Omnipotent Data

Chapter 428

In fact, since the 1940s, relevant road scholars began to incorporate probability theory methods into the design and analysis of structures, and gradually developed into traditional theories about structural reliability.

For the normal design, normal construction and normal use of the pavement structure, the probability that the surface deflection and the bottom bending stress of the pavement will not exceed their allowable values ​​within the time when the pavement reaches the specified design cumulative standard axle load The reliability of pavement structure often said.

Although probability theory and fuzzy mathematics belong to two different branches of the field of mathematics, the connection between them is very low.

The application of probability theory in road structure analysis and the application of simple derivation to fuzzy mathematics in road structure analysis are completely whimsical.

Cheng Nuo obviously would not be ignorant to do so.

But there are some things that Cheng Nuo can learn from.

As the reliability of asphalt pavement structure is not only random, but also fuzzy, the reliability of asphalt pavement structure is a fuzzy random reliability.

The concepts and theorems of the Monte Carlo method, extreme value theory, and the J-C method for approximate derivation are equally applicable in the calculation of fuzzy mathematics.

…………

In the conference room, under the interest of several big men, Cheng Nuo slowly said, "I think the fuzzy reliability theory can be applied to the analysis of pavement structure."

"First, give the failure membership function of the asphalt pavement structure. As everyone knows, the membership function number (Z) has many forms."

"But we are discussing the study of asphalt pavement structure. Then, using the reduced half-normal membership function can better reflect the characteristics of the fuzzy failure zone of the asphalt pavement structure with road surface deflection as the control index. The mathematical expression is (Z )={1, Z≤a

(Z)={e^(-k(z-a)^2), Z>a, k<0. "

Cheng Nuo said, everyone listened.

Some people nodded as they listened, obviously agreeing with Cheng Nuo's ideas.

But Cheng Nuo hasn't finished speaking yet, and it is difficult for several people to draw conclusions temporarily.

Seeing that no one has come forward to refute for the time being, Cheng Nuo raised the corner of his mouth, and he became more confident as he spoke, "After getting the expression of the reduced-half-normal membership function, the following is to use the road surface deflection value as the control index, and get it through derivation Asphalt pavement structure failure probability Pf, the fuzzy reliability can be easily obtained: PS=1-Pf=1-∫(+∞, -∞)fz(Z)(Z)dZ=1-∫……”

A preliminary calculation formula for the fuzzy reliability of the asphalt pavement structure was derived, and Cheng Nuo's narration entered the final stage.

The final derivation process is not difficult, it can even be said to be quite simple.

When the previous professor was stating his point of view, Cheng Nuo had already got the result by writing and drawing in the notebook.

"Introducing the two concepts of the limit function of the structural reliability calculation of the asphalt pavement and the probability density function formula of Z, taking the fuzzy number a to 0 and deriving it, we can get the fuzzy reliability Ps and the structural resistance, as well as the load effect. The relationship between the function function Z composed of S: Ps=Φ(z/σz)!"

"As for the judgment of the critical value, the range of the critical interval should be determined according to the actual situation (for the actual situation in the project."

"If the statistics of the function function of the asphalt pavement structure (mean Z and standard deviation σZ) are known, the failure fuzzy interval of the pavement structure can be preliminarily defined, and combined with the distribution of the fuzzy failure probability map of the asphalt pavement structure, the asphalt pavement structure can be further limited The range of the critical interval is used to ensure the safety of the structure."

"That's all I want to talk about, thank you!"

After Cheng Nuo finished speaking, he let out a sigh of relief.

The scene was strangely quiet for ten seconds.

Pop pop

Professor Ji, who was sitting in the main seat, looked at Cheng Nuo with a smile and applauded gently.

Happiness!

Then, applause echoed like a tide.

Professor Fang applauded while looking at Cheng Nuo with encouragement and relief.

Professor Zhou secretly gave Cheng Nuo a thumbs up.

Cheng Nuo scratched his head, a little at a loss.

This is... what happened?

He doesn't think that he has launched the "protagonist's speech" as the master skill. It is not so much that Cheng Nuo was stating his own point of view just now, but rather that he was telling a fact that does exist in theory.

It is feasible to apply fuzzy mathematics to asphalt pavement structure analysis.

What Cheng Nuo did was to change the viewpoint that was denied by the public to get affirmation in another way.

Cheng Nuo didn't think he could bear so many enthusiastic applause.

Some flattered Cheng Nuo pressed his hands down in the void, beckoning everyone not to stop!

Professor Yuki took the lead, and everyone's applause was even more enthusiastic.

Cheng Nuo's expression was a little helpless.

Since you were so enthusiastic, he had no choice but to accept it.

But, I really didn’t do anything?

Several journalists from the journals sitting at the door of the conference room, although they couldn't figure out what happened, they raised their cameras and shot Cheng Nuo ka ka ka ka.

Cheng Nuo immediately sat up straight, adjusted his hair style by the way, and smiled kindly at the camera.

After more than ten seconds, everyone's applause gradually ceased.

Professor Ji couldn't hide the smile on his face, and said enthusiastically to Cheng Nuo, "Student Cheng Nuo, what you said just now is really rigorous and accurate!"

what? Cheng Nuo!

Except for Professor Fang and Professor Zhou, all of the thirty or so present were shocked.

They turned their heads, and Cheng Nuo's young face overlapped with the same face in their memory.

They all said suddenly, "It's really Cheng Nuo!"

As a big news in the mathematics world during the recent period, they have no reason not to know Cheng Nuo's name.

But it may be that he didn't think about this place at the beginning, so after Professor Ji revealed his identity as Cheng Nuo, the crowd recognized him.

After all, they are discussing applied mathematics in this meeting.

As far as they know, Cheng Nuo's field of research is in basic mathematics, and everyone has not heard of Cheng Nuo's return to China, and it is reasonable to recognize Cheng Nuo before they have time.

At first, everyone was surprised at why a young man would come up with a flawless theory ~www.readwn.com~ to affirm the plan that was originally rejected by them. But if this young man was Cheng Nuo, then it was over.

However, having said that, why did Cheng Nuo appear here?

Suddenly, someone thought of something and suddenly turned to look at Professor Fang who was sitting on the chair with a smile.

According to rumors, the sudden emergence of mathematics genius was a direct disciple of Professor Fang from Tsinghua...

Everyone figured it out in an instant, but a bitter smile appeared on the corners of their lips.

You said, Cheng Nuo, even if you go to a large conference like the International Mathematicians Conference, no matter how much you toss, it is impossible to steal all the limelight.

But we are just a small academic conference that can't be smaller. It doesn't matter if you toss like this, all the limelight is instantly robbed by Cheng Nuo alone.

Now it seems that even his teacher, Professor Fang, has been concealed by Cheng Nuo today.

As for the reason, it lies in the huge economic benefits that Cheng Nuo's proposal can create!