technological heresy

Chapter 5 Two Methods
Ning Qing took the question handed over by Mr. Luo, and quickly glanced at it. This is a question about predicting the remaining discharge time of a lead-acid battery. A basic sampling data chart is given in the question, which also greatly reduces the problem. difficulty.

Sure enough, the mathematical modeling competition in high school is not difficult.

For the sponsoring companies, it probably didn't really think that a group of high school students could really help them solve technical problems.The main focus is on the selection of mathematical thinking talents.

Then Ning Qing began to carefully read the stem of the question.

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

已知酸铅电池的基本情况与要求：1、已知20A、30A、40A……100A的电流强度下，电池放电时间随电压的变化；
2. Definition of MRE: According to the maximum interval not exceeding 0.005V, extract 202 sample points, and the average error between the discharge time of the model and the discharge time of the sample corresponding to these voltage values;

3. During the discharge process of the lead-acid battery at a constant current intensity, the voltage decreases monotonously with the discharge time until the rated minimum protection voltage is Uo, and Uo=9V is selected for this test.

Problems to be solved: 1. Give the relationship between voltage and time variation under nine current intensities from 20A to 100A; and extract 202 sample points that meet the conditions, and give nine average relative errors (MRE) respectively;
2. Establish a mathematical model of the discharge curve with any constant current intensity between 20A-100A, and use MRE to evaluate the accuracy of the model;
3. The same battery is discharged from full charge with the same current intensity under different attenuation states. According to the known new battery state, attenuation state 1 and attenuation state 2, the remaining discharge time of attenuation state 3 is predicted. "

After the question is the table made using MATLAB.Very good, the name of the software is the same as that on Earth, which makes Ning Qing feel an inexplicable sense of intimacy.

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

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

"Have you finished reading it? How difficult do you think this question is for you?" Luo Zhen asked while sitting at the desk, looking at Ning Qing with a glass of water.

"It's not difficult. Including programming, it will take about five days for me alone, but it will delay the class." Ning Qing's cautious temperament allowed Ning Qing to give himself two more days.

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

"Ahem... Ning Qing, I don't want you to solve this problem, you just need to tell me about 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?"

"For the mathematical modeling competition of the high school group, each group will arrange a special programming instructor. At least before you get the tickets for the international competition, the specific program is actually the least important part." Luo Zhen explained sentence.

Ning Qing nodded, probably understood the meaning of mathematical modeling in the senior high school group, and answered: "Actually, I have two ideas. The first idea is to use MATLAB to draw the voltage versus time diagram corresponding to each current intensity, and the different The current discharge curve in the state. Here you can list the chemical equation first...

Moreover, Figure 1 can easily prove Problems 2 and 0, and Figure 3 can prove that the new battery state is basically similar to the discharge curves of Decay State [-] and Decay State [-], and the curves must conform to the exponential function model.After the data is obtained, the rationality of the model is verified by MATLAB fitting, and whether the variance is approximately [-].And building a model based on this can predict the remaining discharge time of decay state [-]. "

After finishing speaking, Ning Qing paused, changed the topic manuscript paper in his hand to the picture one, and said again: "The second way of thinking is similar to the previous one. It is known that the voltage decreases monotonously with the discharge time, so the voltage increases monotonously with the remaining discharge time. , with time as the ordinate and current-voltage change as the abscissa, a relational graph 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 obtaining the graphics, introduce a passivation mechanism, the tail data does not participate in the modeling process, directly delete the first 10% of the data given in the question stem, and only refer to the next 90% to build the model, and then use the polynomial model Y=A1*X^ n+A2*X^n-1...An-1*X+An for fitting.

Where Y is the remaining discharge time, and then the quadratic function polynomial is substituted into the fitting until a satisfactory result is obtained.This solves problem one, and problem two uses..."

Ning Qing pointed to the data on the chart and began to talk, and took a pen from Luo Zhen's desk, and began to write down many mathematical formulas in the blank space of the topic.

No way, if he was still in the rocket class, it would be easy to sign up.But for a student who only scored 87 points at the end of last semester's mathematics test, he really needs to show enough persuasiveness to participate in this mathematical modeling.

When Ning Qing was explaining his problem-solving ideas to Luo Zhen, neither of them noticed that Yan Zhengming, who was still correcting the paper just now, had walked behind Ning Qing, and was also listening to Ning Qing's explanation in great surprise.

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

Ning Qing had too little time to think.For a mathematical modeling competition question, even if they personally do it from analyzing the question to finding a solution to the problem, and giving the solution idea, it is normal for one or two hours.

This is also the reason why Luo Zhen planned to let Ning Qing spend the whole evening self-study to think.

Who would have thought that Ning Qing would just start explaining his thoughts after reading the topic...

This is a little too much. Of course, there is also a possibility that Ning Qing has seen the same topic before.But this question is just a question that Luo Zhen randomly selected from the test questions of the World Mathematical Contest in recent years, and this question is also a foreign test question.

But what made Luo Zhen unable to figure it out was that Ning Qing also directly gave two ways of solving the problem, which sounded quite reasonable.Luo Zhen's reference book for choosing the topic only gave one way to solve the problem, which is not too different from Ning Qing's second one.

Fortunately, Ning Qing quickly explained his thoughts clearly, and then began to summarize: "In fact, the two thoughts have their own advantages and disadvantages. The first one is better than the simple one, but the accuracy of the results obtained is worse than the second one. A few. So if it is a real competition and there is enough time, I will tend to use the second way of thinking, so that it will be more convincing when the thesis is written and defended.”

"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, looked at Ning Qing in confusion and asked.

This question seems familiar...

Ning Qing could only take a deep breath, and perfunctoryly said with the same reason: "Well, Teacher Luo, in fact, I can do all the questions, but I just don't want to start writing."

Well, this time the explanation seems to be more reasonable.

(End of this chapter)