This installment of my simulation explanation will likely be the last unless something of general interest arises. The earlier posts described what the variables were and how to obtain them from the downloaded data from the MFMP site. The data from that source is used to directly calculate the a,b, and c coefficients as well as obtain a starting point estimate for the Pin variable. I have intentionally chosen a set of transformed curve axis such that the original 'c' coefficient is zeroed out. When this condition exists, the modified constant coefficient term of the final quadratic expression reduces to just c'= Pin/Cap.
A review of the various variables show that there are related to either the static power output versus temperature equation or the time domain portion. Please note that I tend to use the terms Pin and Pout interchangeably since the calibration is expected to be performed without excess heat being generated by the device so they would be equal under that condition. Static variables are a, b, c, Kint, and Pin. All five of these terms are derived from static calibration measurements of the downloaded data. If you review the installments below you will see how these terms are obtained. Pin is self evident since that is the input power applied to the device. The a,b, and c were generated by a graph trend line second order fit relating the temperature of the outer glass test point to the power input. I have chosen to make the temperature the X variable and the power input as the Y variable. The Kint is determined by the initial temperature and associated power from which the step emerges. For instance, if you begin with an input power of 10 watts and proceed to 30 watts, the Kint value is adjusted to match the beginning simulation temperature associated with the 10 watt power level. The other two variables, Cap and TC, are related to the time varying behavior of the simulation. The value of Cap is directly related to the energy storage mechanism of the cell. If you know the temperature rise required to store a certain number of joules of energy, then you can calculate the equivalent Cap. This value also is the one that I use when I simulate the behavior with a spice program. The TC variable is used to represent the delay that occurs between the calculated exponentially rising curve that represents the solution to the differential equation and the monitor point chosen to sample that variable. When an input step of power is applied to the cell, there is essentially no delay before the internal energy of the cell begins to rise. For this reason the calculated simulation curve begins to immediately rise in synchronization to the power step. But, the temperature at the outer glass monitor takes time to respond to this drive. Also, there is quantization error in the time steps that are included within the downloaded data. It is not unusual to see these steps 8 seconds or more apart. This throws an extra unknown that needs to be compensated for in order to get excellent temperature tracking. Note that I transform the time axis so that time equals zero when the power step is applied. There is much more information that could be written about the operation of the program, but this will have to suffice for now. The optimization of the variables is a key operation to perform when using my simulation tool. You should note that I am performing an LMS curve fit to get the best match of program run to input data. I calculate the 'sum of the differences squared' for this operation. The actual number and location in time of the sum terms can be adjusted depending upon where you are most interesting in the matching of the data. Most of the time the input data is limited to a thousand points or less and I use all of the available pairs for the optimization. On occasion, I am interested in the initial rising edge of the transient response, particularly if it appears as though excess power is being generated that increased with time. I ask the program to fit the starting edge and then observe how quickly the excess power is increasing or decreasing with time. For the present argument let's assume that we have data to fit which is well behaved with time. I typically enter the Pin variable to the step final level. It is generally possible to estimate the Kint to generate a curve that begins somewhat near the actual value demonstrated by the measured data. If I feel like playing around a bit, I just optimize the Kint with Excel solver so that the initial temperature calculated by my program matches the downloaded data. This works very well provided that you also have entered the Pin before the optimization begins. After this step is completed, a curve could be displayed that is reasonably close to the actual physical run. But, we want to know more accurately what the actual power input really is (here I refer to Pin plus Pexcess) as well as to obtain a close fit for the displayed curve and the real world. The data solver in Excel does a remarkable job of adjusting the variables so that the calculated curve matches the downloaded one. I just optimize the LMS value toward 0 by allowing solver to vary the Pin, Kint, Cap, and TC. It plugs away for a few seconds and then tells me it can not find a perfect match. Generally the match is quite good however so I accept the values that solver finds and the task is completed. A plot of the error function demonstrates how closely the delayed function matches the real life values and it typically looks flat with the exception of noise that is riding upon the input data. I include a simple one pole RC equivalent filter to smooth the displayed data. The RC can be adjusted to either increase or decrease the smoothing and I generally place the variable below a graph that displays both filtered and raw error signals. I like to plot a second graph which shows the raw temperature data, calculated curve, and the delayed curve versus time. In this manner, it is possible to review how well the program generated fit matches the real life data. If for some reason something looks strange in the output, you have a display that helps debug the operation. It is seldom necessary for me to need to debug the curve fitting, but it is comforting to know that the file performed as required. When the optimization is completed, you will see that the Pin variable has been modified from what you initially entered. A stable calibrated run generally yields a final value that is within a few tenths of a watt from the downloaded data provided the calibration run is accurate and good values determined for a, b, and c. This operation can actually be used to verify that you in fact do have accurate values for the parameters and is thus valuable. If you know that there is no excess power being generated due to the set up, then I would expect an accurate match to Pin. One of the beauties of this technique is that in the future, if the calibration drifts, the program will clearly show that fact. The Pin will not match up to what is known to be used in that case. Once the program is calibrated and matches a calibration step accurately, then you are ready to measure excess power. Just enter the latest downloaded data that might have excess power contained within and let the program do its optimization as described above. The Pin that the program estimates is then modified by the additional power due to LENR and shows up as perturbation away from the ideal curve fit at points in time that correspond to excess power or absorbed power. So, you can see variation in average Pin as the modification to the actual Pin given with the data set, as well as see where the curves divert from each other indicating heat that is produced. Once you have performed several curve fits, you will become comfortable with the best procedure and gain confidence in your usage of the program. There is no substitute for taking the time to learn by trying since supplying the best description for the operation of my program is difficult at best. Ask questions either in private or in this list and I will answer in like fashion. Dave -----Original Message----- From: David Roberson <dlrober...@aol.com> To: dlroberson <dlrober...@aol.com> Sent: Sat, Jan 19, 2013 9:52 pm Subject: Re: [Vo]:Simulation of Celani Replication by MFMP This is the third installment of my explanation of how to use my simulation program. The last time I left those interested with a task of determining the roots of the primed coefficients. Those primed values are in the last installment which is below this one. The solution to the quadratic equation yields a first root that is positive referred to as R2 = 181.2596. The negative root of the equation yields R1 = -350.751. Next, there is an additional value required to simulate the cell behavior and I refer to it as Wreal. This is the actual real frequency of the fundamental exponential natural response. The solution consists of this fundamental frequency plus an infinite series of its harmonics that all contribute to the time domain response. In actuality, only the first few terms are important as each falls off rapidly due to the affect of the integration constant Kint. You calculate the Wreal with the following terms. Wr= square root of ( b' ^2 - 4 * a' * c'). Using the values given below of a'=-6.4 E-6, b'= -.00109, and c'= .409318 one obtains a Wr = .003425. I have mentioned an exponential time constant that the curves follow in earlier posts which is the inverse of this term, in this case it is 1 / .003425 which is 291.96 seconds. This should not be confused with the delay TC below. Once the 5 values discussed have been determined you can generate the actual time domain curve that the outer glass temperature follows (or any other with proper adjustments). It is best to generate the curve in two steps so that the internal energy storage mechanism is followed by the delay associated with the monitor point. Using two steps permits you to observe the operation of the test device and ensure that nothing weird is fouling up your end results. The equation for the first step is as follows: F(t) = R2 - (R2 - R1) * ( e ^ (-1.0 * Wr * t + Kint) ) / ( 1 - e^ (-1.0 * Wr * t + Kint) ). Careful observation of this equation demonstrates that the value of R2 is the temperature that the device obtains after a long time has elapsed and the transient portion of the equation approaches a value of zero. The Kint is the integration constant and in this case is a negative number of the following value; Kint = -1.63. Please refer to the other variable values in the paragraphs above. You most likely noticed the ratio of exponential terms and wonder how that results in an infinite series of harmonics. This is how it works. 1 / ( 1 - X) is equal to( 1 + X + X^2 + X^3 + ...). If you then multiply this by X you end up with ( X + X^2 + X^3 + X^4 + ...). As long as you restrict the value of X to below 1, the series converges. In our case the X is replaced by the exponential term which is e^(-1.0 * Wr * t + Kint). If you experiment with this relationship you can see the range of values that Kint can have which results in a convergent series. Once you have generated the time domain expression above and entered it into Excel along with a time axis, you are most of the way there. You can plot the value of F(t) versus time and observe how the internal temperature of the cell behaves. We see an attenuated version of the actual temperature that exists within the cell due to heat flow through thermal resistances. It is not clear exactly what the internal temperature reaches, but I suspect that the un attenuated value is related to the gas temperature itself. It is suggested that the mica might be a bit higher due to conduction and radiation from the heated wires but I can only speculate about this issue. Some of the time domain runs of my program simulating the mica temperature have a characteristic that tends to support this hypothesis. The power applied to the cell can not have a delay directly applied to it since the energy instantly begins to appear within the cell. For example, if you apply 100 watts of input power then 100 joules per second of energy starts to flow into the cell heating it up. I realize that there is inductance in the leads as well as capacitance to ground that do cause delays in the microsecond range, but we are monitoring operation that is measured in the many seconds time frame so I use the word instant with a wink. My favorite monitor point is the outer glass temperature and this reading is subject to a relatively long heating delay before the glass reflects the internal temperature. Each temperature monitor has a different delay associated with it and I have experimented with them all and find the outer glass the easiest to work with. A time constant that reflects the heating delay of the monitor point must be added after the differential equation solution to obtain excellent temperature tracking. I accomplish this function by including a very simple single pole low pass digital delay mechanism. The end result of this operation is that the input waveform is subjected to a low pass filter with a delay equal to the TC(time constant) discussed below. I think this function is pretty much self explanatory and I will leave it up to you to follow its operation by reviewing the Excel file that I have deposited in the newvortex-moderated group. If you have difficulty finding this file, email me and I will be happy to assist. This is a good stopping point for this installment. In the next one I will talk about how to manipulate the file to obtain the best curve tracing which allows excellent observation of the cell performance. Dave -----Original Message----- From: David Roberson <dlrober...@aol.com> To: dlroberson <dlrober...@aol.com> Sent: Wed, Jan 16, 2013 10:43 pm Subject: Re: [Vo]:Simulation of Celani Replication by MFMP It is a good time to add another installment to my explanation of the simulation program for the Celani replication cells. A review of the original attached post should be conducted prior to attempting to follow this latest one. I am assuming that you now have obtained values that I label a,b, and c from the Excel trend line associated with data pairs of glass outer surface temperature as the X variable and power input as Y. A typical set of values is a=.001719, b=.291356, and c=-7.52999. These were obtained from a recent calibration test run and are representative. I want to introduce 4 additional variables that you will use to complete the simulation. The first is Pin, which is self explanatory. This variable is actually inputted as the power applied at the step up. The solution that I am introducing with this series is only good for a step up in power. Another exists for a step down, but I am concentrating upon the increases in power currently. Later I can post the alternate step if anyone is particularly interested. A typical value for Pin is 101.7589 watts as a maximum. It is best to include a power that falls within the range of the calibration data used. The second new variable is Cap. This is the actual capacitance that appears within my spice simulation that matches the Excel curve quite well. The value is closely associated with the energy storage mechanism within the cell and determines how quickly the reflected temperature within the cell rises as a result of the addition of extra input energy. For a recent run this value was determined to be 267 Farads. The third variable I am introducing is named Kint. This variable is the constant of integration that is obtained when the differential equation is integrated. The value is instrumental in establishing the initial condition of the curve at t=0. The solution begins at a temperature that is associated with Kint and proceeds toward its final steady state value as time approaches infinity. A typical value for Kint is -1.63. The last variable needed to simulate the cell temperature as a function of time is named TC(time constant). I analyzed the behavior of the temperature curves at each of the various test points such as mica, well and glass out. It was apparent that the effective internal temperature of the cell was displayed at each of these points after a time delay that depended upon how long it takes to heat up the monitor point to a stable value. The behavior is exactly that same as a low pass filter with a cutoff frequency associated with TC. For this reason I have included a simple one pole filter equivalent that lines up the edges to obtain excellent accuracy. For a recent test run the value that I found for TC was 52.8 seconds. The next step I perform is to transform the original a,b, and c values to a new set that I call the prime set for convenience. I do this to allow me to reduce the errors that tend to creep up when too many variables show up in the calculation cells of Excel. The transform is quite simple in this case. The a' value is -1.0*a/Cap. The b'=-1.0*b/Cap, and the c' is obtained as follows: c'=(Pin - c) / Cap. For the program run I am using as an example the actual values determined for these transforms are a' = -6.4 E -6, b' = -.00109, and c' = .409318. Now that all the variables have been introduced and typical values listed, it is time to take the next step. Start by finding the roots to the quadratic equation formed by using the prime values listed above. I call these roots R1 and R2. I consider R2 the most interesting one and it has a positive value that equals the steady state temperature that the cell reaches after a long time has elapsed. I will allow interested persons to calculate these for themselves for a bit of practice. This is a good point to break for this installment since questions may arise that need to be answered before I proceed. Anyone wanting to duplicate my process should have calculated the values of the roots, R1 and R2 and have initial estimates for Kint as well as TC. The typical values shown are obtained from my program FC0103 (29) for my reference. Let me know if any questions arise. Dave -----Original Message----- From: David Roberson <dlrober...@aol.com> To: vortex-l <vortex-l@eskimo.com> Sent: Thu, Jan 3, 2013 5:02 pm Subject: [Vo]:Simulation of Celani Replication by MFMP Recently I have been simulating the time domain response of the Celani replication cells that are being tested by the MFMP and am getting excellent results. My purpose is to detect any excess power that may emanate from the cells as the temperature sweeps upwards due to power increases. I suspect that the time domain behavior will be dramatically different if additional power is effectively added to the drive as a result of excess power generation. My hypothesis is yet to be confirmed and I felt like it was time to reveal my process for others to share the fun and help with the large amount of data that is coming available. I hope to publish several posts as time permits that will allow other interested parties to duplicate my system and perhaps find answers to a few questions that remain. For this particular description I am using Excel, in others I have used LTSpice and the results agree to a reasonable level of confidence. I also, generated a simple numerical integration procedure which also matched the others. Three different techniques that demonstrate very similar results must be good for something. And, they fall closely to the calibration data on the MFMP site. The technique to be described is the solution to a non linear differential equation of the following form: dx/(a*x^2+b*x+c)=dt . The closed form solution to this equation is in the form of an exponential series similar to this: x(t)=k1 + k2*(e^(w*t+c1) + (e^(w*t+c1))^2 + (e^(w*t+c1))^3 +.....). This mess can be simplified to an equation of this sort: x(t)=k3 + k4*(e^(w*t+c1))/(1-e^(w*t+c1)) which is how I enter the information into my Excel chart. Notice that there are two pieces to the solution, one is a constant and the second one is the transient behavior. The constant is that actual final value that the temperature reaches if a very long time is applied to the system allowing the transient portion to approach zero. The second part fades away with time, and as a result will follow a certain path that can be carefully matched to the real world revealing any excess heating. I should mention that I have been forced to add a short lived transient to the equation solution to counter the initial edge delay which does not appear normally with the exponential expression. On some of my testing, I have just waited out the time required for this transient to pass so that I do not have to include it. The time constant is typically 30 to 40 seconds, but depends upon the cell design. It would be a good exercise for others to speculate as to what causes this delay. My current thoughts are that it is the time required for a pulse of heat added to the cell to mix within the gas and finally impact the outside glass. To replicate my file, you need to find values for the constants of the equation: P(T)=a*T^2+b*T+c. Where P(T) is power as a function of the Outside Glass Temperature(T) of the cell. These coefficients can be easily determined by analyzing a calibration run for the cell of interest. I obtain the data from the live feed of the MFMP site averaged over a 30 second window. They usually start with a step of very nearly 0 watts and the associated temperature at the outer glass wall and then step the input power upwards until they reach about 103 watts. This procedure yields several steps and thus pairs of values that can then be placed into a X-Y chart. I take my readings generally from the second to last constant input power point proceeding a power step upwards. I like to use the individual point plot for the X-Y plot so that it is clear where the trend line intercepts these for an indication of a good curve match. Open the chart modification box with the trend line options showing and select polynomial of second order. Choose to show the equation on your chart as well as the R^2 value for confirmation. I edit the trend line label so that my numbers are displayed with 6 or more decimal places. The values you desire are shown associated with the quadratic equation displayed on the chart. I call these a,b, and c which are modified by the next process that will be given on a following post. If there are questions please do not hesitate to post them as I will do my best to answer. Once you apply this technique, you will be amazed at the closeness with which the theory follows the real world results. On many tests, I find it difficult to detect an indication of the underlying transient curve that is many times greater than the noise surrounding the ideal response. Dave
