Equation Solution High Performance by Design 




A Straightforward Verification of JUNE5
[Posted by JennChing Luo on Mar. 17, 2009 ]
Some experts in the field of nondestructive evaluation asked me a common question how I could prove the method I derived for
JUNE5,
which is a tool to evaluate insitu stiffness and mass. That is a good question. I never submitted the method for a peer review. When I worked at universities, I published my works in journals which went through a process of 'peer review'. JUNE5 was developed after I left academic work, and I never published the method. A verification is always possible. Here suggests a reliable and straightforward method to verify JUNE5.
BACKGROUND Two terms, insitu stiffness and insitu mass, are mentioned previously. Some readers who do not major in structural mechanics may have no idea about in situ stiffness and mass. In situ stiffness and insitu mass are two properties which are crucial to a determination of structural condition, health, and response to potential impact, and to determine whether a structure is safe for services. In situ stiffness and mass are two important properties, and we must have them for a determination of structural strength. For purpose of discussion, here uses the word 'parameters' for insitu stiffness and mass. A question up to this point is whether the technology, before JUNE5, allowed us to evaluate those two parameters. The answer is NO. Some readers may wonder if those two parameters cannot be evaluated, how could we design a structure? The fact is that design of a structure never considered those parameters. What was considered in design process was theoretical expression. A problem is that theoretical value is not in situ value. In a design process, we never evaluated those two parameters. The parameters are assumed in design. After a structure has been well constructed, the structure definitely has values for those two parameters. It could be realized that structural strength should be determined by actual parameters, not by theoretical expression. The next question for us to consider is if technology allowed us to evaluate actual parameters in the past. The answer is NO. Some readers may further wonder if technology did not allow us to evaluate actual parameters, how could we make sure a structure was safe for services? A surprising answer is by 'visible inspection'. A friend of mine, a structural engineer, told me he was assigned to inspect a steel bridge. He was hanged in the air, and used a hammer to find out deteriorated spots. That is a highly 'unpleasant' and dangerous assignment. 'Visible inspection' completely replies on inspector's opinion. Fear also may make an inspection carelessly, especially hidden damage is invisible. Every rational person must reject visible inspection. Unfortunately, we had no other choice in the past. Due to lack of technology to evaluate actual parameters, there were tragic accidents. For an example, according to Wikipedia, on 25 May 2002, China Airlines Flight 611, a Boeing 747, broke into pieces in midair and crashed, killing all aboard. The final investigation report, which China Airlines disputed, found that the accident was the result of structural failure. The report found that on 7 February 1980, the accident aircraft suffered damage from a tailstrike accident, and the repair doubler did not extend beyond the entire damaged area enough to restore the overall structural strength. Consequently, after repeated cycles of depressurization and pressurization during flight, the weakened hull gradually started to crack and finally broke open in midflight on 25 May 2002. This is an example to show visible inspection is insufficient to evaluate structural strength. We cannot rely on visible inspection. The repair doubler could be visibly seen, but visible inspection cannot determine whether the damage had been repaired to a necessary strength. JUNE5 introduces a new technology to evaluate in situ stiffness and mass, by which a structural strength can be analyzed. Some people raise a reasonable doubt. A TECHNOLOGY WE NEED Some experts expressed their interest in JUNE5, and asked for a verification of JUNE5. Many governmental grant agencies, for example, National Science Foundation, Department of Defense, DARPA, NASA, and others also had shown great interests in researches into nondestructive evaluation, and had awarded many grants to universities and institutes. Before I started JUNE5, I also submitted a few proposals for small business innovation research. All my proposals were denied. Many researches, sponsored by grant agencies, were published. To the best of my knowledge, no technology, other than JUNE5, was published to evaluate in situ stiffness and mass. Most publications, sponsored by grant agencies, focused on locating damage, based on observation criteria. Locating damage is insufficient to monitor structural strength. For example, even if a damage can be located and after a repair, the structural strength remains undetermined. We need to evaluate in situ stiffness and mass to analyze whether a repair has restored its design strength. Evaluation of structural strength is not limited to damaged structures. Strength of undamaged structures also needs to be monitored to determine their service span. By in situ stiffness and mass, we can determine the strength of a new structure; we could determine the strength of a, for example, 10yearold structure. In situ stiffness and mass are two important parameters that allow us to determine structural strength. Evaluation of in situ stiffness and mass is a big challenge. We need to apply indirect evaluation, which is similar to indirectly measure earth mass. It is impossible for us to build a scale to measure earth mass. Generally, it is impossible for us to directly evaluate in situ stiffness and mass, either. The method I derived writes in situ stiffness and mass in terms of partial ordinates of mode shapes with cyclic frequencies of the first few modes. The derivation could prove it converges. We can have a more accurate result if more ordinates and modes are applied to an evaluation. I never published the method. The derivation also may lead to an innovative method to condense algebraic eigenvalue equation. As mentioned before, all my proposals submitted for small business innovation research for this research were denied. It is reasonable for people to doubt for no proof. The following suggests a straightforward proof. A STRAIGHTFORWARD VERIFICATION Since the method is never published, here suggests a straightforward verification, direct test. JUNE5 applies partial ordinates with cyclic frequencies of the first few modes to evaluate in situ stiffness and mass. For example, we have 4 sensors to monitor vibration, and have the following 4 ordinates of the first two modes: / \  x_{11} x_{12}   x_{21} x_{22}   x_{31} x_{32}   x_{41} x_{42}  \ / We start at applying the above 4 ordinates to evaluate in situ stiffness and mass. Then, we apply the in situ stiffness and mass to motion equation, and get the solution to compare with testing result. Some people may argue those 4 ordinates are applied in the process of evaluation of in situ stiffness and mass, already known in the evaluation process, and it may be a cheat, and like to see a verification against an ordinate that is not applied in the evaluation process. We can make such verification, too. For example, we can apply 3 ordinates to evaluate in situ stiffness and mass and keep one ordinate for verification. For example, we apply the followiong 3 ordinates for evaluation of in situ stiffness and mass: / \  x_{11} x_{12}   x_{21} x_{22}   x_{31} x_{32}  \ / After evaluating in situ stiffness and mass by three ordinates, we apply in situ stiffness and mass into motion equation and solve the first two modes. Then, extract the 4 ordinates where sensors apply, i.e., corresponding to x_{11}, x_{21}, x_{31}, and x_{41}, from the first mode as: / \  y_{11}   y_{21}   y_{31}   y_{41}  \ / / \ / \  x_{11}   y_{11}   x_{21}  = α y_{21}   x_{31}   y_{31}  \ / \ / Direct testing is a straightforward method to verify JUNE5. Mathematical derivation has shown approximation converges with more ordinates and more modes. 
