Edge detection in the potential field using the correlation coefficients of multidirectional standard deviations

Most edge-detection methods rely on calculating gradient derivatives of the potential field, a process that is easily affected by noise and is therefore of low stability. We propose a new edge-detection method named correlation coefficient of multidirectional standard deviations（CCMS） that is solely based on statistics. First, we prove the reliability of the proposed method using a single model and then a combination of models. The proposed method is evaluated by comparing the results with those obtained by other edge-detection methods. The CCMS method offers outstanding recognition, retains the sharpness of details, and has low sensitivity to noise. We also applied the CCMS method to Bouguer anomaly data of a potash deposit in Laos. The applicability of the CCMS method is shown by comparing the inferred tectonic framework to that inferred from remote sensing（RS） data.

Weighted Parameterized Correlation Coefficients of Indeterminacy Fuzzy Multisets and Their Multicriteria Group Decision Making Method with Different Decision Risks

Real-life data introduce noise,uncertainty,and imprecision to statistical projects;it is advantageous to consider strategies to overcome these information expressions and processing problems.Neutrosophic(indeterminate)numbers can flexibly and conveniently represent the hybrid information of the partial determinacy and partial indeterminacy in an indeterminate setting,while a fuzzy multiset is a vital mathematical tool in the expression and processing of multi-valued fuzzy information with different and/or same fuzzy values.If neutrosophic numbers are introduced into fuzzy sequences in a fuzzy multiset,the introduced neutrosophic number sequences can be constructed as the neutrosophic number multiset or indeterminate fuzzy multiset.Motivated based on the idea,this study first proposes an indeterminate fuzzy multiset,where each element in a universe set can be repeated more than once with the different and/or identical indeterminate membership values.Then,we propose the parameterized correlation coefficients of indeterminate fuzzy multisets based on the de-neutrosophication of transforming indeterminate fuzzy multisets into the parameterized fuzzy multisets by a parameter(the parameterized de-neutrosophication method).Since indeterminate decision-making issues need to be handled by an indeterminate decision-making method,a group decision-making method using the weighted parameterized correlation coefficients of indeterminate fuzzy multisets is developed along with decision makers’different decision risks(small,moderate,and large risks)so as to handle multicriteria group decision-making problems in indeterminate fuzzy multiset setting.Finally,the developed group decision-making approach is used in an example on a selection problem of slope design schemes for an open-pit mine to demonstrate its usability and flexibility in the indeterminate group decision-making problem with indeterminate fuzzy multisets.

ON TESTING THE EQUALITY OF K MULTIPLE AND PARTIAL CORRELATION COEFFICIENTS

Coutsourides (1980) derives an ad hoc nuisance parameter removal test for testing the equality of two multiple correlation coefficients of two independent p variate normal populations, under the assumption that a sample of size n is available from each population. He also extends his ad hoc nuisance parameter removal test to the testing of the equality of two multiple correlation matrices. This paper presents likelihood ratio tests for testing the equality of k multiple correlation coefficients, and also k partial correlation coefficients.

ASSESSMENT OF LOCAL INFLUENCE FOR GENERALIZED CORRELATION COEFFICIENTS

In this paper, we study local influence analysis for Zhang's generalized correlation coefficients and Hotelling's generalized correlation coefficient by using approach. of local influence analysis suggested by Shi (1991), i.e., generalized influence function (GIF) and generalized Cook distance (GCD). An example is given to illustrate our results.

A Simulation Based Comparison of Correlation Coefficients with Regard to Type I Error Rate and Power

In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.

Correlation Study of Operational Data and System Performance of District Cooling System with Ice Storage

The district cooling system (DCS) with ice storage can reduce the peak electricity demand of the business district buildings it serves, improve system efficiency, and lower operational costs. This study utilizes a monitoring and control platform for DCS with ice storage to analyze historical parameter values related to system operation and executed operations. We assess the distribution of cooling loads among various devices within the DCS, identify operational characteristics of the system through correlation analysis and principal component analysis (PCA), and subsequently determine key parameters affecting changes in cooling loads. Accurate forecasting of cooling loads is crucial for determining optimal control strategies. The research process can be summarized briefly as follows: data preprocessing, parameter analysis, parameter selection, and validation of load forecasting performance. The study reveals that while individual devices in the system perform well, there is considerable room for improving overall system efficiency. Six principal components have been identified as input parameters for the cold load forecasting model, with each of these components having eigenvalues greater than 1 and contributing to an accumulated variance of 87.26%, and during the dimensionality reduction process, we obtained a confidence ellipse with a 95% confidence interval. Regarding cooling load forecasting, the Relative Absolute Error (RAE) value of the light gradient boosting machine (lightGBM) algorithm is 3.62%, Relative Root Mean Square Error (RRMSE) is 42.75%, and R-squared value (R2) is 92.96%, indicating superior forecasting performance compared to other commonly used cooling load forecasting algorithms. This research provides valuable insights and auxiliary guidance for data analysis and optimizing operations in practical engineering applications. .

The Application of Pearson Correlational Analysis Method in Air Quality Analysis of Beijing-Tianjin-Hebei Region

Based on the analysis of monitoring data on six pollution indexes of SO2, NO2, CO, O3, PM10 and PM2.5 from 53 monitoring points in 7 cities, including Beijing, Tianjin, Shijiazhuang, etc., from April 8 of 2014 to July 23 of 2014, this article adopted Pearson correlation coefficient method to determine the relevance among each pollutant of these cities with the help of SPSS. The results showed that such three leading indexes as SO2, PM10 and PM2.5 had strong correlation in Beijing, Tianjin and main cities of Hebei. Finally, some suggestions and preventive measures for the cooperative governance of air pollution in Beijing-Tianjin-Hebei Region were put forward, hoping this can help them.

A new heat transfer correlation for flow boiling in helically coiled tubes

Based on the superposition principle of the nucleate boiling and convective heat transfer terms,a new correlation is developed for flow boiling heat transfer characteristics in helically coiled tubes.The effects of the geometric and system parameters on heat transfer characteristics in helically coiled tubes are investigated by collecting large amounts of experimental data and analyzing the heat transfer mechanisms. The existing correlations are divided into two categories,and they are calculated with the experimental data.The Dn factor is introduced to take into account the effect of a complex geometrical structure on flow boiling heat transfer.A new correlation is developed for predicting the flow boiling heat transfer coefficients in the helically coiled tubes,which is validated by the experimental data of R134a flow boiling heat transfer in them;and the average relative error and root mean square error of the new correlation are calculated.The results show that the new correlation agrees well with the experimental data,indicating that the new correlation can be used for predicting flow boiling heat transfer characteristics in the helically coiled tubes.

Stochastic resonance based on correlation coefficient in parallel array of threshold devices

The phenomenon of stochastic resonance （SR） based on the correlation coefficient in a parallel array of threshold devices is discussed. For four representative noises： the Gaussian noise, the uniform noise, the Laplace noise and the Cauchy noise, when the signal is subthreshold, noise can improve the correlation coefficient and SR exists. The efficacy of SR can be significantly enhanced and the maximum of the correlation coefficient can dramatically approach to one as the number of the threshold devices in the parallel array increases. Two theorems are presented to prove that SR has some robustness to noises in the parallel array. These results further extend the applicability of SR in signal processing.

The Physical Significance of the Synthetic Running Correlation Coefficient and Its Applications in Oceanic and Atmospheric Studies

In order to study the temporal variations of correlations between two time series,a running correlation coefficient(RCC)could be used.An RCC is calculated for a given time window,and the window is then moved sequentially through time.The current calculation method for RCCs is based on the general definition of the Pearson product-moment correlation coefficient,calculated with the data within the time window,which we call the local running correlation coefficient(LRCC).The LRCC is calculated via the two anomalies corresponding to the two local means,meanwhile,the local means also vary.It is cleared up that the LRCC reflects only the correlation between the two anomalies within the time window but fails to exhibit the contributions of the two varying means.To address this problem,two unchanged means obtained from all available data are adopted to calculate an RCC,which is called the synthetic running correlation coefficient(SRCC).When the anomaly variations are dominant,the two RCCs are similar.However,when the variations of the means are dominant,the difference between the two RCCs becomes obvious.The SRCC reflects the correlations of both the anomaly variations and the variations of the means.Therefore,the SRCCs from different time points are intercomparable.A criterion for the superiority of the RCC algorithm is that the average value of the RCC should be close to the global correlation coefficient calculated using all data.The SRCC always meets this criterion,while the LRCC sometimes fails.Therefore,the SRCC is better than the LRCC for running correlations.We suggest using the SRCC to calculate the RCCs.

Improvement of Similarity Measure： Pearson Product-Moment Correlation Coefficient

Aim To study the reason of the insensitiveness of Pearson product-momentcorrelation coefficient as a similarity measure and the method to improve its sensitivity. MethodsExperimental and simulated data sets were used. Results The distribution range of the data setsinfluences the sensitivity of Pearson product-moment correlation coefficient. Weighted Pearsonproduct-moment correlation coefficient is more sensitive when the range of the data set is large.Conclusion Weighted Pearson product-moment correlation coefficient is necessary when the range ofthe data set is large.

Narrowband time delay estimation based on correlation coefficient

The problems of time delay estimation of narrowband signals are presented. The disadvantages of the existing algorithms are analyzed, and a new narrowband time delay estimating algorithm based on correlation coefficient is proposed. The original time delay information is transfered into the delay between the autocorrelation and cross-correlation function, and the precise estimating result by wave-comparison is given. The algorithm proposed here is also compared with other algorithms and its advantages over other algorithms are proved. The theoretical analysis and simulation show the effectiveness of the proposed algorithm.

Mathematical Proof of the Synthetic Running Correlation Coefficient and Its Ability to Reflect Temporal Variations in Correlation

The running correlation coefficient(RCC)is useful for capturing temporal variations in correlations between two time series.The local running correlation coefficient(LRCC)is a widely used algorithm that directly applies the Pearson correlation to a time window.A new algorithm called synthetic running correlation coefficient(SRCC)was proposed in 2018 and proven to be rea-sonable and usable;however,this algorithm lacks a theoretical demonstration.In this paper,SRCC is proven theoretically.RCC is only meaningful when its values at different times can be compared.First,the global means are proven to be the unique standard quantities for comparison.SRCC is the only RCC that satisfies the comparability criterion.The relationship between LRCC and SRCC is derived using statistical methods,and SRCC is obtained by adding a constraint condition to the LRCC algorithm.Dividing the temporal fluctuations into high-and low-frequency signals reveals that LRCC only reflects the correlation of high-frequency signals;by contrast,SRCC reflects the correlations of high-and low-frequency signals simultaneously.Therefore,SRCC is the ap-propriate method for calculating RCCs.

Wet-Dry Runoff Correlation in Western Route of South-to-North Water Diversion Project,China

The Western Route of the South-to-North Water Diversion Project is an important trans-basin diversion project to transfer water from the upstream Yangtze River and its tributaries （water-exporting area）, to the upstream of the Yellow River （water- importing area）. The long-term hydrologieal data from 14 stream gauging stations in the Western Route area and techniques including the pre-whitening approach, non-parametric test, Bayes, law, variance analysis extrapolation, and Wavelet Analysis are applied to identify the streamflow eharacteristics and trends, streamflow time series cross-correlations, wetness-dryness encountering probability, and periodicities that occurred over the last 50 years. The results show that the water-exporting area, water- importing area, and the streteh downstream of the water-exporting have synehronization in high-low flow relationship, whereas they display non- synchronization in long-term evolution. This corresponds to the complicated and variable climate of the plateau region. There is no obvious increasing or decreasing trend in runoff at any gauging station. The best hydrological eompensation probability for rivers where water is diverted is about 25% to lO%, and those rivers influenced significantly by diversion are the Jinsha and Yalong rivers. Proper planning and design of compensation reservoirs for the water-exporting area and stretch downstream of the water- exporting area can increase the hydrological compensation possibility from water-exporting area to the water-importing area, and reduce the impact on the stretch of river downstream of the water- exporting area.

Reliability Sensitivity-based Correlation Coefficient Calculation in Structural Reliability Analysis

The correlation coefficients of random variables of mechanical structures are generally chosen with experience or even ignored,which cannot actually reflect the effects of parameter uncertainties on reliability.To discuss the selection problem of the correlation coefficients from the reliability-based sensitivity point of view,the theory principle of the problem is established based on the results of the reliability sensitivity,and the criterion of correlation among random variables is shown.The values of the correlation coefficients are obtained according to the proposed principle and the reliability sensitivity problem is discussed.Numerical studies have shown the following results：（1） If the sensitivity value of correlation coefficient ρ is less than（at what magnitude 0.000 01）,then the correlation could be ignored,which could simplify the procedure without introducing additional error.（2） However,as the difference between ρs,that is the most sensitive to the reliability,and ρR,that is with the smallest reliability,is less than 0.001,ρs is suggested to model the dependency of random variables.This could ensure the robust quality of system without the loss of safety requirement.（3） In the case of ｜Eabs｜ρ0.001 and also ｜Erel｜ρ0.001,ρR should be employed to quantify the correlation among random variables in order to ensure the accuracy of reliability analysis.Application of the proposed approach could provide a practical routine for mechanical design and manufactory to study the reliability and reliability-based sensitivity of basic design variables in mechanical reliability analysis and design.

LARGE DEVIATION FOR THE EMPIRICAL CORRELATION COEFFICIENT OF TWO GAUSSIAN RANDOM VARIABLES

In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random variables X, Y with the means EX, EY （both known）, wherein the author gives two kinds of different proofs and gets the same results.

Zonal Differences in Correlation Patterns Between Soil Organic Carbon and Climate Factors at Multi-extent

Studying the relationship between climate factors and soil organic carbon （SOC） is vitally important. However, how SOC responses to climate （temperature and precipitation） at cohesive extents is poorly studied. Two transects of approximately the same length （transect P and transect T） were selected to examine the variation of SOC content in relation to mean annual temperature （MAT） and mean annual precipitation （MAP）. The coefficients of partial correlation between SOC density and MAT （Rt） and MAP （Rp） were determined to quantify the relationships between SOC density and the two climate factors. The results indicated that for transect T, Rt was statistically significant once the extent level was greater than or equal to two fundamental extent units, while for transect P, Rp showed statistical significance only at extent levels which were greater than two fundamental extent traits. At the same extent levels but in different transects, Rts exhibited no zonal difference, but Rps did once the extent level was greater than two fundamental extent units. Therefore, to study the relationship between SOC density and different climate factors, different minimum extent levels should be ex- amined. The results of this paper could deepen the understanding of the impacts that SOC pool has on terrestrial ecosystem and global carbon cycling.

Correlation Degree and Correlation Coefficient of Multi-Output Functions

We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency, the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multioutput functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

We study the correlation between detrended fluctuation analysis（DFA） and the Lempel-Ziv complexity（LZC） in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.

A Correlation Coefficient Approach for Evaluation of Stiffness Degradation of Beams Under Moving Load

This paper presents a new approach using correlation and cross-correlation coefficients to evaluate the stiffness degradation of beams under moving load.The theoretical study of identifying defects by vibration methods showed that the traditional methods derived from the vibration measurement data have not met the needs of the actual issues.We show that the correlation coefficients allow us to evaluate the degree and the effectiveness of the defects on beams.At the same time,the cross-correlation model is the basis for determining the relative position of defects.The results of this study are experimentally conducted to confirm the relationship between the correlation coefficients and the existence of the defects.In particular,the manuscript shows that the sensitivity of the correlation coefficients and cross-correlation is much higher than the parameters such as changes in stiffness(EJ)and natural frequency values(Δf).This study suggests using the above parameters to evaluate the stiffness degradation of beams by vibration measurement data in practice.