Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): I. Mathematical Framework

This work presents the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “nth-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the nth-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the nth-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the nth-FASAM-N methodology becomes identical to the extant nth CASAM-N (“nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the nth-FASAM-N and the nth-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the nth-FASAM-N and the nth-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.

Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): II. Illustrative Example

This work highlights the unparalleled efficiency of the “nth-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The nth-FASAM-N methodology is compared to the extant “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-CASAM-N) showing that: (i) the 1st-FASAM-N and the 1st-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1st-LASS);(ii) the 2nd-FASAM-N methodology is considerably more efficient than the 2nd-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2nd-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2nd-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3rd-FASAM-N methodology is even more efficient than the 3rd-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3rd-FASAM-N methodology, while the application of the 3rd-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the nth-FASAM-N and the nth-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.

Optimal Design of Bicycle Frame Parameters Considering Biomechanics

With the development of technology and the change of market demands,the trend in middle and high grade bicycle manufacturing is developed toward small-volume,multi-species,and customer-oriented production.Therefore,human element should be fully considered in design so that the bicycle has the best cycling performance for the specific rider.Currently,customized design is difficult to achieve since feature parameters of the rider are not included in the design.The design of bicycle frame is the most important in bicycle design.The relative positions among the saddle,handlebar and central axis are defined as the bicycle three-pivot,they are the main parameters in bicycle frame design.In conventional bicycle design,frame parameters are merely relevant to bicycle types.On the basis of the principles of biomechanics and ergonomics knowledge,this paper presents a design method for bicycle three-pivot considering feature parameters of the rider by dynamic simulation.Firstly,a dynamic model of rider-bicycle system is built for a special rider,and a serial of simulation experiments is designed by uniform test method.Then,a mathematical model is built between the three-pivot position and the square of lower limb muscle stress by using simulation and regression analysis of the rider-bicycle system.The optimal three-pivot position parameters are obtained by setting the minimal of the square of the lower limb muscle stress as the objective.Therefore,the optimal parameters are gained for the specific rider.Finally,various results are gained for different riders based on the same design process.The function between feature parameters of the rider and the optimum three-pivot position parameters is built by regression.Bicycle design considering biomechanics can be divided into three main steps：calculating the three-pivot position,designing the geometrical structure of the bicycle frame and analyzing frame strength,and selecting appropriate parts and assembling the bicycle.Bicycle design considering biomechanics changes the conventional bicycle design and realizes customized design by considering human element in the design process.

Bayesian prediction of potential depressions in the Erlian Basin based on integrated geophysical parameters

In this study,we analyzed the geological,gravity,magnetic,and electrical characteristics of depressions in the Erlian Basin.Based on the results of these analyses,we could identify four combined feature parameters showing strong correlations and sensibilities to the reservoir oil-bearing conditions:the average residual gravity anomaly,the average magnetic anomaly,the average depth of the conductive key layer,and the average elevation of the depressions.The feature parameters of the 65 depressions distributed in the whole basin were statistically analyzed:each of them showed a Gaussian distribution and had the basis of Bayesian theory.Our Bayesian predictions allowed the defi nition of a formula to calculate the posterior probability of oil occurrence in the depressions based on the combined characteristic parameters.The feasibility of this prediction method was verifi ed by considering the results obtained for the 22 drilled depressions.Subsequently,we were able to determine the oilbearing threshold of hydrocarbon potential for the depressions in the Erlian Basin,which can be used as a standard for quantitative optimizations.Finally,the proposed prediction method was used to calculate the probability of hydrocarbons in the other 43 depressions.Based on this probability and on the oil-bearing threshold,the fi ve depressions with the highest potential were selected as targets for future seismic explorations and drilling.We conclude that the proposed method,which makes full use of massive gravity,magnetic,electric,and geological data,is fast,eff ective,and allows quantitative optimizations;hence,it will be of great value for the comprehensive geophysical evaluation of oil and gas in basins with depression group characteristics.

Identification of serous ovarian tumors based on polarization imaging and correlation analysis with clinicopathological features

Ovarian cancer is one of the most aggressive and heterogeneous female tumors in the world,and serous ovarian cancer(SOC)is of particular concern for being the leading cause of ovarian cancer death.Due to its clinical and biological complexities,ovarian cancer is still considered one of the most di±cult tumors to diagnose and manage.In this study,three datasets were assembled,including 30 cases of serous cystadenoma(SCA),30 cases of serous borderline tumor(SBT),and 45 cases of serous adenocarcinoma(SAC).Mueller matrix microscopy is used to obtain the polarimetry basis parameters(PBPs)of each case,combined with a machine learning(ML)model to derive the polarimetry feature parameters(PFPs)for distinguishing serous ovarian tumor(SOT).The correlation between the mean values of PBPs and the clinicopathological features of serous ovarian cancer was analyzed.The accuracies of PFPs obtained from three types of SOT for identifying dichotomous groups(SCA versus SAC,SCA versus SBT,and SBT versus SAC)were 0.91,0.92,and 0.8,respectively.The accuracy of PFP for identifying triadic groups(SCA versus SBT versus SAC)was 0.75.Correlation analysis between PBPs and the clinicopathological features of SOC was performed.There were correlations between some PBPs(δ,β,q_(L),E_(2),rqcross,P_(2),P_(3),P_(4),and P_(5))and clinicopathological features,including the International Federation of Gynecology and Obstetrics(FIGO)stage,pathological grading,preoperative ascites,malignant ascites,and peritoneal implantation.The research showed that PFPs extracted from polarization images have potential applications in quantitatively differentiating the SOTs.These polarimetry basis parameters related to the clinicopathological features of SOC can be used as prognostic factors.

Classification of wood surface texture based on Gauss-MRF Model

The basal theory of Gauss-MRF is expounded and 2-5 order Gauss MRF models are established. Parameters of the 2-5 order Gauss-MRF models for 300 wood samples＇ surface texture are also estimated by using LMS. The data analysis shows that： 1） different rexture parameters have a clear scattered distribution, 2） the main direction of texture is the direction represented by the maximum parameter of Gauss-MRF parameters, and 3） for those samples having the same main direction, the finer the texture is, the greater the corresponding parameter is, and the smaller the other parameters are; and the higher the order of Gauss-MRF is, the more clearly the texture is described. On the condition of the second order Gauss MRF model, parameter B1, B2 of tangential texture are smaller than that of radial texture, while B3 and B4 of tangential texture are greater than that of radial texture. According to the value of separated criterion, the parameter of the fifth order Gauss-MRF is used as feature vector for Hamming neural network classification. As a result, the ratio of correctness reaches 88%.

Polarimetry feature parameter deriving from Mueller matrix imaging and auto-diagnostic signicance to distinguish HSIL and CSCC

High-grade squamous intraepithelial lesion(HSIL)is regarded as a serious precancerous state of cervix,and it is easy to progress into cervical invasive carcinoma which highlights the importance of earlier diagnosis and treatment of cervical lesions.Pathologists examine the biopsied cervical epithelial tissue through a microscope.The pathological examination will take a long time and sometimes results in high inter-and intra-observer variability in outcomes.Polarization imaging techniques have broad application prospects for biomedical diagnosis such as breast,liver,colon,thyroid and so on.In our team,we have derived polarimetry feature parameters(PFPs)to characterize microstructural features in histological sections of breast tissues,and the accuracy for PFPs ranges from 0.82 to 0.91.Therefore,the aim of this paper is to distinguish automatically microstructural features between HSIL and cervical squamous cell carcinoma(CSCC)by means of polarization imaging techniques,and try to provide quantitative reference index for patho-logical diagnosis which can alleviate the workload of pathologists.Polarization images of the H&E stained histological slices were obtained by Mueller matrix microscope.The typical path-ological structure area was labeled by two experienced pathologists.Calculate the polarimetry basis parameter(PBP)statistics for this region.The PBP statistics(stat PBPs)are screened by mutual information(MI)method.The training method is based on a linear discriminant analysis(LDA)classier whichnds the most simplied linear combination from these stat PBPs and the accuracy remains constant to characterize the specic microstructural feature quantitatively in cervical squamous epithelium.We present results from 37 clinical patients with analysis regions of cervical squamous epithelium.The accuracy of PFP for recognizing HSIL and CSCC was 83.8%and 87.5%,respectively.This work demonstrates the ability of PFP to quantitatively charac-terize the cervical squamous epithelial lesions in the H&E pathological sections.Signicance:Polarization detection technology provides an effcient method for digital pathological diagnosis and points out a new way for automatic screening of pathological sections.

Correlation of image textures of a polarization feature parameter and the microstructures of liver fibrosis tissues

Mueller matrix imaging is emerging for the quantitative characterization of pathological microstructures and is especially sensitive to fibrous structures.Liver fibrosis is a characteristic of many types of chronic liver diseases.The clinical diagnosis of liver fibrosis requires time-consuming multiple staining processes that specifically target on fibrous structures.The staining proficiency of technicians and the subjective visualization of pathologists may bring inconsistency to clinical diagnosis.Mueller matrix imaging can reduce the multiple staining processes and provide quantitative diagnostic indicators to characterize liver fibrosis tissues.In this study,a fibersensitive polarization feature parameter(PFP)was derived through the forward sequential feature selection(SFS)and linear discriminant analysis(LDA)to target on the identification of fibrous structures.Then,the Pearson correlation coeffcients and the statistical T-tests between the fiber-sensitive PFP image textures and the liver fibrosis tissues were calculated.The results show the gray level run length matrix(GLRLM)-based run entropy that measures the heterogeneity of the PFP image was most correlated to the changes of liver fibrosis tissues at four stages with a Pearson correlation of 0.6919.The results also indicate the highest Pearson correlation of 0.9996 was achieved through the linear regression predictions of the combination of the PFP image textures.This study demonstrates the potential of deriving a fiber-sensitive PFP to reduce the multiple staining process and provide textures-based quantitative diagnostic indicators for the staging of liver fibrosis.

Application of Particle Swarm Optimization to Fault Condition Recognition Based on Kernel Principal Component Analysis

Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal kernel function parameter. We first comprehensively considered within-class scatter and between-class scatter of the sample features. Then, the fitness function of an optimized kernel function parameter is constructed, and the particle swarm optimization algorithm with adaptive acceleration （CPSO） is applied to optimizing it. It is used for gearbox condi- tion recognition, and the result is compared with the recognized results based on principal component analysis （PCA）. The results show that KPCA optimized by CPSO can effectively recognize fault conditions of the gearbox by reducing bind set-up of the kernel function parameter, and its results of fault recognition outperform those of PCA. We draw the conclusion that KPCA based on CPSO has an advantage in nonlinear feature extraction of mechanical failure, and is helpful for fault condition recognition of complicated machines.

Recognition of multi-carrier OFDM and single-carrier with alpha-stable distribution noise

In order to identify the multi-carrier orthogonal frequency division multiplexing(OFDM) and the single-carrier signal in the non-Gaussian noise environment, different features of the two signals are analyzed in terms of five parameters: generalized normalized fourth-order cumulant, the maximum value of the instantaneous amplitude power spectral density, absolute standard deviation of instantaneous phase on the section with weak signals, and position and numbers of the generalized cyclic spectrum's peak. The recognition method of the multi-carrier OFDM and single-carrier signal is proposed in the environment with alpha-stable distribution noise. Simulation results show that the recognition rate of the multi-carrier OFDM can reach 100% when the mixed signal to noise ratio(MSNR) is greater than-5 dB and the recognition rate can reach 90% for the single-carrier when the MSNR is greater than 2 dB.

An improved empirical wavelet transform method for rolling bearing fault diagnosis

Empirical wavelet transform(EWT)based on the scale space method has been widely used in rolling bearing fault diagnosis.However,using the scale space method to divide the frequency band,the redundant components can easily be separated,causing the band to rupture and making it difficult to extract rolling bearing fault characteristic frequency effectively.This paper develops a method for optimizing the frequency band region based on the frequency domain feature parameter set.The frequency domain feature parameter set includes two characteristic parameters:mean and variance.After adaptively dividing the frequency band by the scale space method,the mean and variance of each band are calculated.Sub-bands with mean and variance less than the main frequency band are combined with surrounding bands for subsequent analysis.An adaptive empirical wavelet filter on each frequency band is established to obtain the corresponding empirical mode.The margin factor sensitive to the shock pulse signal is introduced into the screening of empirical modes.The empirical mode with the largest margin factor is selected to envelope spectrum analysis.Simulation and experiment data show this method avoids over-segmentation and redundancy and can extract the fault characteristic frequency easier compared with only scale space methods.

Application of biomonitoring and support vector machine in water quality assessment

The behavior of schools of zebrafish （Danio rerio） was studied in acute toxicity environments. Behavioral features were extracted and a method for water quality assessment using support vector machine （SVM） was de- veloped. The behavioral parameters of fish were recorded and analyzed during one hour in an environment of a 24-h half-lethal concentration （LC50） of a pollutant. The data were used to develop a method to evaluate water quality, so as 6＋ 2＋ to give an early indication of toxicity. Four kinds of metal ions （Cu2~, Hg2~, Cr , and Cd ） were used for toxicity testing. To enhance the efficiency and accuracy of assessment, a method combining SVM and a genetic algorithm （GA） was used. The results showed that the average prediction accuracy of the method was over 80% and the time cost was acceptable. The method gave satisfactory results for a variety of metal pollutants, demonstrating that this is an effective approach to the classification of water quality.

Cooperative automatic modulation recognition in cognitive radio

In this article, a new effective method of cooperative modulation recognition （CMR） is proposed to recognize different modulation types of primary user for cognitive radio receivers. In the cognitive radio （CR） system, two CR users respectively send their feature parameters to the cooperative recognition center, which is composed of back propagation neural network （BPNN）. With two users＇ cooperation and the application of an error back propagation learning algorithm with momentum, the center improves the performance of modulation recognition, especially when one of the CR users＇ signal-to-noise ratio （SNR） is low. To measure the performance of the proposed method, simulations are carried out to classify different types of modulated signals corrupted by additive white Gaussian noise （AWGN）. The simulation results show that this cooperation algorithm has a better recognition performance than those without cooperation.