A Soft Sensor-Based Fault-Tolerant Control on the Air Fuel Ratio of Spark-Ignition Engines

The air/fuel ratio (AFR) regulation for spark-ignition (SI) engines has been an essential and challenging control problem for engineers in the automotive industry. The feed-forward and feedback scheme has been investigated in both academic research and industrial application. The aging effect can often cause an AFR sensor fault in the feedback loop, and the AFR control performance will degrade consequently. In this research, a new control scheme on AFR with fault-tolerance is proposed by using an artificial neural network model based on fault detection and compensation, which can provide the satisfactory AFR regulation performance at the stoichiometric value for the combustion process, given a certain level of misreading of the AFR sensor

Practical shape optimization for turbine and compressor blades

The shape optimization of blades is a crucial step within the design cycle of a whole turbomachine. This paper is a report on a joint project between academia and industry leading to an efficient solution software for this problem to be used in the daily work of concerned engineers. The problem description and solution method, characterized as a partially reduced SQP method, as well as numerical results are presented

On limited memory SQP methods for large scale constrained nonlinear least squares problems

This paper describes limited memory Sequential Quadratic Programming methods (LSQP) for a large scale equality constrained nonlinear least squares problem. By introducing additional variables, the original problem is transformed into a general equality constrained nonlinear programming problem with a simple objective. This is then solved by a limited memory variation of SQP methods. This overcomes one of the major drawbacks of the traditional SQP method, where a large matrix needs to be stored, and combines the best performance of the Gauss-Newton and Quasi-Newton methods by a suitable choice of the Lagrangian Hessian approximation. Our numerical tests indicate that the new method is faster than the reduced Hessian (RSQP) method, and is better able to use additional storage to accelerate convergence. For some problems it approaches the performance of the full Hessian SQP (FSQP) method adapted for least squares problems in Schittkowski. However, his method cannot cope with problems with very many observations

Nonlinear programming without a penalty function or a filter

A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate that the method performs well

A comparative study of null-space factorizations for sparse symmetric saddle point systems

Null-space methods for solving saddle point systems of equations have long been used to transform an indefinite system into a symmetric positive definite one of smaller dimension. A number of independent works in the literature have identified that we can interpret a null-space method as a matrix factorization. We review these findings, highlight links between them, and bring them into a unified framework. We also investigate the suitability of using null-space factorizations to derive sparse direct methods, and present numerical results for both practical and academic problems

Parameter and state model reduction for Bayesian statistical inverse problems

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 113-118).Decisions based on single-point estimates of uncertain parameters neglect regions of significant probability. We consider a paradigm based on decision-making under uncertainty including three steps: identification of parametric probability by solution of the statistical inverse problem, propagation of that uncertainty through complex models, and solution of the resulting stochastic or robust mathematical programs. In this thesis we consider the first of these steps, solution of the statistical inverse problem, for partial differential equations (PDEs) parameterized by field quantities. When these field variables and forward models are discretized, the resulting system is high-dimensional in both parameter and state space. The system is therefore expensive to solve. The statistical inverse problem is one of Bayesian inference. With assumption on prior belief about the form of the parameter and an assignment of normal error in sensor measurements, we derive the solution to the statistical inverse problem analytically, up to a constant of proportionality. The parametric probability density, or posterior, depends implicitly on the parameter through the forward model. In order to understand the distribution in parameter space, we must sample. Markov chain Monte Carlo (MCMC) sampling provides a method by which a random walk is constructed through parameter space. By following a few simple rules, the random walk converges to the posterior distribution and the resulting samples represent draws from that distribution. This set of samples from the posterior can be used to approximate its moments.(cont.) In the multi-query setting, it is computationally intractable to utilize the full-order forward model to perform the posterior evaluations required in the MCMC sampling process. Instead, we implement a novel reduced-order model which reduces in parameter and state. The reduced bases are generated by greedy sampling. We iteratively sample the field in parameter space which maximizes the error in full-order and current reduced-order model outputs. The parameter is added to its basis and then a high-fidelity forward model is solved for the state, which is then added to the state basis. The reduction in state accelerates posterior evaluation while the reduction in parameter allows the MCMC sampling to be conducted with a simpler, non-adaptive 3 Metropolis-Hastings algorithm. In contrast, the full-order parameter space is high-dimensional and requires more expensive adaptive methods. We demonstrate for the groundwater inverse problem in 1-D and 2-D that the reduced-order implementation produces accurate results with a factor of three speed up even for the model problems of dimension N ~~500. Our complexity analysis demonstrates that the same approach applied to the large-scale models of interest (e.g. N > 10⁴) results in a speed up of three orders of magnitude.by Chad Eric Lieberman.S.M

Optimal allocation of static and dynamic reactive power support for enhancing power system security

Power systems over the recent past few years, has undergone dramatic revolution in terms of government and private investment in various areas such as renewable generation, incorporation of smart grid to better control and operate the power grid, large scale energy storage, and fast responding reactive power sources. The ongoing growth of the electric power industry is mainly because of the deregulation of the industry and regulatory compliance which each participant of the electric power system has to comply with during planning and operational phase. Post worldwide blackouts, especially the year 2003 blackout in north-east USA, which impacted roughly 50 million people, more attention has been given to reactive power planning. At present, there is steady load growth but not enough transmission capacity to carry power to load centers. There is less transmission expansion due to high investment cost, difficulty in getting environmental clearance, and less lucrative cost recovery structure. Moreover, conventional generators close to load centers are aging or closing operation as they cannot comply with the new environmental protection agency (EPA) policies such as Cross-State Air Pollution Rule (CSAPR) and MACT. The conventional generators are getting replaced with far away renewable sources of energy. Thus, the traditional source of dynamic reactive power support close to load centers is getting retired. This has resulted in more frequently overloading of transmission network than before. These issues lead to poor power quality and power system instability. The problem gets even worse during contingencies and especially at high load levels. There is a clear need of power system static and dynamic monitoring. This can help planners and operators to clearly identify severe contingencies causing voltage acceptability problem and system instability. Also, it becomes imperative to find which buses and how much are they impacted by a severe contingency. Thus, sufficient static and dynamic reactive power resource is needed to ensure reliable operation of power system, during stressed conditions and contingencies. In this dissertation, a generic framework has been developed for filtering and ranking of severe contingency. Additionally, vulnerable buses are identified and ranked. The next task after filtering out severe contingencies is to ensure static and dynamic security of the system against them. To ensure system robustness against severe contingencies optimal location and amount of VAR support required needs to be found. Thus, optimal VAR allocation needs to be found which can ensure acceptable voltage performance against all severe contingency. The consideration of contingency in the optimization process leads to security constrained VAR allocation problem. The problem of static VAR allocation requirement is formulated as minlp. To determine optimal dynamic VAR installation requirement the problem is solved in dynamic framework and is formulated as a Mixed Integer Dynamic Optimization (MIDO). Solving the VAR allocation problem for a set of severe contingencies is a very complex problem. Thus an approach is developed in this work which reduces the overall complexity of the problem while ensuring an acceptable optimal solution. The VAR allocation optimization problem has two subparts i.e. interger part and nonlinear part. The integer part of the problem is solved by branch and bound (B&B) method. To enhance the efficiency of B&B, system based knowledge is used to customize the B&B search process. Further to reduce the complexity of B&B method, only selected candidate locations are used instead of all plausible locations in the network. The candidate locations are selected based upon the effectiveness of the location in improving the system voltage. The selected candidate locations are used during the optimization process. The optimization process is divided into two parts: static optimization and dynamic optimization. Separating the overall optimization process into two sub-parts is much more realistic and corresponds to industry practice. Immediately after the occurrence of the contingency, the system goes into transient (or dynamic) phase, which can extend from few milliseconds to a minute. During the transient phase fast acting controllers are used to restore the system. Once the transients die out, the system attains steady state which can extend for hours with the help of slow static controllers. Static optimization is used to ensure acceptable system voltage and system security during steady state. The optimal reactive power allocation as determined via static optimization is a valuable information. It\u27s valuable as during the steady state phase of the system which is a much longer phase (extending in hours), the amount of constant reactive power support needed to maintain steady system voltage is determined. The optimal locations determined during the static optimization are given preference in the dynamic optimization phase. In dynamic optimization optimal location and amount of dynamic reactive power support is determined which can ensure acceptable transient performance and security of the system. To capture the true dynamic behavior of the system, dynamic model of system components such as generator, exciter, load and reactive power source is used. The approach developed in this work can optimally allocate dynamic VAR sources. The results of this work show the effectiveness of the developed reactive power planning tool. The proposed methodology optimally allocates static and dynamic VAR sources that ensure post-contingency acceptable power quality and security of the system. The problem becomes manageable as the developed approach reduces the overall complexity of the optimization problem. We envision that the developed method will provide system planners a useful tool for optimal planning of static and dynamic reactive power support that can ensure system acceptable voltage performance and security