Chapter 5 Two methods

Author: Bucket of Pudding

Chapter 5 Two methods

Ning Qing took the question handed over by Teacher Luo and quickly glanced at it. This was a question about predicting the remaining discharge time of lead-acid batteries. The question gave a basic sampling data chart, which also greatly shortened the question.

of difficulty.

Sure enough, the mathematical modeling competition at the high school level is not very difficult.

For the sponsoring companies, they probably don't really think that a group of high school students can really help them solve technical problems. The main thing is to select mathematical thinking talents.

Then Ning Qing began to read the main part of the question carefully.

"After a century of development, acid-lead batteries have been widely used in many fields of human social life. During the discharge process of acid-lead batteries with a constant current, the voltage will decrease monotonically with the discharge time until the rated minimum protection voltage.

The basic situation and requirements of the acid lead battery are known: 1. It is known that the battery discharge time changes with the voltage under the current intensity of 20A, 30A, 40A...100A;

2. MRE definition: Extract 202 sample points at a maximum interval of no more than 0.005V. The average first alignment error between the model discharge time corresponding to these voltage values ​​and the sample discharge time;

3. When the lead-acid battery is discharged at a constant current intensity, the voltage decreases monotonically with the discharge time until the rated minimum protection voltage is Uo. Uo=9V was selected for this test.

Problems that need to be solved: 1. Give the relationship between voltage changes with time at nine current intensities from 20A to 100A; and extract 202 sample points that meet the conditions, and give nine mean relative errors (MRE) respectively;

2. Establish a mathematical model of the discharge curve with any constant current intensity between 20A and 100A, and use MRE to evaluate the accuracy of the model;

3. The same battery starts to discharge from full charge at the same current intensity in different attenuation states. Based on the known new battery state, attenuation state 1 and attenuation state 2, predict the remaining discharge time of attenuation state 3. "

After the question, there was a table made using MATLAB. It was very good. The name of the software was the same as on Earth, which gave Ning Qing an inexplicable sense of intimacy.

After browsing through the topic, Ning Qing looked at Luo Zhen inquiringly.

Although the question is not difficult in his opinion, and can even be said to be simple, it is a Taoist modeling question after all. To solve this problem, he will need about three days alone, but this time is very tight. The main thing is that he has to first

Get to know the world of essay formats.

"Have you finished reading? How difficult do you think this question is for you?" Looking at each other, Luo Zhen sat at the desk, picked up the water glass and looked at Ning Qing and asked.

"It's not difficult. Including programming, it would take me about five days by myself, but it would delay class." Ning Qing's cautious temper allowed her to give herself two more days.

"Pfft..." Probably because the tea leaves were too hot, Luo Zhen accidentally spit them out.

"Ahem... Ning Qing, I'm not asking you to solve this problem. You just need to briefly tell me your solution. Well, is there enough time for self-study tonight?" Luo Zhen asked.

Ning Qing glanced at Luo Zhen in surprise and said, "But the modeling competition requires programming, right?"

"In the high school mathematical modeling competition, each group will be assigned a dedicated programming instructor. At least until you get the tickets for the international competition, the specific procedures are actually the least important link." Luo Zhen explained.

sentence.

Ning Qing nodded, roughly understanding the meaning of mathematical modeling in the high school group, and replied: "Actually, I have two ideas. The first idea is to use MATLAB to draw a graph of the voltage changes over time corresponding to each current intensity, as well as different

State current discharge curve. Here you can list the chemical equation first...

Moreover, Figure 1 can easily prove questions 1 and 2. Figure 2 can prove that the new battery state is basically similar to the discharge curves of decay state 1 and decay state 2. The curve must conform to the exponential function model. After obtaining the data, simulate it through MATLAB

Together, we can verify the rationality of the model and see if the variance is approximately 0. By building a model based on this, we can predict the remaining discharge time in decay state 3."

After saying that, Ning Qing paused for a moment, changed the paper in his hand to the picture, and said again: "The second idea is almost the same as before. It is known that the voltage decreases monotonically with the discharge time, so the voltage increases monotonically with the remaining discharge time.

, with time as the ordinate and current-voltage change as the abscissa, a relationship curve can be drawn;

If you want to improve the accuracy of the model coefficients, you can increase the time unit from minutes to days. After the graph is obtained, a passivation mechanism is introduced. The tail data does not participate in the modeling process. The first 10% of the data given in the question stem is directly deleted.

After quoting, 90% of the model is established, and then the polynomial model Y=A1*X^n+A2*X^n-1...An-1*X+An is used for fitting.

Among them, Y is the remaining discharge time, and then use the quadratic function polynomial to substitute into the fitting until a satisfactory result is obtained. In this way, the first problem can be solved, and the second problem can be solved using..."

Ning Qing pointed at the data on the chart and started talking. He also took a pen from Luo Zhen's desk and started writing many mathematical formulas in the blank space of the question.

There is no way, if he is still in the rocket class, it is probably very simple to register. But for a student who only scored 87 points at the end of the mathematics test last semester, he really needs to show enough ability to participate in this mathematical modeling test.

Persuasiveness.

Just when Ning Qing was explaining his problem-solving ideas to Luo Zhen, neither of them noticed that Yan Zhengming, who had just been correcting the paper, had already walked behind Ning Qing and listened to Ning Qing's explanation in great surprise.

It can be seen that the expressions of the two teachers at this time are extremely confused.

Ning Qing's time for thinking was too short. For a mathematical modeling competition problem, even if they personally analyze the problem, find the solution, and provide ideas for solving the problem, one or two hours is normal.

This is also the reason why Luo Zhen just planned to let Ning Qing spend a whole evening studying in self-study to think about it.

Who would have thought that Ning Qing just read the question and started to explain his ideas...

This is a little too much. Of course, there is a possibility that Ning Qing has seen the same question before. But this question was just a question that Luo Zhen randomly picked among the test questions of the World Mathematics Competition in recent years, and this question is still

Foreign test questions.

But what makes Luo Zhen confused is that Ning Qing also directly gave two ideas for solving the problem, which sounded quite reasonable. The reference book for Luo Zhen's topic selection also only gave one idea for solving the problem, which was different from Ning Qing's.

The second one is pretty much the same.

Fortunately, Ning Qing quickly explained his ideas clearly, and then began to summarize: "Both ideas actually have their own advantages and disadvantages. The first one is better in simplicity, but the accuracy of the results obtained is worse than the second one."

Some. So if it is a real competition and I have enough time, I will tend to use the second idea, so that the paper will be more convincing when I defend it after writing it."

"Ning Qing, I remember that you only scored 63 points in the math test at the beginning of school this year?" Luo Zhen raised his head and looked at Ning Qing in confusion and asked.

This question seems familiar...

Ning Qing could only take a deep breath and said perfunctorily with the same reason: "Well, Teacher Luo, I can actually do the questions, but I just don't want to write."

Well, this explanation seems to be more reasonable.
Chapter completed!