In this paper, we develop and validate a method to identify computationally efficient site- and patient-specific models of ultrasound thermal therapies from MR thermal images. The models of the specific absorption rate of the transduced energy and the temperature response of the therapy target are identified in the reduced basis of proper orthogonal decomposition of thermal images, acquired in response to a mild thermal test excitation. The method permits dynamic reidentification of the treatment models during the therapy by recursively utilizing newly acquired images. Such adaptation is particularly important during high-temperature therapies, which are known to substantially and rapidly change tissue properties and blood perfusion. The developed theory was validated for the case of focused ultrasound heating of a tissue phantom. The experimental and computational results indicate that the developed approach produces accurate low-dimensional treatment models despite temporal and spatial noises in MR images and slow image acquisition rate.

Supercapacitors are emerging new devices for many applications, either as main energy sources or as energy buffers, due to their high power density. To study possible applications of supercapacitors, a terminal model describing the dynamic behavior of supercapacitors is required. In this paper, a simple electrical equivalent circuit model (ECM) is proposed based on the conventional supercapacitor RC branches model. Moreover, a nonlinear optimization algorithm is presented to identify the model parameters. The proposed modeling and identification method was validated with supercapacitor experimental results. The proposed method can be used to simulate and predict the dynamic performance of a super capacitor, assess its energy storage capability. It can also be used in the design of energy management system of many supercapacitor applications, such as, capacitive deionization (CDI), hybrid/electric vehicles.

Fractional order differential equations (FODE) provides a more flexible approach to describe dynamic systems. However, the extra flexibility poses a difficult problem in system identification, which requires not only the estimation of model coefficients but also the determination of fractional orders. They are coupled nonlinearly. In addition, the model coefficients in a FODE are shown nonlinearly coupled with respect to the often used Sum Squared Error (SSE) objective function. In this article, a two-layer approach is designed to estimate fractional orders and model coefficients iteratively. An intermediate step that estimates model coefficients is also introduced to address the nonlinear coupling of coefficients in a SSE. In the subsequent simulation for electrochemical systems, it is found that prior knowledge on physical systems being modeled is necessary to create optimization constraints and justify the results.

In this article, we introduce a powerful software tool Engineering Equation Solver (EES) and apply it to create steady state and dynamic models for a reverse osmosis (RO) desalination system. EES is a general equation-solving program that can numerically solve thousands of coupled nonlinear algebraic equations. It can also be used to solve differential equations and optimization problems. In RO desalination system design, amount of coupled differential equations related to mass balance and momentum balance need to be solved to develop system model. Hence, by applying EES to solve differential equations is a very efficient and effective method to build RO desalination system model. Comparing with Matlab, EES has the advantage of easy programming and fast convergence speed. It significantly reduces the time spending for programming to solve nonlinear equations and researchers can focus on RO system optimal design and analysis.

In accelerated & controlled cooling (ACC) process, the relationship between plate point's temperature and the manipulated variable, plate velocity, is complicate and nonlinear with a time delay. A novel Model Predictive Control (MPC) is developed for precise control of the plate point's final temperature (FT) with fast computational speed. The control objective of time-temperature curve (plate temperature evolution) is converted into a space distribution of plate temperature along cooling line, which simplifies the ACC model to a linear model then does beneficial to employ MPC directly for optimizing the FT of plate points. The predictive horizon and control horizon of MPC is reduced to one or two sample time since the space distribution of plate temperature contains the future information of plate point's temperature, then dramatically reduce the computational burden. The simulation result shows the efficiency of the proposed method.