Chapter 92: Theoretical Level Improvement (2-in-1)

Maybe it's because of the attempt when I was just reborn, or maybe it's because the management ability has improved from a blank LV0 to LV1.

In short, the subsequent formation of the research team and the process of assigning tasks to the 606 Institute and the 410 Factory were much smoother than Chang Haonan imagined.

After all, the engineers who can work in these places have tested their abilities and experience, and it is much easier than when they took Zhou Shuwan and Zhang Man, two undergraduates.

When it comes to the calculation method and the content of the experiment, it is basically a simple point.

So that evening, the team responsible for the research of the first part of the moving blade upper end sweep and the lower end of the forward bending technology has already begun to work.

After assigning the last part of the task, Chang Haonan finally dragged his tired body out of the office temporarily assigned to him, preparing to go back to his residence in 601 to rest.

From the day of the accident on prototype 01 until now, he hasn't slept a single night.

There are still a lot of problems left for him to solve, and many parts are not easy even with the help of the system, even if the experimental part has been stripped out, and the numerical simulation part alone costs him 50 points.

The main limitation is, of course, the level of computers in this era.

The complexity of the flow field involved in each scheme he gave is different, the grazing blades have different grazing heights and grazing angles, and the bending blades are also modified with different bending heights and angles, and the number of meshes automatically generated by each blade is about 900,000 before the optimization of the system.

Not to mention 1996, even if it is placed in 2006, it is definitely a number that can make people feel full of blood pressure directly after hearing it.

And the pressure on this thing is greater than the previous design improvements to the wing.

In the process of retrofitting the No. 04 prototype with a new wing, the two prototypes 01 and 03 are still in non-stop test flight work, but they need to make some adjustments to the test subjects.

However, the engine, as the heart of the aircraft, had such a big accident as last time, and even almost led to the complete loss of the No. 01 prototype, and it is obviously impossible to continue the test flight work until the problem is solved.

Every day of delay in this can cause immeasurable damage.

"Whew-"

Chang Haonan exhaled a breath of turbidity, feeling the already cool evening breeze at the end of August in the north, and couldn't help but speed up his pace.

Just as he was about to enter the dormitory building, the doorman on duty at the door suddenly stopped him from behind.

"Permanent worker!"

Although Chang Haonan is not a regular employee of the 601 Institute, most of the non-technical personnel do not understand the more complicated twists and turns, so they are basically referred to as X work.

"This comrade...... Something? ”

Chang Haonan, who heard his name, stopped, turned around, and saw a uniformed security guard who looked about the same age as him running out of the sentry box with something in his hand.

"This is a letter to you, because I didn't write the specific dormitory number, so I left it with the doorman."

"Letter?"

Chang Haonan took the brown paper envelope from the other party's hand a little dazedly, and couldn't see what was written on it clearly in the dim light.

Not too many people know about his work in the 601 Institute, and it seems that anyone who knows about it can contact him directly through Yang Fenghat.

"Excuse me, comrade."

"It's okay, just come to me and sign it to confirm that you have received it."

A few minutes later.

With a soft click, Chang Haonan opened the door of the dormitory.

After returning from exhaustion, the first thing he did was to throw himself on the bed and lay down for half an hour.

But today, after a short struggle when going upstairs, Chang Haonan decided to see what the letter was.

Light the lamp.

Although it has been a few months since he was reborn, and he has gradually become accustomed to this era without mobile internet, he still feels strange when he actually sees a letter with a stamp on it.

The sender's column is filled with "Xu Yang, Institute of Computing Technology, Chinese Academy of Sciences".

The pen handwriting is very beautiful.

"No wonder ......"

Chang Haonan said to himself while opening the letter.

I know that he works in the 601 Institute, but there is no way to contact him by phone so that he needs to send a letter, and it seems that the only person who needs to send a letter is the other party.

The folded letter was nearly 20 pages, a thickness that made him frown.

"Forget it, it's all dismantled, let's see what she writes and then rest......"

Because the action of unfolding the letter was so fast, he didn't even have time to remember whether there was any bloody plot flashing in his mind at that moment, and he saw the title at the top of the first page.

Research on an Extended Kalman Filter Algorithm Based on Differential Evolution Algorithm

Abstract:Extended Kalman filter has been widely used in engineering practice and other fields, but the accuracy of this algorithm is not high due to the error caused by the assumption that the process noise is fixed. An improved EKF algorithm is studied, which mainly assumes that the process noise is obtained from the filtering results and observations, and then uses the differential evolution algorithm to optimize the variance of the process noise to improve the filtering accuracy......

The results show that the improved extended Kalman filter algorithm reduces the state estimation bias and obtains a relatively ideal filtering effect......

"Shhhh

"I kind of regret opening this letter......"

Chang Haonan rubbed his slightly swollen temples, put the letter on the table, and got up to leave the bedroom.

He was going to make a cup of strong tea.

I'm afraid tonight's rest will be in the soup again.

……

A few hours later.

Chang Haonan looked at the letterhead that had been marked with red and blue pencils, and the notebook full of notes written next to him, and drank the last bitter sip of tea in the thermos cup.

It can only be said that Xu Yang is worthy of being a doctor who returned from UCB, and he personally participated in the development process of the differential evolution algorithm.

In terms of the level of ability shown by the other party, it doesn't seem to be an exaggeration to say that she has a system with the same style as herself.

The ability to draw inferences is quite strong.

The content of the letter is not complicated to say:

After seeing Chang Haonan's improvement of the differential evolution algorithm, Xu Yang proposed a new idea, and wanted to discuss the feasibility and application prospects with the latter.

To put it simply, filtering is the operation of filtering out the frequency of a specific band in a signal, which is an important measure to suppress and prevent interference, and is almost an essential process for all behaviors that require the emission of electromagnetic signals.

In fact, the least-squares method learned in high school mathematics is a classical filtering method, but it is not stable because it only considers the relationship between measurement and state.

Later, the Kalman filter was born for linear systems where noise obeys the Gaussian distribution, and it soon became one of the most widely used filtering methods in engineering due to its high efficiency and accuracy.

However, because the original Kalman filter was only applicable to linear systems, many people later extended it to make this widely acclaimed filtering algorithm also applicable to nonlinear systems.

One of the most typical is the extended Kalman filter algorithm (EKF), that is, the system equation is expanded with Taylor series, ignoring the second-order and higher-order terms, when the nonlinear system is close to the linear form, and then the standard Kalman filter algorithm is used to estimate the state of the system.

Obviously, the computational amount of the EKF algorithm is not large, and it is not difficult to implement, but the EKF is prone to serious oscillations and even divergence for strong nonlinear systems.

By the mid-90s, the engineering community had basically seen the limits of the EKF algorithm and began to think about improving the EKF algorithm or creating a new Kalman filter algorithm.

The new algorithm proposed by Xu Yang uses an improved differential evolution algorithm to select the variance of the process noise before filtering, which greatly reduces the state estimation bias and can achieve an accuracy far beyond the EKF algorithm by virtue of the computational effort slightly larger than that of the traditional EKF algorithm.

As an aeronautical engineer, Chang Haonan's previous understanding of filtering algorithms was limited to the application level, and his understanding of the basic principles was not profound, but if he only looked at the process of selecting the process noise through the differential evolution algorithm, it should be no problem.

Raising his head and looking at the horizon that had turned white, the tiredness that had just been suppressed by the strong tea finally came up.

Chang Haonan decided to take a break and then find a few books to study them completely before replying.

On the one hand, the optimization of the shape design of the blades of the turbojet 14 compressor has just begun, and most of the work at this stage is done by the engineers of the 606 Institute. Moreover, because of the existence of the system, as long as the code written by Chang Haonan is correct, there is no need to debug, which is the ability to envy countless programmers, and the most time-consuming part of him is not programming, but waiting for the calculation results, so there is enough time to do this.

On the other hand, although the algorithm Xu Yang came up with has little effect on the current engine improvement, it is the basis for a series of technologies such as precision-guided weapon strapdown seeker, radar data link, missile inertial navigation system solution, etc., which are closely related to Chang Haonan's previous pessimistic progress of the imitation A bomb - Thunderbolt 11 semi-active radar-guided air-to-air missile.

If there is no bullet, it will not be able to form combat effectiveness.

If it can be realized, it may be of great help to solve the problem of insufficient target test accuracy that has plagued it for a long time.

It's just dozing to send pillows.

"Maybe the weapon system of the 83 Project can also see hope within this year......

This was Chang Haonan's last thought before falling asleep.

……

The next morning, Chang Haonan left the dormitory after washing, preparing to go straight to the library, borrow some materials, and continue to study the idea proposed by Xu Yang.

In particular, the second half is related to the Kalman filter.

But full of anticipation, when I went out, I happened to meet Yao Mengna, who had also just opened the door of the room.

The two looked at each other.

"Why did Team Leader Chang go out so late? Don't you have to prepare meeting materials in advance? ”

Yao Mengna locked the door, and there was a bit of amusement in her tone.

After hearing this, Chang Haonan was stunned for a moment, and then slapped his forehead heavily.

The identity of a manager is something to get used to, and after decades of being a screwman, he is inexperienced in this area, and his mind is full of algorithm-related things after reading letters all night, causing him to almost forget about the meeting this morning.

This meeting was even proposed by himself last night.

Fortunately, I was reminded by Yao Mengna when I went out today, and the entire task assignment process was in Chang Haonan's mind, so it was not enough to delay the big event.

However, he did not show any frustration, and only took a breath and pointed to his head.

"No, the knowledge is all in the head, just start assigning tasks when you get there."

……

However, in the end, the duration of this morning meeting still exceeded Chang Haonan's estimate.

It wasn't until after lunchtime that he found what he was looking for from the library and returned to a computer room that had been set aside for him in the computing center.

With a clear idea that the idea was feasible, Chang Haonan didn't even need to use the system, and he quickly found the part he wanted from the stack of materials he picked up.

In fact, with the current system level, there is no way to carry out two projects at the same time, so this time he can only rely on himself.

It was almost the whole afternoon, and Chang Haonan was almost always analyzing and calculating ideas on scratch paper.

"Constant ......"

When Yao Mengna pushed the door in and was about to ask him to go to dinner, she only saw the back of a person who was struggling to write.

After a moment's hesitation, she pursed her lips and gently closed the door again.

At this time, Chang Haonan had completed the entire calculation process, and took out a stack of letter paper from the side to write a reply.

The content on the scratch paper just now was quite sloppy, even if he read it the next day, I am afraid that he might not be able to understand it.

In the original timeline, the unscented Kalman filter algorithm (UKF) was developed to solve the problem of large linear truncation error of the EKF algorithm.

Chang Haonan's original idea was to use this algorithm to combine with Xu Yang's noise variance optimization, which should be a very important breakthrough in the field of information extraction.

However, with the deepening of his understanding of the algorithm, he found that the mathematical derivation process of the UKF algorithm in theory is not rigorous, and after several calculations and simulations, it is proved that the value in the high-dimensional state is still not stable enough.

In the process of studying and researching the Kalman filter method, a flash of inspiration gave him a more subtle idea:

"Huishu respectfully understands that the idea of using the improved differential evolution algorithm to automatically adjust the variance matrix of the process noise matrix is quite novel, and it has been proved to have good estimation accuracy after numerical simulation, but there are still some problems in the EKF filtering algorithm itself......"

"Since EKF needs to find Jacobian matrices, the specific form of the nonlinear function must be known exactly, and it cannot be black-box encapsulated."

"It is difficult to find Jacobian matrices because the derivatives of the nonlinear functions of the equations of state and the observed equations cannot be found in many practical problems."

“……”

"According to Bayesian theory and Spherical-Radial Cubature rules, the integration in the Cartesian coordinate system can be converted into a spherical-radial integral, and a set of deterministic sampling points can be used to estimate the state by propagating nonlinear equations, and the specific steps are as follows:"

"Step 1: Determine the initial value of filtering: X0=E(X),P0=E[(X0-X0)(X0-X0)^T ]......"

"In the second step, calculate the volume point at the time of k-1, P(k-1|k-1)=S(k-1)S(k-1)^T, where S(k-1) is obtained by the Cholessky decomposition of P(k-1|k-1), and for the volumetric Kalman filter algorithm, the point set ξ and the corresponding weights are ......"

Time passed minute by minute, and at the beginning, Chang Haonan still needed to write for a while before stopping to think for a while, but as the calculation process progressed, his whole train of thought became more and more fluent, and he seemed to have entered a state similar to "flow".

So much so that when he finally wrote "Hurry this first, let it be later" at the end of the letter and sign his name, he saw the dinner on the table next to him that he didn't know who had packed it back.

"I used to think that forgetting to sleep and eat was a figure of speech......"

Chang Haonan thought of himself who forgot to sleep last night and forgot to eat tonight, shook his head with a smile, and then folded the letter and put it aside.

When he opened the lunch box, he glanced at his system panel by the way, and then froze in place.

[Research points: 110.]

Theoretical level: LV2 (500/10000)

Engineering Experience: LV1 (270/1000)

Management capability: LV1 (100/1000)

Comprehensive ability: LV1

Projects in progress:1

Items that can be carried out: 0]

For this is the first time since his rebirth that the experience of the [theoretical level] has increased.

And it's 500 points at a time!

You know, the things he wrote on hand haven't even been shown to the second person, and they haven't had any real impact yet.

"Looks like I've got a big job this time......"

Chang Haonan leaned back in the chair, broke the disposable chopsticks, rubbed the back of his somewhat sour neck, and muttered to himself.

I was driving late on the road just now.,I always thought that the UKF algorithm was proposed in 2000.,As a result, I see today that it was proposed in 1991.,So the plot about the improvement of the Kalman filter method has to be adjusted.,But now the details have been re-straightened out.,No problem.。

(End of chapter)