Towards greater accuracy in individual-tree mortality regression

Background mortality is an essential component of any forest growth and yield model. Forecasts of mortality contribute largely to the variability and accuracy of model predictions at the tree, stand and forest level. In the present study, I implement and evaluate state-of-the-art techniques to increase the accuracy of individual tree mortality models, similar to those used in many of the current variants of the Forest Vegetation Simulator, using data from North Idaho and Montana. The first technique addresses methods to correct for bias induced by measurement error typically present in competition variables. The second implements survival regression and evaluates its performance against the traditional logistic regression approach. I selected the regression calibration (RC) algorithm as a good candidate for addressing the measurement error problem. Two logistic regression models for each species were fitted, one ignoring the measurement error, which is the “naïve” approach, and the other applying RC. The models fitted with RC outperformed the naïve models in terms of discrimination when the competition variable was found to be statistically significant. The effect of RC was more obvious where measurement error variance was large and for more shade-intolerant species. The process of model fitting and variable selection revealed that past emphasis on DBH as a predictor variable for mortality, while producing models with strong metrics of fit, may make models less generalizable. The evaluation of the error variance estimator developed by Stage and Wykoff (1998), and core to the implementation of RC, in different spatial patterns and diameter distributions, revealed that the Stage and Wykoff estimate notably overestimated the true variance in all simulated stands, but those that are clustered. Results show a systematic bias even when all the assumptions made by the authors are guaranteed. I argue that this is the result of the Poisson-based estimate ignoring the overlapping area of potential plots around a tree. Effects, especially in the application phase, of the variance estimate justify suggested future efforts of improving the accuracy of the variance estimate. The second technique implemented and evaluated is a survival regression model that accounts for the time dependent nature of variables, such as diameter and competition variables, and the interval-censored nature of data collected from remeasured plots. The performance of the model is compared with the traditional logistic regression model as a tool to predict individual tree mortality. Validation of both approaches shows that the survival regression approach discriminates better between dead and alive trees for all species. In conclusion, I showed that the proposed techniques do increase the accuracy of individual tree mortality models, and are a promising first step towards the next generation of background mortality models. I have also identified the next steps to undertake in order to advance mortality models further.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

Analysis of in-cylinder pressure transducer data quality utilizing a SIDI turbocharged engine

In-cylinder pressure transducers have been used for decades to record combustion pressure inside a running engine. However, due to the extreme operating environment, transducer design and installation must be considered in order to minimize measurement error. One such error is caused by thermal shock, where the pressure transducer experiences a high heat flux that can distort the pressure transducer diaphragm and also change the crystal sensitivity. This research focused on investigating the effects of thermal shock on in-cylinder pressure transducer data quality using a 2.0L, four-cylinder, spark-ignited, direct-injected, turbo-charged GM engine. Cylinder four was modified with five ports to accommodate pressure transducers of different manufacturers. They included an AVL GH14D, an AVL GH15D, a Kistler 6125C, and a Kistler 6054AR. The GH14D, GH15D, and 6054AR were M5 size transducers. The 6125C was a larger, 6.2mm transducer. Note that both of the AVL pressure transducers utilized a PH03 flame arrestor. Sweeps of ignition timing (spark sweep), engine speed, and engine load were performed to study the effects of thermal shock on each pressure transducer. The project consisted of two distinct phases which included experimental engine testing as well as simulation using a commercially available software package. A comparison was performed to characterize the quality of the data between the actual cylinder pressure and the simulated results. This comparison was valuable because the simulation results did not include thermal shock effects. All three sets of tests showed the peak cylinder pressure was basically unaffected by thermal shock. Comparison of the experimental data with the simulated results showed very good correlation. The spark sweep was performed at 1300 RPM and 3.3 bar NMEP and showed that the differences between the simulated results (no thermal shock) and the experimental data for the indicated mean effective pressure (IMEP) and the pumping mean effective pressure (PMEP) were significantly less than the published accuracies. All transducers had an IMEP percent difference less than 0.038% and less than 0.32% for PMEP. Kistler and AVL publish that the accuracy of their pressure transducers are within plus or minus 1% for the IMEP (AVL 2011; Kistler 2011). In addition, the difference in average exhaust absolute pressure between the simulated results and experimental data was the greatest for the two Kistler pressure transducers. The location and lack of flame arrestor are believed to be the cause of the increased error. For the engine speed sweep, the torque output was held constant at 203 Nm (150 ft-lbf) from 1500 to 4000 RPM. The difference in IMEP was less than 0.01% and the PMEP was less than 1%, except for the AVL GH14D which was 5% and the AVL GH15DK which was 2.25%. A noticeable error in PMEP appeared as the load increased during the engine speed sweeps, as expected. The load sweep was conducted at 2000 RPM over a range of NMEP from 1.1 to 14 bar. The difference in IMEP values were less 0.08% while the PMEP values were below 1% except for the AVL GH14D which was 1.8% and the AVL GH15DK which was at 1.25%. In-cylinder pressure transducer data quality was effectively analyzed using a combination of experimental data and simulation results. Several criteria can be used to investigate the impact of thermal shock on data quality as well as determine the best location and thermal protection for various transducers.