Based on M-Copula Reliability Analysis of Random Load Correlation

To improve the performance of a conventional rescue equipment, we designed a novel multi-functional rescue end-effector comprising a separation mechanism and a grasping mechanism. The failure causes of the separation mechanism are analyzed, and three main failure modes are determined. Meanwhile, their performance functions are established as well. To solve the complex correlations among multiple failure modes, a novel mixed copula function that can capture the upper and lower tail dependencies simultaneously is proposed, which comprises the Gumbel copula and the Clayton copula. Further, a novel procedure that adopts the non-parametric kernel density estimation (NKDE) technique to estimate the probability density function (PDF) and the cumulative distribution function (CDF) for each performance function of the separation mechanism is proposed. The parameters of the mixed copula function are estimated using the method of maximum likelihood estimation. Subsequently, to further study the separation mechanism’s reliability during working, a time-variant parameter estimation method is introduced to build the time-variant mixed copula function. Finally, both the reliability and time-variant reliability of the separation mechanism are analyzed via the proposed integral methods. Comparisons with other analysis schemes show that the proposed integral method is not only effective but also efficient in analyzing the reliability of our target mechanism.

Aiming at the problem that the existing modeling methods cannot accurately describe the probabilistic modeling of the joint power output of thermal-storage concentrating-photovoltaic solar power (CSP-PV) system. In this paper, based on the complementarity and correlation of CSP and PV power output in space and time, a method for establishing a probabilistic model of CSP-PV joint power output based on non-parametric Kernel Density Estimation and Copula function is proposed. First, the model is based on the historical data of CSP and PV, and uses non-parametric Kernel Density Estimation methods to establish the probability density functions of CSP and PV respectively; Then, according to the correlation between CSP and PV power output, the Copula function is used to establish the probability model of CSP-PV joint power output. Finally, the Nash-Sutcliffe efficiency, Root mean square error and Euclidean distance are used as evaluation indicators to determine the optimal Copula model. Taking the historical actual data of Jiuquan New Energy Base as an example, the simulation calculation shows the effectiveness and feasibility of the method in this paper.

To evaluate the impact of the randomness and correlation of photovoltaic (PV) and load on AC/DC systems with a multiport current flow controller (M-CFC), this paper proposes a probabilistic optimal power flow calculation for AC/DC systems based on a nonparametric kernel density estimation. First, according to the M-CFC model, the DC power flow calculation method with M-CFC was deduced, and its influence on line loss was analyzed. Second, a nonparametric kernel density estimation with an adaptive bandwidth was used to accurately describe the probability distribution of the PV and load, and correlation samples of the PV and load were obtained by the mixed copula function. Then an optimization model that considers system loss and static security was established, and a fast nondominated sorting genetic algorithm based on the elite strategy (NSGA-II) was used to calculate the multi-objective probability optimal power flow of the AC/DC system. Finally, a case study was performed on the modified IEEE39 bus system using measured PV and load data. We verified the nonparametric kernel density estimation with an adaptive bandwidth can better adapt to random component uncertainty, and M-CFC can improve the static security of the system.

Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models

Most studies in wind integration ignore either the temporal or spatial correlation of the power data, which decreases the accuracy of the results. The objective of this paper is to model and verify the temporal correlation of wind power data using Copula and nonparametric kernel density estimation (KDE). A model for reconstructing wind power time series is proposed based on Copula theory. This model preserves the time correlation characteristics of the original wind power sequence as much as possible, which facilitates the subsequent research on the uncertainty of evolution over time. Then, based on the nonparametric KDE and maximum likelihood estimation algorithm, by selecting appropriate correlation coefficients, a time correlation model of Gaussian Copula is established and applied to the actual dataset of a wind farm in GEFCOM2014. Finally, the boxwhisker plot and the autocorrelation function are used to verify the uncertainty characteristics of the reconstructed sequence, and the accuracy of the fit is further proved by the root mean square error in both short-term and long-term case studies. From the comparison with original time series data, as well as the numerical results, the effectiveness of the proposed method is illustrated.

Worldwide Equity Risk Forecasting with GARCH Models

Fault detection in non-stationary processes is a timely research topic in industrial process monitoring. The core objective of this research is to tackle anomaly detection in non-stationary industrial processes with manipulated set-point changes and uncertainties in the prior knowledge about the statistical nature of the measurements. In this research, the fault detection problem is investigated from an unsupervised perspective and a modified PCA approach is proposed. This method utilizes the base-line loading matrices and an upper bound to be determined for the variation range of time-series to relax the assumption on stationary characteristics. Hence, the mean used for normalizing the time-series are adaptively updated (using soft-calculation) without any need for a high-complexity recalibration procedure as needed in other existing adaptive/recursive PCA methods. Moreover, the first- and second-order error indices are introduced to monitor the statistical behaviour of process measurements. To develop a more reliable system condition indicator, an overall health index is given based on the proposed features using a non-parametric kernel density estimator (KDE). The proposed approach does not require a heavy online calculation in comparison with the existing adaptive solutions and it can successfully detect faults from healthy measurements’ mean changes. Finally, an alarm generator algorithm is presented which generates two alarm types, caution and actual fault for processes operators, utilizing the proposed overall health index. The effectiveness of the modified PCA approach is validated by both numerical examples and industrial case studies.

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric univariate kernel density estimation method to the interpoint distances to estimate the density around a data member. Our clustering algorithm is simple in its formation and easy to apply resulting in well-defined clusters. The algorithm starts with objective selection of the initial cluster representative and always converges independently of this choice. The method finds the number of clusters itself and can be used irrespective of the nature of underlying data by using an appropriate interpoint distance measure. The cluster analysis can be carried out in any dimensional space with viability to high-dimensional use. The distributions of the data or their interpoint distances are not required to be known due to the design of our procedure, except the assumption that the interpoint distances possess a density function. Data study shows its effectiveness and superiority over the widely used clustering algorithms.

Roughly capturing the general trend of load changes leads to large prediction errors. To address this, a power system power prediction error optimization model based on a self-supervised learning temporal convolutional network is proposed. A feature extraction unit containing modules such as self-attention is constructed to implicitly represent historical power interaction information through multi-dimensional transformation and calculation. Various operations are combined, and a mutual information maximization unit is constructed. After preprocessing and training, latent temporal features of power are mined. Based on a temporal convolutional network integrating multiple convolutions, an attention mechanism and autoregressive components are introduced, integrating linear and nonlinear components. The Dropout method is used to reduce overfitting, thus constructing a power prediction model. The nonparametric statistical kernel density estimation method is used to model the deviation probability distribution, calculate the deviation interval probability, analyze the effective deviation, and then adjust the model parameters accordingly, completing the construction of the power system power prediction error optimization model. Experiments show that the predicted curve of the proposed method has a high degree of fit with the actual curve. Key indicators such as MAE, RMSE, and MAPE are all controlled within 2%. Compared with the comparison methods, its residual curve fluctuates more closely around the zero value with small fluctuations, and the R 2 value is significantly higher, significantly reducing the prediction error.

With the increasingly severe global climate change problem, accurate monitoring and assessment of carbon emissions have become increasingly critical. However, the measurement of carbon emissions is often accompanied by uncertainty and errors, and the statistical characteristics of these errors require further investigation. This paper aims to explore the error probability statistical modeling of the electric carbon coupling relationship and to quantify and analyze the associated error by developing a non-parametric kernel density estimation model. Analysis of actual data from coal-fired power plants demonstrates that the proposed model effectively fits the coupling errors between electricity generation and carbon emissions.

In the linear model y = x′β + u where x is a regressor vector and E(u | x)= 0, we estimate β in E(y | x)= x′β However, the assumption of the linear model, or any nonlinear model for that matter, is a strong one. In nonparametric regression, we try to estimate E(y | x) without specifying the functional form. Since $$E(y{\kern 1pt} |{\kern 1pt} x) = \smallint y \cdot f(y|x)dy = \smallint y \cdot \{ f(y,x)/f(x)\} dy $$ (1.1) if we can estimate f(y, x) and f(x), we can also estimate E(y | x). In this chapter, we study nonparametric density estimation for x as a prelude to nonparametric regression in the next chapter. We will assume that x has a continuous density function f (x) If x is discrete, one can estimate P(x = x 0) either with the same estimation method used for the continuous case or with the number of observations with x i = x 0. There are several nonparametric density estimation methods available. The most popular is “kernel density estimation method” which we explore mainly. Other methods will be examined briefly in the last section. See Prakasa Rao (1983), Silverman (1986), Izenman (1991), Rosenblatt (1991) and Scott (1992) for more on nonparametric density estimation in general.

With the increasing proportion of wind power access in southern China, the impact of the randomness and volatility of wind power generation on power system operation cannot be ignored. Therefore, it is necessary to study the characteristics and random distribution of wind power generation in southern China. Firstly, the influence of time and geographical factors on wind power generation characteristics is analyzed. Secondly, an improved non-parametric kernel density estimation method considering the optimal bandwidth selection of kernel function is proposed to establish the random distribution models of wind power generation in five southern provinces under multiple time scales. The evaluation index system of model fitting effect is also established. Thirdly, the effectiveness of the improved non-parametric kernel density estimation method proposed is verified by comparing with two parameter estimation methods based on typical empirical distribution function. Finally, the differences of probability characteristics of wind power generation in different provinces of southern China are analyzed by daily, quarterly and annual time scales, which can play an auxiliary role in decision-making of power system dispatching, power planning, site selection and capacity determination of wind farms.

Estimators for derivatives associated with a density function can be useful in identifying its modes and inflection points. In addition, these estimators play an important role in plug-in methods associated with bandwidth selection in nonparametric kernel density estimation. In this paper, we extend the nonparametric class of density estimators proposed by Mynbaev and Martins-Filho (2010) to the estimation of m-order density derivatives. Contrary to some existing derivative estimators, the estimators in our proposed class have a full asymptotic characterization, including uniform consistency and asymptotic normality. An expression for the bandwidth that minimizes an asymptotic approximation for the estimators’ integrated squared error is provided. A Monte Carlo study sheds light on the finite sample performance of our estimators and contrasts it with that of density derivative estimators based on the classical Rosenblatt–Parzen approach.

Purpose This study aims to investigate the coupling coordination relationship between new infrastructure construction (NIC) and high-quality development (HQD) from the perspective of urban agglomerations, analyse its spatial-temporal evolution characteristics and reveal the underlying driving mechanisms. Design/methodology/approach This study focuses on the Shandong Peninsula urban agglomeration. By creating an indicator system for NIC and HQD, the study explores the coupling coordination degree (CCD) by employing the entropy weight approach and CCD model. Furthermore, it analyses the spatial-temporal evolution characteristics and influencing factors by using nonparametric kernel density estimation, the Dagum Gini coefficient and the Tobit panel regression model. Findings 1) Over time, the developmental levels of NIC and HQD within urban agglomerations and their CCD have shown a steady upward trend. (2) In terms of spatial distribution, the CCD between NIC and HQD within urban agglomerations exhibits a “core-periphery” structure. (3) The CCD of NIC and HQD is influenced by various factors. Originality/value Current research mainly emphasises national and provincial levels, exhibiting a paucity of studies centred on urban agglomerations. Most studies emphasise the effect of NIC on specific fields, indirectly exploring its role in HQD. However, a systematic understanding of the overall development trends of both is lacking. This study provides quantitative support for policies aimed at building a modern NIC system and advancing HQD collaboratively within urban agglomerations.

Mixture models have been widely used for data clustering. However, commonly used mixture models are generally of a parametric form (e.g., mixture of Gaussian distributions or GMM), which significantly limits their capacity in fitting diverse multidimensional data distributions encountered in practice.We propose a non-parametric mixture model (NMM) for data clustering in order to detect clusters generated from arbitrary unknown distributions, using non-parametric kernel density estimates. The proposed model is non-parametric since the generative distribution of each data point depends only on the rest of the data points and the chosen kernel. A leave-one-out likelihood maximization is performed to estimate the parameters of the model. The NMM approach, when applied to cluster high dimensional text datasets significantly outperforms the state-of-the-art and classical approaches such as K-means, Gaussian Mixture Models, spectral clustering and linkage methods.