Change Point Detection for Process Data Analytics Applied to a Multiphase Flow Facility

Change point detection becomes increasingly important because it can support data analysis by providing labels to the data in an unsupervised manner.In the context of process data analytics,change points in the time series of process variables may have an important indication about the process operation.For example,in a batch process,the change points can correspond to the operations and phases defined by the batch recipe.Hence identifying change points can assist labelling the time series data.Various unsupervised algorithms have been developed for change point detection,including the optimisation approachwhich minimises a cost functionwith certain penalties to search for the change points.The Bayesian approach is another,which uses Bayesian statistics to calculate the posterior probability of a specific sample being a change point.The paper investigates how the two approaches for change point detection can be applied to process data analytics.In addition,a new type of cost function using Tikhonov regularisation is proposed for the optimisation approach to reduce irrelevant change points caused by randomness in the data.The novelty lies in using regularisation-based cost functions to handle ill-posed problems of noisy data.The results demonstrate that change point detection is useful for process data analytics because change points can produce data segments corresponding to different operating modes or varying conditions,which will be useful for other machine learning tasks.

Comparative Analysis of Climatic Change Trend and Change-Point Analysis for Long-Term Daily Rainfall Annual Maximum Time Series Data in Four Gauging Stations in Niger Delta

The aim of this study is to establish the prevailing conditions of changing climatic trends and change point dates in four selected meteorological stations of Uyo, Benin, Port Harcourt, and Warri in the Niger Delta region of Nigeria. Using daily or 24-hourly annual maximum series (AMS) data with the Indian Meteorological Department (IMD) and the modified Chowdury Indian Meteorological Department (MCIMD) models were adopted to downscale the time series data. Mann-Kendall (MK) trend and Sen’s Slope Estimator (SSE) test showed a statistically significant trend for Uyo and Benin, while Port Harcourt and Warri showed mild trends. The Sen’s Slope magnitude and variation rate were 21.6, 10.8, 6.00 and 4.4 mm/decade, respectively. The trend change-point analysis showed the initial rainfall change-point dates as 2002, 2005, 1988, and 2000 for Uyo, Benin, Port Harcourt, and Warri, respectively. These prove positive changing climatic conditions for rainfall in the study area. Erosion and flood control facilities analysis and design in the Niger Delta will require the application of Non-stationary IDF modelling.

Detecting Climate Change Trend, Size, and Change Point Date on Annual Maximum Time Series Rainfall Data for Warri, Nigeria

The study focused on the detection of indicators of climate change in 24-hourly annual maximum series (AMS) rainfall data collected for 36 years (1982-2017) for Warri Township, using different statistical methods yielded a statistically insignificant positive mild trend. The IMD and MCIMD downscaled model’s time series data respectively produced MK statistics varying from 1.403 to 1.4729, and 1.403 to 1.463 which were less than the critical Z-value of 1.96. Also, the slope magnitude obtained showed a mild increasing trend in variation from 0.0189 to 0.3713, and 0.0175 to 0.5426, with the rate of change in rainfall intensity at 24 hours duration as 0.4536 and 0.42 mm/hr.year (4.536 and 4.2 mm/decade) for the IMD and the MCIMD time series data, respectively. The trend change point date occurred in the year 2000 from the distribution-free CUSUM test with the trend maintaining a significant and steady increase from 2010 to 2015. Thus, this study established the existence of a trend, which is an indication of a changing climate, and satisfied the condition for rainfall Non-stationary intensity-duration-frequency (NS-IDF) modeling required for infrastructural design for combating flooding events.

Probabilistic modeling of multifunction radars with autoregressive kernel mixture network

The task of modeling and analyzing intercepted multifunction radars(MFRs)pulse trains is vital for cognitive electronic reconnaissance.Existing methodologies predominantly rely on prior information or heavily constrained models,posing challenges for non-cooperative applications.This paper introduces a novel approach to model MFRs using a Bayesian network,where the conditional probability density function is approximated by an autoregressive kernel mixture network(ARKMN).Utilizing the estimated probability density function,a dynamic programming algorithm is proposed for denoising and detecting change points in the intercepted MFRs pulse trains.Simulation results affirm the proposed method's efficacy in modeling MFRs,outperforming the state-of-the-art in pulse train denoising and change point detection.

Does Biochar Addition Influence the Change Points of Soil Phosphorus Leaching?

Phosphorus change point indicating the threshold related to P leaching, largely depends on soil properties. Increasing data have shown that biochar addition can improve soil retention capacity of ions. However, we have known little about weather biochar amendment influence the change point of P leaching. In this study, two soils added with 0, 5, 10, 20, and 50 g biochar kg-1 were incubated at 25℃ for 14 d following adjusting the soil moisture to 50% water-holding capacity （WHC）. The soils with different available P values were then obtained by adding a series of KH2PO4 solution （ranging from 0 to 600 mg P kg-1 soil）, and subjecting to three cycles of drying and rewetting. The results showed that biochar addition significantly lifted the P change points in the tested soils, together with changes in soil pH, organic C, Olen-P and CaC12-P but little on exchangeable Ca and Mg, oxalate-extractable Fe and Al. The Olsen-P at the change points ranged from 48.65 to 185.07 mg kg-1 in the alluvial soil and 71.25 to 98.65 mg kg^-1 in the red soil, corresponding to CaCl2-P of 0.31-6.49 and 0.18-0.45 mg L~, respectively. The change points of the alluvial soil were readily changed by adding biochar compared with that of the red soil. The enhancement of change points was likely to be explained as the improvement of phosphate retention ability in the biochar-added soils.

Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

Damage Position of Concrete Beam Based on Test of Even Change Point

The quantitative analysis of damage position of concrete beam is established.The method of damage position free of models used in this paper is based on the variations of strain mode and test of even change point.The discrete model and the position criterion are presented.Numerical example is conducted,the result demonstrates that the method of damage position is correct and effective.

Recognition Method for Change Point of Traffic Flow Linear Regressions

Recognition method of traffic flow change point was put forward based on traffic flow theory and the statistical change point analysis of multiple linear regressions. The method was calibrated and tested with the field data of Liantong Road of Zibo city to verify the validity and the feasibility of the theory. The results show that change point method of multiple linear regression can make out the rule of quantitative changes in traffic flow more accurately than ordinary methods. So, the change point method can be applied to traffic information management system more effectively.

Non-Stationary Trend Change Point Pattern Using 24-Hourly Annual Maximum Series (AMS) Precipitation Data

This paper mainly investigated the basic information about non-stationary trend change point patterns. After performing the investigation, the corresponding results show the existence of a trend, its magnitude, and change points in 24-hourly annual maximum series (AMS) extracted from monthly maximum series (MMS) data for thirty years (1986-2015) rainfall data for Uyo metropolis. Trend analysis was performed using Mann-Kendall (MK) test and Sen’s slope estimator (SSE) used to obtain the trend magnitude, while the trend change point analysis was conducted using the distribution-free cumulative sum test (CUSUM) and the sequential Mann-Kendall test (SQMK). A free CUSUM plot date of change point of rainfall trend as 2002 at 90% confidence interval was obtained from where the increasing trend started and became more pronounced in the year 2011, another change point year from the SQMK plot with the trend intensifying. The SSE gave an average rate of change in rainfall as 2.1288 and 2.16 mm/year for AMS and MMS time series data respectively. Invariably, the condition for Non-stationary concept application is met for intensity-duration-frequency modeling.

RATE OF CONVERGENCE FOR MULTIPLE CHANGEPOINTS ESTIMATION OF MOVING-AVERAGE PROCESSES

In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, associated and negatively associated sequences under suitable conditions.

Limit Distribution of the φ-Divergence Based Change Point Estimator

The assumption of stationarity is too restrictive especially for long time series. This paper studies the change point problem through a change point estimator based on the φ-divergence which provides a rich set of distance like measures between pairs of distributions. The change point problem is considered in the following sub-fields: the problem of divergence estimation, testing for the homogeneity between two samples as well as estimating the time of change. The asymptotic distribution of the change point estimator is estimated by the limiting distribution of a stochastic process within given bounds through asymptotic theory surrounding the likelihood theory. The distribution is found to converge to that of a standardized Brownian bridge process.

Consistency of the <i>φ</i>-Divergence Based Change Point Estimator

This paper utilizes a change-point estimator based on the φ-divergence. Since we seek a near perfect translation to reality, then locations of parameter change within a finite set of data have to be accounted for since the assumption of stationary model is too restrictive especially for long time series. The estimator is shown to be consistent through asymptotic theory and finally proven through simulations. The estimator is applied to the generalized Pareto distribution to estimate changes in the scale and shape parameters.

A New Method for Determining Threshold in Using PGCEVD to Calculate Return Values of Typhoon Wave Height

In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.

Flow regime changes in three catchments with different landforms following ecological restoration in the Chinese Loess Plateau

The Chinese Loess Plateau is known as one of the most severe soil erosion regions in the world.Two ecological restoration projects,i.e.,the integrated soil conservation project since the 1970s and the''Grain for Green''project since 1999,have been progressively implemented to control the soil erosion in this area.Ecological restoration has greatly changed flow regime over the past five decades.However,the mechanism of how flow regime responds to ecological restoration among landforms remains poorly understood.In this study,we investigated the temporal dynamics of flow regime in three catchments,i.e.,Wuqi,Honghe and Huangling hydrological stations,respectively representing the loess hilly-gully,loess table-gully and rocky mountain(covered by secondary forest)areas in the Chinese Loess Plateau,using daily hydrological data during the 1960s–2010s.The nonparametric Mann-Kendall test,Pettitt's test and daily flow series were used to investigate the changes of flow regime.Significantly negative trends of annual streamflow were detected at the Wuqi and Honghe stations,except for the Huangling station.The annual baseflow at the Wuqi station showed a significantly positive trend whereas a significantly negative trend was observed at the Honghe station,and there was no significant trend at the Huangling station.It was interesting that baseflow index significantly increased during the whole period in all catchments.However,the trends and change points of daily flow series derived by different percentages of exceedance and extreme series in different consecutive days varied among individuals.Based on the change points analysis of annual streamflow,we divided data series into three periods,i.e.,the baseline period(from 1959 and 1963 to 1979,PI),the integrated soil conservation period(1980–1999,PII)and the''Grain for Green''period(2000–2011,PIII).We found that streamflow decreased due to the reduction of high streamflow(exceeding 5%of time within a year)and median streamflow(50%)in PII and PIII at the Wuqi and Honghe stations.However,low flow(95%)increased in PII and PIII at the Wuqi station while decreased at the Honghe station.Streamflow change at the Huangling station was more stable,thus potentially resulting in much less soil erosion in the forestry area than in the other areas.The great improvement in ecological environment on the Chinese Loess Plateau revealed the advantages of ecological restoration in reducing flood amount and compensating streamflow at a regional scale.

Identification of Dominant Climate Variables on Spatiotemporal Variation in Reference Evapotranspiration on the Loess Plateau,China

Reference evapotranspiration(ET_(0))is a vital component in hydrometeorological research and is widely applied to various aspects,such as water resource management,hydrological modeling,irrigation deployment,and understanding and predicting the influence of hydrologic cycle variations on future climate and land use changes.Quantifying the influence of various meteorological variables on ET_(0) is not only helpful for predicting actual evapotranspiration but also has important implications for understanding the impact of global climate change on regional water resources.Based on daily data from 69 meteorological stations,the present study analyzed the spatiotemporal pattern of ET_(0) and major contributing meteorological variables to ET_(0) from 1960 to 2017 by the segmented re-gression model,Mann-Kendall test,wavelet analysis,generalized linear model,and detrending method.The results showed that the annual ET_(0) declined slightly because of the combined effects of the reduction in solar radiation and wind speed and the increase in vapor pressure deficit(VPD)and average air temperature in the Loess Plateau(LP)during the past 58 yr.Four change points were detected in 1972,1990,1999,and 2010,and the annual ET_(0) showed a zigzag change trend of‘increasing-decreasing-increasing-decreasing-increasing’.Wind speed and VPD played a leading role in the ET_(0) changes from 1960 to 1990 and from 1991 to 2017,respectively.This study confirms that the dominant meteorological factors affecting ET_(0) had undergone significant changes due to global climate change and vegetation greening in the past 58 years,and VPD had become the major factor controlling the ET_(0) changes on the LP.The data presented herein will contribute to increasing the accuracy of predictions on future changes in ET_(0).

Interpurchase Time of Customer Behavior in Cloud Computing

Cloud computing is an increasingly popular paradigm for accessing computing resources. For marketing application, this paper proposes a dynamic model of customer interpurchase time with geometric distribution. This model considers that there is a change point in interpurchase time and two types of probability density functions are demonstrated （time decreasing before changing; time increasing after changing）. With the description of change point, Bernoulli and Poisson distributions also are discussed in the model construction.

Change-point detection for expected shortfall in time series

Expected shortfall(ES)is a popular risk measure and plays an important role in risk and portfolio management.Recently,change-point detection of risk measures has been attracting much attention in finance.Based on the self-normalized CUSUM statistic in Fan,Glynn and Pelger(2018)and the Wild Binary Segmentation(WBS)algorithm in Fryzlewicz(2014),this paper proposes a variant WBS procedure to detect and estimate change points of ES in time series.The strengthened Schwarz information criterion is also introduced to determine the number of change points.Monte Carlo simulation studies are conducted to assess the finite-sample performance of our variant WBS procedure about ES in time series.An empirical application is given to illustrate the usefulness of our procedure.

Testing for Change Points in Partially Linear Models

In this paper we provide a method to test the existence of the change points in the nonparametric regression function of partially linear models with conditional heteroscedastic variance. We propose the test statistic and establish its asymptotic properties under some regular conditions. Some simulation studies are given to investigate the performance of the proposed method in finite samples. Finally, the proposed method is applied to a real data for illustration.

Nonparametric Inference in a Simple Change-point Model

In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfrac{1}{n}$\tfrac{1}{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.