Tag Archives: Engineering design

Time series analysis tools in Visual Process Analytics: Cross correlation

Two time series and their cross-correlation functions
In a previous post, I showed you what autocorrelation function (ACF) is and how it can be used to detect temporal patterns in student data. The ACF is the correlation of a signal with itself. We are certainly interested in exploring the correlations among different signals.

The cross-correlation function (CCF) is a measure of similarity of two time series as a function of the lag of one relative to the other. The CCF can be imagined as a procedure of overlaying two series printed on transparency films and sliding them horizontally to find possible correlations. For this reason, it is also known as a "sliding dot product."

The upper graph in the figure to the right shows two time series from a student's engineering design process, representing about 45 minutes of her construction (white line) and analysis (green line) activities while trying to design an energy-efficient house with the goal to cut down the net energy consumption to zero. At first glance, you probably have no clue about what these lines represent and how they may be related.

But their CCFs reveal something that appears to be more outstanding. The lower graph shows two curves that peak at some points. I know you have a lot of questions at this point. Let me try to see if I can provide more explanations below.

Why are there two curves for depicting the correlation of two time series, say, A and B? This is because there is a difference between "A relative to B" and "B relative to A." Imagine that you print the series on two transparency films and slide one on top of the other. Which one is on the top matters. If you are looking for cause-effect relationships using the CCF, you can treat the antecedent time series as the cause and the subsequent time series as the effect.

What does a peak in the CCF mean, anyways? It guides you to where more interesting things may lie. In the figure of this post, the construction activities of this particular student were significantly followed by analysis activities about four times (two of them are within 10 minutes), but the analysis activities were significantly followed by construction activities only once (after 10 minutes).

Time series analysis tools in Visual Process Analytics: Autocorrelation

Autocorrelation reveals a three-minute periodicity
Digital learning tools such as computer games and CAD software emit a lot of temporal data about what students do when they are deeply engaged in the learning tools. Analyzing these data may shed light on whether students learned, what they learned, and how they learned. In many cases, however, these data look so messy that many people are skeptical about their meaning. As optimists, we believe that there are likely learning signals buried in these noisy data. We just need to use or invent some mathematical tricks to figure them out.

In Version 0.2 of our Visual Process Analytics (VPA), I added a few techniques that can be used to do time series analysis so that researchers can find ways to characterize a learning process from different perspectives. Before I show you these visual analysis tools, be aware that the purpose of these tools is to reveal the temporal trends of a given process so that we can better describe the behavior of the student at that time. Whether these traits are "good" or "bad" for learning likely depends on the context, which often necessitates the analysis of other co-variables.

Correlograms reveal similarity of two time series.
The first tool for time series analysis added to VPA is the autocorrelation function (ACF), a mathematical tool for finding repeating patterns obscured by noise in the data. The shape of the ACF graph, called the correlogram, is often more revealing than just looking at the shape of the raw time series graph. In the extreme case when the process is completely random (i.e., white noise), the ACF will be a Dirac delta function that peaks at zero time lag. In the extreme case when the process is completely sinusoidal, the ACF will be similar to a damped oscillatory cosine wave with a vanishing tail.

An interesting question relevant to learning science is whether the process is autoregressive (or under what conditions the process can be autoregressive). The quality of being autoregressive means that the current value of a variable is influenced by its previous values. This could be used to evaluate whether the student learned from the past experience -- in the case of engineering design, whether the student's design action was informed by previous actions. Learning becomes more predictable if the process is autoregressive (just to be careful, note that I am not saying that more predictable learning is necessarily better learning). Different autoregression models, denoted as AR(n) with n indicating the memory length, may be characterized by their ACFs. For example, the ACF of AR(2) decays more slowly than that of AR(1), as AR(2) depends on more previous points. (In practice, partial autocorrelation function, or PACF, is often used to detect the order of an AR model.)

The two figures in this post show that the ACF in action within VPA, revealing temporal periodicity and similarity in students' action data that are otherwise obscure. The upper graphs of the figures plot the original time series for comparison.

Seeing student learning with visual analytics

Technology allows us to record almost everything happening in the classroom. The fact that students' interactions with learning environments can be logged in every detail raises the interesting question about whether or not there is any significant meaning and value in those data and how we can make use of them to help students and teachers, as pointed out in a report sponsored by the U.S. Department of Education:
New technologies thus bring the potential of transforming education from a data-poor to a data-rich enterprise. Yet while an abundance of data is an advantage, it is not a solution. Data do not interpret themselves and are often confusing — but data can provide evidence for making sound decisions when thoughtfully analyzed.” — Expanding Evidence Approaches for Learning in a Digital World, Office of Educational Technology, U.S. Department of Education, 2013
A radar chart of design space exploration.
A histogram of action intensity.
Here we are not talking about just analyzing students' answers to some multiple-choice questions, or their scores in quizzes and tests, or their frequencies of logging into a learning management system. We are talking about something much more fundamental, something that runs deep in cognition and learning, such as how students conduct a scientific experiment, solve a problem, or design a product. As learning goes deeper in those directions, data produced by students grows bigger. It is by no means an easy task to analyze large volumes of learner data, which contain a lot of noisy elements that cast uncertainty to assessment. The validity of an assessment inference rests on  the strength of evidence. Evidence construction often relies on the search for relations, patterns, and trends in student data.With a lot of data, this mandates some sophisticated computation similar to cognitive computing.

Data gathered from highly open-ended inquiry and design activities, key to authentic science and engineering practices that we want students to learn, are often intensive and “messy.” Without analytic tools that can discern systematic learning from random walk, what is provided to researchers and teachers is nothing but a DRIP (“data rich, information poor”) problem.

A scatter plot of action timeline.
Recognizing the difficulty in analyzing the sheer volume of messy student data, we turned to visual analytics, a whole category of techniques extensively used in cutting-edge business intelligence systems such as software developed by SAS, IBM, and others. We see interactive, visual process analytics key to accelerating the analysis procedures so that researchers can adjust mining rules easily, view results rapidly, and identify patterns clearly. This kind of visual analytics optimally combines the computational power of the computer, the graphical user interface of the software, and the pattern recognition power of the brain to support complex data analyses in data-intensive educational research.

A digraph of action transition.
So far, I have written four interactive graphs and charts that can be used to study four different aspects of the design action data that we collected from our Energy3D CAD software. Recording several weeks of student work on complex engineering design challenges, these datasets are high-dimensional, meaning that it is improper to treat them from a single point of view. For each question we are interested in getting answers from student data, we usually need a different representation to capture the outstanding features specific to the question. In many cases, multiple representations are needed to address a question.

In the long run, our objective is to add as many graphic representations as possible as we move along in answering more and more research questions based on our datasets. Given time, this growing library of visual analytics would develop sufficient power to the point that it may also become useful for teachers to monitor their students' work and thereby conduct formative assessment. To guarantee that our visual analytics runs on all devices, this library is written in JavaScript/HTML/CSS. A number of touch gestures are also supported for users to use the library on a multi-touch screen. A neat feature of this library is that multiple graphs and charts can be grouped together so that when you are interacting with one of them, the linked ones also change at the same time. As the datasets are temporal in nature, you can also animate these graphs to reconstruct and track exactly what students do throughout.

The National Science Foundation funds SmartCAD—an intelligent learning system for engineering design

We are pleased to announce that the National Science Foundation has awarded the Concord Consortium, Purdue University, and the University of Virginia a $3 million, four-year collaborative project to conduct research and development on SmartCAD, an intelligent learning system that informs engineering design of students with automatic feedback generated using computational analysis of their work.

Engineering design is one of the most complex learning processes because it builds on top of multiple layers of inquiry, involves creating products that meet multiple criteria and constraints, and requires the orchestration of mathematical thinking, scientific reasoning, systems thinking, and sometimes, computational thinking. Teaching and learning engineering design becomes important as it is now officially part of the Next Generation Science Standards in the United States. These new standards mandate every student to learn and practice engineering design in every science subject at every level of K-12 education.
Figure 1

In typical engineering projects, students are challenged to construct an artifact that performs specified functions under constraints. What makes engineering design different from other design practices such as art design is that engineering design must be guided by scientific principles and the end products must operate predictably based on science. A common problem observed in students' engineering design activities is that their design work is insufficiently informed by science, resulting in the reduction of engineering design to drawing or crafting. To circumvent this problem, engineering design curricula often encourage students to learn or review the related science concepts and practices before they try to put the design elements together to construct a product. After students create a prototype, they then test and evaluate it using the governing scientific principles, which, in turn, gives them a chance to deepen their understanding of the scientific principles. This common approach of learning is illustrated in the upper image of Figure 1.

There is a problem in the common approach, however. Exploring the form-function relationship is a critical inquiry step to understanding the underlying science. To determine whether a change of form can result in a desired function, students have to build and test a physical prototype or rely on the opinions of an instructor. This creates a delay in getting feedback at the most critical stage of the learning process, slowing down the iterative cycle of design and cutting short the exploration in the design space. As a result of this delay, experimenting and evaluating "micro ideas"--very small stepwise ideas such as those that investigate a design parameter at a time--through building, revising, and testing physical prototypes becomes impractical in many cases. From the perspective of learning, however, it is often at this level of granularity that foundational science and engineering design ultimately meet.

Figure 2
All these problems can be addressed by supporting engineering design with a computer-aided design (CAD) platform that embeds powerful science simulations to provide formative feedback to students in a timely manner. Simulations based on solving fundamental equations in science such as Newton’s Laws model the real world accurately and connect many science concepts coherently. Such simulations can computationally generate objective feedback about a design, allowing students to rapidly test a design idea on a scientific basis. Such simulations also allow the connections between design elements and science concepts to be explicitly established through fine-grained feedback, supporting students to make informed design decisions for each design element one at a time, as illustrated by the lower image of Figure 1. These scientific simulations give the CAD software tremendous disciplinary intelligence and instructional power, transforming it into a SmartCAD system that is capable of guiding student design towards a more scientific end.

Despite these advantages, there are very few developmentally appropriate CAD software available to K-12 students—most CAD software used in industry not only are science “black boxes” to students, but also require a cumbersome tool chaining of pre-processors, solvers, and post-processors, making them extremely challenging to use in secondary education. The SmartCAD project will fill in this gap with key educational features centered on guiding student design with feedback composed from simulations. For example, science simulations can be used to analyze student design artifacts and compute their distances to specific goals to detect whether students are zeroing in towards those goals or going astray. The development of these features will also draw upon decades of research on formative assessments of complex learning.

A stock-and-flow model for building thermal analysis

Figure 1. A stock-and-flow model of building energy.
Our Energy3D CAD software has two built-in simulation engines for performing solar energy analysis and building thermal analysis. I have extensively blogged about solar energy analysis using Energy3D. This article introduces building thermal analysis with Energy3D.

Figure 2. A colonial house.
The current version of the building energy simulation engine is based on a simple stock-and-flow model of building energy. Viewed from the perspective of system dynamics—a subject that studies the behavior of complex systems, the total thermal energy of a building is a stock and the energy gains or losses through its various components are flows. These gains or losses usually happen via the energy exchange between the building and the environment through the components. For instance, the solar radiation that shines into a building through its windows are inputs; the heat transfer through its walls may be inputs or outputs depending on the temperature difference between the inside and the outside.

Figure 3. The annual energy graph.
Figure1 illustrates how energy flows into and out of a building in the winter and summer, respectively. In order to maintain the temperature inside a building, the thermal energy it contains must remain constant—any shortage of thermal energy must be compensated and any excessive thermal energy must be removed. These are done through heating and air conditioning systems, which, together with ventilation systems, are commonly known as HVAC systems. Based on the stock-and-flow model, we can predict the energy cost of heating and air conditioning by summing up the energy flows in various processes of heat transfer, solar radiation, and energy generation over all the components of the building such as walls, windows, or roofs and over a certain period of time such as a day, a month, or a year.

Figure 2 shows the solar radiation heat map of a house and the distribution of the heat flux density over its building envelope. Figure 3 shows the results of the annual energy analysis for the house shown in Figure 2.

More information can be found in Chapter 3 of Energy3D's User Guide.

Common architectural styles supported by Energy3D


Energy3D supports the design of some basic architectural styles commonly seen in New England, such as Colonial and Cape Cod. Its simple 3D user interface allows users to quickly sketch up a house with an aesthetically pleasing look -- with only mouse clicks and drags (and, of course, some patience). This makes it easy for middle and high school students to create meaningful, realistic designs and learn science and engineering from these authentic experiences -- who wants to keep doing those cardboard houses that look nothing like a real house for another 100 years?

The true enabler of science learning in Energy3D is its analytic capability that can tell students the energy consequences of their designs while they are working on them. Without this analytical capability, learning would have been cut short at architectural design (which undeniably is the fun part of Energy3D that entices students to explore many different design options that entertain the eyes). With the analytical capability, the relationship between form and function becomes a major driving force for student design. It is at this point that an Energy3D project becomes an engineering design project.

Architectural design, which focuses on designing the form, and engineering design, which focuses on designing the function, are equally important in both educational and professional practices. Students need to learn both. After all, the purpose of design is to meet various people's needs, including their aesthetic needs. This principle of coupling architectural design and engineering design is of generic importance as it can be extended to the broader case of integrating industrial design and engineering design. It is this coupling that marries art, science, and usability.

We are working on providing a list of common architectural styles that can be designed using Energy3D. These styles, four of them are shown in this article, show only the basic form of each style. Each should only take less than an hour to sketch up for beginners. If you want, you can derive more complex and detailed designs for each style.

Simulating cool roofs with Energy3D

Fig. 1: Solar absorption of colors.
Cool roofs represent a simple solution that can save significant air-conditioning cost and help mitigate the urban heat island effect, especially in hot climates. Nobel Prize winner and former Secretary of Energy Steven Chu is a strong advocate of cool roofs. It was estimated that painting all the roofs and pavements around the world with reflective coatings would be "equivalent to getting 300 millions cars off the road!"

With Version 4.0 of Energy3D (BTW, this version supports 200+ worldwide locations -- with 150+ in the US), you can model cool roofs and evaluate how much energy you can save by switching from a dark-colored roof to a light-colored one. All you need to do is to set the colors of your roofs and other building blocks. Energy3D will automatically assign an albedo value to each building block according to the lightness of its color.

Figure 1 shows five rectangles in different gray colors (upper) and their thermal view (lower). In this thermal view, blue represents low energy absorption, red represents high energy absorption, and the colors in-between represents the energy absorption at the level in-between.

Now let's compare the thermal views of a black roof and a white roof of a cape code house, as shown in Figure 2. To produce Figure 2, the date was set to July 1st, the hottest time of the year in northern hemisphere, and the location was set to Boston.

Fig. 2: Compare dark and white roofs.
How much energy can we save if we switch from a perfectly black roof (100% absorption) to a perfectly white roof (0% absorption)? We can run the Annual Energy Analysis Tool of Energy3D to figure this out in a matter of seconds. The results are shown in Figure 3. Overall, the total yearly energy cost is cut from 6876 kWh to 6217 kWh for this small cape code house, about 10% of saving.

Figure 3 shows that the majority of savings comes from the reduction of AC cost. The reason that the color has no effect on heating in the winter is because the passive solar heat gains through the windows in this well-insulated house is enough to keep it warm during the sunshine hours. So the additional heat absorbed by the black roof in the same period doesn't offset the heating cost (it took me quite a while to figure out that this was not a bug in our code but actually the case in the simulation).

Fig. 3: Compare heating and AC costs (blue is white roof).
Of course, this result depends on other factors such as the U-value and thermal mass of the roof. In general, the better the roof is insulated, the less its color impacts the energy cost. With Energy3D, students can easily explore these design variables.

This new feature, along with others such as the heat flux visualization that we have introduced earlier, represents the increased capacity of Energy3D for performing function design using scientific simulations.

Here is a video that shows the heating effect on roofs of different colors.

Visualization of heat flux in Energy3D using vector fields

Fig. 1: Winter in Boston
One of the strengths of our Energy3D CAD software is its 3D visualizations of energy transfer. These visualizations not only allow students to see science concepts in action in engineering design, but also provide informative feedback for students to make their design choices based on scientific analyses of their design artifacts.

Fig. 2: Summer in Boston
A new feature has been added to Energy3D to visualize heat transfer across the building envelope using arrays of arrows. Each arrow represents the heat flux at a point on the surface of the building envelope. Its direction represents the direction of the heat flux and its length represents the magnitude of the heat flux, calculated by using Fourier's Law of Heat Conduction. Quantitatively, the length is proportional to the difference between the temperatures inside and outside the building, as well as the U-value of the material.

Fig. 3: Winter in Miami
The figures in this post show the heat flux visualizations of the same house in the winter and summer in Boston and Miami, respectively. Like the solar radiation heat map shown in the figures, the heat flux is the daily average. The U-value of the windows is greater than those of the walls and roof. Hence, you can see that the heat flux vectors in the winter sticking out of the windows are much longer than those sticking out of the walls or roof. In the summer, the heat flux vectors point into the house but they are much shorter, agreeing with the fact that Boston's summer is not very hot.

Fig. 4: Summer in Miami
Now move the same house to Miami. You can see that even in the winter, the daily average heat flux points inside the house, agreeing with the fact that Miami doesn't really have a winter. In the summer, however, the heat flux into the house becomes significantly large.

These visualizations give students clear ideas about where a house loses or gains energy the most. They can then adjust the insulation values of those weak points and run simulations to check if they have been fixed or not. Compared with just giving students some formulas or numbers to figure out what they actually mean to science and engineering practices, experiential learning like this should help students develop a true understanding of thermal conduction and insulation in the context of building science and technology.

Here is a YouTube video of the heat flux view.

A 16-year-old’s designs with Energy3D

This post needs no explanation. The images say it all.

All these beautiful structures were designed from scratch (NOT imported from other sources) by Cormac Paterson using our Energy3D CAD software.

He is only 16 years old. (We have his parents' permission to reveal his name and his work.)

From conceptual design to detailed design with Energy3D

Figure 1: Empire State Building
An important objective of our Energy3D software is to explore how to create CAD software that support students to practice the full cycle of engineering design from conceptual design to detailed design in a single piece of software. We believe that interactive 3D visualizations and simulations provided by CAD tools are cognitively important for K-12 students who have little prior knowledge about the subject of design or the process of design to develop some sense of them -- through practice. Instantaneous visualizations of the results of their actions within the CAD software can give students some concrete clues to develop, share, and refine their ideas directly within a visual design space.

Although there have been some cautions about the use of CAD software in design education, my take is that, in the very early stage of grassroots design education, the problem is not that students are handicapped by a design tool; the problem is that they lack ideas to start with or skills to put their ideas into actions and should be aided by an intelligent design tool (in addition to a teacher, of course). A good CAD tool will be very instructive in this stage. Only after students rise to a certain expert level will the limitations of the CAD software begin to emerge. Often in the K-12 settings, the time constraint does not allow the majority of students to reach that level through conventional instruction, however. Hence, it is likely that the positive effects of using CAD software in K-12 engineering education will outweigh the negative effects, letting alone that students will learn important computer design and modeling skills that will be extremely useful to their future STEM careers.
Figure 2: Freedom Tower

But not all CAD software were created equal. Many CAD software have been developed for professional engineers and are not appropriate for K-12 applications, even though many software vendors have managed to enter the K-12 market in recent years. Given the rise of engineering in K-12 schools, it is probably the right time to rethink how to develop a CAD platform that supports design, learning, and assessment from the ground up.

Our Energy3D CAD software has provided us a powerful platform to ponder about these questions. From the beginning of this project back in 2010, we had been envisioning a CAD platform that integrates conceptual design, detailed design, collaborative design, numerical analysis, designer modeling, machine learning, and digital fabrication. After four years' continuous work, the software can now do not only conceptual design like a sketch tool but also detailed design like a production CAD program (look at the details in Figure 3). In terms of education, this means that it has a very short learning curve that allows all students to translate their ideas into computer models in a short amount of time and, meanwhile, a very deep design space that allows some of the willing students to advance to an expert level. With these capacities, we are now conducting leading-edge data mining research to investigate how to facilitate the transition. The research will eventually translate into novel software features of the CAD program.
Figure 3: Kendall Square

Cormac Paterson, a brilliant high school student from Arlington, MA, has demonstrated these possibilities. He has created many designs with Energy3D that are showcased in our model repository, including all the designs shown in the figures of this post.