Article

Anomaly Detection and Cleaning of Highway Elevation Data from Google Earth Using Ensemble Empirical Mode Decomposition

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Abstract

Elevation information and its derivation, such as grade, are very important in analyses of traffic operation, safety performance, and energy consumption on highways. Google Earth (GE) is considered a reliable source of elevation information of ground surface and highway elevation. Data were extracted from GE. However, the authors found that raw GE elevation data on highways contains various anomalies and noises. The primary objective of this study was to evaluate the use of the ensemble empirical mode decomposition (EEMD) method for anomaly detection and cleaning of highway elevation data extracted from GE. Three interstate highways' segments were studied, and typical anomalies that existed in raw GE elevation data were identified. The EEMD method was then applied to decompose elevation data into different compositions with different details of original data, which were determined into those containing true information or white noise. The modeling results showed that the EEMD method was effective in excluding noises and obtaining accurate elevation data. Findings of this study can help transport authorities to create an accurate elevation data set for all highways or other road classes.

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For many years the Butterworth lowpass filter has been used to smooth many kinds of biomechanical data, despite the fact that it is underdamped and therefore overshoots and/or undershoots data during rapid transitions. A comparison of the conventional Butterworth filter with a critically damped filter shows that the critically damped filter not only removes the undershooting and overshooting, but has a superior rise time during rapid transitions. While analog filters always create phase distortion, both the critically damped and Butterworth filters can be modified to become zero-lag filters when the data are processed in both the forward and reverse directions. In such cases little improvement is realized by applying multiple passes. The Butterworth filter has superior 'roll-off' (attenuation of noise above the cutoff frequency) than the critically damped filter, but by increasing the number of passes of the critically damped filter the same 'roll-off' can be achieved. In summary, the critically damped filter was shown to have superior performance in the time domain than the Butterworth filter, but for data that need to be double differentiated (e.g. displacement data) the Butterworth filter may still be the better choice.
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Due to the envelope fitting problem exists in the process of empirical mode decomposition, an improved algorithm was proposed which could eliminate the undershoot phenomenon exactly. Firstly, in this improved algorithm, the cubic spline interpolation was used to determine the regions of undershoot which generated during the execution of envelope fitting. Secondly, the envelope intervals of undershoot regions were compensated by the monotone piecewise cubic polynomial interpolation. The original signal could be wrapped tightly by this modified envelope, which did not affect the characteristics of signal itself, and could keep the smoothness of previous envelope as well as possible. The simulation results showed that the undershoot phenomenon caused by cubic spline interpolation could be effectively eliminated and the envelope could be obtained better by this algorithm. In addition, the accuracy of empirical mode decomposition could be further improved.
Article
Filtering out the noise in traffic collision data is essential in reducing false positive rates (i.e., requiring safety investigation of sites where it is not needed) and can assist government agencies in better allocating limited resources. Previous studies have demonstrated that denoising traffic collision data is possible when there exists a true known high collision concentration location (HCCL) list to calibrate the parameters of a denoising method. However, such a list is often not readily available in practice. To this end, the present study introduces an innovative approach for denoising traffic collision data using the Ensemble Empirical Mode Decomposition (EEMD) method which is widely used for analyzing nonlinear and nonstationary data. The present study describes how to transform the traffic collision data before the data can be decomposed using the EEMD method to obtain set of Intrinsic Mode Functions (IMFs) and residue. The attributes of the IMFs were then carefully examined to denoise the data and to construct Continuous Risk Profiles (CRPs). The findings from comparing the resulting CRP profiles with CRPs in which the noise was filtered out with two different empirically calibrated weighted moving window lengths are also documented, and the results and recommendations for future research are discussed.
Article
Short-term passenger flow forecasting is a vital component of transportation systems. The forecasting results can be applied to support transportation system management such as operation planning, and station passenger crowd regulation planning. In this paper, a hybrid EMD–BPN forecasting approach which combines empirical mode decomposition (EMD) and back-propagation neural networks (BPN) is developed to predict the short-term passenger flow in metro systems. There are three stages in the EMD–BPN forecasting approach. The first stage (EMD Stage) decomposes the short-term passenger flow series data into a number of intrinsic mode function (IMF) components. The second stage (Component Identification Stage) identifies the meaningful IMFs as inputs for BPN. The third stage (BPN Stage) applies BPN to perform the passenger flow forecasting. The historical passenger flow data, the extracted EMD components and temporal factors (i.e., the day of the week, the time period of the day, and weekday or weekend) are taken as inputs in the third stage. The experimental results indicate that the proposed hybrid EMD–BPN approach performs well and stably in forecasting the short-term metro passenger flow.
Article
The empirical mode decomposition (EMD) and Hilbert spectrum are a new method for adaptive analysis of non-linear and non-stationary signals. This paper applies this method to vibration signal analysis for localised gearbox fault diagnosis. We first study the properties of the recently developed B-spline EMD as a filter bank, which is helpful in understanding the mechanisms behind EMD. Then we investigate the effectiveness of the original and the B-spline EMD as well as their corresponding Hilbert spectrum in the fault diagnosis. Vibration signals collected from an automobile gearbox with an incipient tooth crack are used in the investigation. The results show that the EMD algorithms and the Hilbert spectrum perform excellently. They are found to be more effective than the often used continuous wavelet transform in detection of the vibration signatures.
Article
The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean. Next, the confidence limit is defined as a range of standard deviations from this mean. However, such a confidence limit is valid only for linear and stationary processes. Furthermore, in order for the ergodic assumption to be valid, the subsections have to be statistically independent. For non-stationary and nonlinear processes, such an analysis is no longer valid. The confidence limit of the method here termed EMD/HSA (for empirical mode decomposition/Hilbert spectral analysis) is introduced by using various adjustable stopping criteria in the sifting processes of the EMD step to generate a sample set of intrinsic mode functions (IMFs). The EMD technique acts as a pre-processor for HSA on the original data, producing a set of components (IMFs) from the original data that equal the original data when added back together. Each IMF represents a scale in the data, from smallest to largest. The ensemble mean and standard deviation of the IMF sample sets obtained with different stopping criteria are calculated, and these form a simple random sample set. The confidence limit for EMD/HSA is then defined as a range of standard deviations from the ensemble mean. Without evoking the ergodic assumption, subdivision of the data stream into short sections is unnecessary; hence, the results and the confidence limit retain the full-frequency resolution of the full dataset. This new confidence limit can be applied to the analysis of nonlinear and non-stationary processes by these new techniques. Data from length-of-day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied. By providing a confidence limit for this new approach, a stable range of stopping criteria for the decomposition or sifting phase (EMD) has been established, making the results of the final processing with HSA, and the entire EMD/HSA method, more definitive.
Article
Recently, advanced navigation systems have been developed that provide users the ability to select not only a shortest-distance route and even the shortest-duration route (on the basis of real-time traffic congestion information) but also routes that minimize fuel consumption as well as greenhouse gas and pollutant emissions. In these ecorouting systems, fuel consumption and emission attributes are estimated for roadway links on the basis of the measured traffic volume, density, and average speed. Instead of standard travel time or distance attributes, these link attributes are then used as cost factors when an optimal route for any particular trip is selected. In addition to roadway congestion attributes, road grade factors also have an effect on fuel consumption and emissions. This study evaluated the effect of road grade on vehicle fuel consumption (and thus carbon dioxide [CO(2)] emissions). The real-world experimental results show that road grade does have significant effects on the fuel economy of light-duty vehicles both at the roadway link level and at the route level. Comparison of the measured fuel economy between a flat route and example hilly routes revealed that the vehicle fuel economy of the flat route is superior to that of the hilly routes by approximately 15% to 20%. This road grade effect will certainly play a significant role in advanced ecorouting navigation algorithms, in which the systems can guide drivers away from steep roadways to achieve better fuel economy and reduce CO(2) emissions.
Article
A microscopic model of freeway rear-end crash risk is developed based on a modified negative binomial regression and estimated using Washington State data. Compared with most existing models, this model has two major advantages: (1) It directly considers a driver's response time distribution; and (2) it applies a new dual-impact structure accounting for the probability of both a vehicle becoming an obstacle (Po) and the following vehicle's reaction failure (Pf). The results show for example that truck percentage-mile-per-lane has a dual impact, it increases Po and decreases Pf, yielding a net decrease in rear-end crash probabilities. Urban area, curvature, off-ramp and merge, shoulder width, and merge section are factors found to increase rear-end crash probabilities. Daily vehicle miles traveled (VMT) per lane has a dual impact; it decreases Po and increases Pf, yielding a net increase, indicating for example that focusing VMT related safety improvement efforts on reducing drivers' failure to avoid crashes, such as crash-avoidance systems, is of key importance. Understanding such dual impacts is important for selecting and evaluating safety improvement plans for freeways.
Article
Empirical mode decomposition (EMD) is a self-adaptive analysis method for nonlinear and non-stationary signals. It may decompose a complicated signal into a collection of intrinsic mode functions (IMFs) based on the local characteristic time scale of the signal. The EMD method has attracted considerable attention and been widely applied to fault diagnosis of rotating machinery recently. However, it cannot reveal the signal characteristic information accurately because of the problem of mode mixing. To alleviate the mode mixing problem occurring in EMD, ensemble empirical mode decomposition (EEMD) is presented. With EEMD, the components with truly physical meaning can be extracted from the signal. Utilizing the advantage of EEMD, this paper proposes a new EEMD-based method for fault diagnosis of rotating machinery. First, a simulation signal is used to test the performance of the method based on EEMD. Then, the proposed method is applied to rub-impact fault diagnosis of a power generator and early rub-impact fault diagnosis of a heavy oil catalytic cracking machine set. Finally, by comparing its application results with those of the EMD method, the superiority of the proposed method based on EEMD is demonstrated in extracting fault characteristic information of rotating machinery.
Article
The empirical mode decomposition (EMD) is reviewed and some questions related to its effective performance are discussed. Its interpretation in terms of AM/FM modulation is done. Solutions for its drawbacks are proposed. Numerical simulations are carried out to empirically evaluate the proposed modified EMD.
Article
Standard exposition of Empirical Mode Decomposition (EMD) is usually done within a continuous-time setting whereas, in practice, the eective implementation always operates in discrete-time. The purpose of this contribution is to summarize a number of results aimed at quantifying the influence of sampling on EMD. The idealized case of a sampled pure tone is first considered in detail and a theoretical model is proposed for upper bounding the approx- imation error due to finite sampling rates. A more general approach is then discussed, based on the analysis of the nonlinear operator that underlies the EMD (one step) sifting process. New explicit, yet looser, bounds are obtained this way, whose parameters can be estimated directly from the analyzed signal. Theoretical predictions are compared to simulation results in a number of well-controlled numerical experiments.
Article
A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturally without any a priori subjective criterion selection as in the intermittence test for the original EMD algorithm. This new approach utilizes the full advantage of the statistical characteristics of white noise to perturb the signal in its true solution neighborhood, and to cancel itself out after serving its purpose; therefore, it represents a substantial improvement over the original EMD and is a truly noise-assisted data analysis (NADA) method.
Article
Huang's data-driven technique of empirical mode decomposition (EMD) is given a filter bank interpretation from two complementary perspectives. First, a stochastic approach operating in the frequency domain shows the spontaneous emergence of an equivalent dyadic filter bank structure when EMD is applied to the versatile class of fractional Gaussian noise processes. Second, a similar structure is observed when EMD is operated in the time domain on a deterministic pulse. A detailed statistical analysis of the observed behavior is carried out involving extensive numerical simulations that suggest a number of applications. New EMD-based approaches are used to estimate the scaling exponents in the case of self-similar processes, to perform a fully data-driven spectral analysis, and to denoise-detrend signals that contain noise.
Article
In addition to multi-vehicle accidents, large trucks are also prone to single-vehicle accidents on the mountainous interstate highways due to the complex terrain and fast-changing weather. By integrating both historical data analysis and simulations, a multi-scale approach is developed to evaluate the traffic safety and operational performance of large trucks on mountainous interstate highways in both scales of individual vehicle as well as traffic on the whole highway. A typical mountainous highway in Colorado is studied for demonstration purposes. Firstly, the ten-year historical accident records are analyzed to identify the accident-vulnerable-locations (AVLs) and site-specific critical adverse driving conditions. Secondly, simulation-based single-vehicle assessment is performed for different driving conditions at those AVLs along the whole corridor. Finally, the cellular-automaton (CA)-based simulation is carried out to evaluate the multi-vehicle traffic safety as well as the operational performance of the traffic by considering the actual speed limits, including the differential speed limits (DSL) at some locations. It is found that the multi-scale approach can provide insightful and comprehensive observations of the highway performance, which is especially important for mountainous highways.
Article
There has been an abundance of research that has used Poisson models and its variants (negative binomial and zero-inflated models) to improve our understanding of the factors that affect accident frequencies on roadway segments. This study explores the application of an alternate method, tobit regression, by viewing vehicle accident rates directly (instead of frequencies) as a continuous variable that is left-censored at zero. Using data from vehicle accidents on Indiana interstates, the estimation results show that many factors relating to pavement condition, roadway geometrics and traffic characteristics significantly affect vehicle accident rates.
Article
Recent research has shown that the wavelet transform (WT) can potentially be used to extract partial discharge (PD) pulses from severe noise. However, the method is more complex than the Fourier transform (FT), and requires expertise and experience to be applied to produce its best effect. The authors have previously published algorithms for selection of the most appropriate mother wavelet and for automatic determination of threshold values for applying the WT to PD measurement denoising. The present paper is to present an improved methodology to apply the discrete wavelet transform (DWT) with better denoising effect to PD measurement. Firstly the paper describes the structure of DWT's filter pairs. It then analyses the frequency bands of the wavelet coefficients in approximations and details, and energy distribution of a PD signal along each of the levels following the DWT. Finally a DWT-based denoising method is proposed and justified. Results prove that, with the proposed methodology, in conjunction with the algorithms proposed by the authors to select optimal mother wavelet and threshold values, significant improvement in denoising effect can be achieved.
Modeling the probability of freeway rear-end crash occurrence
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Analyzing the impact of grade on fuel consumption for the national interstate highway system
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