Stability Analysis - Science topic

@Erik Eberhardt

That is a very general question. any geotechnical book has the basic principles. Check, Soil Strength and Slope Stability book by J. Michael Duncan, Stephen G. Wright Thomas L. Brandon.

In this code, the SEIR model is represented by a system of ordinary differential equations (ODEs). The `ode45` function is used to solve these equations numerically over the given time span `tspan`. The results are then plotted to visualize the dynamics of the population compartments over time. You can modify the parameter values, initial conditions, and time span to fit your specific scenario. Additionally, you may consider incorporating additional features or extensions to the basic SEIR model as per the requirements of your analysis. I hope this code helps you get started with the SEIR model in MATLAB!Certainly! Here's a basic MATLAB code implementation of the SEIR model for infectious disease simulations:matlab % SEIR Model Parameters beta = 0.8; % Infection rate gamma = 0.2; % Recovery rate sigma = 0.1; % Incubation rate % Initial conditions N = 1000; % Total population I0 = 1; % Initial infected individuals E0 = 0; % Initial exposed individuals R0 = 0; % Initial recovered individuals S0 = N - I0 - E0 - R0; % Initial susceptible individuals % Time vector tspan = 0:1:100; % Time span of simulation % Function representing the SEIR model seir = @(t, y) [-beta * y(1) * y(2)/N; % Susceptible equation beta * y(1) * y(2)/N - sigma * y(2); % Exposed equation sigma * y(2) - gamma * y(3); % Infected equation gamma * y(3)]; % Recovered equation % Solve the differential equations [t, y] = ode45(seir, tspan, [S0, E0, I0, R0]); % Plotting the results plot(t, y(:, 1), 'b', 'LineWidth', 2); % Susceptible hold on; plot(t, y(:, 2), 'y', 'LineWidth', 2); % Exposed plot(t, y(:, 3), 'r', 'LineWidth', 2); % Infected plot(t, y(:, 4), 'g', 'LineWidth', 2); % Recovered legend('Susceptible', 'Exposed', 'Infected', 'Recovered'); xlabel('Time'); ylabel('Population'); title('SEIR Model Simulation'); grid on;

Dear Salah Mokred It is in this case, as indicated by Wolfgang R. Dick, because the journal that cited one of your papers is not listed in RG database of journal titles (the journal is too new and just started volume 1, issue 1).

What you can try to 'speed things up' is that you could ask one of the authors https://www.researchgate.net/profile/Kadir-Dogansahin-2 to upload the paper and then most likely the reference (and thereby your citation) will be picked up.

Best regards.

See Chapter 3 of the following book:

Thank you Dear Nikoloas and Vahid for your reply. I will check the recommended books and paper.

Micro-seismic investigation definitely pave the way for assesment of dynamic stability of caverns. However, the signals should be recorded and interpreted on daily basis and with due care & precision.

For control optimization. If you need a fast response and settling time, ITAE or ISE might be more suitable. If you prioritize a smooth response and lower control effort, IAE could be a better choice.

1. Im not sure if its logical, but as it is doesnt effect the stability slope much. If you predict it higher and repeat calculation, you could get much different results (less stable slope). So if you dont have any data and you want to play it safe, take into account higher level of water.

Questions 2 and 3 were already answered by others.

- The first step of analyzing a dynamical system is proving its well-posedness. That is, the existence and uniqueness of the solution and its continuity with respect to the inputs: the initial conditions, the parameters of the dynamical system, the spatial domain (in the case of spatiotemporal dynamics), etc. In the case of systems governed by nonlinear ODEs, various theorems can provide such a result under suitable global/local Lipschitz conditions on the dynamics. In the case of systems governed by reaction-diffusion systems, an adapted approach based on semigroup theory is usually used.

- From the first step, one can conclude that there are many solutions that can be obtained based on the considered initial condition and the input parameters. The aim of Lyapunov stability theory is to establish conditions under which these solutions have a common asymptotic behavior at a large time.

- Note that in order to proceed with the Lyapunov approach, one needs to establish the existence of equilibrium points. That is, solutions of the dynamical system, which are not depending on time. To obtain these points, for the case of ODEs, one needs to solve a system of nonlinear algebraic equations. While for the case of reaction-diffusion systems, the task is more delicate as it requires the solvability of a nonlinear elliptic problem.

- Conclusively, an intermediate step in the Lyapunov approach is to merely provide the existence of solutions not depending on time. These solutions are not important because they neglect the time dependency which is crucial when it comes to "dynamical" systems, but are of great importance when it comes to investigating the asymptotic behavior.

If you want to prove the stability without linearization, you can use Lyapunov theory.

Anuj Kumar

You can make three main columns- Genotype, (Year x location i.e. 2015 Karnal, 2015 Meerut, 2015 Varanasi, 2016 Karnal, 2016 Meerut, 2016 Varanasi) as the second column which will be Environment (6 Environments) and the third column is Replication. Then 4th to nth columns will be your traits.

Then you can do AMMI-based ANOVA using the Agriolae package in R. Mean data for the same can be used for GGE biplots like Which won where/Mean vs Stability etc. in the GGEBiplotGUE package in R.

You can also use the Metan package in R for this purpose and additionally it gives different stability parameters.

Feel free to ask, if have any doubt.

Good luck!

Irfan Qaisar thank yor for the recommendation

hi,

kindly refer this lik:

Chengyong Gong Thank you professor. I am still an entry level engineer. graduated from school just recently. Looking for some mentoring from fellow engineers here.

I agree with the responses! Additionally, all the factors influencing the shear key resistance should be taken into account in the calculation, in order to get high precise results and thus properly ensure the dam stability!

Dear Kuldeep,

Nice to hear about your research work..your question is what type of triaxial test is to be conducted for soil samples collected from landslide. It is simple understanding that if you need to verify the short term stability of slope than you need to conduct CU test or if you want to verify the long term stability slope than use CD test results. As you know CU test is quick as compared to CD test..so depending upon your design requirements you have to use either CU or CD test..ok all the best..

Hi dear Kuldeep Dutta

Check out the following software:

Hi Tee Su Yee

Yes, there is. You can find many articles in the engineering journals, typically in the field of systems and control. In electrical and mechanical systems, many Lyapunov function candidates can be constructed using the 'energy' concepts. For constrained systems, Barrier Lyapunov Function candidates are usually proposed.

Dear Tarek R. Khalifa

Lyapunov function is a point-wise measure of energy, whereas, cost-functional is an interval-based measure of energy. In this sense, you may connect them by assuming Lyapunov function as an explicit function in time which could get a negative decay-rate assuming V=x^2, and then a closed-form dissipation as; V_dot=-K*V(t) for stabilizing a system, see my pre-print at the URL:

Meanwhile, optimal quadratic cost functional, minimizes energy as a sum of the squared state and control signal during a time-interval as; J=int(x^2+u^2).dt, from zero to T. Please see the paper:

Nonlinear Optimal Control: A Control Lyapunov Function and Receding Horizon Perspective (1999)

The control performance could be different through the two scopes, and the energy consumption could be also different.

Hello

Check the dynamic boundary conditions and damping and mesh size.

Give me more information on your project!

Best,

Rashiddel

Lecturer FLAC 2D - 3D software

Dear Himali Singh

Yes, these articles might be useful to connect all the dots together, have a look:

1. https://www.sciencedirect.com/topics/engineering/extended-kalman-filter

2. https://www.degruyter.com/document/doi/10.1515/rnam-2018-0004/html

3. https://www.researchgate.net/publication/287158261_A_general_extended_Kalman_filter_for_simultaneous_estimation_of_system_and_unknown_inputs

Kind Regards

Qamar Ul Islam

I suggest that you graph the function in question and try to find the Laplace transform of the graph.

Dear Sudar Mani G

The following article will help you:

Thanks for suggesting the books.

Hello Chang-Duo Liang

It is also a unavoidable problem that took place in my desgining controller. From my perpective point, based on an observer, the positive gain "K" can be devised as a time-varying gain. More specifically, when the observer has been completely conducted, the positive gain "K" can be assigned a sufficiently small value to reduce the control overshoot.

However, it is still a difficult problem for me to relieve the control overshoot before the observer takes effect. I sincerely hope that this answer can help you effecively.

AMMI and GGE biplot analysis can be used

Thanks for the suggestion.

consult

As I know, Governors, who are tasked with increasing or decreasing the output of generators in the event of a decrease or increase in network frequency, set up a Dead Band so that they do not act in exchange for small changes in frequency. This will prevent the equipment from malfunctioning. Because the governor is a mechanical device anyway, and if he wants to react to any small change in the network frequency, it will break down very quickly.

But, my Question is how can it be implemented in a system and how can we do System Frequency Response assessment with that?

If by 'stability constraint' it is meant 'restriction on the Courant number', clearly this only refers to discretized convection (I prefer to say 'advection') equations. Any other term that you have in your (spatially) discretized problem may entail other, possibly more restrictive, stability conditions. A linear source term like

the right hand side of

y'=-k*y

entails a stability restriction of the kind | k* h| < constant where h is the time step

and the constant depends on the time discretization method (constant =2 for explicit Euler). A source term that does not depend on the solution, like the right hand side of

y'=f(t)

where t is time interpreted as the independent variable strictly speaking does not entail a stability constraint, since the discretization of this equation is equivalent to the computation of a definite integral of f. However, if your time step h is such that the behaviour of f is not properly sampled (imagine for example f(t)=cos(omega*t) with omega = O(10) and h=O(1) ) then your discretization will never be giving you accurate results and h must be reduced to sample f properly.

Very interesting question! Follow

I am not aware of this model since i hail from Agronomy background. You can read the following article for further information.

Mr.Koushik,

Slope stability analysis in PLAXIS software can be performed by varying the ground water level with respect to time and study the response due to change in ground water level. This depicts the water level before and after rainfall. If you want to simulate debris flow in analysis, first you need to select the region that would fall after rainfall..this can be simulated by applying displacement as boundary conditions and study the response due to change in displacements within the selected region. i suggest you to read PLAXIS manual and collect literature related to your study is available. Find attached the paper related to the work for your reference. all the best in your research..

Are you trying to do a parametric study or working on an actual project? Do you have data on the piezometric levels in the slope?

If you still didnt get response then my answer is applicable.

1. Try to look for velocity spectrum in Kangra Earthquake papers. Even if papers dont share data, get the figures.

2. Extract data from figures.

3. Use this load under dynamic load conditions...

4. Select time query points.

5. Run the analysis.

Dear Dr. Maysam,

I think that the probabilistic and sensitivity analysis may be enough. But, for intensive results and comparisons, you have to consider the statistical analysis. The choice may depend on the nature of your application and research work.

Good Luck!

Hi Dr. Chak,

Thank you for your answer. It will be highly appreciated if you can support further (if possible, please examine the attached Simulink file in Matlab208A format).

My algorithm (the block with light-blue background) receives three-phase bipolar signals in addition to a fourth slowly changing positive signal. The frequency of the three-phase signal can change between zero to a known upper bound (changing rate is limited to a known limit as well). The algorithm's objective is to continually track the phase angle of the input three-phase signals. By stability is meant, the algorithm can keep tracking of the phase angle of the input signals infinitely!

The process within the algorithm is highly nonlinear and as I said only the Simulink numerical model is available (attached)

PROGRAM GENES:

http://arquivo.ufv.br/dbg/genes/genes.htm

http://arquivo.ufv.br/dbg/genes/Genes_EUA.htm

Here are many methods, select according to your need.

Good luck.

First, before designing an observer-based control scheme, you have to ensure that the separation principle holds for that. If the separation principle holds, then we can say the stability can be guaranteed individually, i.e for controller and observer.

Ok, l understand

Karsten Fleck

how can be performed process corner analysis or monte carlo simulation in sram cell design ?

what it will provide?

please reply

There are many companies around the world flying different Lidar scanners for different purposes and they only exist because indeed someone is prepared to pay good money for the data. Many of those are multi-million dollar aerial systems in aircraft or helicopter, i think you are looking at UAV based solution though.

To attempt any freelance work with the Lidar unit you mentioned would be a waste of time however, the data precision and accuracy would not be considered good enough for the majority of end users.

A much higher level unit such as the Riegl Mini-VUX or the VUX-1UAV would operate well in that environment and with an appropriate IMU and GNSS/RTK system produce survey grade results of some value to an end user.

Dear Mr. Tiwari, I hope all is going well. I have recently published a series of papers regarding Multi-Environment Trial Analysis. In my first paper ( ) we combined the feature of AMMI and BLUP models into a new stability measure called WAASB. In the second paper ( ) I've proposed a multi-trait stability index aiming at selecting stable genotypes based on multiple traits. To facilitate the implementation of these indexes I've been developing an R package called "metan" (https://tiagoolivoto.github.io/metan/), which also includes code for AMMI analysis. I hope it helps you. Any suggestion/criticism will be welcome. Best regards,

Hello Lv July ,no I haven't got to resolve the question. I was only able to compare the total RNA yield between the serum and plasma samples, and on an average I found that plasma had way more higher RNA than the serum. In general, people are inclined more towards using plasma for exosome studies, because serum is subject to coagulation.

Idealizing the earthquake forces by static forces is an approximate approach and is applicable only when there is one dominant mode shape of the structure.

Please elaborate why you want to do it this way

Hi, there are pro and cons for each software.

Slope/w is widely used tool due to easiness and less cost. This program is developed based on Limit Equilibrium methods. The limit equilibrium method of slices is based purely on the principle of statics; that is, the summation of moments, vertical forces, and horizontal forces. The method says nothing about strains and displacements, and as a result it does not satisfy displacement compatibility. Due to this, we don't know the deformation of stable and unstable slope.

FLAC is finite difference method and needs a lot of time to generate model, meshing and assiging suitable constitutive model and to run. In FLAC you can write the program as per your /client requirement. It is more versatile and much costlier than Slope/w.

OK, thanks a lot Engineers

Attached you will find the required model. You will find four versions of identical main network. We already used this system for studying the dynamical aspects of integrating solar-PV sources to this system,

Good luck

Thank you, Mohamed-Mourad Lafifi and DJILANI KOBIBI Youcef Islam.

Good morninhg

I found those reaserches

Maybe are helpfull

Ingrid

Norms don't go to zero, unless error is always zero at all time instants.

The time-integral criteria are generic and comprehensive tools to evaluate the performance of a control system.

a system may have good rise time, but poor settling time. or vice versa. other basic criteria to evaluate the performance of a system are the overshoot, the steady state error. but all of these describe only one characteristic

time-integral criteria are generic and comprehensive. they allow comparing between different controller designs or even different controller structure.

as mentioned in an earlier answer, the physical meaning of these criteria is: each one is a function of the error profile (in time) of the output.

Hi Dana Afshar

You can use the following command and put your file name instead of "Dynamic.tcl"

! OpenSees.exe "Dynamic.tcl"

Dear Muhammed,

Slope stability consists of numerous methodologies including Limit Equilibrium Method (LEM), Finite Element Method (FEM), Boundary Element Method (BEM), Rigid Element Method (REM), Limit Analysis Method (LAM), Discrete Element Method (DEM) as well as hyprid methodologies such as Finite-Discrete Element Method (FDEM) and many others that I may have forgot to mention.

These methodologies have all some advantages and disadvantages over one another. Infact hyprid theories have been continuously developed to overcome these facts. Many software packages have been written over the years but almost all of them have some limitations in every methodologies they represent, because developers need to simplfy the complex algortihms as much as possible to decrease mainly the time consumption of the development. Also please bear in mind that they are generally written commercially.

As I mentioned every theory have some limitations, considering LEM cannot represent the post failure situation of an instability nor the mechanism. Also, It ignores the deformation characteristics of the materials and many assumptions need to be made such as inter-slice force fucntions to represent the magnitude of forces between each slice.

Additionally, you need to have decent understanding of each theories to be able to develop a new method, which I honestly think that there is no need at this time since many analytical solutions are already present.

Best Regards

Bekir SF

' I just need to add required extra surfactant ' - ideally you remove part of the continuous phase for dilution. It's surfactant content is different from the overall surfactant content because depending on droplet size distribution considerable amount is adsorbed onto oil droplets or even distributed into the oil phase.

Should be better to dilute with plain water.

GeoStudio is fine. You don't need a license to use the (limited) students version

Dear Dr. Kaushik Kumar,

Yes, you can check equality of means using MINiTAB.

Regards

Vishwanath

We have proposed a numerical method (denoted as MEM) for solving the

Nonlinear Dynamic problems. If you would like, you can view our published articles in this field entitled "dynamic analysis of SDOF systems using modified energy method". By the way, the presented idea is also generalized to MDOF systems in another study, which is available on my research-gate account.

if you need more information, please let me know.

Regards,

Jalili

Dear@ Vidal Marvin Gabriel Cabasal Gabriel

Please visit the following links

Best Regards

By definition, a slope fails with a FoS going below 1.0. As long as the FoS is above 1.0, a slope is considered stable. Thus, I do not see how your figure could be drawn.

Of course, the FoS is a simplification and can not be measured directly. However, the definition is rather clear and if you follow it a FoS>1 relates to zero probability of failure.

I think the following papers may helpful for you.

best regards

Dear Mr.Hassan,

The influence of intermediate stress in 3D analysis will influence the factor of safety of slope. The factor of safety of 3D based analysis is lower than the 2D based slope analysis. all the best in your research..

Dear Arshad and other contributors,

I think the remarks are relevant. Pointing out Nichols chart (by Itzhak) was really nice. Let me add a few remarks which could turn out to be important. I mention them from many years experience in class room... I know these are recurrent doubts.

1) Bode diagrams are one way of graphically representing the frequency response of a LTI (linear time-invariant) system, which is by definition, the Fourier Transform of the impulse response of the system;

2) Although Matlab will provide a Bode Plot for an unstable system, such a plot should not be interpreted as a frequency response, because an unstable system does not respond sinusoidally to a sinusoidal input. Mathematically, the impulse response of an unstable system is not an absolutely integrable signal and the corresponding Fourier Transform does not converge.

3) Out of technicalities and into stability... Supose a system with frequency response G(jw), if it has a frequency response then it is stable by definition;

4) Now what seems to be implied in your question is how to use a Bode Diagram of G(jw) to establish the stability of G(jw)/1+G(jw), which is the frequency response of the closed-loop system. Practically all the answers given were provided assuming this (which is the most natural interpretation).

5) Making a long story short: if the system is open-loop unstable, then Bode Diagrams are not the best way of addressing stability either of the open or of the closed-loop. If the loop transfer function is open-loop stable, then, yes, you will find the answer to the stability of the closed-loop system by measuring the gain and or phase-margins.

6) This is valid for both, continuous- and discrete-time systems, although we cannot use the concepts of asymptotes (straight line approximations) to plot Bode Diagrams for discrete-time systems.

Regards.

Luis

While doing some research incident to producing a scientific biography of Galileo [cf. citation in my profile], I came across a Coriolis-type phenomenon that Galileo investigated, that is, the apparent deflection of an object moving along a longitude line or, to a lesser extent, moving in a direction that has a north-south component, which can be expected to deflect to the right in the northern hemisphere and to the left in the southern. This Coriolis deflection can be attributed in part to Earth’s eastward rotation -- a phenomenon that Galileo strove mightily to demonstrate with many arguments -- and I would expect this deflection to apply to your " dust molecular clouds".

To use one of Galileo’s favorite examples, that of a projected cannonball, if fired to the north from the equator it would land somewhat east of the meridian on which it was fired. Due to the tangential velocity of a point on Earth varying with latitude the cannonball can be expected to travel eastward faster at the Equator than does its more northerly target or landing point. And mutatis mutandis for a cannonball fired to the South.

Here I have only “scratched the surface” of the issue; i.e., there is much more to be said about Coriolis force. For the sake of brevity I will resist the temptation to further discuss it here but instead refer you to a scholarly article that has the most comprehensive history and development of this topic of which I am presently aware [Anders O. Persson, “The Coriolis Effect: Four centuries of conflict between common sense and mathematics”, History of Meteorology 2, 2005”]. I hope this helps.

$e^{w_0 A t}$ is bounded by and exponential decreasing function in the case of A hurwitz. so after some time $T1$will be less than any constant , in particular 1/(w_0^{n+1}).

Hi Tang ,

You might be interested in the "ready to use" CMIP5 data for climate change impact modeling we provide.

https://theclimatedatafactory.com/product/near-surface-air-temperature-over-singapore-singapore-annual-trend-of-historical-gridded-observations-and-climate-projections-from-cmip5-models/

There is also daily min/max temperature and solar radiation (and soon wind and relative humidity).

Please note that those are not high resolution data (scale is 50km x 50km). Our "City data" are useful for quick exploration of past and future climate conditions at a specific location. There are intended to inform about possible trends and support qualitative assessments.   

The methods and process we use to generate this data from the original CMIP5 data are described in this report: https://www.researchgate.net/publication/322888233_Bias_Adjusting_Climate_Model_Projections

All the best

I think it is the simplest way.

Initially you have to do a little attention, but once you understand the system it is very simple. In these years I have done many tests of stability using this system.

ANOVA partitions total variability represented by total sum of squares SSt into four components: (1) sum of squares due to genotype SSg (2) sum of squares due to environment SSenv (3) sum of squares due the genotypexenvironment interaction SSgxe (4) sum of squares due to error SSe. The ratio of each sum of squares to SSt is the proportion each variable contributes to the total variability respectively. Note that the proportions add up to 1.

When a matrix is multiplied with a vector, it does do things 1. rotation 2. scaling. you can easily visualize it by multiplying a two dimensional vector with a 2x2 matrix (y=Ax) and see that y is a rotated and scaled version of x. When the dimension increases then you can't visualize it. SVD kind of helps u in finding out the the basis for the axis of rotation (U and V*) and singular value matrix (S) says the importance of that basis. So from SVD of matrix A, u can say that how it will rotate or scale the x.

The straight forward application is PCA or dimension reduction. If u can find that in certain axis there is no change then u can simply ignore that because they are not important. You can link the SVD to eigen value decomposition where eigen value decomposition is only for square matrix where as the SVD is valid for all the matrices.

This is my intuition to SVD and hope it helps.

BW

Yes, I used the original PST by Chow in stability analysis of muli-machine systems. This was during my PhD study in 2003. Later, I decided to use the PSAT as it has a GUI, more capabilities, and more components. Currently, the PST is significantly developed, but I didn't use it yet. I am also thinking to try the POUYA package.

This link may help

https://link.springer.com/article/10.1007%2Fs10846-013-9915-6.

Also refer prefiltering concept

Hi Waheed,

Thanks for your reply.

Since you have designed a Lyapunov-based integral backstepping controller for the 4^th-order MISO system, what exactly is your difficulty in checking the stability of the control system?

I was attempting to apply finite differences in a linear ODE with dirichlet BCs and I could not find something regarding stability check in the literature so far. I guess even for the simple case where you assume boundaries of the type y(0)=0 , y(L)=0 where (0,L) is the grid, you can not use the Von Neuman analysis correct?