Piecewise Linear Trend Research Articles

Continuous Health Monitoring of Reinforced Concrete Bridge Deck based on Traffic Load-induced Acoustic Emission

This paper presents continuous bridge deck monitoring based on b-value obtained from traffic load-induced acoustic emission (AE) signals. Using the self powered AE system that we developed, we have observed traffic load-induced AE on an actual bridge for five years. The developed self-powered AE system demonstrated that long-term traffic load-induced AE measurements over five years could be performed without an external power source. Traffic load-induced AEs measured irregularly by event-driven measurement were accumulated, and b-values were calculated. We used an additive regression model that accounts for piecewise linear trends and seasonality to extract long-term trends accurately. Over the past five years, the bridge has deteriorated. In addition, repairs were made during the period. As a result of this monitoring, we determined the relationship between the damage condition of the bridge and the b-value trend obtained from the traffic load-induced AEs. The results confirmed that the b-value based on traffic load-induced AE corresponds well with the damage conditions on the underside of the deck slab or in a shallow area inside it.

Randomized Trial of the Effectiveness of Videoconferencing-Based Versus Message-Based Psychotherapy on Depression.

The authors compared the engagement, clinical outcomes, and adverse events of text or voice message-based psychotherapy (MBP) versus videoconferencing-based psychotherapy (VCP) among adults with depression. The study used a sequential multiple-assignment randomized trial design with data drawn from phase 1 of a two-phase small business innovation research study. In total, 215 adults (ages ≥18 years) with depression received care from Talkspace, a digital mental health care company. Participants were initially randomly assigned to receive either asynchronous MBP or weekly VCP. All therapists provided evidence-based treatments such as cognitive-behavioral therapy. After 6 weeks of treatment, participants whose condition did not show a response on the Patient Health Questionnaire-9 or was rated as having not improved on the Clinical Global Impressions scale were randomly reassigned to receive either weekly VCP plus MBP or monthly VCP plus MBP. Longitudinal mixed-effects models with piecewise linear time trends applied to multiple imputed data sets were used to address missingness of data. Participants who were initially assigned to the MBP condition engaged with their therapists over more weeks than did participants in the VCP condition (7.8 weeks for MBP vs. 4.9 weeks for VCP; p<0.001). No meaningful differences were observed between the two groups in rates of change by 6 or 12 weeks for depression, anxiety, disability, or global ratings of improvement. Neither treatment resulted in any adverse events. MBP appears to be a viable alternative to VCP for treating adults with depression.

Self-exciting threshold -valued autoregressive processes for non-stationary time series of counts

To handle non-stationary integer-valued time series of counts with piecewise characteristics and linear trends, this paper introduced a class of self-exciting threshold Z -valued autoregressive processes. The process is defined with a free type distribution for the innovation, which enhances the flexibility of the model. The basic probabilistic and statistical properties of the proposed model are discussed. Conditional least squares (CLS) estimator and modified quasi-likelihood (MQL) estimator, as well as their asymptotic properties are obtained. A searching algorithm for estimating the threshold parameter is also provided. Some simulation studies are conducted to show the performances of the proposed methods. Finally, an application to a real data example is provided.

Determining a Piecewise Linear Trend of a Nonstationary Time Series Based on Intelligent Data Analysis. II. Machine Experiments and Solution of the Practical Problem

Determining a Piecewise Linear Trend of a Nonstationary Time Series Based on Intelligent Data Analysis. II. Machine Experiments and Solution of the Practical Problem

Determining a Piecewise Linear Trend of a Nonstationary Time Series Based on Intelligent Data Analysis. I. Description and Substantiation of the Method

Determining a Piecewise Linear Trend of a Nonstationary Time Series Based on Intelligent Data Analysis. I. Description and Substantiation of the Method

ВИЗНАЧЕННЯ КУСКОВО-ЛІНІЙНОГО ТРЕНДУ НЕСТАЦІОНАРНОГО ЧАСОВОГО РЯДУ НА ОСНОВІ ІНТЕЛЕКТУАЛЬНОГО АНАЛІЗУ ДАНИХ. II. МАШИННI ЕКСПЕРИМЕНТИ ТА РОЗВ’ЯЗАННЯ ПРАКТИЧНОЇ ЗАДАЧІ

The article describes the results of the approbation of the method of constructing a piecewise-linear trend, which can have breaks at the switching points as well as be continuous at these points, i.e., represent a linear flow. An example of applying the method for constructing a linear regression with switches, which has two independent variables with a trend, is considered. The problem of spline approximation of the time series of logarithms of the number of infected people with COVID-19 in Ukraine is stated and solved. Keywords: trend, regression, switch point, spline, real-time calculation.

A study on estimating piecewise linear trend model using the simple moving average of differenced time series

A study on estimating piecewise linear trend model using the simple moving average of differenced time series

A study on estimating piecewise linear trend model using the simple moving average of differenced time series

A study on estimating piecewise linear trend model using the simple moving average of differenced time series

Long‐Term Variations and Residual Trends in the E, F, and Sporadic E (Es) Layer Over Juliusruh, Europe

AbstractUsing 63 and 56 yr of continuous observations, we investigate the long‐term oscillations and residual linear trends, respectively, in the E‐ and F‐region ionosonde measured parameters of frequencies and height over Juliusruh, Europe. Using the Lomb‐Scargle periodogram (LSP) long‐term variations are estimated before the trend calculation. We found that the amplitude of the annual oscillation is higher than the 11‐yr solar cycle variation in the critical frequencies of the daytime E (foE) and Es (foEs) layers. In the F‐region, except for daytime hmF2, and nighttime foF2, the amplitude of the 11‐yr solar cycle variation is higher than the annual oscillation. The combination of the LSP estimated periods and their corresponding amplitudes and traditional regression analysis are used to construct a model for E‐ and F‐region ionospheric parameters. The modeled estimates are in good agreement with the observations. The trend calculation is derived by applying a least‐squares fit analysis to the residuals, subtracting the model from the observation. In the F‐region, both day (nighttime) foF2 and hmF2 show negative trends of −4.44 ± 1.78 (−4.30 ± 1.63) kHz/yr and −413 ± 47 (−574 ± 75) m/yr, respectively. The Piecewise linear trend of foF2 provides negative and positive trends in 1964–1996 and 1997–2019, respectively. In the E‐region, foEs show a negative trend of −2.00 ± 0.61 kHz/yr. The present investigation suggests that the greenhouse cooling effect and negative trend in the atomic oxygen (O) as well as wind shear variability could be the main drivers for the observed negative trends in the hmF2, foF2, and foEs, respectively.

Diffusion in intact secondary cell wall models of plants at different equilibrium moisture content

Secondary plant cell walls are composed of carbohydrate and lignin polymers, and collectively represent a significant renewable resource. Leveraging these resources depends in part on a mechanistic understanding for diffusive processes within plant cell walls. Common wood protection treatments and biomass conversion processes to create biorefinery feedstocks feature ion or solvent diffusion within the cell wall. X-ray fluorescence microscopy experiments have determined that ionic diffusion rates are dependent on cell wall hydration as well as the ionic species through non-linear relationships. In this work, we use classical molecular dynamics simulations to map the diffusion behavior of different plant cell wall components (cellulose, hemicellulose, lignin), ions (Na+, K+, Cu2+, Cl−) and water within a model for an intact plant cell wall at various hydration states (3–30 wt% water). From these simulations, we analyze the contacts between different plant cell wall components with each other and their interaction with the ions. Generally, diffusion increases with increasing hydration, with lignin and hemicellulose components increasing diffusion by an order of magnitude over the tested hydration range. Ion diffusion depends on charge. Positively charged cations preferentially interact with hemicellulose components, which include negatively charged carboxylates. As a result, positive ions diffuse more slowly than negatively charged ions. Measured diffusion coefficients are largely observed to best fit piecewise linear trends, with an inflection point between 10 and 15% hydration. These observations shed light onto the molecular mechanisms for diffusive processes within secondary plant cell walls at atomic resolution.

A statistical method for estimating piecewise linear sales trends

A statistical method for estimating piecewise linear sales trends

Trend patterns of HBsAg kinetics in chronic hepatitis B patients during nucleos(t)ide analogue therapy based on ARMA models

BackgroundTrend pattern analysis are lacking for hepatitis B surface antigen (HBsAg) kinetics in chronic hepatitis B (CHB) patients during nucleos(t)ide analogue (Nuc) therapy. We evaluated the trend patterns of HBsAg kinetics by time series analysis and forecasting times to HBsAg seroclearance accordingly. MethodsA total of 116 CHB patients with documented three-month HBsAg levels during the previous more than five years of Nuc therapy were included. The piecewise linear trends of the autoregressive-moving average (ARMA) model were used for time series analysis of HBsAg kinetics trends. Best fitted models were created for each patient using HBsAg datasets with backtracking capability. Predicted time to HBsAg seroclearance was calculated accordingly. ResultsFour trend patterns of HBsAg kinetics were found: no trend (n = 22, 19.0%), single trend (n = 16, 13.8%), biphasic trend with rapid-slow decline (n = 56, 48.2%) and biphasic trend with rise-decline (n = 22, 19.0%). Except for no-trend patients, the trend became slow reduction as HBsAg declined. Only 6.1% of patients continued rapid decline when the initial HBsAg of the last trend reached <100 IU/mL. Last trend slopes < −10 and rise-decline patterns indicate greater chances of achieving HBsAg seroclearance within two years. ConclusionBest fitted ARMA models of HBsAg kinetics can be created individually for patients during Nuc therapy. About 67.2% patients have biphasic trend patterns, suggesting the dynamic nature of HBsAg kinetics over time. Trend patterns and last trend slopes predict individual times to HBsAg seroclearance.

Multiple Changepoint Analysis of COVID-19 Infection Progression and Related Deaths in the Small Island State of Malta

In December 2019, in the city of Wuhan (China), Severe Acute Respiratory Syndrome Coronavirus - 2 (SARS-CoV−2), a virus that causes what is known as Coronavirus Disease 2019 (better known as COVID-19), emerged. In a few months the virus spread around the world becoming a global pandemic that has shaken the world. On Malta (a nation consisting of an archipelago of islands of approximately 500000 people), which is the case study of this analysis, the first case was identified on 7/3/2020. In this paper, we shall fit a piecewise linear trend model to the log-scale of cumulative cases and deaths due to COVID-19 in Malta by implementing the SN-NOT changepoint model. This model combines the self-normalisation (SN) technique, which is used to test whether there is a single change-point in the linear trend of a time series, with the Narrowest Over Threshold algorithm (NOT) to achieve multiple change-point in the linear trend. Through analysis of news reports and other sources of information, estimated change-points are then compared to potential factors such as health restrictions, mass events, government policy and population behaviour that have affected these changes, in order to determine the efffect of these factors on the spread of the disease.

L 1common trend filtering: an extension

common trend filtering enables us to estimate a common continuous piecewise linear trend and the corresponding factor loading coefficients of multiple time series simultaneously. In this paper, we extend this by replacing the identifying restriction with an alternative identifying restriction and develop an algorithm for solving this new problem. As the new identifying restriction is linear, it can include other linear restrictions of parameters. Using this modification, e.g. we can estimate the vector of the factor loading coefficients so that its two entries will equal, which current common trend filtering cannot handle. We also provide a way of specifying the tuning parameter of the new problem and empirically illustrate how well the algorithm works.

Modelling the COVID-19 Infection Trajectory: A Piecewise Linear Quantile Trend Model

AbstractWe propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based approach is robust to outliers, captures heteroscedasticity (commonly exhibited by COVID-19 infection curves) and automatically delivers both point and interval forecasts with minimal assumptions. Building on a self-normalized (SN) test statistic, this paper proposes a novel segmentation algorithm for multiple change-point estimation. Theoretical guarantees such as segmentation consistency are established under mild and verifiable assumptions. Using the proposed method, we analyse the COVID-19 infection curves in 35 major countries and discover patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. A simple change-adaptive two-stage forecasting scheme is further designed to generate short-term prediction of COVID-19 cumulative new cases and is shown to deliver accurate forecast valuable to public health decision-making.

Statistically-Based Trend Analysis of MTInSAR Displacement Time Series

Current multi-temporal interferometric Synthetic Aperture Radar (MTInSAR) datasets cover long time periods with regular temporal sampling. This allows high-rate and non-linear trends to be observed, which typically characterize pre-failure warning signals. In order to fully exploit the content of MTInSAR products, methods are needed for the automatic identification of relevant changes along displacement time series and the classification of the targets on the ground according to their kinematic regime. This work reviews some of the classical procedures for model ranking, based on statistical indices, which are applied to the characterization of MTInSAR displacement time series, and introduces a new quality index based on the Fisher distribution. Then, we propose a procedure to recognize automatically the minimum number of parameters needed to model a given time series reliably within a predefined confidence level. The method, though general, is explored here for polynomial models, which can be used in particular to approximate satisfactorily and with computational efficiency the piecewise linear trends that are generally used to model warning signals preceding the failure of natural and artificial structures. The algorithm performance is evaluated under simulated scenarios. Finally, the proposed procedure is also demonstrated on displacement time series derived by the processing of Sentinel-1 data.

The influence of Antarctic ice loss on polar motion: an assessment based on GRACE and multi-mission satellite altimetry

Increasing ice loss of the Antarctic Ice Sheet (AIS) due to global climate change affects the orientation of the Earth’s spin axis with respect to an Earth-fixed reference system (polar motion). Here the contribution of the decreasing AIS to the excitation of polar motion is quantified from precise time variable gravity field observations of the Gravity Recovery and Climate Experiment (GRACE) and from measurements of the changing ice sheet elevation from altimeter satellites. While the GRACE gravity field models need to be reduced by noise and leakage effects from neighboring subsystems, the ice volume changes observed by satellite altimetry have to be converted into ice mass changes. In this study we investigate how much individual gravimetry and altimetry solutions differ from each other. We show that due to combination of individual solutions systematic and random errors of the data processing can be reduced and the robustness of the geodetic derived AIS polar motion excitations can be increased. We investigate the interannual variability of the Antarctic polar motion excitation functions by means of piecewise linear trends. We find that the long-term behavior of the three ice sheet subregions: EAIS (East Antarctic Ice Sheet), WAIS (West Antarctic Ice Sheet) and APIS (Antarctic Peninsula Ice Sheet) is quite different. While APIS polar motion excitations show no significant interannual variations during the study period 2003-2015, the trend of the WAIS and EAIS polar motion excitations increased in 2006 and again in 2009 while it started slightly to decline in 2013. AIS mass changes explain about 45% of the observed magnitude of the polar motion vector (excluding glacial isosatic adjustment). They cause the pole position vector to drift along 59^{circ } East longitude with an amplitude of 2.7 mas/yr. Thus the contribution of the AIS has to be considered to close the budget of the geophysical excitation functions of polar motion.

Ell _{1} Common Trend Filtering

The ell _{1} trend filtering enables us to estimate a continuous piecewise linear trend of univariate time series. This filter and its variants have subsequently been applied in various fields, including astronomy, climatology, economics, electronics, environmental science, finance, and geophysics. Although the ell _{1} trend filtering can estimate a continuous piecewise linear trend of univariate time series, it cannot estimate a common continuous piecewise linear trend of multiple time series. This paper develops a statistical procedure that enables us to estimate it, which is a multivariate extension of the ell _{1} trend filtering. We provide an algorithm for estimating it and a clue to specify the tuning parameter of the procedure, both required for its application. We also (i) numerically illustrate how well the algorithm works, (ii) provide an empirical illustration, and (iii) introduce a generalization of our novel method.

Compositional trend filtering

Trend filtering is known as the technique for detecting piecewise linear trends in univariate time series. This technique is extended to the setting of compositional data, which are multivariate data where only the relative information is of importance. According to this, we formulate the problem and present a procedure how to efficiently solve it. To show the usefulness of this method, we consider the number of COVID-19 infections in several European countries in a chosen time period.

Time series analysis of COVID-19 infection curve: A change-point perspective

In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (Baranowski et al., 2019) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.