Omnipotent Data

Chapter 428

In fact, from the 1940s onwards, relevant road scholars began to apply the method of probability theory to the design and analysis of structures, and gradually developed into a traditional theory on structural reliability.

For pavement structures with normal design, normal construction and normal use, the probability that the deflection of the pavement surface and the bending-tensile stress at the bottom of the layer do not exceed their allowable values ​​respectively within the time when the pavement reaches the specified design cumulative standard axle load times is our It is often said that the pavement structure reliability.

Although probability theory and fuzzy mathematics belong to two different branches of the field of mathematics, their connection with each other is very low.

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

Cheng Nuo was obviously not ignorant enough to do this.

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

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

Those idea theorems such as Monte-Carlo method, extreme value theory, and J-C method of approximate derivation are also applicable in the calculation of fuzzy mathematics.

…………

In the conference room, under the watchful eyes of several bigwigs, Cheng Nuo said slowly, "I think that 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 we all know, the number of membership functions (Z) has various forms."

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

(Z)={e^(-k(z-a)^2), Z\u003ea, k\u003c0. "

Cheng Nuo spoke, and everyone listened.

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

But Cheng Nuo hadn't finished talking, and it was difficult for them to draw conclusions.

Seeing that no one has come forward to refute yet, Cheng Nuo raised the corner of his mouth, becoming more confident as he spoke.

"After obtaining the expression of the reduced half-normal membership function, the following is to use the road surface deflection value as the control index, and obtain the probability Pf of asphalt pavement structure damage through derivation, then the fuzzy reliability can be easily obtained: PS= 1-Pf=1-∫(+∞,－∞)fz(Z)(Z)dZ=1-∫..."

After deriving the preliminary formula for calculating the fuzzy reliability of the asphalt pavement structure, Cheng Nuo's presentation came to an end.

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

While the professor in front was stating his point of view, Cheng Nuo had already come to the result by writing and drawing in his notebook.

"Introduce the two concepts of the limit function of the reliability calculation of asphalt pavement structure and the probability density function formula of Z, take the value of fuzzy number a as 0, and deduce it, you can get the fuzzy reliability Ps and structural resistance, as well as the load effect The relation of functional function Z composed of S: Ps=Φ(z/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 function function of the asphalt pavement structure (mean value Z and standard deviation σZ) are known, the failure fuzzy interval of the pavement structure can be initially limited, 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 wanted to say, thank you!"

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

The scene was eerily quiet for more than ten seconds.

clap clap

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

Clap clap!

Then, there was a wave of applause echoing like a tide.

Professor Fang applauded while looking at Cheng Nuo with encouraging and gratifying eyes.

Professor Zhou secretly gave Cheng Nuo a thumbs up.

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

This is... what happened?

He didn't think he had activated the "Protagonist's Speech" skill. Rather than saying that Cheng Nuo was stating his point of view just now, it was better to say that he was telling a fact that actually existed in theory.

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

What Cheng Nuo did was to gain affirmation in a different way from a point of view that was denied by everyone.

Cheng Nuo didn't think he could handle the warm applause from so many big bosses.

Cheng Nuo, who was a little flattered, pressed his hands down and signaled everyone not to, stop!

With Professor Ji taking the lead, the applause of the crowd was even more enthusiastic.

Cheng Nuo's expression was a little helpless.

Since everyone was so enthusiastic, he had no choice but to accept it frankly.

But, what did I really do?

Several journalists from the periodical and newspaper office sitting at the door of the meeting room, although they didn't understand what happened, they still raised their cameras and took continuous pictures of Cheng Nuo.

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

After more than ten seconds of clapping, the applause of the crowd gradually subsided.

The smile on Professor Ji's face couldn't be hidden, and he said enthusiastically to Cheng Nuo, "Student Cheng Nuo, what you just said was really rigorous and accurate!"

What? Cheng Nuo!

Except for Professor Fang and Professor Zhou, all the more than 30 people present were shocked.

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

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

As a big news in the mathematics world recently, they had 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 Cheng Nuo's identity, everyone recognized him.

After all, their meeting was about applied mathematics.

As far as they knew, Cheng Nuo's field of research was basic mathematics, and no one had heard of Cheng Nuo's return to China, so it was reasonable not to recognize Cheng Nuo for a while.

Originally, everyone was surprised why a young man would come up with a flawless theory to affirm the plan that was originally denied by them. But if this young man is Cheng Nuo, then it makes sense.

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

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

According to rumors, that mathematical genius who suddenly appeared was a direct disciple of Professor Fang of Tsinghua University...

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

You said, Cheng Nuo, you can go to a big conference like the International Congress of Mathematicians to make a fuss, no matter how much you make a fuss, it is impossible to steal all the limelight.

But we are just a small academic conference, so it doesn't matter if you make such a fuss, Cheng Nuo will steal all the limelight in an instant.

From the looks of it now, even his teacher, Professor Fang, was overshadowed by today's Cheng Nuo.

As for the reason, it was because of the huge economic benefits that Cheng Nuo's proposal could create!