By Béla Lipták, PE, CONTROL Columnist THE SECOND
installment in this two-part series illustrates an assumed artificial neural network (ANN) model of the U.S. economy (See Chart below).
[The first part, “Automation Engineers Can Control the Economy
,” ran in CONTROL, Sept. ’05, p. 47.] The model is assumed to have four manipulated variables (MVs), five disturbance variables (DVs), and two controlled variables (CVs). These output CVs are assumed to be gross domestic product (GDP) or the LEI. They are a function of the input (manipulated and disturbance) variables. The relationship between the output CVs and the input MVs and DVs is described by gains applied at the nodes located in one or more hidden layer(s) in the model. The gains (and biases) applied at these nodes reflect the influence a particular input has on a particular output CV. If one or more input variables are changing, their effect on a CV is a function of their weights (gains) at biases at the corresponding nodes.
"Using an artificial neural network (ANN) model on the U.S. economy would be more scientific, more accurate, less influenced by political considerations, and consequently less prone to increasing the federal debt on future generations."
The ANN model must also reflect the fact that some input variables will quickly influence the outputs (cost of oil, interest rates, war, etc.), while other inputs tend to evolve slowly (fiscal or trade policies). This is because it takes longer to accumulate the effects of trade policy changes than to handle interest rate changes.
In process control, the time for an input variable to show 63% of its full effect on the controlled variable is called its time constant. There is also a period during which the input has no effect at all on the controlled variable. This is called its dead time. It can be short, as in the case of some political event, or it can be long. For example, if the quality of our scientific education is allowed to deteriorate, it will take years before this will start to affect the economy by making our society less competitive. CNET has reported that at its recent international computing machinery contest, the best U.S. team placed 17th among participating teams of university students from around the world. Click the image above to view an enlarged .pdf version of this chart.Tuning the Economy’s ANN Controller
The gains at the figure’s nodes describe the proportional response of the ANN controller to an error (ef), which is the difference between the set point and the actual value of the controlled variable (LEI or GDP). The integral action of this controller responds to the past history of an error, such as the effect of accumulated budget deficits on the LEI, by integrating the area under the error curve. The role of the derivative action is to anticipate the future, and take corrective action based on what would happen if the correction wasn’t made. The most significant example of this is looking at the rate that we in the U.S. are borrowing from our children and grandchildren, and the effect of this national debt if it’s left uncorrected.
Most processes oscillate with a cycle period of about four dead times. Naturally, in multivariable processes, it’s the combined effect of the gains and dead times of the many input variables that determine the cycle period of the process. Therefore, to obtain the probable cycle period and amplitude of the process, the ANN model has to be trained on historical data.
The main limitation in most multivariable, nonlinear processes is that historical data for training the ANN model don’t exist. In the case of the U.S. economy, however, there is detailed data available covering the last several decades. Of course, the model developed using that data would only reflect the economy’s past dynamics. So, just as one can’t control based on feed forward alone, one can’t fully anticipate the economy’s future based on past performance. This is why the figure also contains a feedback component, where the self-correcting feedback (em) is continuously applied to correct and update the ANN model.
One can only speculate how much value an ANN model and its recommendations would have on the nation. What is less debatable is the fact that it would be more scientific, more accurate, less influenced by political considerations, and consequently less prone to increase the debt on future generations, which politicians tend to do. What we do know is that such a complex process, if it was an industrial one, would never be controlled in the manual, based on the on-off manipulation of one variable, such as the periodic interest rate adjustments made by the U.S. Federal Reserve and its Chairman Alan Greenspan.
The other facts we do know are that the price to earnings (P/E) ratio of our securities is around 26. This ratio has not been that high since 1927. We also know that our national debt is approximately three years’ worth of the GDP, and that our high-tech imports exceed our exports. This alone should be sufficient reason to take advantage of the available and proven know-how of the process control profession to double-check the projections and corrective actions proposed by our economists and politicians.
, process control consultant, is also editor of the Instrument Engineer’s Handbook and is seeking new co-authors for the forthcoming new edition of that multi-volume work.