Chapter 425

In fact, since the 1940s of last century, the relevant road scholars have started to penetrate the probability theory into the design and analysis of structure, and gradually developed into the traditional theory of structural reliability.

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

Although probability theory and fuzzy mathematics belong to two different branches in mathematics field, their relationship is very low.

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

And cheno was obviously not ignorant to do so.

But there are some things that cheno 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.

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

…………

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

"First, the failure membership function of asphalt pavement structure is given. As you all know, the number of membership functions μ (z) is in various forms. "

"But we are talking about the study of asphalt pavement structure, so the use of reduced semi normal 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

br > μ (z) ={e^ (-k (z-a) ^2), z > A, K < 0. "

"And Cheng Nuo said, listen to all.

Some people nodded while listening, obviously agreeing with cheno.

But Cheng Nuo has not yet told, and a few people are not good at concluding for a while.

See that no one has come out to refute for a while. The more confident the Chengnuo mouth is, the more confident it is, "after the expression of reduced semi normal membership function is obtained, the following is to take the deflection value of road surface as the control index, and then the probability PF of Asphalt Pavement structure failure can be obtained by derivation. Then fuzzy reliability can be easily obtained: PS = 1-pf = 1- (∞, - ∞) FZ (z) μ (z) dz=1- ∫..."

The formula of fuzzy reliability of asphalt pavement structure is derived, and the narration of cheno will enter the closing stage.

The final derivation process is not difficult, and even quite simple.

When the former professor stated his point of view, cheno had already come to the conclusion by writing and drawing in his notebook.

"The paper introduces the two concepts of limit function and probability density function formula of Z for the calculation of structural reliability of asphalt pavement. Taking the fuzzy number a as 0 value, we can get the relationship between fuzzy reliability PS and structural resistance R, and the function function Z composed of load effect s: ps= Φ (μ Z σ z)!"

"As for the determination of critical value, the range of critical range shall be determined according to the actual situation (for the actual situation in the project)

"If the statistics of the function function of asphalt pavement structure (mean μ Z and standard deviation σ z) are known, the failure fuzzy interval of pavement structure can be preliminarily limited. Combined with the distribution of fuzzy failure probability map of asphalt pavement structure, the range between critical areas of asphalt pavement structure can be further limited to ensure the safety of the structure."

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

After Cheng Nuo finished this sentence, he took a slight relief.

The scene was eerie and quiet for more than ten seconds.

Professor Ji, who sat in the main position, smiled at Cheng Nuo and clapped.

It's a slap!

Then, there was a wave of applause.

Professor Fang applauded and looked at cheno with encouragement and gratification.

Professor Zhou gave Cheng Nuo a thumbs up in the dark.

Cheno scratched his head, a little overwhelmed.

This is What happened?

He does not think that he launched the main public skill of "the leading role speech", rather than saying that cheno was presenting his own views, rather than telling a fact that there is actually in theory.

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

What Cheng Nuo did was to get affirmation by changing the view that he was denied by the public.

Cheno doesn't think he can afford so many big applause.

Some of the flattered Chengnuo hands empty pressure, to signal that you do not, stop!

Professor Ji led the round, and the applause was more enthusiastic.

Cheng Nuo's expression was a little helpless.Since you are so enthusiastic, he has to accept it.

But what am I really doing?

Some reporters from the periodical newspaper office sitting at the door of the conference room, although they did not understand what happened, still held up their cameras and took pictures of Cheng Nuoka.

Cheng Nuo immediately sat up straight and straightened his hair, smiling genially at the camera.

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

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

What? Cheng Nuo!

More than 30 of you, except for Professor Fang and Professor Zhou, are all shocked.

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

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

As a big news in the field of mathematics recently, there is no reason why they don't know Cheng Nuo's name.

But maybe he didn't think about this place at the beginning, so after Professor Ji explained his identity as Cheng Nuo, many people recognized him.

After all, this meeting is about applied mathematics.

As far as they know, Cheng Nuo's research field is in basic mathematics. People have not heard of Cheng Nuo's return home, and there is no time to recognize that Cheng Nuo is also reasonable.

At first, people were also surprised why a young man put forward a theory without any flaws to confirm the plan that had been rejected by them. But this young man is Cheng Nuo's words, that said in the past.

But then again, why is Cheng Nuo here?

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

It is said that the sudden emergence of mathematical genius is Professor Fang Qinghua's personal disciple

All of them thought it out in an instant, but a bitter smile appeared in the corner of the mouth.

You said, Cheng Nuo, if you go to the International Conference of mathematicians, you can't win the whole show.

But we are just a small academic conference. It doesn't matter if you make such a fuss. All the limelight is snatched by Cheng Nuo.

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

As for the reason, it is the huge economic benefits that Cheng Nuo proposed!

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