Chapter 1107 I have 3 methods, 3!

It is of course impossible to say that Chang Haonan could fully understand this technology in just a few dozen minutes.

It's just that he is better at distilling the essence of the problem.

With this sentence just now, the subsequent research direction has been basically determined.

That is, error modeling is combined with adaptive compensation in the cutting part, while floating clamping is used in the clamping part to minimize the post-processing deformation caused by the fixed area.

Of course, even so, when it comes to precision, it still can't compare to the work of a master craftsman.

But it is a necessary step to get the aerospace industry to truly scale.

In fact, Yang Weihua also raised concerns in this regard.

Chang Haonan's answer was the same as in the previous meeting at Gaofa Group -

It is possible to carefully select from a batch of products, distinguish several batches with higher consistency, and install them separately on the same engine.

This seemingly wild idea was almost subversive to Yang Weihua, who came from a mechanical processing background.

He stopped packing his things and stood there for a long time:

"When I entered the industry, the first thing my master taught me was standardized processing... Now it seems that it is a bit out of date..."

His tone was full of emotion.

Considering Yang Weihua’s age, he should have entered the industry in the early 1980s, which happened to be the stage when China’s machinery industry was undergoing its second round of large-scale upgrades.

It has been more than twenty years now.

You know, in the early years when my country's processing accuracy was not good, this method of selecting qualified products from a batch of products was implemented.

It is through the efforts of their generation that a relatively complete standardized processing system has been established.

Now we have to go back.

The nostalgic server is open.

“Standardization is certainly correct.”

Chang Haonan also felt the other party's emo and replied with a smile:

"However, for truly high-demand production, even with the most sophisticated production methods, there will always be errors, so strict standardization of processing results is not possible."

"In this case, why don't we change our thinking and implement standardization in the production process, and use production efficiency to make up for the lack of product consistency to a certain extent..."

In this era, most people’s understanding of “high-level production” is still relatively simple.

High precision and good replaceability.

It's still the same as in the eighties.

But in fact, random errors exist even in the field of semiconductor processing, let alone mechanical manufacturing.

There is no shame in being picky.

The key is to be able to choose clearly...

After some guidance, Yang Weihua left the meeting room thoughtfully.

But Wei Yongming didn't seem to have any intention of leaving.

He didn't even put away the laptop on the table.

"Yongming, is there anything else?"

Seeing this, Chang Haonan stopped what he was doing and sat back in his chair.

He and Wei Yongming are of similar age and have known each other for many years, so they are more casual in addressing each other in private.

Wei Yongming didn't waste any words and went straight to the point:

"I just carefully analyzed the clamping method proposed by Lao Yang. If it is refined into a multi-objective optimization problem, there are only three decision variables, but the objective function is completely more than that... Especially for workpieces with a large degree of bending and twisting, there must be at least four or more."

Chang Haonan didn't say anything, but just nodded to indicate that it was correct.

This matter-of-fact look almost made Wei Yongming lose confidence.

However, after calming down, he continued:

"But...using genetic algorithms for multi-objective optimization is generally based on Pareto dominance. As the number of objectives increases, the number of non-dominated solutions in the population will increase exponentially, causing the algorithm's search capability to deteriorate rapidly..."

"I have previously tested the solution of the non-inferior sorting genetic algorithm to the four-dimensional target optimization problem... Even after many rounds of adjustments, it always diverges in the end... or it is a solution with very poor accuracy, and the calculation time is extremely exaggerated. It may not matter to our group, but I am afraid that the production side does not have such a high level of computing power support..."

Wei Yongming opened a PDF file on his computer and turned the screen towards Chang Haonan.

A quick look at the latter revealed that it was a fairly typical grid search problem.

It looked like some kind of random test.

"Indeed it is."

Chang Haonan pushed the computer back:

"From an intuitive geometric point of view, an optimization problem with an m-dimensional objective is equivalent to dividing each dimension of the objective space into r grids. Assuming that the non-dominated solutions of the problem are uniformly distributed, the boundary of the grid Pareto front constitutes the upper bound of the number of particles."

As he spoke, he drew a three-dimensional diagram on paper.

"Obviously, for an optimization problem with M objectives, M*r^(M-1) solutions are needed to form the Pareto frontier. For an optimization problem with 5 objectives, even if we set r to a relatively low value of 25, we still need about a million solutions to characterize the basic Pareto frontier... It is normal that some unexpected results may lead to divergence, or that no results can be obtained after several months of calculation."

Wei Yongming was slightly relieved.

Obviously, it wasn't that his question was too simple, it was just that Chang Haonan seemed to have been mentally prepared:

"Then the next research direction is..."

Unexpectedly, Chang Haonan just shook his head.

“Not sure yet.”

Wei Yongming was immediately shocked.

However, before he could organize his words, he heard Chang Haonan continue:

"I have initially thought of three technical routes, but I don't know which one is more suitable yet..."

"..."

The former wiped the sweat from his forehead and swallowed the words that were about to come out of his mouth:

"You tell me, if it doesn't work we can just give it a try..."

This time, Chang Haonan did not write anything, but took out a notebook that he had prepared long ago:

"First, ... we can enlarge or reduce the objective function value of an individual by a certain ratio and then compare it with other individuals. That is, we can relax the Pareto dominance relationship, so that we can compare the advantages and disadvantages of some non-dominated individuals and enhance the search ability of the algorithm."

Wei Yongming's thoughts also moved quickly:

"This approach can improve the differential evolution algorithm... but it seems to easily cause individuals to fall into a cycle of domination?"

“So it still needs to be improved, and the differential evolution algorithm is not particularly suitable for this type of problem... Anyway, we will study it in detail later.”

Chang Haonan waved his hand and turned to the next page in his notebook:

"You can also use performance evaluation indicators as the objective function to replace the Pareto dominance relationship to guide the search process... However, this type of algorithm can only get one solution each time it runs, and it takes multiple calculations to get the optimal solution set, and it is easy to fall into interval optimality."

"Finally, we don't consider targets that have little impact on the search process or the final optimization results, that is, we reduce the dimension of the objective function. I am personally optimistic about the prospects of this technical route, but there are many mathematical problems that need to be overcome..."

Hearing this, Wei Yongming couldn't help but grumble:

"This is actually a good thing..."

However, Chang Haonan, who had sharp ears, caught it:

"You can't say that."

"After all, we still have to consider the user experience... If the algorithm is too complicated, then it will inevitably encounter obstacles when promoting it in the future..."