Category: Mathematics

Quasi-static Time Series

Quasi-static Time Series

Quasi-static Time Series

08/02/18

“How can we work with time-dependent and discrete data?”

 

Distributed Energy Resources can have many different discrete processes that are time dependent such as solar panels producing usable current and batteries absorbing energy. And sometimes these time-dependent processes might actually have multiple different time periods. Since normal analysis is too difficult to integrate with this, we can use something called Quasi-static Time Series to quantify our data.

Swanson’s Law

Swanson’s Law

Swanson’s Law

07/17/18

“Does solar power price drops have some form of pattern?”

 

Every day it seems that we hear about the price drop of solar power. However, does this price change somehow have a pattern? Well, a solar industrialist known as Richard Swanson was analyzing the data and found that PV module prices drop 20 percent for every doubling of cumulative shipped volume. This phenomenon is known as Swanson’s law and is similar to Moore’s law in Computer Science.

Loss Functions

Loss Functions

Loss Functions

07/03/18

“How can we see the cost of some data?”

 

When we are working with data, we often want to pick the best value. However, it can often be hard to quantify which value has the highest related cost. So how can we use our scientific problem? Well, we can use something called a Loss Function which maps all variables to a particular cost. 

Fitness Functions

Fitness Functions

Fitness Functions

07/02/18

“How can we evaluate a solution as a single figure of merit?”

 

In many fields of science, one of the most important things to do is to evaluate which solution function to a given dataset is the best. However, quantifying this can be very difficult. So how can we use our scientific mindset to solve this problem? Well, we can simply use something called a Fitness Function that can summarize all functions as a single figure of merit. With an easily accessible and quantified set of possible functions, we can pick the best one from the stack. Fitness functions are commonly used in Data Science where there can be a manifold of possible solutions.

Bumpless Transfer

Bumpless Transfer

Bumpless Transfer

07/01/18

“How can we ensure a seamless transition when we turn a PID controller from manual to auto?”

 

Switching a PID controller from Auto to Manual can be very rough for the ongoing process. That’s why engineers have created Bumpless Transfer which allows it to happen completely smoothly.

Genetic Algorithm

Genetic Algorithm

Genetic Algorithm

06/27/18

“How can we find an absolute maximum or minimum using an algorithm?”

 

Finding the absolute maximum and minimum of the function is one of the most important applications of mathematics. However, sometimes this may not be a straightforward task. So how can we use our mathematical mindsets to figure this out? Well, we could start with a few local points. We can then find how good these points are by applying a local function, and then iterate to find new points. We can repeat this process again and again until we arrive at the absolute maximum or minimum. This procedure is known as a Genetic Algorithm and can be applied to all forms of engineering problems, whether it be in energy control systems or aerospace maneuvering.  

Nonlinear Algebra

Nonlinear Algebra

Nonlinear Algebra

06/02/18

“What happens to Linear Algebra when it stops being linear?”

 

Linear Algebra has endless applications. But sometimes our system has equations where one or more variable might have an exponent greater than one or multiple variables might be coupled together. To work with these systems, we can use something called Nonlinear Algebra to simplify and solve.