Refrigeration and chiller optimization is an important and well studied topic in mechanical engineering, mostly taking advantage of physical models, designed on top of over-simpli ed assumptions, over the equipments. Conventional optimization techniques using physical models make decisions of online parameter tuning, based on very limited information of hardware speci cations and external conditions, e.g., outdoor weather. In recent years, new generation of sensors is becoming essential part of new chiller plants, for the rst time allowing the system administrators to continuously monitor the running status of all equipments in a timely and accurate way. e explosive growth of data owing to databases, driven by the increasing analytical power by machine learning and data mining, unveils new possibilities of data-driven approaches for real-time chiller plant optimization.is paper presents our research and industrial experience on the adoption of data models and optimizations on chiller plant and discusses the lessons learnt from our practice on real world plants. Instead of employing complex machine learning models, we emphasize the incorporation of appropriate domain knowledge into data analysis tools, which turns out to be the key performance improver over state-of-the-art deep learning techniques by a signi cant margin. Our empirical *
The commonly made assumption of Gaussian noise is an approximation to reality. In this paper, influence function, an analysis tool in robust statistics, is used to formulate a recursive solution for the filtering of the ARMAX process with generalized t-distribution noise. By being a superset encompassing Gaussian, uniform, t, and double exponential distributions, generalized t-distribution has the flexibility of characterizing noise with Gaussian or non-Gaussian statistical properties. The filter is formulated as a maximum likelihood problem, but instead of solving the optimization problem numerically, influence function approximation is used to obtain a recursive solution to reduce the computational load and facilitate real-time implementation. The influence function equations derived are also useful in determining the variance of the filter and the impact of outliers.
A commonly
made assumption of Gaussian noise is an approximation to reality.
In this paper, we used the influence function in robust statistics
to analyze a parameter estimator that modeled noise with the Generalized
t (GT) distribution instead of the usual Gaussian noise. The analysis
is extended to the case where the estimator designed with probability
density function f(ε) is applied to actual
noise with different probability density function g
k
(ε) at different sampling instance, k, to provide a framework for analysis of outliers. By being
a superset encompassing Gaussian, uniform, t, and double exponential
distributions, GT distribution has the flexibility to characterize
data with non-Gaussian statistical properties. Equations derived are
useful in determining the variance of the estimates and the impact
of outliers. These equations enable us to compute the sample size
needed by the estimator to meet specified variance or to tune the
estimator to limit the impact of outliers. The theory is verified
through simulations and an experiment on the chemical mechanical polishing
of semiconductors.
The generalized t-distribution (GT) is well-known because of its flexibility in transforming into many popular distributions. However, implementation of data reconciliation (DR) estimator using GT noise is somehow difficult due to its complex structure. This work proposes two iterative algorithms to ease the complexity of the GT DR estimator, hence making it easy to implement even in a large-scale problem. We also point out the convergence condition for each algorithm. Some simulation examples are shown to verify the effectiveness of the proposed algorithms on computational time. The results from this work can also be applied to other data reconciliation estimators.
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