Interval Sensitivity Analysis Research Articles

Interval Sensitivity Analysis and Optimization of Magneto-Rheological Damper with Energy Harvesting Characteristics

Interval Sensitivity Analysis and Optimization of Magneto-Rheological Damper with Energy Harvesting Characteristics

Nonlinear dynamic analysis of a seismic vibrator-ground interaction system considering interval uncertainties

Seismic vibrators have wide prospections in geological exploration which can provide useful information of underground conditions for various geotechnical engineering. The enhancement of the exploration performance of the seismic vibrators closely relates to the dynamic response of the vibrator-ground (VG) system. This paper proposes an effective method for the uncertain nonlinear dynamics of the VG system. Firstly, the dynamic model of the VG system with uncertainties is developed based on the solution of the nonlinear soil-baseplate interaction. Then, the fundamental theory of the Chebyshev-based interval method and its implementation in the simulation of the VG dynamics are described. The efficiency and accuracy of the proposed method are validated by comparing with the scanning method. Finally, the effects of the multiple uncertainty parameters, sourced from both the soil conditions and the vibrator structure, on the dynamic response of the VG system are analyzed and discussed in detail. In addition, an interval sensitivity analysis is developed to evaluate and compare the effects of different uncertain parameters. The results indicate that uncertainties greatly influence the dynamics of the VG system, and their effects change with the excitation frequency and also relate to the sources of the uncertainties.

A novel sensitivity index for analyzing the response of numerical models with interval inputs

This study proposes a novel sensitivity index to provide essential insights into numerical models whose inputs are characterized by intervals. Based on the interval model and its normalized form, the interval processes are introduced to define a new sensitivity index. The index can represent the individual or joint influence of the interval inputs on the output of a considered model. A double-loop strategy, based on global metamodeling and optimization, is established to calculate the index. Subsequently, the proposed index is theoretically compared with two other existing indices, and it is experimentally applied to three numerical examples and a practical engineering problem of a honeycomb sandwich radome. The results indicate that the proposed index is an effective tool for interval sensitivity analysis.

Interval sensitivity analysis of joint dynamics in complex built-up structures

The dynamic properties of joints, or inter-component connections, are a principal source of uncertainty when modelling complex built-up structures. In the present paper, we propose an interval-based sensitivity analysis (SA) to establish the contribution, or influence, of a structure’s uncertain joint dynamics towards the uncertainty of its coupled admittance. We choose an interval SA as it overcomes the limitations of conventional local and global methods; accuracy and computation efficiency, respectively. Furthermore, it avoids the need for detailed probabilistic data to describe each joint, which is often unavailable. The proposed interval SA is based on the dual formulation of the sub-structuring problem and utilises the Sherman–Morrison formula to factor out the contribution of an individual joint. A complex interval is used to represent the uncertain joint stiffness and damping, and precise bounds on the assembly’s complex admittance (also operational response) are determined following an application specific algorithm. The relative change between input (joint stiffness and damping) and output (complex admittance) interval area is chosen as a sensitivity metric and used to rank order the uncertain influence of each joint. The method is illustrated by numerical example.

Robust topology optimization of structures under uncertain propagation of imprecise stochastic-based uncertain field

This study introduces a novel computational framework for Robust Topology Optimization (RTO) considering imprecise random field parameters. Unlike the worst-case approach, the present method provides upper and lower bounds for the mean and standard deviation of compliance as well as the optimized topological layouts of a structure for various scenarios. In the proposed approach, the imprecise random field variables are determined utilizing parameterized p-boxes with different confidence intervals. The Karhunen–Loève (K–L) expansion is extended to provide a spectral description of the imprecise random field. The linear superposition method in conjunction with a linear combination of orthogonal functions is employed to obtain explicit mathematical expressions for the first and second order statistical moments of the structural compliance. Then, an interval sensitivity analysis is carried out, applying the Orthogonal Similarity Transformation (OST) method with the boundaries of each of the intermediate variable searched efficiently at every iteration using a Combinatorial Approach (CA). Finally, the validity, accuracy, and applicability of the work are rigorously checked by comparing the outputs of the proposed approach with those obtained using the particle swarm optimization (PSO) and Quasi-Monte-Carlo Simulation (QMCS) methods. Three different numerical examples with imprecise random field loads are presented to show the effectiveness and feasibility of the study.

A Method for Detecting the Randomness of Barkhausen Noise in a Material Fatigue Test Using Sensitivity and Uncertainty Analysis.

The magnetic Barkhausen noise (MBN) signal provides interesting clues about the evolution of microstructure of the magnetic material (internal stresses, level of degradation, etc.). This makes it widely used in non-destructive evaluation of ferromagnetic materials. Although researchers have made great effort to explore the intrinsic random characteristics and stable features of MBN signals, they have failed to provide a deterministic definition of the stochastic quality of the MBN signals. Because many features are not reproducible, there is no quantitative description for the stochastic nature of MBN, and no uniform standards to evaluate performance of features. We aim to make further study on the stochastic characteristics of MBN signal and transform it into the quantification of signal uncertainty and sensitivity, to solve the above problems for fatigue state prediction. In the case of parameter uncertainty in the prediction model, a prior approximation method was proposed. Thus, there are two distinct sources of uncertainty: feature(observation) uncertainty and model uncertainty were discussed. We define feature uncertainty from the perspective of a probability distribution using a confidence interval sensitivity analysis, and uniformly quantize and re-parameterize the feature matrix from the feature probability distribution space. We also incorporate informed priors into the estimation process by optimizing the Kullback–Leibler divergence between prior and posterior distribution, approximating the prior to the posterior. Thus, in an insufficient data situation, informed priors can improve prediction accuracy. Experiments prove that our proposed confidence interval sensitivity analysis to capture feature uncertainty has the potential to determine the instability in MBN signals quantitatively and reduce the dispersion of features, so that all features can produce positive additive effects. The false prediction rate can be reduced to almost 0. The proposed priors can not only measure model parameter uncertainties but also show superior performance similar to that of maximum likelihood estimation (MLE). The results also show that improvements in parameter uncertainties cannot be directly propagated to improve prediction uncertainties.

An approach for accuracy enhancement of five-axis machine tools based on quantitative interval sensitivity analysis

Error compensation is a common method to improve the machining accuracy of five-axis machine tools (FAMTs). Before that, in order to identify the key geometric errors that affect the machining accuracy, sensitivity analysis (SA) in entire machining region or a specified point is usually used. However, since the influence of geometric errors on form errors is different in each interval, the result of SA would be affected, which decreases the compensating accuracy. For this reason, a new approach for accuracy enhancement of FAMTs based on quantitative interval sensitivity analysis (QISA) is presented in this paper. First, based on multi-body system theory and homogeneous transform matrix, the volumetric error model of the FAMT is established. Then, the geometric error model of the FAMT is formulated. Second, development of form error model is involved in this paper to clarify the effect law of geometric error on form error. Moreover, the machining region of S-shaped test piece is divided into five intervals. Then, the QISA method is presented to calculate the sensitivity index of each geometric error and identify key geometric errors at different intervals. Finally, simulations and experiments are conducted to validate the feasibility and effectiveness of the presented method.

Improved reliability analysis method based on the failure assessment diagram

With the uncertainties related to operating conditions, in-service non-destructive testing (NDT) measurements and material properties considered in the structural integrity assessment, probabilistic analysis based on the failure assessment diagram (FAD) approach has recently become an important concern. However, the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored. To obtain more detailed and direct knowledge from the reliability analysis, an improved probabilistic fracture mechanics (PFM) assessment method is proposed. By integrating 2D kernel density estimation (KDE) technology into the traditional probabilistic assessment, the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram. Moreover, a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis. The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack. The results indicate that these two methods can give consistent sensitivities of input parameters, but the interval sensitivity analysis is computationally more efficient. Meanwhile, the point density distribution and its contour are plotted in the FAD, thereby better revealing the characteristics of PFM assessment. This study provides a powerful tool for the reliability analysis of critical structures.

Assessment of uncertainties in substation grounding system using interval mathematics

The paper presents the application of interval mathematics as a new method to, rigorously, address uncertainties associated with designing substation earthing system. While several methods exist to determine the important factors for personnel safety in and around substations such as earth resistance, different potentials of substation earthing grid, these methods usually require data which may be uncertain in nature. To account for such uncertainties the interval mathematics is developed with the integration of input parameters’ uncertainties, in interval format, into the governing standard expressions mentioned on IEEE STD 80-2000. The effects of uncertain inputs within the proposed model are examined for various assumed levels of overall uncertainties. To assess the relative contribution of each uncertain input, an interval sensitivity analysis is carried out. Successful implementation of the proposed method is described for the design and configuration arrangement of a 115/13kV substation earthing rectangular grid with ground rods system.

Sampling interval sensitivity analysis for crack detection by stationary wavelet transform

The purpose of this paper was to analyze the sampling interval sensitivity for crack detection by stationary wavelet transform (SWT) in order to facilitate the identification of crack locations in beam-like structures. SWT is a redundant transform that doubles the number of input samples at each iteration. It has been shown that the SWT decomposition detail coefficient of mode shapes of beam-like structure can provide sensitive crack indication that is useful for damage detection. However, the sampling interval is an important factor that affects the sensitivity of crack detection. Three SWT methods were analyzed, including the method using the SWT of the original mode shape (designated SWT-1), the method using the difference between the detail coefficients of the SWT of the left-half and the reconstructed right-half sets of the mode shapes (designated SWT-2), and the method using the difference between the detail coefficient of the left-half and right-half sets of the interpolated mode shapes (designated SWT-3). The modal responses of damaged beams with single and multiple cracks are computed using the finite element method. The curve of the peak value of SWT detail coefficient versus sampling interval was obtained using a fifth-order polynomial fit method. The effects of crack depth, crack width, and crack locations on the sensitivity of sampling interval on crack detection are investigated. SWT-2 method has a shortcoming in determining whether the cracks are located at the true crack location or its mirror image position at different sampling intervals. In order to overcome this shortcoming, two rules are proposed for the determination of true crack locations and the selection of sampling intervals for single crack or multiple crack detection.