Development of New Global Optimization Algorithms Using Stochastic Level Set Method with Application in: Topology Optimization, Path Planning and Image Processing

A unique mathematical tool is developed to deal with global optimization of a set of engineering problems. These include image processing, mechanical topology optimization, and optimal path planning in a variational framework, as well as some benchmark problems in parameter optimization. The optimization tool in these applications is based on the level set theory by which an evolving contour converges toward the optimum solution. Depending upon the application, the objective function is defined, and then the level set theory is used for optimization. Level set theory, as a member of active contour methods, is an extension of the steepest descent method in conventional parameter optimization to the variational framework. It intrinsically suffers from trapping in local solutions, a common drawback of gradient based optimization methods. In this thesis, methods are developed to deal with this drawbacks of the level set approach. By investigating the current global optimization methods, one can conclude that these methods usually cannot be extended to the variational framework; or if they can, the computational costs become drastically expensive. To cope with this complexity, a global optimization algorithm is first developed in parameter space and compared with the existing methods. This method is called "Spiral Bacterial Foraging Optimization" (SBFO) method because it is inspired by the aggregation process of a particular bacterium called, Dictyostelium Discoideum. Regardless of the real phenomenon behind the SBFO, it leads to new ideas in developing global optimization methods. According to these ideas, an effective global optimization method should have i) a stochastic operator, and/or ii) a multi-agent structure. These two properties are very common in the existing global optimization methods. To improve the computational time and costs, the algorithm may include gradient-based approaches to increase the convergence speed. This property is particularly available in SBFO and it is the basis on which SBFO can be extended to variational framework. To mitigate the computational costs of the algorithm, use of the gradient based approaches can be helpful. Therefore, SBFO as a multi-agent stochastic gradient based structure can be extended to multi-agent stochastic level set method. In three steps, the variational set up is formulated: i) A single stochastic level set method, called "Active Contours with Stochastic Fronts" (ACSF), ii) Multi-agent stochastic level set method (MSLSM), and iii) Stochastic level set method without gradient such as E-ARC algorithm. For image processing applications, the first two steps have been implemented and show significant improvement in the results. As expected, a multi agent structure is more accurate in terms of ability to find the global solution but it is much more computationally expensive. According to the results, if one uses an initial level set with enough holes in its topology, a single stochastic level set method can achieve almost the same level of accuracy as a multi-agent structure can obtain. Therefore, for a topology optimization problem for which a high level of calculations (at each iteration a finite element model should be solved) is required, only ACSF with initial guess with multiple holes is implemented. In some applications, such as optimal path planning, objective functions are usually very complicated; finding a closed-form equation for the objective function and its gradient is therefore impossible or sometimes very computationally expensive. In these situations, the level set theory and its extensions cannot be directly employed. As a result, the Evolving Arc algorithm that is inspired by "Electric Arc" in nature, is proposed. The results show that it can be a good solution for either unconstrained or constrained problems. Finally, a rigorous convergence analysis for SBFO and ACSF is presented that is new amongst global optimization methods in both parameter and variational framework

Real-time estimation of the road bank and grade angles with unknown input observers

This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on 2017-01-24, available online: http://dx.doi.org/10.1080/00423114.2016.1275706This paper proposes an approach for the estimation of the road angles independent from the road friction conditions. The method employs unknown input observers on the roll and pitch dynamics of the vehicle. The correlation between the road angle rates and the pitch/roll rates of the vehicle is also investigated to increase the accuracy. Dynamic fault thresholds are implemented in the algorithm to ensure reliable estimation of the vehicle body and road angles. Performance of the proposed approach in reliable estimation of the road angles is experimentally demonstrated through vehicle road tests. Road test experiments include various driving scenarios on different road conditions to thoroughly validate the proposed approach

A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models

This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on September 28 2016, available online: http://dx.doi.org/10.1080/00423114.2016.1232417In this paper, a vehicle's lateral dynamic model is developed based on the pure and the combined-slip LuGre tyre models. Conventional vehicle's lateral dynamic methods derive handling models utilising linear tyres and pure-slip assumptions. The current article proposes a general lateral dynamic model, which takes the linear and nonlinear behaviours of the tyre into account using the pure and combined-slip assumptions separately. The developed methodology also incorporates various normal loads at each corner and provides a proper tyre–vehicle platform for control and estimation applications. Steady-state and transient LuGre models are also used in the model development and their responses are compared in different driving scenarios. Considering the fact that the vehicle dynamics is time-varying, the stability of the suggested time-varying model is investigated using an affine quadratic stability approach, and a novel approach to define the critical longitudinal speed is suggested and compared with that of conventional lateral stability methods. Simulations have been conducted and the results are used to validate the proposed method

Corner-based estimation of tire forces and vehicle velocities robust to road conditions

The final publication is available at Elsevier via https://doi.org/10.1016/j.conengprac.2017.01.009 © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Recent developments in vehicle stability control and active safety systems have led to an interest in reliable vehicle state estimation on various road conditions. This paper presents a novel method for tire force and velocity estimation at each corner to monitor tire capacities individually. This is entailed for more demanding advanced vehicle stability systems and especially in full autonomous driving in harsh maneuvers. By integrating the lumped LuGre tire model and the vehicle kinematics, it is shown that the proposed corner-based estimator does not require knowledge of the road friction and is robust to model uncertainties. The stability of the time-varying longitudinal and lateral velocity estimators is explored. The proposed method is experimentally validated in several maneuvers on different road surface frictions. The experimental results confirm the accuracy and robustness of the state estimators.Automotive Partnership Canada, Ontario Research Fund, General Motors Co

Longitudinal vehicle state estimation using nonlinear and parameter-varying observers

The final publication is available at Elsevier via https://doi.org/10.1016/j.mechatronics.2017.02.004 © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A corner-based velocity estimation approach is proposed which is used for vehicle’s traction and stability control systems. This approach incorporates internal tire states within the vehicle kinematics and enables the velocity estimator to work for a wide range of maneuvers without road friction information. Tire models have not been widely implemented in velocity estimators because of uncertain road friction and varying tire parameters, but the current study utilizes a simplified LuGre model with the minimum number of tire parameters and estimates velocity robust to model uncertainties. The proposed observer uses longitudinal forces, updates the states by minimizing the longitudinal force estimation error, and provides accurate outcomes at each tire. The estimator structure is shown to be robust to road conditions and rejects disturbances and model uncertainties effectively. Taking into account the vehicle dynamics is time-varying, the stability of the observer for the linear parameter varying model is proved, time-varying observer gains are designed, and the performance is studied. Road test experiments have been conducted and the results are used to validate the proposed approach.Automotive Partnership Canada [APCPJ 395996-09], Ontario Research Fund [ORF-RE-04-039], General Motors Co

Estimation of longitudinal speed robust to road conditions for ground vehicles

This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on June 14 2016 available online: http://dx.doi.org/10.1080/00423114.2016.1178391This article seeks to develop a longitudinal vehicle velocity estimator robust to road conditions by employing a tyre model at each corner. Combining the lumped LuGre tyre model and the vehicle kinematics, the tyres internal deflection state is used to gain an accurate estimation. Conventional kinematic-based velocity estimators use acceleration measurements, without correction with the tyre forces. However, this results in inaccurate velocity estimation because of sensor uncertainties which should be handled with another measurement such as tyre forces that depend on unknown road friction. The new Kalman-based observer in this paper addresses this issue by considering tyre nonlinearities with a minimum number of required tyre parameters and the road condition as uncertainty. Longitudinal forces obtained by the unscented Kalman filter on the wheel dynamics is employed as an observation for the Kalman-based velocity estimator at each corner. The stability of the proposed time-varying estimator is investigated and its performance is examined experimentally in several tests and on different road surface frictions. Road experiments and simulation results show the accuracy and robustness of the proposed approach in estimating longitudinal speed for ground vehicles

Resilient Corner-Based Vehicle Velocity Estimation

© 2017 IEEE. Pirani, M., Hashemi, E., Khajepour, A., Fidan, B., Kasaiezadeh, A., Chen, S.-K., & Litkouhi, B. (2017). Resilient Corner-Based Vehicle Velocity Estimation. IEEE Transactions on Control Systems Technology, 1–11. https://doi.org/10.1109/TCST.2017.2669157This paper presents longitudinal and lateral velocity estimators by considering the effect of the suspension compliance (SC) at each corner (tire) for ground vehicles. The estimators are developed to be resilient to sensor measurement inaccuracies, model and tire parameter uncertainties, switchings in observer gains, and measurement failures. More particularly, the stability of the observer is investigated, and its robustness to road condition uncertainties and sensor noises is analyzed. The sensitivity of the observers' stability and performance to the model parameter changes is discussed. Moreover, the stability of the velocity observers for two cases of arbitrary and stochastic switching gains is investigated. The stochastic stability of the observer in the presence of faulty measurements is also studied, and it is shown that if the probability of a faulty measurement occurring is less than a certain threshold, the observer error dynamics will remain stochastically stable. The performance of the observer and the effect of the SC are validated via several road experiments.Automotive Partnership Canada || Ontario Research Fund || General Motors Co. [grant numbers APCPJ 395996-09 and ORF-RE-04-039

Integrated estimation structure for the tire friction forces in ground vehicles

© IEEE 2017 Hashemi, E., Pirani, M., Khajepour, A., Fidan, B., Kasaiezadeh, A., Chen, S.-K., & Litkouhi, B. (2016). Integrated estimation structure for the tire friction forces in ground vehicles (pp. 1657–1662). IEEE. https://doi.org/10.1109/AIM.2016.7577008This paper presents a novel corner-based force estimation method to monitor tire capacities required for the traction and stability control systems. This is entailed for more advanced vehicle stability systems in harsh maneuvers. A novel estimation structure is proposed in this paper for the longitudinal, lateral, and vertical tire forces robust to the road friction condition. A nonlinear and a Kalman observer is utilized for estimation of the longitudinal and lateral friction forces. The stability and performance of the time-varying estimators are explored and it is shown that the developed integrated structure is robust to model uncertainties and does not require knowledge of the road friction. The proposed method is experimentally tested in several maneuvers on different road surface conditions and the results illustrate the accuracy and robustness of the state estimators.Automotive Partnership Canada, Ontario Research Fund, General Motors Co