Stochastic Time Series Models Research Articles

Characterization of Export Regimes in Concentration–Discharge Plots via an Advanced Time-Series Model and Event-Based Sampling Strategies

Currently, the export regime of a catchment is often characterized by the relationship between compound concentration and discharge in the catchment outlet or, more specifically, by the regression slope in log-concentrations versus log-discharge plots. However, the scattered points in these plots usually do not follow a plain linear regression representation because of different processes (e.g., hysteresis effects). This work proposes a simple stochastic time-series model for simulating compound concentrations in a river based on river discharge. Our model has an explicit transition parameter that can morph the model between chemostatic behavior and chemodynamic behavior. As opposed to the typically used linear regression approach, our model has an additional parameter to account for hysteresis by including correlation over time. We demonstrate the advantages of our model using a high-frequency data series of nitrate concentrations collected with in situ analyzers in a catchment in Germany. Furthermore, we identify event-based optimal scheduling rules for sampling strategies. Overall, our results show that (i) our model is much more robust for estimating the export regime than the usually used regression approach, and (ii) sampling strategies based on extreme events (including both high and low discharge rates) are key to reducing the prediction uncertainty of the catchment behavior. Thus, the results of this study can help characterize the export regime of a catchment and manage water pollution in rivers at lower monitoring costs. We propose a simple stochastic time-series model to represent the export regime of a catchment beyond simple regression. We propose how to get the required data with the least effort when the use of high-frequency in situ analyzers is not feasible or restricted. Sampling strategies based on extreme events are essential for reducing the prediction uncertainty of the catchment behavior.

Statistical guided-waves-based structural health monitoring via stochastic non-parametric time series models

Damage detection in active-sensing, guided-waves-based structural health monitoring (SHM) has evolved through multiple eras of development during the past decades. Nevertheless, there still exist a number of challenges facing the current state-of-the-art approaches, both in the industry as well as in research and development, including low damage sensitivity, lack of robustness to uncertainties, need for user-defined thresholds, and non-uniform response across a sensor network. In this work, a novel statistical framework is proposed for active-sensing SHM based on the use of ultrasonic guided waves. This framework is based on stochastic non-parametric time series models and their corresponding statistical properties in order to readily provide healthy confidence bounds and enable accurate and robust damage detection via the use of appropriate statistical decision-making tests. Three such methods and corresponding statistical quantities (test statistics) along with decision-making schemes are formulated and experimentally assessed via the use of three coupons with different levels of complexity: an Al plate with a growing notch, a carbon fiber-reinforced plastic (CFRP) plate with added weights to simulate local damage, and the CFRP panel used in the Open Guided Waves project, all fitted with piezoelectric transducers under a pitch-catch configuration. The performance of the proposed methods is compared to that of state-of-the-art time-domain damage indices (DIs). The results demonstrate the increased detection sensitivity and robustness of the proposed methods, with better tracking capability of damage evolution compared to conventional approaches, even for damage-non-intersecting actuator–sensor paths. In particular, the Z statistic emerges as the best damage detection metric compared to conventional DIs, as well as the other proposed statistics. Overall, the proposed statistics in this study promise greater damage sensitivity across different components, with enhanced robustness to uncertainties, as well as user-friendly application.

Statistical residual-based time series methods for multicopter fault detection and identification

This paper presents the introduction, investigation, and critical assessment of three data-driven statistical residual-based time series methods for rotor fault detection and identification (FDI) in multicopters. A concise overview of statistical residual-based FDI methods is provided based on scalar (univariate) and vector (multivariate) stochastic time series models. The FDI methods employed in this study are based on identified response-only parametric scalar (univariate) and vector (multivariate) autoregressive (AR) representations of multicopter attitudes (time series), as the external excitation is non-observable, and their corresponding model residuals obtained under the considered healthy and faulty multicopter states. The comparative assessment of the effectiveness of three residual-based statistical FDI methods is presented in the face of external disturbances, namely three different levels of turbulence, and for different rotor fault scenarios. To the authors' best of knowledge, this is the first time that residual-based statistical time series methods are investigated and evaluated with respect to multicopter FDI. The unique characteristics of the presented methods are: (i) the data-driven stochastic identification of the multicopter dynamics under healthy and faulty rotor conditions is based only on the use of multicopter attitude signals, i.e. roll, pitch, and yaw, without the need to use additional aircraft states; (ii) there is no analytical modeling involved and the subsequent development of a stochastic multicopter FDI framework does not require knowledge of the controller effort to detect and classify rotor faults. The fault detection methods based on Vector AutoRegressive (VAR) models exhibit improved performance compared to their scalar counterparts, as indicated by lower false alarms and missed fault rates. In the case of rotor fault identification (classification), the methods that are based on scalar AR models exhibit reduced rotor fault classification accuracy, while the VAR-based methods outperform their scalar counterparts and can achieve a fault identification accuracy of up to 99.6%.

Review of the book Stochastic Models for Time Series by Paul Doukhan

Review of the book <i>Stochastic Models for Time Series</i> by Paul Doukhan

A Stochastic Time-Series Model for Solar Irradiation

We propose a novel stochastic time series model able to explain the stylized features of daily irradation level data in 5 cities in Germany. The model is suitable for applications to risk management of photovoltaic power production in renewable energy markets. The suggested dynamics is a low order autoregressive time series with seasonal level given by an atmospheric clear-sky model. Moreover, we detect a skewness property in the residuals which we explain by a winter-summer regime switch. The stochastic variance is modelled by a seasonally varying GARCH-dynamics. The winter and summer standardized residuals are proposed to be a Gaussian mixture model to capture the bimodal distributions. We estimate the model on the observed data, and perform a validation study. An application to energy markets studying the production at risk for a PV-producer is presented.

Stochastic Models for Radon Daily Time Series: Seasonality, Stationarity, and Long-Range Dependence Detection

In this paper, the presence of seasonality, stationarity, and long-range memory structures are detected in daily radon measurements in a permanent monitoring station in central Italy. The transient dynamics and the seasonality structure are identified by power spectral analysis based on the continuous wavelet transformation and a clear 1-year periodicity emerges. The stationarity in the data is assessed with the Dickey Fuller test; the decay of the estimated autocorrelation function and the estimated Hurst exponent indicate the presence of long-range dependence. All the main characteristics of the data have been properly included in a modelling structure. In particular, an autoregressive fractionally integrated moving average (ARFIMA) model is estimated and compared with the classical ARMA and ARIMA models in terms of goodness of fit and, secondarily, of forecast evaluation. An autoregressive model with a non-integer values of the differencing parameter ($d=0.278$) resulted to be the most appropriate on the basis of Akaike Information Criterion, the diagnostic on the residuals, and the Root Mean Squared Error. The results suggest that there is statistically-significant evidence for not rejecting the presence of long memory in the radon concentration. The radon measurements are better characterised as being stationary, but with long memory and so the statistical dependence decays more slowly than an exponential decay.

Stochastic time-series models for drought assessment in the Gaza Strip (Palestine)

Abstract The Eastern Mediterranean region of the Middle East and North Africa (MENA) is experiencing patterns of major drought due to the effects of rising temperatures and falling precipitation levels. The multiscale drought evaluation Standardized Precipitation Evapotranspiration Index (SPEI) reveals evolving and severe drought from North Africa and the Sinai desert toward the Middle East. While there has been a period without drought between 1970 and 1990, the severity and frequency of drought increased considerably after 1990. Current drought conditions in the Eastern Mediterranean region of MENA are moderate to severe with a 60–100% likelihood of occurrence, according to time parameters. The Gaza Strip is especially vulnerable to the consequences of increasing drought because it is situated in the vicinity of the Sinai Desert; therefore, a downscaled study of drought in the region is essential to implement mitigation measures for the sustainable management and planning of coastal aquifer and agricultural activities in the Gaza Strip. Considerable availability of precipitation time series from various meteorological stations helped provide a local drought study for the Gaza Strip, in accordance with the Standardized Precipitation Index (SPI). The stochastic time-series model of (4,0,1) (5,1,1)12 shows a robust simulator for modeling and forecasting the future trend of precipitation at the nine meteorological stations. In terms of correlation accuracy, the model achieves a correlation (r) of approximately 93–97% in the calibration range and a correlation (r) of about 92–99% in the validation range. In terms of measuring the difference between the values, the root mean squared error (RMSE) of the model results shows that the RMSE was between 7–21 in the calibration range and 11–21 in the validation range. The model reveals a slightly stable trend in precipitation patterns at the northern meteorological stations of Beit Hanon, Beit Lahia, Shati, and Remal. However, declining precipitation tendency was recorded at the southern meteorological stations of Mughraka, Nussirat, Beir Al-Balah, Khanyounis, and Rafah. The SPI-based drought assessment implies that the precipitation annual threshold levels at SPI = 0 drop territorially from 474 mm in the north to about 250 mm in the south of the Gaza Strip. In this study, a representative 12-month local scale SPI12 at an annual precipitation threshold level of 370 mm was formulated to address the drought conditions in the Gaza Strip. Standing on the outputs of the local SPI12 scale might signify that the region of the Gaza Strip risks drought status with an incidence likelihood varying from 8% in the north to 100% in the south. Regular drought is prevalent in the northern governorates, but the hazards of extreme and severe drought are high in the southern areas with an incidence risk of about 83%. Sequentially, southern governorates of Rafah and Khanyounis experience chronic annual drought, while the return period of drought is reported to be every 9–12 years in the northern governorates of the Gaza Strip. The rain-fed years of 1998 and 2010 reported the worst periods of drought, while the period of 2016 showed a good droughtless water balance. Overall, the no-drought status might define the prospective conditions in the governorates of North Gaza, Gaza, and central Gaza over the next 20 years, while Rafah and Khanyounis are anticipated to be under normal to severe drought conditions.

Ordered fuzzy random variables: Definition and the concept of normality

The concept of fuzzy random variable combines two sources of uncertainty: randomness and fuzziness, whereas the model of ordered fuzzy numbers provides a representation of inaccurate quantitative data, and is an alternative to the standard fuzzy numbers model proposed by Zadeh. This paper develops the model of ordered fuzzy numbers by defining the concept of fuzzy random variables for these numbers, called further ordered fuzzy random variables. Thanks to the well-defined arithmetic of ordered fuzzy numbers (existence of neutral and opposite elements) and the introduced ordered fuzzy random variables; it becomes possible to construct fully fuzzy stochastic time series models such as e.g., the autoregressive model or the GARCH model in the form of classical equations, which can be estimated using the least-squares or the maximum likelihood method. Furthermore, the concept of normality of ordered fuzzy random variables and the method to generate pseudo-random ordered fuzzy variables with normal distribution are introduced.

Trend of Betel Leaf Production in Bangladesh: Prospects and Challenges

Betel leaf is one of the important cash crops that gaining popularity in recent time in Bangladesh. This study was conducted to identify the present and future production pattern of betel leaf in Bangladesh as well as its prospects and challenges. Secondary data of 29 years from 1991 to 2019 have been used to specify the production pattern and forecasting of betel leaf at national level by using deterministic, stochastic and dynamic time series model. While the primary data were collected from three sub-districts of the Rajshahi district namely Bagmara, Durgapur and Mohanpur to identify the prospects and challenges through SWOT analysis. This study found significant relationship among betel leaf production, price and annual average temperature of Bangladesh. A total of six growth models of different types were used for forecasting production, cultivation area, and price of betel leaf. Based on the model selection criteria cubic model, quadratic model, and growth model were chosen for initial forecasting of betel leaves production, cultivation area, and price respectively. Among the stochastic model auto regressive integrated moving average ARIMA (0, 1, 0) was fitted well to forecast the production. Finally, a dynamic regression model of ARIMA (1, 1, 0) with dynamic regressors has been used to forecast the production of betel leaf from 2020 to 2023. Forecast values range minimum 202770.41 tons to 296217.14 tons with 95% confidence interval. All the best-fitted models revealed that the production of betel leaf has an upward trend in the future. At the end SWOT analysis was implemented to identify the strengths, weakness, opportunities and threats involved in betel leaf farming which will be helpful for making future national level policy options. Diseases control at the betel leaf garden and access to credit for initial investments were identified as the major challenges for this enterprise.&#x0D; Res. Agric., Livest. Fish.7(2): 209-223, August 2020

Unemployment Rate Forecasting: A Hybrid Approach

Unemployment has always been a very focused issue causing a nation as a whole to lose its economic and financial contribution. Unemployment rate prediction of a country is a crucial factor for the country’s economic and financial growth planning and a challenging job for policymakers. Traditional stochastic time series models, as well as modern nonlinear time series techniques, were employed for unemployment rate forecasting previously. These macroeconomic data sets are mostly nonstationary and nonlinear in nature. Thus, it is atypical to assume that an individual time series forecasting model can generate a white noise error. This paper proposes an integrated approach based on linear and nonlinear models that can predict the unemployment rates more accurately. The proposed hybrid model of the unemployment rate can improve their forecasts by reflecting the unemployment rate’s asymmetry. The model’s applications are shown using seven unemployment rate data sets from various countries, namely, Canada, Germany, Japan, Netherlands, New Zealand, Sweden, and Switzerland. The results of computational tests are very promising in comparison with other conventional methods. The results for asymptotic stationarity of the proposed hybrid approach using Markov chains and nonlinear time series analysis techniques are given in this paper which guarantees that the proposed model cannot show ‘explosive’ behavior or growing variance over time.

Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling.

Fitting mathematical models with a direct connection to experimental observables to the outputs of molecular simulations can be a powerful tool for extracting important physical information from them. In this study, we present two new approaches that use stochastic time series modeling to predict long-time-scale behavior and macroscopic properties from molecular simulation, which can be generalized to other molecular systems where complex diffusion occurs. In our previous work, we studied long molecular dynamics (MD) simulation trajectories of a cross-linked HII phase lyotropic liquid crystal (LLC) membrane, where we observed subdiffusive solute transport behavior characterized by intermittent hops separated by periods of entrapment. In this work, we use our models to parameterize the behavior of the same systems, so we can generate characteristic trajectory realizations that can be used to predict solute mean-squared displacements (MSDs), solute flux, and solute selectivity in macroscopic length pores. First, using anomalous diffusion theory, we show how solute dynamics can be modeled as a fractional diffusion process subordinate to a continuous time random walk. From the MD simulations, we parameterize the distribution of dwell times, hop lengths between dwells, and correlation between hops. We explore two variations of the anomalous diffusion modeling approach. The first variation applies a single set of parameters to the solute displacements and the second applies two sets of parameters based on the solute's radial distance from the closest pore center. Next, we present an approach that generalizes Markov state models, treating the configurational states of the system as a Markov process where each state has distinct transport properties. For each state and transition between states, we parameterize the distribution and temporal correlation structure of positional fluctuations as a means of characterization and to allow us to predict solute MSDs. We show that both stochastic models reasonably reproduce the MSDs calculated from MD simulations. However, qualitative differences between MD and Markov state-dependent model-generated trajectories may in some cases limit their usefulness. With these parameterized stochastic models, we demonstrate how one can estimate the flux of a solute across a macroscopic length pore and, based on these quantities, the membrane's selectivity toward each solute. This work therefore helps to connect microscopic, chemically dependent solute motions that do not follow simple diffusive behavior with long-time-scale behavior, in an approach generalizable to many types of molecular systems with complex dynamics.

Stochastic and analytical approaches for sediment accumulation in river reservoirs

ABSTRACTSediment accumulation in a river reservoir is studied by stochastic time series models and analytical approach. The first-order moving average process is found the best for the suspended sediment discharge time series of the Juniata River at Newport, Pennsylvania, USA. Synthetic suspended sediment discharges are first generated with the chosen model after which analytical expressions are derived for the expected value and variance of sediment accumulation in the reservoir. The expected value and variance of the volume of sediment accumulation in the reservoir are calculated from a thousand synthetic time series each 38 years long and compared to the analytical approach. Stochastic and analytical approaches perfectly trace the observation in terms of the expected value and variability. Therefore, it is concluded that the expected value and variance of sediment accumulation in a reservoir could be estimated by analytical expressions without the cost of synthetic data generation mechanisms.

Comparison of short-term streamflow forecasting using stochastic time series, neural networks, process-based, and Bayesian models

Streamflow forecasts are essential for water resources management. Although there are many methods for forecasting streamflow, real-time forecasts remain challenging. This study evaluates streamflow forecasts using a process-based model (Soil and Water Assessment Tool-Variable Source Area model-SWAT-VSA), a stochastic model (Artificial Neural Network -ANN), an Auto-Regressive Moving-Average (ARMA) model, and a Bayesian ensemble model that utilizes the SWAT-VSA, ANN, and ARMA results. Streamflow is forecast from 1 to 8 d, forced with Quantitative Precipitation Forecasts from the US National Weather Service. Of the individual models, SWAT-VSA and the ANN provide better predictions of total streamflow (NSE 0.60–0.70) and peak flow, but underpredicted low flows. During the forecast period the ANN had the highest predictive power (NSE 0.44–0.64), however all three models underpredicted peak flow. The Bayesian ensemble forecast streamflow with the most skill for all forecast lead times (NSE 0.49–0.67) and provided a quantification of prediction uncertainty.

Groundwater depth monitoring and short-term prediction: applied to El Hamma aquifer system, southeastern Tunisia

In arid and semi-arid areas, such as Tunisia, groundwater depth assessment and monitoring is an important task for groundwater resources sustainable management. The objective of this work is to assess and forecast groundwater depth (GWDs) at short-term, under different impact factors, using stochastic time series (STS) and artificial neural network (ANN). Each model was conceptualized and implemented. Groundwater depth, rainfall, pumping rate and temperature over the period 30 years extending from 1986 to 2016 were used. Root mean squared error, bias, R2, AIC, and BIC were used as sensitivity model performance criteria. Models were implemented, trained, and tested over an observation period and forecasting groundwater depth at short-term over a period 2017–2030. Results show that groundwater abstraction rates increase around 0.46 Mm3/year, whereas a groundwater depth is in continuously drawdown with a rate of 0.3 m/year which requires a monitoring network for sustainable management of water resources. The results are promising and indicate an outstanding suitability of stochastic time series and ANN models for groundwater depth assessment and predictions at short time. The predicted results at short-term will help to draw attention of local authority for clear groundwater sustainable management policy for studied area.

Designing Robust N-of-1 Studies for Precision Medicine: Simulation Study and Design Recommendations.

BackgroundRecent advances in molecular biology, sensors, and digital medicine have led to an explosion of products and services for high-resolution monitoring of individual health. The N-of-1 study has emerged as an important methodological tool for harnessing these new data sources, enabling researchers to compare the effectiveness of health interventions at the level of a single individual.ObjectiveN-of-1 studies are susceptible to several design flaws. We developed a model that generates realistic data for N-of-1 studies to enable researchers to optimize study designs in advance.MethodsOur stochastic time-series model simulates an N-of-1 study, incorporating all study-relevant effects, such as carryover and wash-in effects, as well as various sources of noise. The model can be used to produce realistic simulated data for a near-infinite number of N-of-1 study designs, treatment profiles, and patient characteristics.ResultsUsing simulation, we demonstrate how the number of treatment blocks, ordering of treatments within blocks, duration of each treatment, and sampling frequency affect our ability to detect true differences in treatment efficacy. We provide a set of recommendations for study designs on the basis of treatment, outcomes, and instrument parameters, and make our simulation software publicly available for use by the precision medicine community.ConclusionsSimulation can facilitate rapid optimization of N-of-1 study designs and increase the likelihood of study success while minimizing participant burden.

Dengue Cases in Colombia: Mathematical Forecasts for 2018-2022.

INTRODUCTION Dengue is a disease caused by any one of five virus serotypes and transmitted to humans by the Aedes aegypti mosquito. Climate change and health conditions have combined to make dengue a global public health problem. The situation is especially serious in Colombia, where by week 36 of 2018, dengue incidence was 96 cases per 100,000 population, with a total of 111 deaths. Different mathematical and statistical models have been proposed to understand the dynamics of transmission and consequently to apply control strategies to reduce the number of dengue cases. OBJECTIVE Forecast the number of dengue cases expected in Colombia from 2018 through 2022 with the stochastic Auto-Regressive Integrated Moving Average (ARIMA) model and use the results to adjust the parameters of an ordinary differential equations model in order to determine the disease's basic reproduction number in the year presenting the highest number of dengue cases. METHODS An ecological time series study was conducted to forecast dengue incidence in Colombia from 2018 through 2022. The data were compiled from Colombia's National Health Institute series on dengue cases reported by epidemiological week from 2009 to 2017. The stochastic ARIMA time series model was applied. Forecasts were then analyzed, and the year with the highest number of predicted cases was used to adjust the parameters of an ordinary differential equations model (ODE) through nonlinear least squares regression to calculate the vectorial capacity of the transmitting mosquito. RESULTS Forecasts of the total number of dengue cases per year in Colombia for the following five years were: 32,411 (2018); 88,221 (2019); 56,392 (2020); 47,940 (2021); and 77,344 (2022). The highest number of cases was forecast for 2019. Values for the parameters affecting dengue transmission that year (by the year's four quarters), such as recovery rate (0.0992, 0.0838, 0.1177, and 0.1535, respectively), vectorial capacity of the transmitting mosquito (0.1720, 0.1705, 0.1204, and 0.2147, respectively) and the basic dengue reproduction number (1.73, 2.03, 1.02, and 1.40, respectively) were estimated, indicating that most cases would occur in the second quarter and, since the basic reproduction number values were >1, the disease would persist in the country throughout the entire year. CONCLUSIONS ARIMA model forecasts for 2018 through 2022 predicted the highest incidence of dengue cases in Colombia would occur in 2019. Comparison of ARIMA model forecasts and the ODE model allowed projections of possible variations in dengue cases reported, and the basic reproduction number predicted that dengue would persist throughout 2019. KEYWORDS Arboviruses, climate, dengue, models, theoretical, basic reproduction number, prognosis, Colombia.

Modeling the Effects of Outliers on the Estimation of Linear Stochastic Time Series Model

This study investigates the effects of outliers on the estimates of ARIMA model parameters with particular attention given to the performance of two outlier detection and modeling methods targeted at achieving more accurate estimates of the parameters. The two methods considered are: an iterative outlier detection aimed at obtaining the joint estimates of model parameters and outlier effects, and an iterative outlier detection with the effects of outliers removed to obtain an outlier free series, after which a successful ARIMA model is entertained. We explored the daily closing share price returns of Fidelity bank, Union bank of Nigeria, and Unity bank from 03/01/2006 to 24/11/2016, with each series consisting of 2690 observations from the Nigerian Stock Exchange. ARIMA (1, 1, 0) models were selected based on the minimum values of Akaike information criteria which fitted well to the outlier contaminated series of the respective banks. Our findings revealed that ARIMA (1, 1, 0) models which fitted adequately to the outlier free series outperformed those of the parameter-outlier effects joint- estimated model. Furthermore, we discovered that outliers biased the estimates of the model parameters by reducing the estimated values of the parameters. The implication is that, in order to achieve more accurate estimates of ARIMA model parameters, it is needful to account for the presence of significant outliers and preference should be given to the approach of cleaning the series of outliers before subsequent entertainment of adequate linear time series models.

Stochastic bivariate time series models of waves in the North Sea and their application in simulation-based design

In this paper, we present and evaluate three long-term wave models for application in simulation-based design of ships and marine structures. Designers and researchers often rely on historical weather data as a source for ocean area characteristics based on hindcast datasets or in-situ measurements. The limited access and size of historical datasets reduces repeatability of simulations and analyses, making it difficult to assess the sampling variability of performance and loads on marine vessels and structures. Markov, VAR and VARMA wave models, producing independent long-term time series of significant wave height (Hs) and spectral peak period (Tp), is presented as possible solutions to this problem. The models are tested and compared by addressing how the models affect interpretation of design concepts and the ability to replicate statistical and physical characteristics of the wave process. Our results show that the VAR and VARMA models perform sufficiently in describing design performance, but does not capture the physical process fully. The Markov model is found to perform worst of the tested models in the applied tests, especially for measures covering several consecutive sea states.

On the modeling of the filtered radiative transfer equation in large eddy simulations of lab-scale sooting turbulent diffusion flames

This study investigates the influence of some approximations on the modeling of the filtered absorption and emission terms in an ethylene/air turbulent jet flame. Filtered radiative quantities along characteristic diametric optical paths are computed from corresponding instantaneous radiative quantities obtained by using a stochastic space and time series model. Model results show that the subgrid-scale radiative absorption can be disregarded whatever the filter size. The effects of subgrid-scale fluctuations on the filtered emission term are dominated by the subgrid-scale absorption coefficient-blackbody intensity correlation and the subgrid-scale temperature self-correlation. The former reduces the filtered emission term in regions where soot radiation dominates and enhances it in regions where gas radiation prevails. The latter always increases the filtered emission term. For a filter size typical of engineering applications, model results suggest that the effects subgrid-scale fluctuations on the filtered emission term have to be modeled.

In-Process Monitoring of Material Cross-Contamination Defects in Laser Powder Bed Fusion

The goal of this work is to detect the onset of material cross-contamination in laser powder bed fusion (L-PBF) additive manufacturing (AM) process using data from in situ sensors. Material cross-contamination refers to trace foreign materials that may be introduced in the powder feedstock used in the process due to reasons such as poor cleaning of the machine after previous builds or inadequate quality control during production and storage of the powder. Material cross-contamination may lead to deleterious changes in the microstructure of the AM part and consequently affect its functional properties. Accordingly, the objective of this work is to develop and apply a spectral graph theoretic approach to detect the occurrence of material cross-contamination in real-time as the part is being built using in-process sensors. The central hypothesis is that transforming the process signals in the spectral graph domain leads to early and more accurate detection of material cross-contamination in L-PBF compared to the traditional delay-embedded Bon-Jenkins stochastic time series analysis techniques, such as autoregressive (AR) and autoregressive moving average (ARMA) modeling. To test this hypothesis, Inconel alloy 625 (UNS alloy 06625) test parts were made at Edison Welding Institute (EWI) on a custom-built L-PBF apparatus integrated with multiple sensors, including a silicon photodetector (with 300 nm to 1100 nm optical wavelength). During the process, two types of foreign contaminant materials, namely, tungsten and aluminum particulates, under varying degrees of severity were introduced. To detect cross-contamination in the part, the photodetector sensor signatures were monitored hatch-by-hatch in the form of spectral graph transform coefficients. These spectral graph coefficients are subsequently tracked on a Hotelling T2 statistical control chart. Instances of Type II statistical error, i.e., probability of failing to detect the onset of material cross-contamination, were verified against X-ray computed tomography (XCT) scans of the part to be within 5% in the case of aluminum contaminant particles. In contrast, traditional stochastic time series modeling approaches, e.g., ARMA, had corresponding Type II error exceeding 15%. Furthermore, the computation time for the spectral graph approach was found to be less than one millisecond, compared to nearly 100 ms for the traditional time series models tested.