Confidence Level Based on Ridge Estimator in Process Measurement and Its Application

Ordinary least squares(OLS) algorithm is widely applied in process measurement, because the sensor model used to estimate unknown parameters can be approximated through multivariate linear model. However, with few or noisy data or multi-collinearity, unbiased OLS leads to large variance. Biased estimators, especially ridge estimator, have been introduced to improve OLS by trading bias for variance. Ridge estimator is feasible as an estimator with smaller variance. At the same confidence level, with additive noise as the normal random variable, the less variance one estimator has, the shorter the two-sided symmetric confidence interval is. However, this finding is limited to the unbiased estimator and few studies analyze and compare the confidence levels between ridge estimator and OLS. This paper derives the matrix of ridge parameters under necessary and sufficient conditions based on which ridge estimator is superior to OLS in terms of mean squares error matrix, rather than mean squares error.Then the confidence levels between ridge estimator and OLS are compared under the condition of OLS fixed symmetric confidence interval, rather than the criteria for evaluating the validity of different unbiased estimators. We conclude that the confidence level of ridge estimator can not be directly compared with that of OLS based on the criteria available for unbiased estimators, which is verified by a simulation and a laboratory scale experiment on a single parameter measurement.

Evaluating the confidence level of Traditional Chinese Medicine in nursing undergraduates at Chinese medical university

Objective:To observe the confidence level prevailing with regard to the practice of Traditional Chinese Medicine(TCM)among undergraduate nursing students who have undertaken TCM courses at Shanxi Medical University.Methods:This cross-sectional study was conducted at Shanxi University of Chinese Medicine.A questionnaire survey was administered through the Questionnaire Star website(https://www.questionstar.com/).The confidence level was examined from 6 aspects,namely cognition of TCM culture and theory,advantages and characteristics of TCM diagnosis and treatment,feelings about TCM achievements,personal behaviors related to TCM,attitudes toward Western medicine,and the future of TCM.The mean score of the observed items was calculated,and was found to be positively related to the confidence level concerning TCM(the score was between 1 and 5).Results:A total of 120 participants voluntarily enrolled themselves in the study.The results showed that the mean score of observed items were generally about 4.A relatively strong confidence was shown in understating TCM advantages and characteristics in diagnosis and treatment,and also in feelings toward TCM achievements.Conclusions:The majority of nursing undergraduates had confidence in TCM.However,some aspects such as the understanding of TCM culture and the correlation between TCM and Western medicine may need to be improved through education.

Confidence Level of System Spares OptimizationUsing Fuzzy Theory

To obtain a higher readiness for a complex system, the common method is to store some spares. Confidence level of system spares is an important parameter to control the probability of the spares required. By introducing fuzzy theory, this paper allocates the confidence level of system spares to its subsystems, thus to achieve a rational management of system spares,

Aggregation operators and CRITIC-VIKOR method for confidence complex q-rung orthopair normal fuzzy information and their applications

Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and purchasers is becoming progressively familiar as all industries are moving towards a massive sustainable potential.To handle such sort of developments in supply chain management the involvement of fuzzy settings and their generalisations is playing an important role.Keeping in mind this role,the aim of this study is to analyse the role and involvement of complex q-rung orthopair normal fuzzy(CQRONF)information in supply chain management.The major impact of this theory is to analyse the notion of confidence CQRONF weighted averaging,confidence CQRONF ordered weighted averaging,confidence CQRONF hybrid averaging,confidence CQRONF weighted geometric,confidence CQRONF ordered weighted geometric,confidence CQRONF hybrid geometric operators and try to diagnose various properties and results.Furthermore,with the help of the CRITIC and VIKOR models,we diagnosed the novel theory of the CQRONF-CRITIC-VIKOR model to check the sensitivity analysis of the initiated method.Moreover,in the availability of diagnosed operators,we constructed a multi-attribute decision-making tool for finding a beneficial sustainable supplier to handle complex dilemmas.Finally,the initiated operator's efficiency is proved by comparative analysis.

Reliability Analysis of Wind Turbine Gearbox Based on the Optimal Confidence Limit Method

Based on the zero-failure data of 30 Chinese 1. 5 MW wind turbine gearboxes( WTGs),the optimal confidence limit method was developed to predict the reliability and reliability lifetime of WTG. Firstly,Bayesian method and classical probability estimation method were introduced to estimate the value interval of shape parameter considering the engineering practice. Secondly,taking this value interval into the optimal confidence limit method,the reliability and reliability lifetime of WTG could be obtained under different confidence levels. Finally,the results of optimal confidence limit method and Bayesian method were compared. And the comparison results show that the rationality of this estimated range.Meantime, the rule of confidence level selection in the optimal confidence limit method is provided, and the reliability and reliability lifetime prediction of WTG can be acquired.

Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method

An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.

RANDOMIZATION METHOD OF DETERMINISTIC EQUATION FOR PROBABILITY FRACTURE MECHANICS

In order to obtain any probability of survival for crack growth life, a randomization method of deterministic equation for probability fracture mechanics is presented. According to this method, the deterministic equation of fracture mechanics is randomized to stochastic equation, and the parameters of the stochastic equation are estimated by means of the statistics. Three new kinds of random models to gain the p d a/ d N Δ K curve and the γ p d a/ d N Δ K curve (confidence level probability of survival fatigue crack growth rate stress intensity factor range curve) are proposed by using this randomization method. And the p d a/ d N Δ K curves and the γ p d a/ d N Δ K curves determined by these three models are discussed and compared according to the treatment result of the experimental data from CT specimens. From examples, it is found that the three deterministic fatigue crack growth rate equations determined by these models are very near and in agreement with the traditional deterministic fatigue crack growth rate equation, and these models are effectively and easily used to treat fatigue crack growth rate data.

Application of apparent stress in earthquake prediction

On the basis of the assumption that ω^2 model accords with source displacement spectra of moderate-small shocks, we calculate the apparent stress values of 1 020 moderate-small shocks recorded by the Digital Seismic Network of Yunnan Province by using the low-frequency fiat level and corner frequencies. The results show that the apparent stress is of good significance in earthquake prediction. The moderate-small shock with apparent stress larger than 0.9 MPa can be used as a referential index to predict moderate-strong earthquakes in Yunnan area. And its relevant predictability evaluation （R value） has a high confidence level.

Novel serpentine structure design method considering confidence level and estimation precision

Due to the importance of metal layers in the product yield,serpentine test structures are usually fabricated on test chips to extract parameters for yield prediction.In this paper,the confidence level and estimation precision of the average defect density on metal layers are investigated to minimize the randomness of experimental results and make the measured parameters more convincing.On the basis of the Poisson yield model,the method to determine the total area of all serpentine test structures is obtained using the law of large numbers and the Lindeberg-Levy theorem.Furthermore,the method to determine an adequate area of each serpentine test structure is proposed under a specific requirement of confidence level and estimation precision.The results of Monte Carlo simulation show that the proposed method is consistent with theoretical analyses.It is also revealed by wafer experimental results that the method of designing serpentine test structure proposed in this paper has better performance.

A new via chain design method considering confidence level and estimation precision

For accurate prediction of via yield, via chains are usually fabricated on test chips to investigate issues about vias. To minimize the randomness of experiments and make the testing results more convincing, the confidence level and estimation precision of the via failure rate are investigated in this paper. Based on the Poisson yield model, the method of determining an adequate number of total vias is obtained using the law of large numbers and the de Moivre-Laplace theorem. Moreover, for a specific confidence level and estimation precision, the method of determining a suitable via chain length is proposed. For area minimization, an optimal combination of total vias and via chain length is further determined. Monte Carlo simulation results show that the method is in good accordance with theoretical analyses. Results of via failure rates measured on test chips also reveal that via chains designed using the proposed method has a better performance. In addition, the proposed methodology can be extended to investigate statistical significance for other failure modes.

A Confidence-based Consensus Model for Multi-Attribute Group Decision Making:Exploring the Bounded Trust Propagation and Personalized Adjustment Willingness

Social trust network(STN)and minimum cost consensus(MCC)models have been widely used to address consensus issues in multi-attribute group decision-making(MAGDM)problems with limited resources.However,most researchers have overlooked the decision maker‘(DMs)’confidence levels(CLs)and adjustment willingness implicit in their evaluations.To address these problems,this paper explores a confidence-based MCC model that considers DMs’adjustment willingness in the STN.The proposed model includes several modifications to the traditional trust propagation and consensus optimization models.Firstly,the improved method for measuring CLs of DMs and the confidence-based normalization approach are defined,respectively.Secondly,the bounded trust propagation operator is proposed,which considers the credibility of mediators to complete the STN.Thirdly,the identification rules based on the consensus index and CL are defined,and the MCC model with personalized cost functions and acceptable adjustment thresholds is built to automatically generate adjustment values for non-consensus DMs.Finally,a model to identify the non-cooperative behavior at the element level is established and the hybrid MCC model with persuasion strategies is provided.Finally,a case study is processed to verify the applicability of the proposed model,and comparison and sensitivity analysis are conducted to highlight its benefits.

FUZZY STABILITY ANALYSIS OF MODE COUPLING CHATTER ON CUTTING PROCESS

The influence of fuzzy uncertainty factors is considered on the analysis of chatter occurring during machine tool cutting process. Using fuzzy mathematics analysis methods, a detailed discussion over fuzzy stability analysis problems is presented related to the mode coupling chatter with respect to intrinsic structure fuzzy factors, and the possibility distribution of the fuzzy stability cutting range and the confidence level expressions of the fuzzy stability cutting width are given.

Investigation on Thermal Contact Conductance Based on Data Analysis Method of Reliability

The method of reliability is proposed for the investigation of thermal contact conductance （TCC） in this study. A new defini- tion is introduced, namely reliability thermal contact conductance （RTCC）, which is defined as the TCC value that meets the reliability design requirement of the structural materials under consideration. An experimental apparatus with the compensation heater to test the TCC is introduced here. A practical engineering example is utilized to demonstrate the applicability of the pro- posed approach. By using a statistical regression model along with experimental data obtained from the interfaces of the struc- tural materials GH4169 and K417 used in aero-engine, the estimate values and the confidence level of TCC and RTCC values are studied and compared. The results show that the testing values of TCC increase with interface pressure and the proposed RTCC model matches the test results better at high interface pressure.

A new global land productivity dynamic product based on the consistency of various vegetation biophysical indicators

Changes in land productivity have been endorsed by the Inter Agency Expert Group on Sustainable Development Goals(IAEGSDGs)as key indicators for monitoring SDG 15.3.1.Multiple vegeta-tion parameters from optical remote sensing techniques have been widely utilized across different land productivity decline processes and scales.However,there is no consensus on indicator selection and their effectiveness at representing land productivity declining at different scales.This study proposes a fusion framework that incorporates the trends and consistencies within the four com-monly used remote sensing-based vegetation indicators.We ana-lyzed the differences among the four vegetation parameters in different land cover and climate zones,finally producing a new global land productivity dynamics(LPD)product with confidence level degrees.The LPD classes indicated by the four vegetation indicators(VIs)showed that all three levels(low,medium,and high confidence)of increasing area account for 23.99%of the global vegetated area and declining area account for 7.00%.The Increase high-confidence(HC)area accounted for 2.77%of the total area,and the Decline-HC accounted for 0.35%of the total area.This study demonstrates the accuracy of the high-confidence(HC)area for the evaluation of land productivity decline and increase.The“forest”landcover type and“humid”climate zone had the largest increasing and declining area but had the lowest high-confidence proportion.The data product provides an important and optional reference for the assessment of SDG 15.3.1 at global and regional scales according to the specific application target.

A PROPORTIONAL 3-TUPLE FUZZY LINGUISTIC REPRESENTATION MODEL FOR SCREENING NEW PRODUCT PROJECTS

It is critically important for companies to screen new product projects before they are launched to the market. So far, many approaches have been developed for tackling the process of screening product innovations. Due to uncertain, vague and incomplete information as well as dynamically complex process regarding to new product development （NPD）, a fuzzy linguistic approach employed linguistic assessments and the fuzzy-set-based computation is reasonable for screening new products. However, such a fuzzy linguistic approach faces with various defects and limitations, such as loss of information, failing in considering the aspects related to human nature on uncertain subjective judgments etc. These defects and limitations lead to a dilemma, i.e., it＇s very difficult to screen new product projects reasonably and precisely. In this paper, we propose a notion of proportional 3-tuple to represent a linguistic assessment and related ignoring information, and a preference-preserving proportional 3-tuple transformation for the unification of linguistic assessments represented by proportional 3-tuples between two different linguistic term sets. On this basis, a proportional 3-tuple fuzzy linguistic representation model for screening new product projects is developed. It is shown that the proposed model is flexible to handle uncertain, vague and incomplete information related to screening new product projects. It not only allows evaluators to express their subjective judgments with different confidence levels, but is also able to deal with incomplete linguistic assessments. Ultimately, the proposed model also improves the precision and reasonability of the screening result.

Probabilistic safety assessment of self-centering steel braced frame

The main drawback of conventional braced frames is implicitly accepting structural damage under the design earthquake load, which leads to considerable economic losses. Controlled rocking self-centering system as a modem low-damage system is capable of minimizing the drawbacks of conventional braced frames. This paper quantifies main limit states and investigates the seismic performance of self-centering braced frame using a Probabilistic Safety Assessment procedure. Margin of safety, confidence level, and mean annual frequency of the self-centering archetypes for their main limit states, including PT yield, fuse fracture, and global collapse, are established and are compared with their acceptance criteria. Considering incorporating aleatory examined. Results of the investigation indicate that the provide the adequate margin of safety against exceeding and epistemic uncertainties, the efficiency of the system is design of low- and mid-rise self-centering archetypes could the undesirable limit-states.