Random Balance Designs Research Articles

Prediction of Coal Spontaneous Combustion Hazard Grades Based on Fuzzy Clustered Case-Based Reasoning

Accurate prediction of the coal spontaneous combustion hazard grades is of great significance to ensure the safe production of coal mines. However, traditional coal temperature prediction models have low accuracy and do not predict the coal spontaneous combustion hazard grades. In order to accurately predict coal spontaneous combustion hazard grades, a prediction model of coal spontaneous combustion based on principal component analysis (PCA), case-based reasoning (CBR), fuzzy clustering (FM), and the snake optimization (SO) algorithm was proposed in this manuscript. Firstly, based on the change rule of the concentration of signature gases in the process of coal warming, a new method of classifying the risk of spontaneous combustion of coal was established. Secondly, MeanRadius-SMOTE was adopted to balance the data structure. The weights of the prediction indicators were calculated through PCA to enhance the prediction precision of the CBR model. Then, by employing FM in the case base, the computational cost of CBR was reduced and its computational efficiency was improved. The SO algorithm was used to determine the hyperparameters in the PCA-FM-CBR model. In addition, multiple comparative experiments were conducted to verify the superiority of the model proposed in this manuscript. The results indicated that SO-PCA-FM-CBR possesses good prediction performance and also improves computational efficiency. Finally, the authors of this manuscript adopted the Random Balance Designs—Fourier Amplitude Sensitivity Test (RBD-FAST) to explain the output of the model and analyzed the global importance of input variables. The results demonstrated that CO is the most important variable affecting the coal spontaneous combustion hazard grades.

Synergy of random balance design method and intelligent optimization technique for model updating of the 4 MW offshore wind turbine benchmark

The technical challenges for model updating of real marine engineering structures include the extraction of modal parameters associated with incomplete measurement information and the correction of a large number of structural parameters. As it is difficult to verify the effectiveness of model updating methods for engineering applications, the representative models have to be adopted in finite element (FE) analysis or lab-scale tests, leading to the incomplete reflection of actual structural performances. Based on these factors, a practical model updating method is developed in this study to make full use of field measurement data from a 4 MW offshore wind turbine for the accurate estimation of structural parameters using the random balance designs-Fourier amplitude sensitivity test (RBD-FAST) strategy and an improved particle swarm optimization (IPSO). Leveraging the measured acceleration signals from offshore wind turbines under the conditions including operation, shutdown, collision and typhoon scenarios, the complex exponential decomposition method is applied to accurately extract the time-varying acceleration components (TVAC) for the construction of the frequency response function (FRF). Following that, RBD-FAST is implemented into IPSO with adaptive inertia weights and asynchronously varying learning factors to enable efficient selection of numerous updated physical parameters, thus improving time cost and computational accuracy. The correctness of the proposed method is verified by a numerical jacket platform model. Furthermore, the 4 MW offshore wind turbine benchmark is developed to assess the feasibility of the proposed model updating method using field measured data from different scenarios. Results show that the synergy of RBD-FAST and IPSO in the proposed method can accurately update parameters and minimize a maximum discrepancy of 0.8970% for the first-three orders of natural frequencies between the benchmark and the updated models in the collision scenario. Summarily, the present work provides a potential technique and practical engineering references for model updating of offshore wind turbines subject to harsh marine environments.

A “data-driven uncertainty” computational method to model and predict instabilities of a frictional system

Most of the recently developed methods for predicting instabilities of frictional systems couple stochastic algorithms with the finite element method (FEM). They use random variables to model the uncertainty of input parameters through standard probability laws. Regardless of the fact that advanced numerical schemes are available nowadays, a systematic and accurate method to describe finely the uncertainties upstream the model, and thus predict its response is still missing. In this contribution, we present a data-driven stochastic finite element scheme to predict the dynamic behavior of a rubbing system. The proposed framework relies on data-driven approach and uses four steps. In the first, the measured data are integrated directly, for the uncertainty quantification, by means of the random balance design (RBD). In the second step, the generated stochastic data are evaluated in an iterative way to solve friction-induced vibration problem. In the third step, the resulted data are reordered in such a way that the corresponding values of each measured input parameters are ranked in ascending order. Finally, the Fourier spectrum is introduced on the reordered results to compute the sensitivity indices. Thus, instead of Monte Carlo-based formalism or Fourier Amplitude Sensitivity Test (FAST), the computational cost of the proposed method is kept down to mathcal {O}(N) with N the number of samples. We investigate the efficiency of the suggested solver on a reduced brake system. Altogether, the suggested procedure achieves excellent accuracy at a much reduced computational time compared to the methods available in the literature.

Data-driven multi-step robust prediction of TBM attitude using a hybrid deep learning approach

A robust multi-step TBM attitude prediction approach named convolutional gated-recurrent-unit neural network (C-GRU) is proposed in this research and the random balance design Fourier amplitude sensitivity test method is used for sensitivity analysis to reveal the interaction between input and output of the C-GRU model. A tunnel construction project in Singapore is taken as an example to prove the robustness and effectiveness of the proposed approach. Results indicate that the length of the output sequence of the model can maintain high robustness and accuracy within 21 steps. In the 21-step prediction, the highest R2 can reach 0.9652 while the mean R2 is 0.9004 even though some attitude parameter is with large fluctuations. Each step in the 21-step prediction can maintain a stable accuracy. The data of the past 11 time steps of the TBM attitude parameters are the most sensitive. The proposed method has higher accuracy and robustness than state-of-art time-series based methods.

FRF 기반 부분구조합성법을 이용한 차량 진동성능 강건설계

In this study, a robust design procedure using the FRF-based substructuring (FBS) method was proposed for vehicle vibration performance. In the robust design procedure, global sensitivity analysis was used to obtain the design information of elastomers in structural systems considering uncertainties. The global sensitivity method combines the random balance design method for variance-based sensitivity information and the FRF-based substructuring (FBS) method for the calculation of vibrational responses, which establishes an efficient tool even in complex real structures. Moreover, a multi-objective optimization formulation was applied to obtain the optimal design of elastomers that give robust vibration responses. The objective functions were set to the mean and variance of the vibration responses. The Pareto optimal front was calculated using the non-dominated sorting genetic algorithm-II (NSGA-II). The genetic algorithm design variables were screened using the global sensitivity analysis results for the elastomers. These formulations were applied to a passenger car problem to obtain the optimal design of the engine mount systems. The numerical results showed that the newly introduced feature enhanced the calculation performance and the proposed procedure can be applied successfully in real complex structural problems.

Assembly deviation modelling to predict and trace the geometric accuracy of the precision motion system of a CNC machine tool

Geometric accuracy is the direct embodiment of the assembly deviation of a precision motion system. This paper proposes a novel methodology for predicting the geometric accuracy induced by assembly deviation of a precision motion system and tracing the sensitivity of the assembly deviation with respect to geometric accuracy terms. The small displacement torsor is first characterized as the periodic function of the assembly deviation and dimension parameters of the components of ball-screw feeding system, the vector constraint relationship of the parallel assembly of the feeding system is established, and a spatial propagate model of the assembly deviation for the feeding system is then constructed. A random balance design and Fourier amplitude sensitivity test method are introduced to trace the effect of each assembly feature on the geometric accuracy. The experiments were performed on a single-axis feeding system to verify the effectiveness of the proposed method. This method has the advantage that the mapping relationship between the assembly deviation and geometric accuracy with respect to the instructed position is quantified, and the assembly and adjustment is pertinent to the traceability analysis. The model has the potential to accurately allocate and maintain the machining centre.

On the Global Sensitivity Analysis Methods in Geotechnical Engineering: A Comparative Study on a Rock Salt Energy Storage

The large number of input factors involved in a sophisticated geotechnical computational model is a challenge in the concept of probabilistic analysis. In the context of model calibration and validation, conducting a sensitivity analysis is substantial as a first step. Sensitivity analysis techniques can determine the key factors which govern the system responses. In this paper, three commonly used sensitivity analysis methods are implemented on a sophisticated geotechnical problem. The computational model of a compressed air energy storage, mined in a rock salt formation, includes many input parameters, each with large amount of uncertainties. Sensitivity measures of different variables involved in the mechanical response of the cavern are computed by different global sensitivity methods, namely, Sobol/Saltelli, Random Balance Design, and Elementary Effect method. Since performing sensitivity analysis requires a large number of model evaluations, the concept of surrogate modelling is utilised to decrease the computational burden. In the following, the accuracy levels of various surrogate techniques are compared. In addition, a comparative study on the applied sensitivity analysis methods shows that the applied sensitivity analysis techniques provide identical parameter importance rankings, although some may also give more information about the system behaviour.

First-Order Sensitivity Analysis for Hidden Neuron Selection in Layer-Wise Training of Networks

Multilayer neural networks are current trends in machine learning. Although complex architectures bring high performance, having sparse neurons in each layer can save memory, energy, and computational resources. In this paper, we aim to balance benefits between the complexity of architectures and the sparsity of neurons. An algorithm is proposed to prune neurons in multilayer neural networks through the global sensitivity analysis. Motivated by layer-wise training, we construct autoencoders with linear decoders, so mathematical models of multilayer neural networks can be considered as additive models. Hence, a first-order sensitivity analysis method, called random balance designs (RBD), is employed to select redundant neurons in hidden layers. This paper provides a novel framework to apply RBD in multilayer neural networks. Multiple experimental results demonstrate the generality and effectiveness of the proposed approach on structural learning of neural networks. After removing superfluous hidden neurons, higher accuracy can be obtained in most cases with less computation.

Methods for global sensitivity analysis in life cycle assessment

PurposeInput parameters required to quantify environmental impact in life cycle assessment (LCA) can be uncertain due to e.g. temporal variability or unknowns about the true value of emission factors. Uncertainty of environmental impact can be analysed by means of a global sensitivity analysis to gain more insight into output variance. This study aimed to (1) give insight into and (2) compare methods for global sensitivity analysis in life cycle assessment, with a focus on the inventory stage.MethodsFive methods that quantify the contribution to output variance were evaluated: squared standardized regression coefficient, squared Spearman correlation coefficient, key issue analysis, Sobol’ indices and random balance design. To be able to compare the performance of global sensitivity methods, two case studies were constructed: one small hypothetical case study describing electricity production that is sensitive to a small change in the input parameters and a large case study describing a production system of a northeast Atlantic fishery. Input parameters with relative small and large input uncertainties were constructed. The comparison of the sensitivity methods was based on four aspects: (I) sampling design, (II) output variance, (III) explained variance and (IV) contribution to output variance of individual input parameters.Results and discussionThe evaluation of the sampling design (I) relates to the computational effort of a sensitivity method. Key issue analysis does not make use of sampling and was fastest, whereas the Sobol’ method had to generate two sampling matrices and, therefore, was slowest. The total output variance (II) resulted in approximately the same output variance for each method, except for key issue analysis, which underestimated the variance especially for high input uncertainties. The explained variance (III) and contribution to variance (IV) for small input uncertainties were optimally quantified by the squared standardized regression coefficients and the main Sobol’ index. For large input uncertainties, Spearman correlation coefficients and the Sobol’ indices performed best. The comparison, however, was based on two case studies only.ConclusionsMost methods for global sensitivity analysis performed equally well, especially for relatively small input uncertainties. When restricted to the assumptions that quantification of environmental impact in LCAs behaves linearly, squared standardized regression coefficients, squared Spearman correlation coefficients, Sobol’ indices or key issue analysis can be used for global sensitivity analysis. The choice for one of the methods depends on the available data, the magnitude of the uncertainties of data and the aim of the study.

Global and local sensitivity analyses for coupled thermo–hydro–mechanical problems

SummaryThis paper focuses on the sensitivity analysis for coupled thermo–hydro–mechanical problems employing both local and global sensitivity methods. A derivative‐based method is used in the local sensitivity approach, whereas the random balance designs method is used for the global sensitivity analysis. The main goal is to investigate the effect of uncertainties in the constitutive parameters on the results from nonlinear coupled thermo–hydro–mechanical analyses of unsaturated soil behavior whose modeling generally involves large sets of constitutive relations. Knowing the parameter sensitivity allows to qualitatively assess the validity of the results obtained by computational simulations of high‐risk situations, for example, emerging nuclear waste repositories. Copyright © 2016 John Wiley & Sons, Ltd.

Testing the Sampling-Based NUSS-RF Tool for the Nuclear Data—Related Global Sensitivity Analysis with Monte Carlo Neutronics Calculations

NUSS-RF is a tool for nuclear data uncertainty propagation through neutronics calculations with continuous-energy Monte Carlo codes and ACE-formatted nuclear data libraries. Many existing codes, including the original version of NUSS (Nuclear data Uncertainty Stochastic Sampling), are based on simple random sampling algorithms. The NUSS-RF extension now uses a frequency-based sampling algorithm, called the random balance design (RBD), to analyze individual nuclear data uncertainty contributions in regard to the total output (e.g., keff) uncertainty. The implementation of the RBD method into NUSS-RF is initially verified by comparing the computed individual input variance contributions with analytical solutions for two analytical test cases. As well, it is assessed against the alternative approach based on the use of correlation coefficients. NUSS-RF is then used for an analysis of the Jezebel and Godiva fast-spectrum criticality benchmarks: in a first step, the overall effect of the 239Pu(n,f) and 235U(n,f) cross-section uncertainties on keff is evaluated, while in a second step, the contributions from the individual energy groups are quantified. As an additional verification, the NUSS-RF results are assessed against sensitivity and uncertainty analysis based on perturbation theory, showing good agreement between the two solutions. Finally, the capability of NUSS-RF is demonstrated for ranking the input parameters with respect to their influence on the total uncertainty of the output parameters, taking into account possible correlations between input parameters. Possible future improvements for the current computational scheme are discussed in the conclusions.

NUSS-RF: stochastic sampling-based tool for nuclear data sensitivity and uncertainty quantification

The “blackbox” approach of stochastic sampling (SS) methods for simultaneous nuclear data uncertainty quantification is powerful except it reveals little of the individual uncertainty contributions. In this work, the SS-based tool “NUSS” (nuclear data uncertainty stochastic sampling) developed at PSI is updated to “NUSS- RF” which estimates individual nuclear data uncertainty contributions to the total output uncertainty. The new capability is based on the Random balance design and Fourier amplitude sensitivity testing methods, both belonging to the so-called global sensitivity analysis. First, the implementation of NUSS-RF is tested using a mathematical function, followed by the sensitivity and uncertainty analysis for 235U(n,γ) and 238U(n,γ) cross sections in Godiva and BWR pincell benchmarks, respectively. The results are compared to the deterministic sensitivity/uncertainty “Sandwich Rule” approach which is local. For uncorrelated inputs, both methods have the equivalent interpretation of the input uncertainty contribution (in terms of variance fraction and sensitivity index), hence producing good agreement in the results. For correlated inputs, the discrepancy between the two methods broadens with the extent of the correlations.

Applications of random balance design Fourier amplitude sensitivity test and extended Fourier amplitude sensitivity test in the parameter sensitivity analysis of land surface process model

In this paper, we discuss the applications of random balance design Fourier amplitude sensitivity test (RBD-FAST) and extended Fourier amplitude sensitivity test (EFAST) in the parameter sensitivity analysis of land surface process model. We use the common land model and data of Tongyu station, which is a reference site of CEOP in the semi-arid regions, use five model outputs (sensible heat flux, latent heat flux, surface temperature, temperature of air at 2 m over surface, moisture of air at 2 m over surface) as focus output, and use 11 model parameter (soil depth, the soil proportion of 1-5 layers of soil, the porosity of soil, the max dew depth, the roughness of the air between surface and the canopy, and the drag coefficient under the canopy) as the parameters to be analyzed. After the 10 RBD-FAST experiments, we obtain the first-order sensitivity results, and we gain not only first-order sensitivity but also the total sensitivity after the EFAST experiment. The first-order results of two methods show their consistency. The RBD-FAST takes less computing time and is easy to implemente, while the EFAST also has a more comprehensive and reasonable total sensitivity result. All results above illustrate the applications of both RBD-FAST and EFAST in the parameter sensitivity analysis of land surface model. Researchers can choose the suitable one to solve the different problems.

A self-organizing neuro-fuzzy network based on first order effect sensitivity analysis

As an effective method that can provide the information about the influence of inputs on the variation of output, variance based sensitivity analysis is widely used to determine the structure of neural networks. In the past, the global sensitivity analysis method for the total effect has been used for the structure learning of neural networks and various growing and pruning algorithms have been developed. In this paper, we find that neuro-fuzzy networks have the characteristics of additive models in which the first order effect index of the influence can provide the same comprehensive information as the total effect index, thus we only need to analyze the first order effects of the inputs to their output layers. Based on this observation, many low-cost effective methods for the first order effect global sensitivity can be used in for developing self-organizing neuro-fuzzy networks. Specifically, Random Balance Designs is employed here for sensitivity analysis. In addition, we also introduce the concept of systemic fluctuation of neuro-fuzzy networks to determine whether adjustment is needed for a network. This concept helps us to build a new procedure about the leaning of self-organizing neuro-fuzzy networks and to accelerate its speed of convergence in learning and organizing. Examples of simulations have demonstrated that our proposed method performs better than other existing procedures for self-organizing neuro-fuzzy networks, especially in learning of the network structure.

Bias correction for the estimation of sensitivity indices based on random balance designs

This paper deals with the random balance design method (RBD) and its hybrid approach, RBD-FAST. Both these global sensitivity analysis methods originate from Fourier amplitude sensitivity test (FAST) and consequently face the main problems inherent to discrete harmonic analysis. We present here a general way to correct a bias which occurs when estimating sensitivity indices (SIs) of any order – except total SI of single factor or group of factors – by the random balance design method (RBD) and its hybrid version, RBD-FAST. In the RBD case, this positive bias has been recently identified in a paper by Xu and Gertner [1]. Following their work, we propose a bias correction method for first-order SIs estimates in RBD. We then extend the correction method to the SIs of any order in RBD-FAST. At last, we suggest an efficient strategy to estimate all the first- and second-order SIs using RBD-FAST.

Global sensitivity analysis by polynomial dimensional decomposition

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.

Understanding and comparisons of different sampling approaches for the Fourier Amplitudes Sensitivity Test (FAST)

Fourier Amplitude Sensitivity Test (FAST) is one of the most popular uncertainty and sensitivity analysis techniques. It uses a periodic sampling approach and a Fourier transformation to decompose the variance of a model output into partial variances contributed by different model parameters. Until now, the FAST analysis is mainly confined to the estimation of partial variances contributed by the main effects of model parameters, but does not allow for those contributed by specific interactions among parameters. In this paper, we theoretically show that FAST analysis can be used to estimate partial variances contributed by both main effects and interaction effects of model parameters using different sampling approaches (i.e., traditional search-curve based sampling, simple random sampling and random balance design sampling). We also analytically calculate the potential errors and biases in the estimation of partial variances. Hypothesis tests are constructed to reduce the effect of sampling errors on the estimation of partial variances. Our results show that compared to simple random sampling and random balance design sampling, sensitivity indices (ratios of partial variances to variance of a specific model output) estimated by search-curve based sampling generally have higher precision but larger underestimations. Compared to simple random sampling, random balance design sampling generally provides higher estimation precision for partial variances contributed by the main effects of parameters. The theoretical derivation of partial variances contributed by higher-order interactions and the calculation of their corresponding estimation errors in different sampling schemes can help us better understand the FAST method and provide a fundamental basis for FAST applications and further improvements.

Improving Random Balance Designs For The Estimation Of First Order Sensitivity Indices

The original Random Balance Design (RBD) approach is here further analysed and improved in terms of accuracy of the estimates. The dependency of the algorithm on the tricky parameter M, i.e. the maximum number of frequency harmonics, is eliminated, rendering the procedure fully non parametric.

Extension of the RBD-FAST method to the computation of global sensitivity indices

This paper deals with the sensitivity analysis method named Fourier amplitude sensitivity test (FAST). This method is known to be very robust for the computation of global sensitivity indices but their computational cost remains prohibitive for complex and large dimensional models. Recent developments in the implementation of FAST by use of the random balance designs (RBD) technique have allowed significant reduction of the computational cost. The method is now called RBD-FAST. The drawback of this improvement is that only individual first-order sensitivity indices can be computed. In this article, an extension of RBD is derived for the estimation of any global sensitivity indices of individual factor or group of factors. Several tests are proposed to compare the performances of classical FAST and RBD-FAST.

Calculating first-order sensitivity measures: A benchmark of some recent methodologies

This work compares three different global sensitivity analysis techniques, namely the state-dependent parameter (SDP) modelling, the random balance designs, and the improved formulas of the Sobol’ sensitivity indices. These techniques are not yet commonly known in the literature. Strengths and weaknesses of each technique in terms of efficiency and computational cost are highlighted, thus enabling the user to choose the more suitable method depending on the computational model analysed. Two test functions proposed in the literature are considered. Computational costs and convergence rates for each function are compared and discussed.