Stability Analysis - Science topic

The data were recorded on different agronomical traits on wheat crops with two years and three location. the question is that how to calculate stability, means GxE interaction. And suggest to me which is the best method for stability analysis.

Firstly, try to change the second-order nonlinear system of equations into a first-order linear/nonlinear system of equations, then calculate the eigenvalues of jacobian matrix, if all the eigenvalues have a negative real part , implies the system is stable otherwise unstable.

In fact the ISE, IAE, ITSE, and ITAE indexes depend on the control system performance requirements. Usually, they are used to tune the controller and are problem-dependent. So the controller optimally tuned for ITAE can give worse results in other indexes, and shouldn't be compared with the controller tuned for ISE (for example).

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 Pandit,

In order to model the unsaturated soil behaviour, we have to model it hydromechanically. It means that first, we have to model the hydraulic behaviour of soil in which the soil-water characteristic curve and unsaturated hydraulic is vital to be found. Then, must include the SWCC and unsaturated hydraulic conductivity to simulate the soil behaviour mechanically. For doing this, we can use ABAQUS, Plaxis, GeoStudio package, and ... For more details, you can refer to follows papers:

Dear Sudar Mani G

The following article will help you:

Thanks for suggesting the books.

Thanks

Chang-Duo Liang, try to reduce the value of K. But, as long as Ksign(s) is a bound term, I don't think it can cause any problems or overshoot.

Rember that in sliding mode, one constraint the motion of system to lower-dimensional sliding manifolds. So, overshoot is not commonplace in a good design. i,e. suitably designed sliding surfaces.

Finally, check the initial conditions. Try to choose the ICs on the sliding manifolds.

Regards,

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..

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

Pl. go through attached article.

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.

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

None as I recall. No mass balance is 100% since we don't count the water produced as an example. Thus, 85% is acceptable if it can be justified scientifically.

' 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.

Dear Mr. Tiwari. Yes, I runned AMMI1 analyses.However, in my opinion, GGE is superior than AMMI1, because GGE isolate environmental (E) effects (Did not use aditive effect of E). Thus, the model of GGE consider only the main effect of Genotype plus Genotype Environemnt Interaction (G + GE). If you see articles that used AMMI1, you can see that the E effect correspond for the big part of the sum of square, i.e., you make inference about E and not about genotypes.Thus, I recommend use GGE analyses. In R plataform, you can performed mean vs. instability and ideal genotypes analyses to evaluate genotypes and representativeness vs. discriminating power to evaluate test location. As cited before, for each analyses, different scaling methods can change the inferences of analyses.

You can read the below articles about GGE and AMMI1 to understanding and make conclusions about:

Article 1: "GGE Biplot vs. AMMI Analysis of Genotype-by-Environment Data"

Article 2: "Statistical Analysis of Yield Trials by AMMI and GGE: Further Considerations".

$e^{w_0 A t}$ 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?

The type of analysis depends on the type of soils, on groundwater flows and hydrogeological conditions.

For granular soils (i.e sand or gravel), the slope must be checked only in drained conditions.

For cohesive soils (i.e.clay and silts), there are two possibility. If the soils are dry the slope must be checked only in drained conditions. If the soils are saturated or with groundwater flow the slope must be checked in both undrained and drained conditions.

The idea of dimensionless form is intimately associated with the concept of similarity. Two flows having different values of length scales, flow speeds, or fluid properties can apparently be different but still dynamically similar. Therefore, it is standard to non-dimensionalize the equation by scaling each variable by a “characteristic unit”. This scaling process naturally produces certain non-dimensional combination of these units.

A book which deal with more general nonlinearities is the one written by Drainkov and Hellendorn: http://www.springer.com/gp/book/9783540606918.

With all respect, but although LMI approach is very nice, it has some drawbacks. I actually like it but you may wish to see the book I told you about,

Pl. Send your email so we can communicate properly.  Thanks for response.

Hi Luis,

Your question is a fundamental question.

Many systems are using gain scheduling and... they work, and even fly.

However, the guarantee of stability is something else, SISO or MIMO.

Suppose that you know that your system is stable for any gain from Kmin=1 to Kmax =20.

You have been using the gain K1=5 and, at some point in time, you decide that the gain K2=10 is better. So, if you just switch from K1 to K2 and then STAY at K2, you have a simple LTI stable system with the fixed gain K2=10, which, coming from K1=5, may have a transient response, yet otherwise is stable.

Things are different when your policy requires the system to keep switching between K1 and K2, (or to keep going through other various gain values) when you have no guarantee of stability. Your system may happen to remain asymptotically stable, yet may also perform some limit cycle or even just simply diverge, although the gains remain within the so-called “stable domain.”

Yes, this is the shock that people met when they move from constant gains to nonstationary gains.

People here mentioned adaptive control. Because I am coming from the adaptive control field, I had to deal with this problem. A first adaptive rule, called MTI rule, did exactly this: let the gain change within the admissible domain and use an adaptation rule to fit the right gain to the right situation. The algorithm was implemented on a plane, which flew nicely until… it just crashed.

In spite of the known history, at some point in time, I also “almost” had a proof that stability is guaranteed. I wrote “almost” because it was only until I found my own counterexample. I call this my best and happiest mistake ever, because it forced me to learn a lot about stability with nonstationary and nonlinear systems, and such concepts as passivity, etc, which are essential for stability of nonstationary systems, including adaptive control systems. I does not mean that you cannot guarantee stability with nonstationary gains, yet you must first learn to satisfy the prior conditions that can allow you to guarantee it.

You may want to have a look at the paper

I.  Barkana: “Adaptive Control? But it’s so simple! A Tribute to the Efficiency, Simplicity and Beauty of Adaptive Control,” Journal of Intelligent and Robotic Systems, Vol, 83, No. 1, pp-3-34, July 2016 (Published On-Line October 2015) DOI 10.1007/s10846-015-0299-7

It is about adaptive control, yet this only says that, instead of just switching gains, the tracking error is used to compute the appropriate gains such that the error tends to zero. If you cannot get the paper, you can see the report with same name in my list of publications on Research gate.

Regards,

Itzhak

Hello Biswajit Debnath,

I think the following thesis can help you know the basic level of cell mapping method. 

van der Spek JAW.  Cell mapping methods: modifications and extensions. Ph.D. thesis (Technische Universiteit Eindhoven, 1994)

       Shan Yin

interesant question, I want to proof stability with nonlinear smith predictor. I think is necessary to use Lyapunov method

I presume that you might have found a satisfactory answer by now, but just in case not....

The analysis in the notes from Sweden may be extended easily to higher order systems of linear ODEs. Let us take the original system to be, y'=-ay, (which has a sign change compared withe Swedish note) and therefore we require |1-ah|<1 for stability. We may also write the ODE in the form, (D+a)y=0. But any higher order homogeneous system (such as 10 coupled first order equations, three coupled 2nd order equations and so on) may be reduced to one ODE of the form,

(D+a_1)(D+a_2)(D+a_3)...(D+a_n)y=0,

where the constants, a_1 to a_n, are either real or have some complex conjugate pairs within the list. Then the single equation analysis applies to each of the differential factors, (D+a_i). So for a set of real values for the a_i, the steplength is restricted by that factor with the largest value of a_i.

For more complicated systems I am guessing that no analysis could be done, although it might be possible to do so with some sort of linearisation. But even then, if one were to try to solve y'=-ty numerically with a constant timestep, then forward Euler will always eventually become unstable.

You are welcome, Anirudh.

If you find the answer, would you be able to post a sort summary of it? I think it may be useful for other researchers in this area.