An improved interval model updating method via adaptive Kriging models

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction method.This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods.Therefore,an improved IMU method via the adaptive Kriging models is proposed.This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers.These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is accomplished.During the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity information.Local sampling is then performed in key subspaces based on the maximum mean square error(MMSE)criterion.The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements.The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell.The results show that the updated results of the interval model are in good agreement with the experimental results.

Non-equal-interval direct optimizing Verhulst model that x(n) be taken as initial value and its application

To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.

The burden of upper motor neuron involvement is correlated with the bilateral limb involvement interval in patients with amyotrophic lateral sclerosis:a retrospective observational study

Amyotrophic lateral sclerosis is a rare neurodegenerative disease characterized by the involvement of both upper and lower motor neurons.Early bilateral limb involvement significantly affects patients'daily lives and may lead them to be confined to bed.However,the effect of upper and lower motor neuron impairment and other risk factors on bilateral limb involvement is unclear.To address this issue,we retrospectively collected data from 586 amyotrophic lateral sclerosis patients with limb onset diagnosed at Peking University Third Hospital between January 2020 and May 2022.A univariate analysis revealed no significant differences in the time intervals of spread in different directions between individuals with upper motor neuron-dominant amyotrophic lateral sclerosis and those with classic amyotrophic lateral sclerosis.We used causal directed acyclic graphs for risk factor determination and Cox proportional hazards models to investigate the association between the duration of bilateral limb involvement and clinical baseline characteristics in amyotrophic lateral sclerosis patients.Multiple factor analyses revealed that higher upper motor neuron scores(hazard ratio[HR]=1.05,95%confidence interval[CI]=1.01–1.09,P=0.018),onset in the left limb(HR=0.72,95%CI=0.58–0.89,P=0.002),and a horizontal pattern of progression(HR=0.46,95%CI=0.37–0.58,P<0.001)were risk factors for a shorter interval until bilateral limb involvement.The results demonstrated that a greater degree of upper motor neuron involvement might cause contralateral limb involvement to progress more quickly in limb-onset amyotrophic lateral sclerosis patients.These findings may improve the management of amyotrophic lateral sclerosis patients with limb onset and the prediction of patient prognosis.

Corrected QT interval in cirrhosis:A systematic review and metaanalysis

BACKGROUND Corrected QT(QTc)interval is prolonged in patients with liver cirrhosis and has been proposed to correlate with the severity of the disease.However,the effects of sex,age,severity,and etiology of cirrhosis on QTc have not been elucidated.At the same time,the role of treatment,acute illness,and liver transplantation(Tx)remains largely unknown.AIM To determine the mean QTc in patients with cirrhosis,assess whether QTc is prolonged in patients with cirrhosis,and investigate whether QTc is affected by factors such as sex,age,severity,etiology,treatment,acute illness,and liver Tx.METHODS In the present systematic review and meta-analysis,the searching protocol“{[QTc]OR[QT interval]OR[QT-interval]OR[Q-T syndrome]}AND{[cirrhosis]OR[Child-Pugh]OR[MELD]}”was applied in PubMed,EMBASE,and Google Scholar databases to identify studies that reported QTc in patients with cirrhosis and published after 1998.Seventy-three studies were considered eligible.Data concerning first author,year of publication,type of study,method used,sample size,mean age,female ratio,alcoholic etiology of cirrhosis ratio,Child-Pugh A/B/C ratio,mean model for end-stage liver disease(MELD)score,treatment withβ-blockers,episode of acute gastrointestinal bleeding,formula for QT correction,mean pulse rate,QTc in patients with cirrhosis and controls,and QTc according to etiology of cirrhosis,sex,Child-Pugh stage,MELD score,and liver Tx status(pre-Tx/post-Tx)were retrieved.The Newcastle-Ottawa quality assessment scale appraised the quality of the eligible studies.Effect estimates,expressed as proportions or standardized mean differences,were combined using the randomeffects,generic inverse variance method of DerSimonian and Laird.Subgroup,sensitivity analysis,and meta-regressions were applied to assess heterogeneity.RESULTS QTc combined mean in patients with cirrhosis was 444.8 ms[95%confidence interval(CI):440.4-449.2;P<0.001 when compared with the upper normal limit of 440 ms],presenting high heterogeneity(I2=97.5%;95%CI:97.2%-97.8%);both Egger’s and Begg’s tests showed non-significance.QTc was elongated in patients with cirrhosis compared with controls(P<0.001).QTc was longer in patients with Child-Pugh C cirrhosis when compared with Child-Pugh B and A(P<0.001);Child-Pugh B patients presented longer QTc when compared with Child-Pugh A patients(P=0.003).The MELD score was higher in patients with cirrhosis with QTc>440 ms when compared with QTc≤440 ms(P<0.001).No correlation of QTc with age(P=0.693),sex(P=0.753),or etiology(P=0.418)was detected.β-blockers shortened QTc(P<0.001).QTc was prolonged during acute gastrointestinal bleeding(P=0.020).Tx tended to improve QTc(P<0.001).No other sources of QTc heterogeneity were revealed.CONCLUSION QTc is prolonged in cirrhosis independently of sex,age,and etiology but is correlated with severity and affected byβ-blockers and acute gastrointestinal bleeding.QTc is improved after liver Tx.

Prediction model of interval grey number based on DGM(1,1)

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

Improved unequal interval grey model and its applications

A new method to improve prediction precision of GM（1,1） model with unequal time interval is presented.The grey derivative is multiplied by a parameter to guarantee the time response function satisfying approximately exponential function distribution.To simplify the process of parametric estimation,an approximate value is taken for the multiplied parameter.Then the estimators of coefficient of development and grey action quantity can be derived.At the same time,the principle of the new information priority is also considered.We take the last item of the first-order accumulated generation operator（1-AGO） on raw data sequence as the initial condition in the time response function.Then the new information can be taken full advantage of through the improved initial condition.Some properties of this new model are also discussed.The presented method is actually a combination of improvement of grey derivative and improvement of the initial condition.The results of an example indicate that the proposed method can improve prediction precision prominently.

Intrusion Detection Algorithm Based on Model Checking Interval Temporal Logic

Model checking based on linear temporal logic reduces the false negative rate of misuse detection.However,linear temporal logic formulae cannot be used to describe concurrent attacks and piecewise attacks.So there is still a high rate of false negatives in detecting these complex attack patterns.To solve this problem,we use interval temporal logic formulae to describe concurrent attacks and piecewise attacks.On this basis,we formalize a novel algorithm for intrusion detection based on model checking interval temporal logic.Compared with the method based on model checking linear temporal logic,the new algorithm can find unknown succinct attacks.The simulation results show that the new method can effectively reduce the false negative rate of concurrent attacks and piecewise attacks.

EMPIRICAL LIKELIHOOD-BASED INFERENCE IN LINEAR MODELS WITH INTERVAL CENSORED DATA

An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.

Optimal dispatching method for integrated energy system based on robust economic model predictive control considering source-load power interval prediction

Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.

Uncertain Multidisciplinary Design Optimization on Next Generation Subsea Production System by Using Surrogate Model and Interval Method

The innovative Next Generation Subsea Production System(NextGen SPS)concept is a newly proposed petroleum development solution in ultra-deep water areas.The definition of NextGen SPS involves several disciplines,which makes the design process difficult.In this paper,the definition of NextGen SPS is modeled as an uncertain multidisciplinary design optimization(MDO)problem.The deterministic optimization model is formulated,and three concerning disciplines—cost calculation,hydrodynamic analysis and global performance analysis are presented.Surrogate model technique is applied in the latter two disciplines.Collaborative optimization(CO)architecture is utilized to organize the concerning disciplines.A deterministic CO framework with two disciplinelevel optimizations is proposed firstly.Then the uncertainties of design parameters and surrogate models are incorporated by using interval method,and uncertain CO frameworks with triple loop and double loop optimization structure are established respectively.The optimization results illustrate that,although the deterministic MDO result achieves higher reduction in objective function than the uncertain MDO result,the latter is more reliable than the former.

IFCEM based recognition method for target with interval-overlapped hybrid attributes

When the attributes of unknown targets are not just numerical attributes,but hybrid attributes containing linguistic attributes,the existing recognition methods are not effective.In addition,it is more difficult to identify the unknown targets densely distributed in the feature space,especially when there is interval overlap between attribute measurements of different target classes.To address these problems,a novel method based on intuitionistic fuzzy comprehensive evaluation model(IFCEM)is proposed.For numerical attributes,targets in the database are divided into individual classes and overlapping classes,and for linguistic attributes,continuous interval-valued linguistic term set(CIVLTS)is used to describe target characteristic.A cloud modelbased method and an area-based method are proposed to obtain intuitionistic fuzzy decision information of query target on numerical attributes and linguistic attributes respectively.An improved inverse weighted kernel fuzzy c-means(IWK-FCM)algorithm is proposed for solution of attribute weight vector.The possibility matrix is applied to determine the identity and category of query target.Finally,a case study composed of parameter sensitivity analysis,recognition accuracy analysis.and comparison with other methods,is taken to verify the superiority of the proposed method.

The AMSAA-BISE Model with Gap Intervals

In this paper, the AMSAA-BISE model with missing data is discussed. The ML estimates of model parameters and current MTBF are given, and the chi-squared test and a plot for cumulative number of failures versus cumulative testing time are used to test the goodness of fit for the model. This paper concludes with a numerical example to verify the model.

Stable Routh-Padé-type approximation in model reduction of interval systems

An interval Pade-type approximation is introduced and then Routh-Pade-type method （IRPTM） is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical

Interval standard neural network models for nonlinear systems

A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.

Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function

In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.

New approach to multiple attribute decision making with interval numbers

In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin＇s approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin＇s approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.

Stationarity Intervals of Time-Variant Channel in High Speed Railway Scenario

The non-stationary behavior, caused by the train rmverrent, is the rmin factor for the variation of high speed railway channel. To measure the tirce-variant effect, the parameter of stationarity interval, in which the channel keeps constant or has no great change, is adopted based on Zhengzfiou- Xi＇an （Zhengxi） passenger dedicated line measurement with different train speeds. The stationarity interval is calculated through the definition of Local Region of Stationarity （LRS） under three train ve- locities. Furthermore, the time non-stationary characteristic of high speed pared with five standard railway channel is corn- Multiple-Input MultipleOutput （MIMO） channel models, i.e. Spatial Channel Model （SCM）, extended version of SCM （SCME）, Wireless World Initiative New Radio Phase II （WINNERII）, International Mobile Teleconmnications-Advanced （IMT-Advanced） and WiMAX models which contain the high speed moving scenario. The stationarity interval of real channel is 9 ms in 80% of the cases, which is shorter than those of the standard models. Hence the real channel of high speed railway changes more rapidly. The stationarity intervals of standard models are different due to different modeling methods and scenario def- initions. And the compared results are instructive for wireless system design in high speed railway.

Liver cirrhosis-effect on QT interval and cardiac autonomic nervous system activity

AIM To examine the impact of liver cirrhosis on QT interval and cardiac autonomic neuropathy(CAN). METHODS A total of 51 patients with cirrhosis and 51 controls were examined. Standard 12-lead electrocardiogram recordings were obtained and QT as well as corrected QT interval(QTc) and their dispersions(dQT, dQTc) were measured and calculated using a computer-based program. The diagnosis of CAN was based upon the battery of the tests proposed by Ewing and Clarke and the consensus statements of the American Diabetes Association. CAN was diagnosed when two out of the four classical Ewing tests were abnormal. RESULTS QT, QTc and their dispersions were significantly longer(P < 0.01) in patients with cirrhosis than in controls. No significant differences in QT interval were found among the subgroups according to the etiology of cirrhosis. Multivariate regression analysis after controlling for age, gender and duration of cirrhosis demonstrated significant association between QT and presence of diabetes mellitus [standardized regression coefficient(beta) = 0.45, P = 0.02] and treatment with diuretics(beta = 0.55, P = 0.03), but not with the Child-Pugh score(P = 0.54). Prevalence of CAN was common(54.9%) among patients with cirrhosis and its severity was associated with the Child-Pugh score(r = 0.33, P = 0.02). Moreover, patients with decompensated cirrhosis had more severe CAN that those with compensated cirrhosis(P = 0.03). No significant association was found between severity of CAN and QT interval duration.CONCLUSION Patients with cirrhosis have QT prolongation. Treatment with diuretics is associated with longer QT. CAN is common in patients with cirrhosis and its severity is associated with severity of the disease.