-mass mechanical systems, applying differential equations. This method stands out among the diverse mathematical treatments used to solve this type of engineering problem, both for its demonstrative elegance and capacity to offer a total answer. Likewise, practical engineering examples related to the studied subject were presented and the results were obtained and analyzed by using the mathematical software, Wolfram Mathematica.

Research on input-output evaluation index of high energy consumption main transformer transformation

In order to quantify the input-output evaluation index of high-energy consumption main transformer transformation projects of power grid enterprises, to provide a real, effective, and quantitative basis for investment decisions, the project input and output indexes are measured from the whole life cycle perspective. The whole life cycle cost, including the initial investment and annual operational maintenance cost, is selected as the input evaluation index, and the four dimensions of safety, economics, efficiency, and greenness are considered. The output evaluation index is proposed, combined with the investment effectiveness of typical projects of production technology reform, the potential output analysis indexes under each dimension are sorted out, the full set of output evaluation indexes of production technology reform projects is constructed, the corresponding characteristic indexes of high energy consumption main transformation projects are selected from the full set of indexes, and mathematical evaluation model of input-output analysis of high energy consumption main transformation projects is built. Verify the model through practical engineering examples.

A modified stable node-based smoothed finite element method based on low-quality unstructured mesh

A modified stable node-based smoothed finite element method (M-SNS-FEM) based on linear low-quality unstructured mesh is proposed for two-dimensional elastic static analysis and free vibration analysis. Firstly, the weakened weak formulation based on nodes is considered under finite element background, framing the so-called node-based domains. Secondly, the polygonal smoothing domain around each node is approximated as ellipse for low-quality unstructured mesh, and the locations of auxiliary integration points are further chosen. And then, the integration scheme of M-SNS-FEM is obtained by simplifying the discrete equations acquired by auxiliary integration points. Finally, various problems containing both benchmark cases and practical engineering examples are studied, and the applicability and accuracy of M-SNS-FEM in linear low-quality unstructured mesh can be verified. The results show that the proposed approach can always achieve high accuracy as the mesh quality deteriorates gradually and local mesh deforms sharply.

Generalised Isentropic Relations in Thermodynamics

Isentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations for isentropic transformations in gas dynamics are limited to ideal gases, the inability to analytically describe isentropic processes for non-ideal gases is a fundamental shortcoming. This work presents generalised isentropic relations in thermodynamics based on the work by Kouremenos et al., where three isentropic exponents γPv, γTv and γPT are introduced to replace the ideal gas isentropic exponent γ to incorporate the departure from the non-ideal gas behaviour. The general applicability of the generalised isentropic relations is presented by exploring its connections to existing isentropic models for ideal gases and incompressible liquids. Generalised formulations for the speed of sound, the Bernoulli equation, compressible isentropic flow transformations, and isentropic work are presented thereafter, connecting previously disjoint theories for gases and liquids. Lastly, the generalised expressions are demonstrated for practical engineering examples, and their accuracy is discussed.

Unified reliability-based design optimization with probabilistic, uncertain-but-bounded and fuzzy variables

Reliability-based design optimization (RBDO) is critical in improving the design objective and guaranteeing the safety level of mechanical and engineering structures. However, a large number of multi-source uncertainties exist in the real-world, and their applications pose significant challenges owing to the lack of unity and generality of the RBDO theory and high performance computational methods. This study proposes a unified reliability-based design optimization (URBDO) method to deal with multi-source uncertainties, in which probabilistic, uncertain-but-bounded, and fuzzy parameters are simultaneously considered. First, a novel URBDO model is proposed by combining the probabilistic, non-probabilistic, and fuzzy theories, and it consists of nested quadruple optimization loops. Second, the single-loop URBDO method is further developed based on the Lagrangian function to ease the unaffordable computational burden, where the probabilistic analysis, non-probabilistic analysis, fuzzy analysis, and deterministic optimization are simultaneously implemented. Third, the directional properties of non-probabilistic and fuzzy computations are disclosed, and the directional chaos single-loop method (DCSLM) and conjugate gradient single-loop method (CGSLM) are constructed based on the chaos control theory and conjugate gradient method. Finally, three numerical examples and three practical engineering examples are tested to validate the effectiveness of the proposed URBDO model and the high performances of the DCSLM and CGSLM.

MATLAB‐based program for computation of open‐channel flow profiles

AbstractIn engineering practice, open channel water surface profile data frequently serve as the scientific foundation for engineering design, flood forecasting, reservoir scheduling, and the calculation of dam‐break flood evolution. Water surface profiles in open channels (WSPOC), Matrix Laboratory (MATLAB)‐based software was developed to help students better learn and improve their interest in surface line theory. According to the flow characteristics, the program is divided into two modules: steady flow and unsteady flow. The steady flow module guides students to master the judgment methods of various gradually varying flow types and can program independently to explore the solution process of the water surface profiles. The unsteady flow module is designed to help students learn finite difference methods in computational fluid dynamics (CFD), and allow students to interact with software in engineering cases to achieve the purpose of effectively integrating theory and practice. This software employs MATLAB graphical user interface(GUI) visualization technology to embed students' autonomous programming in crucial phases and transforms abstract concepts and theories into vivid animation demonstrations using CFD simulation tools. Furthermore, the transformation from theory to practice has been realized by providing a large number of practical engineering examples, which may improve students' ability to solve complex engineering problems. Based on the survey results, the user experience and application effect of the software are satisfactory, and the software's design objective has been achieved.

An adaptive hybrid dimension-reduction model and its application for statistical moments estimation of stochastic systems and reliability analysis of structures

From the perspective of accuracy, efficiency and versatility, calculating statistical moments for different forms of performance functions in a unified way remains a challenge, and their accuracy also considerably affects the results of subsequent reliability analysis. In this article, a new dimension-reduction model, termed as adaptive hybrid dimension-reduction model (AH-DRM), is derived to approximate the performance functions with different characteristics relatively accurately. Based on the AH-DRM, a highly flexible point estimation method (PEM), which has good versatility for the various forms of performance function, is developed for statistical moments estimation of stochastic systems. Subsequently, to illustrate the performance of the proposed method for different performance function forms, three examples, including weakly, moderately and strongly nonlinear benchmark examples, are investigated. The results indicate that the proposed method is versatile for each example and can receive desirable accuracy for evaluating the first-four central moments of the performance functions with high efficiency. Finally, the developed PEM is applied to reconstruct the probability density function of the performance function and calculate the reliability of structures with the aid of the saddle-point approximation (SPA) method, and two practical engineering examples are used to verify the applicability of the proposed method in structural reliability analysis.