Chapter 428

In fact, since the forties of the last century, relevant road scholars have begun to integrate the probability theory method into the design and analysis of structures, and gradually developed into traditional theories about structural reliability.

For the pavement structure of normal design, normal construction and normal use, the probability that the surface deflection of the pavement and the bending tensile stress at the bottom of the layer do not exceed its allowable value respectively within the time when the pavement reaches the specified design cumulative standard axle load action times, which is the reliability of the pavement structure that we often say.

Although probability theory and fuzzy mathematics belong to two different branches of mathematics, they are not very related to each other.

It is a completely whimsical idea to apply probability theory to the application of probability theory in road structure analysis, and simple derivation to apply fuzzy mathematics to road structure analysis.

Cheng Nuo would obviously not be ignorant enough to do so.

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

Because the reliability of asphalt pavement structure not only has randomness, but also has fuzziness, the reliability of asphalt pavement structure is a fuzzy random reliability.

Conceptual theorems such as the Monte-Carlo method, the extreme value theory, and the J-C method for approximate derivatives are equally applicable to fuzzy mathematical calculations.

............

In the conference room, under the interested attention of several bigwigs, Cheng Nuo said slowly, "I think that the fuzzy reliability theory can be applied to the analysis of pavement structures. ”

"Firstly, the failure membership function of the asphalt pavement structure is given. As we all know, the number of membership functions μ (Z) comes in many forms. ”

"But we are talking about the study of asphalt pavement structure, so the use of the seminormal membership function can better reflect the characteristics of the fuzzy failure zone of asphalt pavement structure with surface deflection as the control index. The mathematical expression is μ(Z)={1,Z≤a

μ(Z)={e^(-k(z-a)^2)，Z＞a，k＜0。 ”

Cheng Nuo spoke, and everyone listened.

Some people even nodded while listening, obviously agreeing with Cheng Nuo's idea.

But Cheng Nuo hasn't finished talking yet, and it's not good for several people to draw conclusions for the time being.

Seeing that no one stood up to refute it for the time being, the corners of Cheng Nuo's mouth raised, and the more he talked, the more confident he became, "After obtaining the expression of the seminormal membership function, the following is to use the road surface deflection value as the control index, and obtain the probability of asphalt pavement structure failure Pf through derivation, so it is easy to obtain the fuzzy reliability: PS = 1-Pf = 1-∫(+∞,-∞)fz(Z)μ(Z)dZ=1-∫......"

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

This final derivation process is not difficult, and can even be said to be quite simple.

When the professor in front of him was stating his opinion, Cheng Nuo had already come up with the result by writing and drawing in his notebook.

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

As for the determination 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 functional function of the asphalt pavement structure (mean μZ and standard deviation σZ) are known, the failure ambiguity interval of the pavement structure can be preliminarily limited, and then combined with the distribution of the fuzzy failure probability diagram of the asphalt pavement structure, the critical interval range of the asphalt pavement structure can be further limited to ensure the safety of the structure. ”

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

After Cheng Nuo said this, he breathed a sigh of relief.

The scene was eerily quiet for more than ten seconds.

Bang Bang Bang ~~

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

Bang Bang Bang ~~!

Then, there was a tidal wave of applause.

Professor Fang applauded and looked 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 main skill of "the protagonist's speech", not so much that Cheng Nuo was stating his own point of view just now, but that he was telling a fact that does exist in theory.

It is feasible to apply fuzzy mathematics to the structural analysis of asphalt pavement.

What Cheng Nuo did was to change the views that were denied by everyone to gain affirmation in another way.

Cheng Nuo didn't think he could afford the warm applause of so many bigwigs.

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

Professor Ji took the lead, and the applause of the crowd 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 calmly.

But, I really didn't do anything?

Several reporters from periodicals and newspapers sitting at the door of the conference room, although they couldn't understand what was going on, still raised their cameras and took pictures of Cheng Nuo's clicks.

Cheng Nuo immediately sat up straight, straightened his hairstyle by the way, and smiled kindly at the camera.

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

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

What?

The more than 30 people present, except for Professor Fang and Professor Zhou, were all shocked.

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

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

As a big news in the mathematics community in recent times, there is no reason why they should not know Cheng Nuo's name.

But it may be that he didn't think about this place from the beginning, so after Professor Ji revealed Cheng Nuo's identity, everyone recognized him.

After all, they were discussing applied mathematics at this conference.

As far as they knew, Cheng Nuo's field of study was in basic mathematics, and everyone didn't get the news of Cheng Nuo's return to China, so it was reasonable that they didn't recognize Cheng Nuo for a while.

Originally, everyone was surprised why a young man would tell a flawless theory to affirm a plan that they had rejected. But this young man is Cheng Nuo's words, then it is in the past.

However, then again, why did Cheng Nuo appear here?

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

According to rumors, the mathematical genius who suddenly emerged was a disciple of Professor Fang of Tsinghua University......

Everyone figured it out instantly, but a bitter smile immediately appeared on the corner of their mouths.

You said, Cheng Nuo, you can toss at a large-scale meeting like the International Congress of Mathematicians, no matter how much you toss, it is impossible to steal all the limelight.

But we are just a small academic conference, it doesn't matter if you toss it like this, all the limelight was snatched away by Cheng Nuo in an instant.

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

As for the reason, it lies in the huge economic benefits that the plan proposed by Cheng Nuo can create!

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