Search results

To provide an explicit representation for wide‐sense stationary stochastic fields which can be used in stochastic finite element modelling to describe random material properties.

This method represents wide‐sense stationary stochastic fields in terms of multiple Fourier series and a vector of mutually uncorrelated random variables, which are obtained by minimizing the mean‐squared error of a characteristic equation and solving a standard algebraic eigenvalue problem. The result can be treated as a semi‐analytic solution of the Karhunen‐Loève expansion.

According to the Karhunen‐Loève theorem, a second‐order stochastic field can be decomposed into a random part and a deterministic part. Owing to the harmonic essence of wide‐sense stationary stochastic fields, the decomposition can be effectively obtained with the assistance of multiple Fourier series.

The proposed explicit representation of wide‐sense stationary stochastic fields is accurate, efficient and independent of the real shape of the random structure in consideration. Therefore, it can be readily applied in a variety of stochastic finite element formulations to describe random material properties.

This paper discloses the connection between the spectral representation theory of wide‐sense stationary stochastic fields and the Karhunen‐Loève theorem of general second‐order stochastic fields, and obtains a Fourier‐Karhunen‐Loève representation for the former stochastic fields.

This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes.

This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples.

Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems.

The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

Derives a first order perturbation algorithm for the computation of mean values and (co‐) variances of the transient temperature field in conduction heated materials with random field parameters. Considers both linear as well as non‐linear heat conduction problems. The algorithm is advantageous in terms of computer time compared to the Monte Carlo method. The computer time can further be reduced by appropriate transformation of the random vectors resulting from the discretization of the random fields.

This paper aims to analyze the influence of rotated anisotropy on the stability of slope, the random finite element method is used in this study.

The random field is generated by the discrete cosine transform (DCT) method, which can generate random field with different rotated angles conveniently.

Two idealized slopes are analyzed; it is observed that the rotated angle significantly affects the slope failure risk. The two examples support the conclusion that when the orientation of the layers is nearly perpendicular to the slip surface, the slope is in a relative stable condition. The results of heterogeneous slope with two clay layers demonstrate that the rotated angle of lower layer mainly controls the failure mechanism of the slope, and the rotated angle of upper layer exhibits a significant influence on the probability of slope failure.

The method for rotated anisotropy random field generation based on the DCT has a simple expression with few parameters and is convenient for implementation and practical application. The proposed method and the results obtained are useful for analyzing the stability of the heterogeneous slopes in engineering projects.

This paper aims to present a multi-scale stochastic damage model (SDM) for concrete and apply it to the stochastic response analysis of reinforced concrete shear wall structures.

The proposed SDM is constructed at two scales, i.e. the macro-scale and the micro-scale. The general framework of the SDM is established on the basis of the continuum damage mechanics (CDM) at the macro-scale, whereas the detailed damage evolution is determined through a parallel fiber buddle model at the micro-scale. The parallel buddle model is made up of micro-elements with stochastic fracture strains, and a one-dimensional random field is assumed for the fracture strain distribution. To represent the random field, a random functional method is adopted to quantify the stochastic damage evolution process with only two variables; thus, the numerical efficiency is greatly enhanced. Meanwhile, the probability density evolution method (PDEM) is introduced for the structural stochastic response analysis.

By combing the SDM and PDEM, the probabilistic analysis of a shear wall structure is performed. The mean value, standard deviation and the probability density function of the shear wall responses, e.g., shear capacity, accumulated energy consumption and damage evolution, are obtained.

It is noted that the proposed method can reflect the influences of randomness from material level to structural level, and is efficient for stochastic response determination of shear wall structures.

This article presents lessons from social experiments in the US over 30 years testing employment and training, welfare reform and social service programmes and systems. It discusses the challenges in implementing a random assignment study and strategies to overcome them, and also sets out lessons for ensuring that an experiment informs and affects policy. In laying out the ingredients for success, the article argues that creative and flexible research design skills are essential, but that just as important in a complex, real‐world context are operational and political skills, applied both to marketing the experiment in the first place and to helping interpret and promote its findings down the line.

In this paper, special emphasis is given to uncertainties in the evaluation of the structural behavior, looking for a better representation of the system characteristics and quantification of the significance of these uncertainties in structural design. The reliability analysis of reinforced concrete structures is performed taking into account the spatial variability of material properties. The finite element method is used to analyze reinforced concrete structures. A multidimensional non‐Gaussian stochastic field generation model (independent of the finite element mesh) is developed and used. The reliability analysis is carried out employing the first order reliability method. Numerical examples are presented to study how to generate correlated non‐Gaussian stochastic fields and determine the reliability of a reinforced concrete structure with respect to a limit state function.

Liquefaction of soils is defined as significant reduction in shear strength and stiffness due to increase in pore water pressure. This phenomenon can occur in static (monotonic) or dynamic loading patterns. However, in each pattern, the inherent variability of the soil parameters indicates that this problem is of a probabilistic nature rather than being deterministic. The purpose of this paper is to present a method, based on random finite element method, for reliability assessment of static liquefaction of saturated loose sand under monotonic loading.

The random finite element analysis is used for reliability assessment of static liquefaction of saturated loose sand under monotonic loading. The soil behavior is modeled by an elasto-plastic effective stress constitutive model. Independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are selected as stochastic parameters which are modeled using a truncated normal probability density function (pdf).

The probability of liquefaction is assessed by pdf of modified pore pressure ratio at each depth. For this purpose pore pressure ratio is modified for monotonic loading of soil. It is shown that the saturated unit weight is the most effective parameter, within the selected stochastic parameters, influencing the static soil liquefaction.

This research focuses on the reliability analysis of static liquefaction potential of sandy soils. Three independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are considered as stochastic input parameters. A computer model, coded in MATLAB, is developed for the random finite element analysis. For modeling of the soil behavior, a specific elasto-plastic effective stress constitutive model (UBCSAND) was used.

This paper aims to propose a framework for optimizing the pose in the assembly process of the non-ideal parts considering the manufacturing deviations and contact deformations. Furthermore, the accuracy of the method would be verified by comparing it with the other conventional methods for calculating the optimal assembly pose.

First, the surface morphology of the parts with manufacturing deviations would be modeled to obtain the skin model shapes that can characterize the specific geometric features of the part. The model can provide the basis for the subsequent contact deformation analysis. Second, the simulated non-nominal components are discretized into point cloud data, and the spatial position of the feature points is corrected. Furthermore, the evaluation index to measure the assembly quality has been established, which integrates the contact deformations and the spatial relationship of the non-nominal parts’ key feature points. Third, the improved particle swarm optimization (PSO) algorithm combined with the finite element method is applied to the process of solving the optimal pose of the assembly, and further deformation calculations are conducted based on interference detection. Finally, the feasibility of the optimal pose prediction method is verified by a case.

The proposed method has been well suited to solve the problem of the assembly process for the non-ideal parts with complex geometric deviations. It can obtain the reasonable assembly optimal pose considering the constraints of the surface morphological features and contact deformations. This paper has verified the effectiveness of the method with an example of the shaft-hole assembly.

The method proposed in this paper has been well suited to the problem of the assembly process for the non-ideal parts with complex geometric deviations. It can obtain the reasonable assembly optimal pose considering the constraints of the surface morphological features and contact deformations. This paper has verified the method with an example of the shaft-hole assembly.

The different surface morphology influenced by manufacturing deviations will lead to the various contact behaviors of the mating surfaces. The assembly problem for the components with complex geometry is usually accompanied by deformation due to the loading during the contact process, which may further affect the accuracy of the assembly. Traditional approaches often use worst-case methods such as tolerance offsets to analyze and optimize the assembly pose. In this paper, it is able to characterize the specific parts in detail by introducing the skin model shapes represented with the point cloud data. The dynamic changes in the parts' contact during the fitting process are also considered. Using the PSO method that takes into account the contact deformations improve the accuracy by 60.7% over the original method that uses geometric alignment alone. Moreover, it can optimize the range control of the contact to the maximum extent to prevent excessive deformations.

Learning field of events is characterized by the occurrenceof random and uncertain phenomena, all of which have probabilistic distributions. The meaning of learning is exchange by interdependence between interacting agents. Such agents are both the human entities and the non‐human ones. Thus, in a learning field of probabilistic events there are complex forms of interaction between the domains of mind (human cognition) and matter (world‐system). The purpose of this paper is to formalize and study such interactions by the epistemology of unity of being and becoming of relations between given variables in analytical perspective.

The critical argumentation and search in this paper leads to the premise of the episteme of unity of knowledge. It is found singularly in the doctrine of the paired universe of the Quran. The episteme of oneness of the monotheistic law and its consequential forms establish the axiomatic basis of the criterion function representing the phenomenon of probabilistic learning field. The authors refer to this criterion as wellbeing. It conceptualizes and measures the degree of unity of being and becoming that exists between the variables of a specific problem under investigation.

The results of this study formalize the probabilistic model of learning. The simulated evaluation of the probabilistic form of the wellbeing function brings out the synonymous results between unity of knowledge and its impact on the unity of the world‐system induced by the knowledge‐flows. Such a transformation of a world‐system presents the meaning of endogenous (or systemically self‐regenerated) ethics and morality in such broader fields of choices involving embedded learning systems.

The dynamics of pervasive complementarities arising from learning by unity of knowledge, and considerations of ethics and morality remain exogenous factors in economic theory. This paper, instead, has formalized ethical endogeneity in models of decision‐making with probabilistic learning fields that remain embedded in complementarities by interaction and integration across economic, social and ethical systems.