Farshad Harirchi

Model Invalidation for Switched Affine Systems with Applications to Fault and Anomaly Detection

Abstract In this paper, the model (in)validation problem is addressed for the class of switched state space models. We pose the model invalidation problem as a mixed-integer linear program and solve it using the state-of-the-art MILP solvers. Model invalidation is mainly utilized to build trust in the models obtained from system identification. However, we turn our attention to solve another important class of problems using model invalidation approach proposed in this paper. It is shown that the model invalidation approach can be utilized to detect any general fault in cyber-physical systems. Moreover, it is illustrated that knowing the fault model can reduce the complexity of fault detection approach proposed here, if the fault and system model satisfy certain conditions.

Optimal payment sharing mechanism for renewable energy aggregation

Renewable energy aggregation has been introduced as a solution to reduce the uncertainty of this type of sources. In this work we propose a new mechanism to share the profit of the aggregate amongst individual producers. Calculating optimal contract for individual producers and the aggregate is the first requirement in order to propose a payment sharing mechanism that has been addressed in the literature. Different researchers utilized various methods from coalitional game theory to statistical methods to introduce payment sharing mechanisms. In this work we propose a novel payment sharing mechanism that maximizes the aggregate profit in first place. The payments to the individuals are based on their actual production instead of the expected. We also show that this method will pay more to the individuals in average compared to previous methods.

Model (in)validation and fault detection for systems with polynomial state-space models

This paper addresses the problem of (in)validation of polynomial state-space models, that is, checking whether a discrete-time uncertain polynomial state-space model can explain noisy experimental input/output data. We first recast this problem as a polynomial optimization problem and present asymptotically tight invalidation certificates by appealing to well-known moments-based relaxations. In the second part of the paper, we show how a model-based run-time fault detection algorithm can be developed based on a notion of T-detectability, which enables the proposed model invalidation approach to be applied in receding horizon fashion to detect faults. The efficacy of the proposed methods are illustrated with some numerical and practical examples.

Implementation of Nonthreaded Estimation for Run-to-Run Control of High Mix Semiconductor Manufacturing

Semiconductor processing consists of many different unit operations that are combined in a sequence to create the finished product. Many of these unit operations utilize run to run control in order to keep the process within the required manufacturing constraints. Typically, the difference, or bias, between the desired and actual result of processing a particular wafer is affected by not only the particular product being produced, but the prior processing path. Each possible effect is called a context category, and the particular context items relevant for a wafer is called a thread. Because of frequent changes and updates in semiconductor products as well as a large number of product lines, run to run control must deal with a high-mix environment of products, and a large number of threads. Previously, several authors have discussed a method of describing the bias for a particular thread as a sum of context item biases and using a Kalman Filter to estimate these biases. However, two issues with previous implementations have been the observability of the state realization of the bias model, and the computational cost of the Kalman filter. In this paper, we introduce a model formulation that does not require model reduction or the specification of special reference threads, thus easily allowing new threads to be added and old threads removed. In addition, we describe how the problem structure allows the information form of the Kalman filter to be much more computationally efficient. Simulation results illustrate the proposed method.

Characterizing and resolving unobservability in run-to-run control of high mix semiconductor manufacturing

Run to run control is a major tool used in semiconductor manufacturing to keep the unit processes within the required manufacturing constraints. Typically, the difference, or bias, between the desired and actual result of processing a particular wafer is affected by not only the particular product being produced, but the prior processing path, which can complicate the control. Previously, several authors have discussed a method of describing the bias for a particular wafer as a linear combination of fundamental bias causes and then using a Kalman Filter to estimate these biases. One known complication of this method is a system structure that can cause the bias states to be unobservable. In this paper we address a second form of unobservability that can be caused by the production process, (i.e. which products are sent to which tools.) We then analyze two methods for adjusting the estimation process to mitigate this unobservability, one of which is new. The performance of this novel method then will be shown using the simulations.

Guaranteed model-based fault detection in cyber–physical systems: A model invalidation approach

This paper presents a sound and complete fault detection approach for cyber-physical systems represented by hidden-mode switched affine models with time varying parametric uncertainty. The fault detection approach builds upon techniques from model invalidation. In particular, a set-membership approach is taken where the noisy input-output data is compared to the set of behaviors of a nominal model. As we show, this set-membership check can be reduced to the feasibility of a mixed-integer linear programming (MILP) problem, which can be solved efficiently by leveraging the state-of-the-art MILP solvers. In the second part of the paper, given a system model and a fault model, the concept of T-detectability is introduced. If a pair of system and fault models satisfies T-detectability property for a finite T, this allows the model invalidation algorithm to be implemented in a receding horizon manner, without compromising detection guarantees. In addition, the concept of weak-detectability is introduced which extends the proposed approach to a more expressive class of fault models that capture language constraints on the mode sequences. Finally, the efficiency of the approach is illustrated with numerical examples motivated by smart building radiant systems.

Effect of bonus payments in cost sharing mechanism design for renewable energy aggregation

The participation of renewable energy sources in energy markets is challenging, mainly because of the uncertainty associated with the renewables. Aggregation of renewable energy suppliers is shown to be very effective in decreasing this uncertainty. In the present paper, we propose a cost sharing mechanism that entices the suppliers of wind, solar and other renewable resources to form or join an aggregate. In particular, we consider the effect of a bonus for surplus in supply, which is neglected in previous work. We introduce a specific proportional cost sharing mechanism, which satisfies the desired properties of such mechanisms that are introduced in the literature, e.g., budget balancedness, ex-post individual rationality and fairness. In addition, we show that the proposed mechanism results in a stable market outcome. Finally, the results of the paper are illustrated by numerical examples.

Optimal input design for affine model discrimination with applications in intention-aware vehicles

This paper considers the optimal design of input signals for the purpose of discriminating among a finite number of affine models with uncontrolled inputs and noise. Each affine model represents a different system operating mode, corresponding to unobserved intents of other drivers or robots, or to fault types or attack strategies, etc. The input design problem aims to find optimal separating/discriminating (controlled) inputs such that the output trajectories of all the affine models are guaranteed to be distinguishable from each other, despite uncertainty in the initial condition and uncontrolled inputs as well as the presence of process and measurement noise. We propose a novel formulation to solve this problem, with an emphasis on guarantees for model discrimination and optimality, in contrast to a previously proposed conservative formulation using robust optimization. This new formulation can be recast as a bilevel optimization problem and further reformulated as a mixed-integer linear program (MILP). Moreover, our fairly general problem setting allows the incorporation of objectives and/or responsibilities among rational agents. For instance, each driver has to obey traffic rules, while simultaneously optimizing for safety, comfort and energy efficiency. Finally, we demonstrate the effectiveness of our approach for identifying the intention of other vehicles in several driving scenarios.

On the Initialization of Threaded Run-to-Run Control of Semiconductor Manufacturing

Run-to-run control is a major tool used in semiconductor manufacturing to keep the unit processes within the required manufacturing constraints. Typically, the difference or bias between the desired and actual result of processing a particular wafer is affected by not only the particular product being produced, but also the prior processing path. Each unique combination of effects is called a thread, and in threaded run-to-run control a separate exponentially weighted moving average controller is applied for each thread. One of the challenges of threaded control is the initialization of the bias estimate for a new thread. Automated initialization methods prevent the cost of manual initialization or utilizing a pilot run, but at the risk of producing outliers in the initialized runs. On the other hand, the manual initialization or using pilot runs incur an extra expense. In this paper, we study a new approach for initialization of the threads by combining the threaded and nonthreaded control strategies. This method avoids the cost associated with manual initialization methods and improves the efficiency of automated methods. Finally, the simulation results will demonstrate the efficiency of the proposed method in comparison with other techniques.

Passive Diagnosis of Hidden-Mode Switched Affine Models with Detection Guarantees via Model Invalidation

Smart systems, ranging from smart homes to infrastructure networks such as traffic and power networks, are examples of cyber-physical systems that are oftentimes safety critical, yet prone to system failures. This chapter contributes to the area of passive fault detection and isolation for such systems, modeled as hybrid dynamical systems, from a model invalidation perspective. In particular, we present a model-based approach for guaranteed detection and isolation of generic faults in cyber-physical systems, where both the systems and the faults are represented by hidden-mode switched affine models with time-varying parametric uncertainty subject to process and measurement noise. We show that model invalidation based fault detection and isolation can be reduced to the feasibility of a mixed-integer linear programming (MILP) problem, which can be solved efficiently by leveraging state-of-the-art MILP solvers. In addition, for a given pair of models (system and/or fault models), we introduce the notion of T-distinguishability and show that the T-distinguishability test for any pair of models also reduces to a feasibility check of a MILP problem. Using this property, we show that the satisfaction of the T-distinguishability property with a finite T allows us to implement the model invalidation algorithm using only data from a finite horizon with guarantees of fault detection and isolation in a receding horizon manner. Finally, building on these results, a real-time fault detection and isolation scheme is presented, which runs multiple model invalidation problems simultaneously at run-time with guarantees for the detection and isolation delays when identifying specific faults.