Non-probabilistic Uncertainty Research Articles

Interval strategy-based regularization approach for force reconstruction with multi-source uncertainties

A force reconstruction method for uncertain structures instead of direct measurement is proposed in this paper. Considering the multi-source uncertainties as unknown-but-bounded (UBB) parameters including unknown structural dynamics and measurement errors, this study proposed a novel force reconstruction method using an interval strategy-based regularization approach with truncated singular value decomposition (TSVD). To overcome the drawbacks of incompleted models and limited information, the overall modelling and inversion of the interval force are reconstructed based on the non-probabilistic uncertainty theory. First, The interval uncertainty-based kernel function for force inversion is deduced using the second-order interval perturbation method, in which the uncertainties of the reconstructed force originate from the uncertain singular values and measurement errors. Based on the regularization of the TSVD, the interval bounds of the singular values can be accurately obtained. Combining the two typical regularization approaches, a novel interval strategy-based regularization approach is proposed to optimize the best regularization parameter based on the uncertain interval distribution of singular values. This novel strategy can not only balance the two typical regularization approaches but also reduce the burden of force inversion. Two numerical examples including a truss and space capsule are applied to access the proposed method, and the estimated accurate force can prove the effectiveness.

Free Vibration Analysis of Arches with Interval-Uncertain Parameters

The dynamic characteristics of a structure serve as a crucial foundation for structural assessment, fault diagnosis, and ensuring structural safety. Therefore, it is imperative to investigate the impacts of uncertain parameters on the dynamic performance of structures. The dynamic characteristics of arches with uncertain parameters are analyzed in this paper. The uncertain parameters are regarded as non-probabilistic uncertainties and represented as interval variables. A model of an arch considering interval-uncertain parameters is built, and kinematic equations are established. The natural frequencies are obtained using the differential quadrature (DQ) method, and the relationships between natural frequency, radius, and central angle are also analyzed. On this basis, the Chebyshev polynomial surrogate (CPS) model is employed to solve the uncertain dynamic problem, and the natural frequencies are seen to be the objective functions of the CPS model. The accuracy verification of the model is achieved by comparison with the Monte Carlo simulation (MCS). Simulations are carried out considering different uncertainties, and the results show that the bounds of natural frequencies are influenced not only by the types of uncertain parameters, but also by their combinations.

Exploration of cross-border e-commerce live streaming and local culture dissemination model based on cluster analysis

Abstract This paper first constructs the logical architecture and implementation mechanism of cross-border e-commerce live streaming and local cultural communication and proposes a cultural communication influence model based on clustered ellipsoid and spatial cluster analysis. By using first-order linear approximation and PMA for non-probabilistic uncertainty cultural communication analysis, the optimal global solution of the system response is solved. Finally, the results of cross-border e-commerce live streaming and local cultural communication power are discussed by specifically analyzing the characteristic quantities of cultural communication structure and local cultural communication effect. The results show that the maximum value is 39.8034 in the TOP20 of local culture communication power, the mean value is 17.3431 in the communication effect dimension, and the mean value is 16.17 in the communication structure dimension. This paper provides a new model to explore for cross-border e-commerce live streaming and local culture communication.

A new hybrid approach to study heat and mass transfer in porous medium influenced by imprecisely defined parameters

The present work discusses a hybrid approach of Successive Overrelaxation (SOR) with Finite Element Method (FEM) in presence of non-probabilistic uncertainties. In order to address the heat and mass transfer problem in porous media with fuzzy environment, the proposed SOR FFEM has been applied. Here, the imprecise parameters have taken in terms of TFNs and the convergence analysis of the proposed technique is performed. The parameters viz. Rayleigh number (Ra), Radiation parameter (Rd) and Lewis's number (Le) are considered as uncertain and discussed in case study. Different combinations of uncertain parameters are considered for investigation and the sensitivity analysis of the same is observed. It is noted that the stream function (ψ‾) is sensitive when Ra is fuzzy. Similarly, the stream function (ψ‾) and temperature (T‾) both are exhibiting sensitivity when Rd is fuzzy. Additionally, the stream function (ψ‾) is sensitive when Le is fuzzy. As comparing all the cases, it is observed that, stream function (ψ‾) is more sensitive in all three circumstances that is a small change in value can be affect more.

Non-Probabilistic Uncertainty and Correlation Propagation Analysis Methods Based on Multidimensional Parallelepiped Model

In engineering practice, the uncertainty and correlation may coexist in the input parameters, as well as in the output responses. To address such cases, several methods are developed for the non-probabilistic uncertainty and correlation propagation analysis in this study. In the proposed methods, the multidimensional parallelepiped model (MPM) is introduced to quantify the uncertainty and correlation of input parameters. In the uncertainty propagation analysis, three methods are presented to calculate the interval bounds of output responses. Among the methods, the Monte Carlo uncertainty analysis method (MCUAM) is firstly presented as a reference method, and then the first-order perturbation method (FOPM) is employed to promote the computational efficiency, and the sub-parallelepiped perturbation method (SPPM) is further developed to handle the correlated parameters with large uncertainty. In the correlation propagation analysis, the Monte Carlo correlation analysis method (MCCAM) is proposed based on the MPM and Monte Carlo simulation, which aims to compute the correlation among different output responses. The uncertainty domains between any two responses can also be constructed by the MCCAM. The effectiveness of the proposed methods on dealing with the uncertainty and correlation propagation problems is demonstrated by three numerical examples.

Vagueness in Goals-of-Care Conferences for Critically Ill Patients: Types of Hedge Language Used by Physicians.

Hedge language is a category of language that refers to words or phrases that make statements "fuzzier." We sought to understand how physicians use hedge language during goals-of-care conferences in the ICU. Secondary analysis of transcripts of audio-recorded goals-of-care conferences in the ICU. Thirteen ICUs at six academic and community medical centers in the United States. Conferences were between clinicians and surrogates of incapacitated, critically ill adults. Four investigators performed a qualitative content analysis of transcripts using deductive followed by inductive methods to identify types of hedge language used by physicians, then coded all instances of hedge language across 40 transcripts to characterize general patterns in usage. We identified 10 types of hedge language: numeric probabilistic statement ("there's an 80% chance"), qualitative probabilistic statement ("there's a good chance"), nonprobabilistic uncertainty statement ("hard to say for her"), plausibility shield ("we expect"), emotion-based statement ("we're concerned"), attribution shield ("according to Dr. X"), adaptor ("sort of"), metaphor ("the chips are stacking up against her"), time reference ("too soon to tell"), and contingency statement ("if we are lucky"). For most types of hedge language, we identified distinct subtypes. Physicians used hedge language frequently in every transcript (median: 74 hedges per transcript) to address diagnosis, prognosis, and treatment. We observed large variation in how frequently each type and subtype of hedge language was used. Hedge language is ubiquitous in physician-surrogate communication during goals-of-care conferences in the ICU and can be used to introduce vagueness to statements in ways beyond expressing uncertainty. It is not known how hedge language impacts decision-making or clinician-surrogate interactions. This study prioritizes specific types of hedge language for future research based on their frequency and novelty.

Robust topology optimization with interval field model: on the spatially varied non-probabilistic uncertainty of material property, loading and geometry

Robust topology optimization with interval field model: on the spatially varied non-probabilistic uncertainty of material property, loading and geometry

Non-probabilistic credible set model for structural uncertainty quantification

A non-probabilistic credible set model for uncertainty quantification structural parameters is proposed in this paper. The developed method surpasses the probabilistic uncertainty quantification method and traditional non-probabilistic uncertainty quantification method by providing both the distribution range of uncertain structural parameters and the corresponding credibility for scant samples, thereby reducing the computation time and improving the credibility of the uncertainty quantification process. The average inverse-distance information entropy, the expanded uncertainty and credibility are introduced to establish a one-dimensional non-probabilistic credible set uncertainty quantification procedure. The basic theory of non-probabilistic sets and a correlation analysis of multidimensional uncertain parameters are reviewed. This theory and analysis are used to develop a multidimensional non-probabilistic credible set uncertainty quantification method. The optimal non-probabilistic set is searched to determine the local coordinate system. The multidimensional uncertainty quantification is subsequently transformed to a one-dimensional uncertainty quantification. A civil aircraft wing structure case, a stiffened plate case and a dynamic case are utilized to verify the feasibility of applying the developed method to various engineering problems.

A credible interval analysis method for uncertain structures under nonprobabilistic framework

In this paper, a novel credible structural interval analysis method is proposed. Traditionally, nonprobabilistic uncertainties are modeled as interval or convex models, and no description of their credibility is given. Based on credible nonprobability uncertainty theory, the credible interval and ellipsoid are quantified to model irrelevant and relevant uncertain structural parameters. An efficient adaptive kriging (EAK) method is developed to solve the interval dynamic responses of structures with credible intervals and ellipsoids. In contrast to existing propagation methods, the proposed EAK method shares the samples of different time steps to improve the computational efficiency. A numerical example and two engineering applications are used to show the validity, accuracy and efficiency of the proposed method. Comparisons show that the proposed method can effectively calculate interval dynamic responses with credibility and is competitive when addressing nonlinear or coupled structural systems.

Non-Probabilistic Uncertainty Quantification of Fiber-Reinforced Composite Laminate Based on Micro- and Macro-Mechanical Analysis

In this paper, the main aim is to study and predict macro elastic mechanical parameters of fiber-reinforced composite laminates by combining micro-mechanical analysis models and the non-probabilistic set theory. It deals with uncertain input parameters existing in quantification models as interval variables. Here, several kinds of micro-mechanical mathematical models are introduced, and the parameter vertex solution theorem and the Monte Carlo simulation method can be used to perform uncertainty quantification of macro elastic properties for composites. In order to take the correlations between macro elastic properties into consideration, the obtained limited sample points or experimental data are utilized on the basis of the grey mathematical modeling theory, where correlated uncertain macro parameters can be treated as a closed and bounded convex polyhedral model. It can give out a clear analytical description for feasible domains of correlated macro elastic properties in the process of uncertainty quantification. Finally, two numerical examples are carried out to account for the validity and feasibility of the proposed quantification method. The results show that the proposed method can become a powerful and meaningful supplement for uncertainty quantification of composite laminates and provide data support for further uncertainty propagation analysis.

Uncertainty quantification method for elastic wave tomography of concrete structure using interval analysis

This paper presents a non-probabilistic uncertainty quantification method for the elastic wave tomography of concrete structures. An interval analysis model is applied to establish the relationship between the measurement error and identified tomography images. Measurements of parameters such as travel time and wave amplitude are modeled as intervals described by their upper and lower boundaries. Based on the straight-ray assumption of the wave propagation path, the relationship between wave velocity and travel time measurements is described by a set of linear equations. The inversion linear equation is converted into an extended fuzzy linear equation using interval analysis. Subsequently, a simultaneous iterative reconstruction technique is applied to solve this fuzzy linear equation. In contrast to the traditional methods, the obtained tomography images are described in terms of the upper and lower boundaries. Finally, numerical simulation and experimental investigation using several plain concrete models are conducted to verify the proposed approach.

Constrained Fuzzy Power Flow Applied to Transmission Congestion

The deregulation of the electricity industry, the increasing penetration of renewable energy resources, and the presence of new stakeholders, such as Electric Vehicles (EV), make managing transmission system congestion critical. In this context, load flow methodologies that consider non-probabilistic uncertainty due to a lack of data (particularly concerning EV) seem to be a handy tool to analyze network congestion situations and to support electrical network planning. The congestion of the branches is related to the load and generation of the network buses. Still, the congestion of a specific branch may not be related to the load and generation on the neighbouring buses. In this line, Fuzzy Power Flow (FPF) is suitable for identifying congestion situations in the transmission system and the branches responsible for such cases when probabilistic models may not describe uncertainty. This paper uses an FPF model, a non-linearized Constrained Fuzzy Power Flow (CFPF), to characterize congestion situations in transmission network planning. The application of the CFPF to analyze congestion situations is a novelty. The results of that application may be used to define the reinforcement of the most appropriate branches to achieve specific suitability of the network in the face of a diverse set of uncertainties. Furthermore, the dual values provided by Lagrange multipliers resulting from the CFPF optimization problem are used to identify the most promising options to mitigate congestion situations.

Vibration Reliable Control and Design Optimization Under Non-Probabilistic Uncertainties

Vibration Reliable Control and Design Optimization Under Non-Probabilistic Uncertainties

Interval-based optimal trajectory tracking control method for manipulators with clearance considering time-dependent reliability constraints

The soaring operating performance of robotic manipulators renders the significance of advanced controller design. However, the uncertainty in practice would unavoidably lead to the failure of manipulators. Meanwhile, the general statistical analysis to uncertainty may be too complicated or tricky and to virtually realize. In this paper, a non-probabilistic uncertainty quantification approach is proposed to simplify the process of system uncertainties. The corresponding response range is attended by collocation method with advantages upon precision and efficiency. Later, a time-dependent reliability (TDR) evaluation is presented by the first-passage theory. The controller design of manipulator system is built with the widely used PID control with the constraint of TDR to ensure manipulator's normal operation under the trajectory tracking course. The proposed method innovates in simplification and precision of uncertainty quantification and response evaluation, as well as the non-probabilistic time-dependent reliability constraints which well suit for controller design for manipulator systems. Three numerical examples are presented to prove the function and effectiveness of the proposed design approach.

Subjective Trusts for the Control of Mobile Robots under Uncertainty.

The paper deals with the methods of handling imperfect information and the control of mobile robots acting under uncertainty. It is assumed that the robots act in autonomous regime and are controlled internally without referring the externally defined probabilities of the states and actions. To control the activity of the robots, we suggest the novel multi-valued logic techniques based on the recently developed measures, known as the subjective trusts. In addition to specification of the robots’ movements, such a technique allows for direct definition of the robots’ swarming using the methods of artificial neural networks with mobile neurons. The suggested methods are verified by numerical simulations and running examples. The resulting framework forms a basis for processing non-probabilistic uncertainties and making individual decisions with imperfect information.

Lightweight design process considering assembly connection and non-probabilistic uncertainty with its application to machine structural design

Owing to the complexity of machines, lightweight structural design needs to consider the influence of assembly connection and non-probabilistic uncertainty in material properties. This study suggests a novel lightweight design process that incorporates these two factors. In this process, the assembly connection was modelled with the finite element model and validated by experiments. The non-probabilistic uncertainty was described using the multidimensional parallelepiped model, and then the corresponding non-probabilistic reliability-based design optimization method was applied to ensure the safety of structures. The proposed design process was applied to the structural design of the upper beam of a forming machine. The results showed that ignoring the assembly connection and non-probabilistic uncertainty may lead to an unsafe structural design, and thus they should be considered in the lightweight structural design of machines. Moreover, the weight reduction by 30.43% for the upper beam achieved using the proposed method demonstrated its effectiveness.

Novel data-driven method for non-probabilistic uncertainty analysis of engineering structures based on ellipsoid model

For the various engineering structures with non-probabilistic uncertain parameters, the ellipsoid modeling is a momentous analysis method considering parameter cross-dependency. To efficiently procure a more precise analysis results based on ellipsoid model, this paper proposes a novel data-driven strategy for uncertainty quantification and propagation. Firstly, a similarity distribution-based identification method is presented to eliminate the data deviation caused by outliers. For the problem with dispersed samples, a fuzzy equivalence relation-based clustering method is subsequently introduced, where the number of clusters is adaptively determined by the prior similarity levels. On the basis of the above data preprocessing procedure, a more precise multi-ellipsoid modeling framework is constructed, in which the statistical information of existing samples is utilized to derive the explicit expression of ellipsoid models. Meanwhile, to improve the computational efficiency of uncertainty propagation analysis under the multi-ellipsoid model, the back propagation artificial neural network (BPANN) is constructed as the surrogate model of the original time-consuming simulation model. Eventually, two numerical examples are provided to investigate the effectiveness of the proposed methods.

A novel dynamic model updating method for composite laminate structures considering non-probabilistic uncertainties and correlations

This paper presents a novel dynamic model updating procedure to efficiently update the intervals and non-probabilistic correlation coefficients matrix (NPCCM) of modal parameters, and establish its accurate and reliable uncertainty boundary. To accomplish these features, an ellipsoidal convex model is adopted to quantify the non-probabilistic uncertainties and correlations of the measured multi-responses, and the dynamic model updating problem for composite laminate structures is divided into an interval updating problem and a correlation updating problem. Then, a performance measure approach (PMA) and the non-probabilistic covariance propagation equations are developed to achieve the intervals and NPCCM of the calculated responses respectively. By using optimization algorithms to reduce the errors of the intervals and the NPCCM between the measured modal responses and calculated modal responses, the intervals and the NPCCM of modal parameters can be updated effectively, and their multidimensional ellipsoidal model can be established eventually. To improve the stability and efficiency of the updating processes, the Sobol sensitivity analysis method is applied to determine the important modal parameters, and an optimal polynomial response surface model is developed to replace the original complex structures. An experimental example for composite laminate structure is investigated to verify the effectiveness and accuracy of the proposed method.

Preface to the Special Issue on “Applications of Fuzzy Optimization and Fuzzy Decision Making”

During the last decades, fuzzy optimization and fuzzy decision making have gained significant attention, aiming to provide robust solutions for problems in making decisions and achieving complex optimization characterized by non-probabilistic uncertainty, vagueness, ambiguity and hesitation [...]

A non-probabilistic uncertainty analysis method based on ellipsoid possibility model and its applications in multi-field coupling systems

Non-probabilistic methods are usually more appropriate and feasible than probabilistic methods to quantify and propagate uncertainty with small samples in many engineering problems. However, some non-probabilistic methods are easily affected by an outlier in uncertainty quantification and only estimate the bounds of output responses in a feasible region in uncertainty propagation. Moreover, some such methods ignore the situation that its sample points have the characteristic of clustering to the center, which significantly affects the accuracy of uncertainty quantification and propagation. In this study, a novel non-probabilistic uncertainty analysis method is proposed to solve the situation and obtain detailed information within the response interval during the process of uncertainty propagation for some problems with small samples. First, an ellipsoid possibility model (EPM) including multiple ellipsoid domains is established using the estimated covariance matrix and predefined scaling rule, which takes into consideration the distribution characteristic of the sample points. The possibilities of all established ellipsoid domains can be calculated by transforming the oblique ellipsoid space into the standard ellipsoid space. Then, two uncertainty propagation approaches based on the established EPM are presented to obtain the interval of an uncertain response and the possibility on all the possible values of the system response, respectively. Finally, the calculation results based on the proposed uncertainty analysis method are in good agreement with those of the MCS in three numerical examples and two engineering applications. The comparison results with three traditional non-probabilistic methods demonstrate that the proposed non-probabilistic uncertainty analysis method is accurate and practical.