RE: [Vo]:Non Linear Model of Celani Device
Dave: That 1000 second sine wave period is ~16.7 minutes… Is it an artifact of the model, or are there any physical properties of the materials used that would account for that oscillatory period? Any insight to its cause? Does the period decrease with time? -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 2:32 PM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device OK Mark, Yes, the model does depend upon having accurate parameters obtained by calibration. The model will need to be modified if the cell is changed, but that is to be expected since it attempts to match the performance of the cell. I just began working on the EU cell and the results are pretty good so far. My first attempt was to use the calibration run on 12/7/2012 to define the quadratic values. They again were accurate to R^2=.9998 or so which is pretty good. With these a, b, c terms I used my model to predict the time domain response. The first run with with the power changing from .036 watts to 28.9 watts during the calibration run matched with an error of .5 degrees or so. I think the 0 power level gives the program a tough point to work with. Next I went from 28.8 watts to 38.6 watts for the second step of their run. Here the curve was beautiful as with the USA cell. The noise level was less than .25 volts with a sinusoidal addition again that dominated the noise. The period of the sine wave was roughly 1000 seconds. I would estimate that the sine wave was about equal to the average noise alone. I am very encouraged by these results. It will be most interesting when my simulation is applied to the systems with expected excess power. It should stand out very well against the calibration data. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 4:25 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Thanks Dave! So one sigma is ~0.25 degsC, and that’s for several thousand points, so confidence level is high… No need for any other calcs at this time; just wanted to get an idea of the level of uncertainty. Your model and the noise level are tied to the experimental setup and process; if any changes are made to the setup, your model may no longer apply… but I’m sure you know all that! Hope the ones doing the tests understand all this… -Mark From: David Roberson [mailto:dlrober...@aol.com mailto:dlrober...@aol.com? ] Sent: Tuesday, December 25, 2012 11:24 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I just let Excel run a standard deviation for all the points of the data series throughout the range of the experiment and obtained .24916 degrees C. This includes a time frame that begins at 0 seconds and continues to 9541 seconds. Each point is typically 2 to 3 seconds away from it's neighbors. The total number is 5508 data points for the standard deviation calculation. Do you wish for me to perform additional tests upon the output? Dave -Original Message- From: David Roberson dlrober...@aol.com To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:08 pm Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I can give you a hint as to how well the model matches the actual real life data. I have plotted a curve of the difference between the actual data and my model prediction. The difference looks like random noise that is more or less evenly distributed about 0 volts throughout the entire power input to temperature output transition. This includes the case I analyzed beginning at 48.2 watts and ending with 82.7 watts. I see no evidence of any curvature associated with the error between my simulation and the real data. There is a small, almost sinusoidal, signal hidden deeply within the noise that continues throughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in the vicinity of .5 degrees C while the average of the flat noise is more in line with .2 degrees C. Perhaps I should make a plot of the output and send it for you to review. It is pretty impressive to see consistent noise when the large time domain transition signal is balanced out. My mention of the possible excess power is based upon my having to include an additional 1 watt of input power for my model to achieve the perfect match. It is quite obvious that the extra power is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at 2200 hours according to my download from the MFMP replication site. I used the history points for my curve fitting and analysis. I fitted the transition between the two power levels shown above. I just took a look at the small noisy sinusoidal signal hidden within the noise and it appears to be in the ballpark of 2000
Re: [Vo]:Non Linear Model of Celani Device
Good question Mark, I put together a quick one pole digital filter with a time constant of 100 seconds to take a closer look at the waveform. Reducing the noise made it a lot easier to see and now I would revise my earlier estimate of the period. I see a relatively large negative going spike that appears to be repeated one good time while my data ends before the next. The time between these peaks is 4047 seconds. An additional positive sharp peak that seems to track the first set also is seen. The actual curve generated by my model is entirely smooth and does not demonstrate the spikes so the noise seen is hidden within the data. It is difficult to describe the shape of the remaining filtered noise except to say that it roughly appears like 1/f or 1/f^2 noise. My filter has taken out most of the high frequency noise. Would it be helpful if I were to make a jpeg of the data or filtered data and send it directly to you or others that are interested? Many might benefit from the charts as well and I have not yet placed this type of information on sites within the web for others to link. That is one area that I need to seriously work upon. For the time being, you or someone else might wish to offer assistance. I suspect that you will be amazed by the complete elimination of the transient waveform underlying the data. I can see no evidence of the transition due to approximately 40 watts of extra input power. The non linear differential equation plus one additional time constant must be a perfect model for the system. Thanks for asking about the shape of the low frequency sine like waveform as it convinced me to perform additional filtering. This addition to my model is quite helpful for its presentation. If needed, I can perform additional filtering with a much sharper cut off frequency. For the record, my data is now being filtered by a single pole low pass with a cut off of .00159 Hertz(TC=100 seconds). Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Wed, Dec 26, 2012 1:04 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave: That 1000 second sine wave period is ~16.7 minutes… Is it an artifact of the model, or are there any physical properties of the materials used that would account for that oscillatory period? Any insight to its cause? Does the period decrease with time? -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 2:32 PM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device OK Mark, Yes, the model does depend upon having accurate parameters obtained by calibration. The model will need to be modified if the cell is changed, but that is to be expected since it attempts to match the performance of the cell. I just began working on the EU cell and the results are pretty good so far. My first attempt was to use the calibration run on 12/7/2012 to define the quadratic values. They again were accurate to R^2=.9998 or so which is pretty good. With these a, b, c terms I used my model to predict the time domain response. The first run with with the power changing from .036 watts to 28.9 watts during the calibration run matched with an error of .5 degrees or so. I think the 0 power level gives the program a tough point to work with. Next I went from 28.8 watts to 38.6 watts for the second step of their run. Here the curve was beautiful as with the USA cell. The noise level was less than .25 volts with a sinusoidal addition again that dominated the noise. The period of the sine wave was roughly 1000 seconds. I would estimate that the sine wave was about equal to the average noise alone. I am very encouraged by these results. It will be most interesting when my simulation is applied to the systems with expected excess power. It should stand out very well against the calibration data. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 4:25 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Thanks Dave! So one sigma is ~0.25 degsC, and that’s for several thousand points, so confidence level is high… No need for any other calcs at this time; just wanted to get an idea of the level of uncertainty. Your model and the noise level are tied to the experimental setup and process; if any changes are made to the setup, your model may no longer apply… but I’m sure you know all that! Hope the ones doing the tests understand all this… -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 11:24 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I just let Excel run a standard deviation for all the points of the data series throughout the range of the experiment and obtained .24916 degrees C
Re: [Vo]:Non Linear Model of Celani Device
On Dec 25, 2012, at 11:15, David Roberson dlrober...@aol.com wrote: During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. Interesting discussion concerning the model you've been working on. Concerning the second-order equation, what you're describing sounds quite similar to the equation Ed Storms proposes in his Calorimetry 101 paper. I believe he is consciously ignoring radiative losses. Concerning the calculation of the error, there is the error of the fit of your curve with the MFMP data, and there is the error of the MFMP instrumentation (I assume). The error of the latter is related to the scatter in their calibration runs and is of two kinds -- stochastic and systematic. I believe that the instrumentation error could easily swamp out 1W purported XP. Concerning the 40 second constant you're adding, I wonder if this is related to the time the system requires to reach equilibrium; when you're calibrating the device, I think you need steps that last long enough for the cell to attain a new equilibrium after the change in input power. In a live cell, I suspect this same characteristic of the operation of the cell would manifest itself as a kind of momentum. Forty seconds might be too short to be this, however. Eric
Re: [Vo]:Non Linear Model of Celani Device
Eric, Originally I was expecting to have a forth order relationship due to radiation but it did not happen. I have made numerous curve fits to the data shown on the live site of the MFMP and it always fits to a nearly perfect quadratic. The typical R^2 value is .9998 with the values. I just completed another fit to the latest USA calibration run and then used my solution to the non linear differential equation along with a short time constant adjustment for the leading edge and it is virtually a perfect match to their data. I used the transition of input power from 58.6 watts to 79.9 watts. The temperature began at 127.5 degrees C and ended at 153.3 degrees C. I applied a digital filter with a time constant of 100 seconds to the error data and the end result is quite good. The worst case error is + and - .4 degrees C over the complete time range. The end noise appears random about the zero error line and has the appearance of 1/f or 1/f^2 electronic noise. I do not see any evidence of the transition waveform in the final result so the differential equation solution must be ideal. I wonder if the remaining noise is due to supply output voltage noise? Of course slow changing long term noise of this nature most likely contains effects due to ambient air currents, etc. I think that I will be capable of detecting excess power is it is compared to this same calibration cell. 1 watt stands out quite well. The time domain technique should be more sensitive to changes within the cell than just one average temperature reading. I have no idea of how accurate their power measurements are, but DC can be determined very accurately. The time ahead will be interesting. Dave -Original Message- From: Eric Walker eric.wal...@gmail.com To: vortex-l vortex-l@eskimo.com Sent: Wed, Dec 26, 2012 9:08 pm Subject: Re: [Vo]:Non Linear Model of Celani Device On Dec 25, 2012, at 11:15, David Roberson dlrober...@aol.com wrote: During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. Interesting discussion concerning the model you've been working on. Concerning the second-order equation, what you're describing sounds quite similar to the equation Ed Storms proposes in his Calorimetry 101 paper. I believe he is consciously ignoring radiative losses. Concerning the calculation of the error, there is the error of the fit of your curve with the MFMP data, and there is the error of the MFMP instrumentation (I assume). The error of the latter is related to the scatter in their calibration runs and is of two kinds -- stochastic and systematic. I believe that the instrumentation error could easily swamp out 1W purported XP. Concerning the 40 second constant you're adding, I wonder if this is related to the time the system requires to reach equilibrium; when you're calibrating the device, I think you need steps that last long enough for the cell to attain a new equilibrium after the change in input power. In a live cell, I suspect this same characteristic of the operation of the cell would manifest itself as a kind of momentum. Forty seconds might be too short to be this, however. Eric
Re: [Vo]:Non Linear Model of Celani Device
During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. This seemed strange, but now I realize that it is required to compensate for the displacement of the rising edge due to the above delay. It is necessary to add back the initial plug of energy lost when the best differential equation solution is followed. This ideal solution for the best overall data match must start at a value that is below the actual temperature of the cell at t=0 in order to accommodate the delayed behavior. The addition of this missing energy is exactly the amount required! So now I can say with confidence that there exists a delay mechanism which retards the reading of the temperature at the outer glass surface. This delay is in addition to the ideal non linear differential equation solution time domain response which is discussed below. So, another way to envision the effect is to realize that it takes 30 to 40 seconds before the addition of heat applied to the cell is registered at that test point. An exponential smoothing (filtering) factor is applied. My suspicion is that the extra pulse of heat must be distributed within the gas and then result in a temperature reading at the outer glass monitor after heating the envelop. The heating of the other structure elements may also be involved in the overall action. A careful review of the waveform hints that the test might be demonstrating an excess power of about 1 watt during the experiment that supplied the data. This is a small amount of excess power and only additional, careful analysis would enable me to be sure. At least it is in the right direction! My virtually perfect curve fit to the data tends to support this conclusion. Merry Christmas! Dave -Original Message- From: David Roberson dlrober...@aol.com To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:13 am Subject: [Vo]:Non Linear Model of Celani Device The data has been flooding in from the MFMP and I have been seeking a time domain model of the system behavior when power to the Celani replication device is modified. Most of my effort has been exerted by analyzing the rising edge of the time domain waveform when the drive power is stepped up by a significant amount. The temperature follows a certain path as it ramps up to the value required to balance the input and output power of the cell. We have been fortunate in this particular case to find that the relationship between temperature and input power is well behaved and follows a second order curve to a remarkable degree. It is not uncommon to see a curve fit with R^2=. or better in many independent test runs. I initially was expecting to see a power series that included a forth order term of significance due to the S-B radiation equation. This has not ever been dominate in any test and I still am trying to understand why this is true. For the time being I will accept this gift happily. A quick glance at the shape of the rising edge of the temperature curve suggests that it follows an exponential. I thus began my model by making that assumption and got fairly reasonable results. It was always evident that my curve fit contained holes, but a couple of degrees of error did not seem too excessive at that time. Being a perfectionist, I decided to improve the situation and to determine how well a model could match the real life test. I very soon added a second exponential to the mix and noticed that the fit improved remarkably. Also, I noticed that the second real frequency was close to the second harmonic of the first one determined by my earlier work. A light went off inside my head and I realized that this would be expected since the non linearity is mainly of second order in the relationship between variables. Now, I saw that the accuracy of my model was becoming very acceptable. There remained a short period of time at the initial power increase where the fit was not as good as I hoped. To fix this problem I added another exponential with an associated time constant of about 40 seconds. With this model, I could obtain an excellent match between my simulation and the real world data. I could have left it in this state, but it is hard to accept imperfection. To pursue the matter further I used a LTSpice model of the system. I guessed correctly in my first try with the model and was rewarded with a well behaved simulation that included the second order distortion effects. This model was used for a significant time as it matched the real world waveforms everywhere except for the initial short
RE: [Vo]:Non Linear Model of Celani Device
Dave: Can you perform some stats on the model vs reality and give us the std deviation? -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 9:15 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. This seemed strange, but now I realize that it is required to compensate for the displacement of the rising edge due to the above delay. It is necessary to add back the initial plug of energy lost when the best differential equation solution is followed. This ideal solution for the best overall data match must start at a value that is below the actual temperature of the cell at t=0 in order to accommodate the delayed behavior. The addition of this missing energy is exactly the amount required! So now I can say with confidence that there exists a delay mechanism which retards the reading of the temperature at the outer glass surface. This delay is in addition to the ideal non linear differential equation solution time domain response which is discussed below. So, another way to envision the effect is to realize that it takes 30 to 40 seconds before the addition of heat applied to the cell is registered at that test point. An exponential smoothing (filtering) factor is applied. My suspicion is that the extra pulse of heat must be distributed within the gas and then result in a temperature reading at the outer glass monitor after heating the envelop. The heating of the other structure elements may also be involved in the overall action. A careful review of the waveform hints that the test might be demonstrating an excess power of about 1 watt during the experiment that supplied the data. This is a small amount of excess power and only additional, careful analysis would enable me to be sure. At least it is in the right direction! My virtually perfect curve fit to the data tends to support this conclusion. Merry Christmas! Dave -Original Message- From: David Roberson dlrober...@aol.com To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:13 am Subject: [Vo]:Non Linear Model of Celani Device The data has been flooding in from the MFMP and I have been seeking a time domain model of the system behavior when power to the Celani replication device is modified. Most of my effort has been exerted by analyzing the rising edge of the time domain waveform when the drive power is stepped up by a significant amount. The temperature follows a certain path as it ramps up to the value required to balance the input and output power of the cell. We have been fortunate in this particular case to find that the relationship between temperature and input power is well behaved and follows a second order curve to a remarkable degree. It is not uncommon to see a curve fit with R^2=. or better in many independent test runs. I initially was expecting to see a power series that included a forth order term of significance due to the S-B radiation equation. This has not ever been dominate in any test and I still am trying to understand why this is true. For the time being I will accept this gift happily. A quick glance at the shape of the rising edge of the temperature curve suggests that it follows an exponential. I thus began my model by making that assumption and got fairly reasonable results. It was always evident that my curve fit contained holes, but a couple of degrees of error did not seem too excessive at that time. Being a perfectionist, I decided to improve the situation and to determine how well a model could match the real life test. I very soon added a second exponential to the mix and noticed that the fit improved remarkably. Also, I noticed that the second real frequency was close to the second harmonic of the first one determined by my earlier work. A light went off inside my head and I realized that this would be expected since the non linearity is mainly of second order in the relationship between variables. Now, I saw that the accuracy of my model was becoming very acceptable. There remained a short period of time at the initial power increase where the fit was not as good as I hoped. To fix this problem I added another exponential with an associated time constant of about 40 seconds. With this model, I could obtain an excellent match between my simulation and the real world data. I could have left it in this state, but it is hard to accept imperfection. To pursue the matter further I used a LTSpice model of the system. I guessed correctly in my first try
Re: [Vo]:Non Linear Model of Celani Device
Mark, I can give you a hint as to how well the model matches the actual real life data. I have plotted a curve of the difference between the actual data and my model prediction. The difference looks like random noise that is more or less evenly distributed about 0 volts throughout the entire power input to temperature output transition. This includes the case I analyzed beginning at 48.2 watts and ending with 82.7 watts. I see no evidence of any curvature associated with the error between my simulation and the real data. There is a small, almost sinusoidal, signal hidden deeply within the noise that continues throughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in the vicinity of .5 degrees C while the average of the flat noise is more in line with .2 degrees C. Perhaps I should make a plot of the output and send it for you to review. It is pretty impressive to see consistent noise when the large time domain transition signal is balanced out. My mention of the possible excess power is based upon my having to include an additional 1 watt of input power for my model to achieve the perfect match. It is quite obvious that the extra power is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at 2200 hours according to my download from the MFMP replication site. I used the history points for my curve fitting and analysis. I fitted the transition between the two power levels shown above. I just took a look at the small noisy sinusoidal signal hidden within the noise and it appears to be in the ballpark of 2000 seconds in period. Maybe this corresponds to the cycle time for the heating system. I guess I can attempt an RMS noise measurement which will be next on my list. The small sinusoidal interference will color that result a bit. I will report the results of the test when completed. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 12:18 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave: Can you perform some stats on the model vs reality and give us the std deviation? -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 9:15 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. This seemed strange, but now I realize that it is required to compensate for the displacement of the rising edge due to the above delay. It is necessary to add back the initial plug of energy lost when the best differential equation solution is followed. This ideal solution for the best overall data match must start at a value that is below the actual temperature of the cell at t=0 in order to accommodate the delayed behavior. The addition of this missing energy is exactly the amount required! So now I can say with confidence that there exists a delay mechanism which retards the reading of the temperature at the outer glass surface. This delay is in addition to the ideal non linear differential equation solution time domain response which is discussed below. So, another way to envision the effect is to realize that it takes 30 to 40 seconds before the addition of heat applied to the cell is registered at that test point. An exponential smoothing (filtering) factor is applied. My suspicion is that the extra pulse of heat must be distributed within the gas and then result in a temperature reading at the outer glass monitor after heating the envelop. The heating of the other structure elements may also be involved in the overall action. A careful review of the waveform hints that the test might be demonstrating an excess power of about 1 watt during the experiment that supplied the data. This is a small amount of excess power and only additional, careful analysis would enable me to be sure. At least it is in the right direction! My virtually perfect curve fit to the data tends to support this conclusion. Merry Christmas! Dave -Original Message- From: David Roberson dlrober...@aol.com To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:13 am Subject: [Vo]:Non Linear Model of Celani Device The data has been flooding in from the MFMP and I have been seeking a time domain model of the system behavior when power to the Celani replication device is modified. Most of my effort has been exerted by analyzing the rising edge of the time domain waveform when the drive
RE: [Vo]:Non Linear Model of Celani Device
Dave, You have made a very interesting analysis. What your model say when a +8W apparent excess heat was reported with EU cell? Can your model able to calculate the apparent excess power anytime? Not when equilibrium has been reached. For the data, did you take the US cell or EU cell? US cell is currently less interesting has the celanis wire seems to be fried. Merry Christmas, Arnaud _ From: David Roberson [mailto:dlrober...@aol.com] Sent: mardi 25 décembre 2012 20:08 To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I can give you a hint as to how well the model matches the actual real life data. I have plotted a curve of the difference between the actual data and my model prediction. The difference looks like random noise that is more or less evenly distributed about 0 volts throughout the entire power input to temperature output transition. This includes the case I analyzed beginning at 48.2 watts and ending with 82.7 watts. I see no evidence of any curvature associated with the error between my simulation and the real data. There is a small, almost sinusoidal, signal hidden deeply within the noise that continues throughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in the vicinity of .5 degrees C while the average of the flat noise is more in line with .2 degrees C. Perhaps I should make a plot of the output and send it for you to review. It is pretty impressive to see consistent noise when the large time domain transition signal is balanced out. My mention of the possible excess power is based upon my having to include an additional 1 watt of input power for my model to achieve the perfect match. It is quite obvious that the extra power is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at 2200 hours according to my download from the MFMP replication site. I used the history points for my curve fitting and analysis. I fitted the transition between the two power levels shown above. I just took a look at the small noisy sinusoidal signal hidden within the noise and it appears to be in the ballpark of 2000 seconds in period. Maybe this corresponds to the cycle time for the heating system. I guess I can attempt an RMS noise measurement which will be next on my list. The small sinusoidal interference will color that result a bit. I will report the results of the test when completed. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 12:18 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave: Can you perform some stats on the model vs reality and give us the std deviation? -Mark From: David Roberson [mailto:dlrober...@aol.com mailto:dlrober...@aol.com? ] Sent: Tuesday, December 25, 2012 9:15 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. This seemed strange, but now I realize that it is required to compensate for the displacement of the rising edge due to the above delay. It is necessary to add back the initial plug of energy lost when the best differential equation solution is followed. This ideal solution for the best overall data match must start at a value that is below the actual temperature of the cell at t=0 in order to accommodate the delayed behavior. The addition of this missing energy is exactly the amount required! So now I can say with confidence that there exists a delay mechanism which retards the reading of the temperature at the outer glass surface. This delay is in addition to the ideal non linear differential equation solution time domain response which is discussed below. So, another way to envision the effect is to realize that it takes 30 to 40 seconds before the addition of heat applied to the cell is registered at that test point. An exponential smoothing (filtering) factor is applied. My suspicion is that the extra pulse of heat must be distributed within the gas and then result in a temperature reading at the outer glass monitor after heating the envelop. The heating of the other structure elements may also be involved in the overall action. A careful review of the waveform hints that the test might be demonstrating an excess power of about 1 watt during the experiment that supplied the data. This is a small amount of excess power and only additional, careful analysis would enable me to be sure. At least it is in the right direction
Re: [Vo]:Non Linear Model of Celani Device
Mark, I just let Excel run a standard deviation for all the points of the data series throughout the range of the experiment and obtained .24916 degrees C. This includes a time frame that begins at 0 seconds and continues to 9541 seconds. Each point is typically 2 to 3 seconds away from it's neighbors. The total number is 5508 data points for the standard deviation calculation. Do you wish for me to perform additional tests upon the output? Dave -Original Message- From: David Roberson dlrober...@aol.com To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:08 pm Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I can give you a hint as to how well the model matches the actual real life data. I have plotted a curve of the difference between the actual data and my model prediction. The difference looks like random noise that is more or less evenly distributed about 0 volts throughout the entire power input to temperature output transition. This includes the case I analyzed beginning at 48.2 watts and ending with 82.7 watts. I see no evidence of any curvature associated with the error between my simulation and the real data. There is a small, almost sinusoidal, signal hidden deeply within the noise that continues throughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in the vicinity of .5 degrees C while the average of the flat noise is more in line with .2 degrees C. Perhaps I should make a plot of the output and send it for you to review. It is pretty impressive to see consistent noise when the large time domain transition signal is balanced out. My mention of the possible excess power is based upon my having to include an additional 1 watt of input power for my model to achieve the perfect match. It is quite obvious that the extra power is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at 2200 hours according to my download from the MFMP replication site. I used the history points for my curve fitting and analysis. I fitted the transition between the two power levels shown above. I just took a look at the small noisy sinusoidal signal hidden within the noise and it appears to be in the ballpark of 2000 seconds in period. Maybe this corresponds to the cycle time for the heating system. I guess I can attempt an RMS noise measurement which will be next on my list. The small sinusoidal interference will color that result a bit. I will report the results of the test when completed. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 12:18 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave: Can you perform some stats on the model vs reality and give us the std deviation? -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 9:15 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. This seemed strange, but now I realize that it is required to compensate for the displacement of the rising edge due to the above delay. It is necessary to add back the initial plug of energy lost when the best differential equation solution is followed. This ideal solution for the best overall data match must start at a value that is below the actual temperature of the cell at t=0 in order to accommodate the delayed behavior. The addition of this missing energy is exactly the amount required! So now I can say with confidence that there exists a delay mechanism which retards the reading of the temperature at the outer glass surface. This delay is in addition to the ideal non linear differential equation solution time domain response which is discussed below. So, another way to envision the effect is to realize that it takes 30 to 40 seconds before the addition of heat applied to the cell is registered at that test point. An exponential smoothing (filtering) factor is applied. My suspicion is that the extra pulse of heat must be distributed within the gas and then result in a temperature reading at the outer glass monitor after heating the envelop. The heating of the other structure elements may also be involved in the overall action. A careful review of the waveform hints that the test might be demonstrating an excess power of about 1 watt during the experiment that supplied the data. This is a small amount of excess power and only additional, careful
Re: [Vo]:Non Linear Model of Celani Device
Thanks for the compliment. I used data from the US cell since I wanted to improve the model with information that was likely to be quiet. Now that I have this tool working well, it is time to use it to our advantage. The beauty of this analysis is that it operates throughout the entire transition period as the temperature is increasing within the cell. It will work very well to demonstrate whether or not there are any special temperatures of interest that may arise as the temperature is effectively swept. I have not applied it to the EU case yet since I am not sure that a good calibration has been obtained thus far without any excess heating and due to the fact that I just perfected the model. I guess I am getting a bit slow these days. The data I used is shown in the last posting for reference. Now may be the time to begin to analyze the EU data and that will be my next endeavor. The model requires accurately calibrated values for the a, b, and c coefficients of the second order fit for power input versus temperature of the cell. This has been a near perfect second order function for all of the data thus far and I have my fingers crossed that it will continue to be true. If the cells are modified in some manner that changes this behavior drastically then a more difficult differential equation might result. I also need to have at least one curve generated by a change in input power drive such as from 10 watts steady state to 48 watts steady state. This transition information is used to calculate the effective thermal capacity of the cell. With accurate measurements of these parameters I can plot the temperature versus time behavior to a high degree of accuracy. Dave -Original Message- From: Arnaud Kodeck arnaud.kod...@lakoco.be To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:21 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave, You have made a very interestinganalysis. What your model say when a +8W apparent excess heat was reported withEU cell? Can your model able to calculate the apparent excess power anytime? Notwhen equilibrium has been reached. For the data, did youtake the UScell or EU cell? US cell is currently less interesting has the celani’s wireseems to be fried. Merry Christmas, Arnaud From:David Roberson [mailto:dlrober...@aol.com] Sent: mardi 25 décembre2012 20:08 To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Modelof Celani Device Mark, I can give you a hint as to howwell the model matches the actual real life data. I have plotted a curveof the difference between the actual data and my model prediction. Thedifference looks like random noise that is more or less evenly distributedabout 0 volts throughout the entire power input to temperature outputtransition. This includes the case I analyzed beginning at 48.2 watts andending with 82.7 watts. I see no evidence of any curvature associatedwith the error between my simulation and the real data. There is a small,almost sinusoidal, signal hidden deeply within the noise that continuesthroughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in thevicinity of .5 degrees C while the average of the flat noise is more in linewith .2 degrees C. Perhaps I should make a plot of the output and send itfor you to review. It is pretty impressive to see consistent noise whenthe large time domain transition signal is balanced out. My mention of the possible excess poweris based upon my having to include an additional 1 watt of input power for mymodel to achieve the perfect match. It is quite obvious that the extrapower is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at2200 hours according to my download from the MFMP replication site. Iused the history points for my curve fitting and analysis. I fitted thetransition between the two power levels shown above. I just took a lookat the small noisy sinusoidal signal hidden within the noise and it appears tobe in the ballpark of 2000 seconds in period. Maybe this corresponds tothe cycle time for the heating system. I guess I can attempt an RMS noisemeasurement which will be next on my list. The small sinusoidalinterference will color that result a bit. I will report the results ofthe test when completed. Dave -OriginalMessage- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 12:18 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave: Can you perform some stats on the modelvs reality and give us the std deviation? -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 20129:15 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Modelof Celani Device During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30to
RE: [Vo]:Non Linear Model of Celani Device
Im very curious to see your model with data of EU cell when 8W apparent excess was shown. You should give your model to the FMFP. Concerning the a, b and c coefficients, the borosilicate glass will have in this regard a better behaviour. The radiation loss at the 4th power of temperature will play less importance than with the quartz tube. Arnaud _ From: David Roberson [mailto:dlrober...@aol.com] Sent: mardi 25 décembre 2012 20:45 To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device Thanks for the compliment. I used data from the US cell since I wanted to improve the model with information that was likely to be quiet. Now that I have this tool working well, it is time to use it to our advantage. The beauty of this analysis is that it operates throughout the entire transition period as the temperature is increasing within the cell. It will work very well to demonstrate whether or not there are any special temperatures of interest that may arise as the temperature is effectively swept. I have not applied it to the EU case yet since I am not sure that a good calibration has been obtained thus far without any excess heating and due to the fact that I just perfected the model. I guess I am getting a bit slow these days. The data I used is shown in the last posting for reference. Now may be the time to begin to analyze the EU data and that will be my next endeavor. The model requires accurately calibrated values for the a, b, and c coefficients of the second order fit for power input versus temperature of the cell. This has been a near perfect second order function for all of the data thus far and I have my fingers crossed that it will continue to be true. If the cells are modified in some manner that changes this behavior drastically then a more difficult differential equation might result. I also need to have at least one curve generated by a change in input power drive such as from 10 watts steady state to 48 watts steady state. This transition information is used to calculate the effective thermal capacity of the cell. With accurate measurements of these parameters I can plot the temperature versus time behavior to a high degree of accuracy. Dave -Original Message- From: Arnaud Kodeck arnaud.kod...@lakoco.be To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:21 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave, You have made a very interesting analysis. What your model say when a +8W apparent excess heat was reported with EU cell? Can your model able to calculate the apparent excess power anytime? Not when equilibrium has been reached. For the data, did you take the US cell or EU cell? US cell is currently less interesting has the celanis wire seems to be fried. Merry Christmas, Arnaud _ From: David Roberson [mailto:dlrober...@aol.com mailto:dlrober...@aol.com? ] Sent: mardi 25 décembre 2012 20:08 To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I can give you a hint as to how well the model matches the actual real life data. I have plotted a curve of the difference between the actual data and my model prediction. The difference looks like random noise that is more or less evenly distributed about 0 volts throughout the entire power input to temperature output transition. This includes the case I analyzed beginning at 48.2 watts and ending with 82.7 watts. I see no evidence of any curvature associated with the error between my simulation and the real data. There is a small, almost sinusoidal, signal hidden deeply within the noise that continues throughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in the vicinity of .5 degrees C while the average of the flat noise is more in line with .2 degrees C. Perhaps I should make a plot of the output and send it for you to review. It is pretty impressive to see consistent noise when the large time domain transition signal is balanced out. My mention of the possible excess power is based upon my having to include an additional 1 watt of input power for my model to achieve the perfect match. It is quite obvious that the extra power is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at 2200 hours according to my download from the MFMP replication site. I used the history points for my curve fitting and analysis. I fitted the transition between the two power levels shown above. I just took a look at the small noisy sinusoidal signal hidden within the noise and it appears to be in the ballpark of 2000 seconds in period. Maybe this corresponds to the cycle time for the heating system. I guess I can attempt an RMS noise measurement which will be next on my list. The small sinusoidal interference will color that result a bit. I will report the results of the test when completed. Dave
Re: [Vo]:Non Linear Model of Celani Device
I just began working with the EU data. The best calibration I see so far is from 12/7/2012. Do you know of a better time period to use? I will give the model to the MFMP when I have played with it a bit longer. It will be interesting to see how the 8 watt test results behave, and that will be soon I hope. Dave -Original Message- From: Arnaud Kodeck arnaud.kod...@lakoco.be To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 3:25 pm Subject: RE: [Vo]:Non Linear Model of Celani Device I’m very curious tosee your model with data of EU cell when 8W apparent excess was shown. Youshould give your model to the FMFP. Concerning the a, b and ccoefficients, the borosilicate glass will have in this regard a better behaviour.The radiation loss at the 4th power of temperature will play lessimportance than with the quartz tube. Arnaud From:David Roberson [mailto:dlrober...@aol.com] Sent: mardi 25 décembre 2012 20:45 To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Modelof Celani Device Thanks for the compliment. I useddata from the US cell since I wanted to improve the model with information thatwas likely to be quiet. Now that I have this tool working well, it istime to use it to our advantage. The beauty of this analysis is that itoperates throughout the entire transition period as the temperature isincreasing within the cell. It will work very well to demonstrate whetheror not there are any special temperatures of interest that may arise as thetemperature is effectively swept. I have not applied it to the EU case yetsince I am not sure that a good calibration has been obtained thus far withoutany excess heating and due to the fact that I just perfected the model. Iguess I am getting a bit slow these days. The data I used is shown in the lastposting for reference. Now may be the time to begin to analyze the EUdata and that will be my next endeavor. The model requires accurately calibratedvalues for the a, b, and c coefficients of the second order fit for power inputversus temperature of the cell. This has been a near perfect second orderfunction for all of the data thus far and I have my fingers crossed that itwill continue to be true. If the cells are modified in some manner thatchanges this behavior drastically then a more difficult differential equationmight result. I also need to have at least one curve generated by achange in input power drive such as from 10 watts steady state to 48 wattssteady state. This transition information is used to calculate theeffective thermal capacity of the cell. With accurate measurements ofthese parameters I can plot the temperature versus time behavior to a highdegree of accuracy. Dave -OriginalMessage- From: Arnaud Kodeck arnaud.kod...@lakoco.be To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:21 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave, You have made a veryinteresting analysis. What your model say when a +8W apparent excess heat wasreported with EU cell? Can your model able to calculate the apparent excesspower anytime? Not when equilibrium has been reached. For the data, did youtake the UScell or EU cell? UScell is currently less interesting has the celani’s wire seems to befried. Merry Christmas, Arnaud From: David Roberson [mailto:dlrober...@aol.com] Sent: mardi 25 décembre 2012 20:08 To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Modelof Celani Device Mark, I can give you a hint as to howwell the model matches the actual real life data. I have plotted a curveof the difference between the actual data and my model prediction. Thedifference looks like random noise that is more or less evenly distributedabout 0 volts throughout the entire power input to temperature outputtransition. This includes the case I analyzed beginning at 48.2 watts andending with 82.7 watts. I see no evidence of any curvature associatedwith the error between my simulation and the real data. There is a small,almost sinusoidal, signal hidden deeply within the noise that continuesthroughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in thevicinity of .5 degrees C while the average of the flat noise is more in linewith .2 degrees C. Perhaps I should make a plot of the output and send itfor you to review. It is pretty impressive to see consistent noise whenthe large time domain transition signal is balanced out. My mention of the possible excess poweris based upon my having to include an additional 1 watt of input power for mymodel to achieve the perfect match. It is quite obvious that the extrapower is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at2200 hours according to my download from the MFMP replication site. Iused the history points for my curve fitting and analysis. I fitted thetransition between
RE: [Vo]:Non Linear Model of Celani Device
Thanks Dave! So one sigma is ~0.25 degsC, and that's for several thousand points, so confidence level is high. No need for any other calcs at this time; just wanted to get an idea of the level of uncertainty. Your model and the noise level are tied to the experimental setup and process; if any changes are made to the setup, your model may no longer apply. but I'm sure you know all that! Hope the ones doing the tests understand all this. -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 11:24 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I just let Excel run a standard deviation for all the points of the data series throughout the range of the experiment and obtained .24916 degrees C. This includes a time frame that begins at 0 seconds and continues to 9541 seconds. Each point is typically 2 to 3 seconds away from it's neighbors. The total number is 5508 data points for the standard deviation calculation. Do you wish for me to perform additional tests upon the output? Dave -Original Message- From: David Roberson dlrober...@aol.com To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:08 pm Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I can give you a hint as to how well the model matches the actual real life data. I have plotted a curve of the difference between the actual data and my model prediction. The difference looks like random noise that is more or less evenly distributed about 0 volts throughout the entire power input to temperature output transition. This includes the case I analyzed beginning at 48.2 watts and ending with 82.7 watts. I see no evidence of any curvature associated with the error between my simulation and the real data. There is a small, almost sinusoidal, signal hidden deeply within the noise that continues throughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in the vicinity of .5 degrees C while the average of the flat noise is more in line with .2 degrees C. Perhaps I should make a plot of the output and send it for you to review. It is pretty impressive to see consistent noise when the large time domain transition signal is balanced out. My mention of the possible excess power is based upon my having to include an additional 1 watt of input power for my model to achieve the perfect match. It is quite obvious that the extra power is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at 2200 hours according to my download from the MFMP replication site. I used the history points for my curve fitting and analysis. I fitted the transition between the two power levels shown above. I just took a look at the small noisy sinusoidal signal hidden within the noise and it appears to be in the ballpark of 2000 seconds in period. Maybe this corresponds to the cycle time for the heating system. I guess I can attempt an RMS noise measurement which will be next on my list. The small sinusoidal interference will color that result a bit. I will report the results of the test when completed. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 12:18 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave: Can you perform some stats on the model vs reality and give us the std deviation? -Mark From: David Roberson [mailto:dlrober...@aol.com mailto:dlrober...@aol.com? ] Sent: Tuesday, December 25, 2012 9:15 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. This seemed strange, but now I realize that it is required to compensate for the displacement of the rising edge due to the above delay. It is necessary to add back the initial plug of energy lost when the best differential equation solution is followed. This ideal solution for the best overall data match must start at a value that is below the actual temperature of the cell at t=0 in order to accommodate the delayed behavior. The addition of this missing energy is exactly the amount required! So now I can say with confidence that there exists a delay mechanism which retards the reading of the temperature at the outer glass surface. This delay is in addition to the ideal non linear differential equation solution time domain response which is discussed below. So, another way to envision the effect is to realize that it takes 30 to 40 seconds
Re: [Vo]:Non Linear Model of Celani Device
OK Mark, Yes, the model does depend upon having accurate parameters obtained by calibration. The model will need to be modified if the cell is changed, but that is to be expected since it attempts to match the performance of the cell. I just began working on the EU cell and the results are pretty good so far. My first attempt was to use the calibration run on 12/7/2012 to define the quadratic values. They again were accurate to R^2=.9998 or so which is pretty good. With these a, b, c terms I used my model to predict the time domain response. The first run with with the power changing from .036 watts to 28.9 watts during the calibration run matched with an error of .5 degrees or so. I think the 0 power level gives the program a tough point to work with. Next I went from 28.8 watts to 38.6 watts for the second step of their run. Here the curve was beautiful as with the USA cell. The noise level was less than .25 volts with a sinusoidal addition again that dominated the noise. The period of the sine wave was roughly 1000 seconds. I would estimate that the sine wave was about equal to the average noise alone. I am very encouraged by these results. It will be most interesting when my simulation is applied to the systems with expected excess power. It should stand out very well against the calibration data. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 4:25 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Thanks Dave! So one sigma is ~0.25 degsC, and that’s for several thousand points, so confidence level is high… No need for any other calcs at this time; just wanted to get an idea of the level of uncertainty. Your model and the noise level are tied to the experimental setup and process; if any changes are made to the setup, your model may no longer apply… but I’m sure you know all that! Hope the ones doing the tests understand all this… -Mark From: David Roberson [mailto:dlrober...@aol.com] Sent: Tuesday, December 25, 2012 11:24 AM To: vortex-l@eskimo.com Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I just let Excel run a standard deviation for all the points of the data series throughout the range of the experiment and obtained .24916 degrees C. This includes a time frame that begins at 0 seconds and continues to 9541 seconds. Each point is typically 2 to 3 seconds away from it's neighbors. The total number is 5508 data points for the standard deviation calculation. Do you wish for me to perform additional tests upon the output? Dave -Original Message- From: David Roberson dlrober...@aol.com To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 2:08 pm Subject: Re: [Vo]:Non Linear Model of Celani Device Mark, I can give you a hint as to how well the model matches the actual real life data. I have plotted a curve of the difference between the actual data and my model prediction. The difference looks like random noise that is more or less evenly distributed about 0 volts throughout the entire power input to temperature output transition. This includes the case I analyzed beginning at 48.2 watts and ending with 82.7 watts. I see no evidence of any curvature associated with the error between my simulation and the real data. There is a small, almost sinusoidal, signal hidden deeply within the noise that continues throughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in the vicinity of .5 degrees C while the average of the flat noise is more in line with .2 degrees C. Perhaps I should make a plot of the output and send it for you to review. It is pretty impressive to see consistent noise when the large time domain transition signal is balanced out. My mention of the possible excess power is based upon my having to include an additional 1 watt of input power for my model to achieve the perfect match. It is quite obvious that the extra power is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at 2200 hours according to my download from the MFMP replication site. I used the history points for my curve fitting and analysis. I fitted the transition between the two power levels shown above. I just took a look at the small noisy sinusoidal signal hidden within the noise and it appears to be in the ballpark of 2000 seconds in period. Maybe this corresponds to the cycle time for the heating system. I guess I can attempt an RMS noise measurement which will be next on my list. The small sinusoidal interference will color that result a bit. I will report the results of the test when completed. Dave -Original Message- From: MarkI-ZeroPoint zeropo...@charter.net To: vortex-l vortex-l@eskimo.com Sent: Tue, Dec 25, 2012 12:18 pm Subject: RE: [Vo]:Non Linear Model of Celani Device
[Vo]:Non Linear Model of Celani Device
The data has been flooding in from the MFMP and I have been seeking a time domain model of the system behavior when power to the Celani replication device is modified. Most of my effort has been exerted by analyzing the rising edge of the time domain waveform when the drive power is stepped up by a significant amount. The temperature follows a certain path as it ramps up to the value required to balance the input and output power of the cell. We have been fortunate in this particular case to find that the relationship between temperature and input power is well behaved and follows a second order curve to a remarkable degree. It is not uncommon to see a curve fit with R^2=. or better in many independent test runs. I initially was expecting to see a power series that included a forth order term of significance due to the S-B radiation equation. This has not ever been dominate in any test and I still am trying to understand why this is true. For the time being I will accept this gift happily. A quick glance at the shape of the rising edge of the temperature curve suggests that it follows an exponential. I thus began my model by making that assumption and got fairly reasonable results. It was always evident that my curve fit contained holes, but a couple of degrees of error did not seem too excessive at that time. Being a perfectionist, I decided to improve the situation and to determine how well a model could match the real life test. I very soon added a second exponential to the mix and noticed that the fit improved remarkably. Also, I noticed that the second real frequency was close to the second harmonic of the first one determined by my earlier work. A light went off inside my head and I realized that this would be expected since the non linearity is mainly of second order in the relationship between variables. Now, I saw that the accuracy of my model was becoming very acceptable. There remained a short period of time at the initial power increase where the fit was not as good as I hoped. To fix this problem I added another exponential with an associated time constant of about 40 seconds. With this model, I could obtain an excellent match between my simulation and the real world data. I could have left it in this state, but it is hard to accept imperfection. To pursue the matter further I used a LTSpice model of the system. I guessed correctly in my first try with the model and was rewarded with a well behaved simulation that included the second order distortion effects. This model was used for a significant time as it matched the real world waveforms everywhere except for the initial short period that required another time constant to fix. Looking at my spice model gave me an interesting idea. I used a capacitor to represent storage of the incoming energy and the node it is connected to reads expected time domain temperature for the outside glass sensor. In parallel with the storage capacitor is a pair of current sources, one representing power applied to the cell, the other power being taken away by the various paths. The draining current source appears as a parallel conductance who's value depends upon the voltage at the temperature node. I, of course, was seeking verification of the time constant associated with the exponential rise waveforms and attempted to use the effective conductance value in parallel with my storage capacitor for a quick check. This lead to the non linear differential equation definition that works so well. It occurred to me that my model could be expressed in the form of a non linear differential equation with a little manipulation of the shape. Basically you have a parallel capacitor being driven by a current source that is paralleled by a non linear conductance. The non linear conductance is neatly defined by the second order equation derived from the calibration runs for the Celani cell. Now, all I had to do was to solve the non linear differential equation that I constructed and insert the initial conditions to define the temperature and power over any time frame. My first thought was yipes! I consulted our favorite source wikipedia to find the solution to unusual integrals. The one I needed to solve was in the form of: Integral dx/(a*x^2+b*x+c) with initial condition of the temperature of the steady state value just prior to the application of an increase in power. I transformed the time scale so that time = 0 was with this application of extra power. It turns out that there is an exact solution to such an equation which you can look up at your convenience to save time and space here. I had to perform some interesting series adjustments to get the curve within the desired temperature band, and I was a bit rusty at first. Finally, a perfect curve was being generated that matched the time domain data extremely well except for that nagging time region at the very
