Modeling

1D PDE Model for Thermal Dynamics in Fluid-Cooled Battery Packs: Numerical Methods and Sensor Placement

Kato, Dylan
Moura, Scott J.
2021

This paper addresses the problem of modeling and estimating state dynamics in coupled battery and thermal cooling systems. We present a coupled diffusion-advection PDE model for fluid-cooled battery packs. A novel numerical method is proposed to simulate this PDE system. The technique is a monolithic integration of the method of characteristics and the Crank-Nicolson update scheme. The numerical scheme is validated with thermal energy conservation and shown to be conservative. We then leverage this numeric scheme to examine the optimal sensor placement problem. We formulate and solve the...

Integrating Electrochemical Modeling with Machine Learning for Lithium-Ion Batteries

Tu, Hao
Moura, Scott
Fang, Huazhen
2021

Mathematical modeling of lithium-ion batteries (LiBs) is a central challenge in advanced battery management. This paper presents a new approach to integrate a physics-based model with machine learning to achieve high-precision modeling for LiBs. This approach uniquely proposes to inform the machine learning model of the dynamic state of the physical model, enabling a deep integration between physics and machine learning. We propose two hybrid physics-machine learning models based on the approach, which blend a single particle model with thermal dynamics (SPMT) with a feedforward neural...

Safe Wasserstein Constrained Deep Q-Learning

Kandel, Aaron
Moura, Scott
2021

This paper presents a distributionally robust Q-Learning algorithm (DrQ) which leverages Wasserstein ambiguity sets to provide idealistic probabilistic out-of-sample safety guarantees during online learning. First, we follow past work by separating the constraint functions from the principal objective to create a hierarchy of machines which estimate the feasible state-action space within the constrained Markov decision process (CMDP). DrQ works within this framework by augmenting constraint costs with tightening offset variables obtained through Wasserstein distributionally robust...

Safe Learning MPC With Limited Model Knowledge and Data

Kandel, Aaron
Moura, Scott J.
2024

This article presents an end-to-end framework for safe learning-based control (LbC) using nonlinear stochastic MPC and distributionally robust optimization (DRO). This work is motivated by several open challenges in LbC literature. Many control-theoretic LbC methods require subject matter expertise (SME), often manifested as preexisting data of safe trajectories or structural model knowledge, to translate their own safety guarantees. In this article, we focus on LbC where the controller is applied directly to a system of which it has no or extremely limited direct experience, toward safety...

Probabilistic Structure of Two-Lane Road Traffic

Daganzo, Carlos F.
1975

In most predictive models for two-lane road traffic, it is assumed that platoons have no physical dimensions, thus restricting their applicability to light traffic where a platoon cannot be long enough to block the progression of the next one. In this paper a model that can be used for heavy traffic is presented. A queueing theory approach in which vehicles are allowed to have physical dimensions yields the platoon length distribution, the delays to fast vehicles, the headway process and the flow density diagram for both the space and time processes. Unlike in other models, the passing...

On Stochastic Models of Traffic Assignment

Daganzo, Carlos F.
Sheffi, Yosef
1977

This paper contains a quantitative evaluation of probabilistic traffic assignment models and proposes an alternate formulation. First, the concept of stochastic-user-equilibration (S-U-E) is formalized as an extension of Wardrop's user-equilibration criterion. Then, the stochastic-network-loading (S-N-L) problem (a special case of S-U-E for networks with constant link costs) is analyzed in detail and an expression for the probability of route choice which is based on two general postulates of user behavior is derived. The paper also discusses the weaknesses of existing S-N-L techniques...

Multinomial Probit and Qualitative Choice: A Computationally Efficient Algorithm

Daganzo, Carlos F.
Bouthelier, Fernando
Sheffi, Yosef
1977

Even though multinomial probit models have many attractive theoretical features and have been proposed for diverse choice problems (such as modal split and route choice in the transportation field), they have never been used in practice due to the lack of an adequate numerical technique for their application. The purpose of this paper is to introduce such a technique and to demonstrate the feasibility of forecasting with multinominal probit models. Our limited computational experience with the proposed numerical technique indicates that it is accurate, and can be efficiently applied to...

An Approximate Analytic Model of Many-to-Many Demand Responsive Transportation Systems

Daganzo, Carlos F.
1978

This paper presents an analytic model to predict average waiting and ridingtimes in urban transportation systems (such as dial-a-bus and taxicabs), which provide non-transfer door-to-door transportation with a dynamically dispatched fleet of vehicles. Three different dispatching algorithms are analyzed with a simple deterministic model, which is then generalized to capture the most relevant stochastic phenomena. The formulae obtained have been successfully compared with simulated data and are simple enough for hand calculation. They are, thus, tools which enable analysts to avoid...

The Statistical Interpretation of Predictions with Disaggregate Demand Models

Daganzo, Carlos F.
1979

This paper discusses an element of forecasting with disaggregate demand models that has received little attention so far; namely, the extent to which the accuracy of the final prediction depends on the accuracy of the calibration process. The paper introduces a numerical technique to evaluate approximate confidence intervals for the expected number of people using a transportation facility and approximate prediction intervals for the actual usage. It is shown that, unless the magnitude of the variance of the estimated parameters is considerably small, the predictions that result may be...

Aggregation with Multinomial Probit and Estimation of Disaggregate Models with Aggregate Data: A New Methodological Approach

Bouthelier, Fernando
Daganzo, Carlos F.
1979

This paper describes an analytic aggregation procedure for disaggregate demand models similar to the one proposed in earlier publications by Westin (1974) and McFadden and Reid (1975). The technique, which uses a multivariate normal approximation for the distribution of the vector of attributes, is based on the multinomial profit algorithm proposed by Daganzo, Bouthelier and Sheffi (1977) and can be applied to an arbitrary number of alternatives. The procedure is computationally so efficient that it enables us to calibrate disaggregate models with aggregate data by maximum likelihood using...