**7. Nonliving material**

#### **7.1 Introduction**

*Noise and Vibration Control - From Theory to Practice*

ogy would never change forever.

we calculate from heartbeat data.

system inherently has.

**5.11 Physiological interpretation**

box-size 270 beat (**Figure 10B**).

**6. Human general population**

Airlangga, Surabaya, Indonesia).

**6.2 SI: reproducibility**

system is alright or not.

**6.1 Ethics**

overlook the details. Both are around 1.

Carlson (1904 Heart physiology on model animals), for example, basics of physiol-

and then one can say, "my computed SI is 1.10" and the other can say, "mine is 0.93." This kind of "contradiction" can happen. But it is NOT a big deal. We need to

If two persons have their own mDFA program, then they analyze the same data,

Regarding mDFA computation, please see the following sections that show what

EKG signal is generated by the cardiac system. Elements in the system are linked to each other. The system cannot work properly without feedback connections. If one can find a scaling-line in the graph (**Figure 10B**), the heart system is working properly. If a line is bending or winding, something is wrong in the body system. We guaranty so. And if a subject is healthy, mDFA tells you that the SI-value is around 1 (1.0). As far as we know, this scaling property of the heart system was first documented in 1982 [8] and then in 1990s [9]. They proposed this nice metric theory. They used a well-known mathematical idea. We must say we moved it forward. But mDFA is based on different concepts—this is the novelty of this research—than Peng's concept as shown below. We just use the scaling property that the cardiac

After finding the slope, linear fitting is necessary to determine SIs. We draw a regression line from box-size 30-beat to 270-beat as the best range for interpreting physiological meaning of heartbeat data [1]. In our study for more than 10 years, SI is "always" obtained from the regression line ranging from box-size 30-beat to

A 30-beat time length corresponds to about 30 s. A 270-beat time length is approximately 3–5 min. We feel sure that life prefers "3–5 min" period length: boxing round fighting time, for 3 min; hit song one musical performance, for 3 min; instant noodles cooking time, for 3 min; and a pain killer medication, coming on 3 min after taking it. We found that it seems convenient and correct that mDFA draws a line within a box-size range [30; 270] (**Figure 10C**) to check if the body

We try to record EKGs of general population including people in the classroom, in the exhibition hall, company-employees, university-employees, and people at a scientific conference venue [1]. Every experimental subject was treated as per the ethical control regulations of universities (Tokyo Metropolitan University; Tokyo Women's Medical University; Universitas Advent Indonesia, Bandung; Universitas

All our data are collected by the author [1, 5, 6]: invertebrate heart study since the 1980s, human data since approximately 2000, and materials data since 2010. The mDFA program was made by a former master student Tanaka [7] in about

**44**

2004.

We learned that mDFA detects abnormality of the heart system. Especially, we learned that a system failure increases SI up from the basic value 1.0. The failure of the heart is generally myocardial cell damage. Myocardial cells are the elementary structure of the system. Analogically, it is like a material that is made by granulated elements [13]. We expected that mDFA might contribute to nonliving system because mDFA works well in the heart.

In **Figure 3**, when a crab heart's cells were damaged by an electrode, the damage caused a significant shift of SI (toward SI = 1.5) (**Figure 3**). In human heart cases, a person who had a surgery due to ventricular septal defect, the cardiac surgery might be a major cause that pushed SI up from normal SI [1] (see a large SI, 1.41, in Section 6.2).

Materials have different properties, meaning each has its own quirks when processing [13] like the hearts.

#### **7.2 Abnormal vibration**

In nonliving material experiments, we use a piezoelectric sensor for vibration detection. It is a mechanical monitoring device made for a cardiac pulse sensor (ADInstruments, Austuraria). The sampling rate is 1 kHz in our heart experiments. The heart beats at about 1 Hz in rate. In turn, a motor rotates ~3000 times per min.

It is 50 Hz oscillation. We set the sampling rate (ADIinstruments) at 20–40 kHz in non-living material experiments. After recording vibration signal, we capture peaks and conduct mDFA as usual.

We use consecutive 2000 peaks for the analysis. We obtained vibration data lasting for about 40–60 s. The methods for both living and nonliving vibration are fundamentally the same.

#### **7.3 Electric motor**

A motor has a design that will safely operate for a long time. We realized that a running motor did not break easily [14]. We therefore covered the motor by glass wool to enhance overheat (**Figure 12**).

We monitor vibration wave travelling through the fixed base by a piezoelectric device. Vibration was analyzed by mDFA, like the heartbeat analysis. **Figure 13** shows results, which demonstrate that abnormality is captured by mDFA. We used a box-size range [30; 270] as in the heartbeat analysis (**Figure 13A**). SI is around 0 when running without overheating (see the periods designated as P–U, **Figure 13**). **Figure 14** shows an example of mDFA.

A sound "bang" occurred at the time of the end of U, and smoking started. It is hazardous. We stopped running the motor at about 10 min (**Figure 13C**). After the bang sound, one can see that SI significantly increases. The motor still ran till 10 min at the same speed although overheated. In **Figure 13C**, one can see that amplitude of signal significantly decreases. We estimate decreased stiffness and durability. It might be plastic's inherent weakness. We later opened the motor. Overheat caused softening of plastic parts inside the motor, especially plastic materials surrounding the brush. Softened plastics may absorb vibration energy more than hard-cold one. **Figure 13B** demonstrates wave patterns. U is much noisier than Q although running speed does not change. It is an induction motor (200 V, 50 Hz).

We found that a box-size range [30; 270] seems to work properly as in the heart. However, the box-size range [130; 270], which is a much narrower range, seems to contribute greatly to capture "warning sign" about "failing" motor (see # in **Figure 13A**). The plotting "130–270" indicates that the "time-window size [130; 270]" detects malfunctioning earlier than other "window sizes" (**Figure 13A**). Moreover, the SI value (see the plotting of "window-size 130–270") increases rapidly in number earlier than the "bang" sounds (**Figure 13A**). This is beyond doubt. But we must say that details are not known for explicit interpretation.

#### **Figure 12.**

*Schematic image of electric motor experiment. A hand-dryer motor (in this study 100 and 200 V tested) is set on a base. A piezoelectric device monitors vibration. The sensor is connected to a logger (ADInstrument). It is the same analysis method as the EKG study, except for a higher sampling rate (20 or 40 kHz).*

**47**

**7.4 Aluminum bar**

*The surge of large increase of SI occurs after Q.*

**Figure 13.**

(TU in **Figure 16**).

(**Figure 17**). This is not like motor (**Figure 13**).

Section 6.2). It is hidden threat. It is a high-risk state.

We test material's toughness or the fracture toughness by changing stress intensity. **Figure 15** shows a diagrammatic image of fracture testing. We set a cantilever. A bar was tightly set on the fixed base (see W, in **Figure 15**). Vibration was applied by a speaker (see S, in **Figure 15**). Vibratory wave was monitored by a piezo device. We apply downward pressure to one end of the bar (see caption of **Figure 15**). **Figure 16** shows the summary of results. There is no load during the time period P. After P, an increase of a load is started. The bar distorts reversibly (Q, R, S in **Figure 16**). At time T, a catastrophic event, an irreversible fracture occurred

*A 200 V motor, overheating experiment. (A) mDFA results. (B) Example waves and peak-identifications. (C) Time zero, run motor. The time period P, heating up is insignificant. Q, Amplitude of signal decrease. Between U and V, a bang sound. Then smoking is started and gradually become worse, then the room was filled with smoke. Motor was stopped before igniting (see Off). It is perhaps fair to say that the time period lengths of R, S, T, and U are not identical. One thus can ignore R, S, T, and U, which do not interfere interpretation of data.* 

**Figure 16C** shows that, at normal state, SI is near 0.5 instead of near zero

In summary, mDFA can monitor shear stress. Q-R-S periods are a period of reversible deflection. Among them, R-S periods are special. It is at a risky time: an elastic state shifts suddenly into an irreversible condition, which is catastrophe.

Before the fracture event, **Figure 16C** shows unique results: SI attains a very high level, 1.2–1.4. This high value of SIs reminds us of ischemic heart disease's SI [1] (see

*mDFA Detects Abnormality: From Heartbeat to Material Vibration*

*DOI: http://dx.doi.org/10.5772/intechopen.85798*

*mDFA Detects Abnormality: From Heartbeat to Material Vibration DOI: http://dx.doi.org/10.5772/intechopen.85798*

#### **Figure 13.**

*Noise and Vibration Control - From Theory to Practice*

and conduct mDFA as usual.

wool to enhance overheat (**Figure 12**).

**Figure 14** shows an example of mDFA.

that details are not known for explicit interpretation.

fundamentally the same.

**7.3 Electric motor**

(200 V, 50 Hz).

It is 50 Hz oscillation. We set the sampling rate (ADIinstruments) at 20–40 kHz in non-living material experiments. After recording vibration signal, we capture peaks

We use consecutive 2000 peaks for the analysis. We obtained vibration data lasting for about 40–60 s. The methods for both living and nonliving vibration are

A motor has a design that will safely operate for a long time. We realized that a running motor did not break easily [14]. We therefore covered the motor by glass

We monitor vibration wave travelling through the fixed base by a piezoelectric device. Vibration was analyzed by mDFA, like the heartbeat analysis. **Figure 13** shows results, which demonstrate that abnormality is captured by mDFA. We used a box-size range [30; 270] as in the heartbeat analysis (**Figure 13A**). SI is around 0 when running without overheating (see the periods designated as P–U, **Figure 13**).

A sound "bang" occurred at the time of the end of U, and smoking started. It is hazardous. We stopped running the motor at about 10 min (**Figure 13C**). After the bang sound, one can see that SI significantly increases. The motor still ran till 10 min at the same speed although overheated. In **Figure 13C**, one can see that amplitude of signal significantly decreases. We estimate decreased stiffness and durability. It might be plastic's inherent weakness. We later opened the motor. Overheat caused softening of plastic parts inside the motor, especially plastic materials surrounding the brush. Softened plastics may absorb vibration energy more than hard-cold one. **Figure 13B** demonstrates wave patterns. U is much noisier than Q although running speed does not change. It is an induction motor

We found that a box-size range [30; 270] seems to work properly as in the heart. However, the box-size range [130; 270], which is a much narrower range, seems to contribute greatly to capture "warning sign" about "failing" motor (see # in **Figure 13A**). The plotting "130–270" indicates that the "time-window size [130; 270]" detects malfunctioning earlier than other "window sizes" (**Figure 13A**). Moreover, the SI value (see the plotting of "window-size 130–270") increases rapidly in number earlier than the "bang" sounds (**Figure 13A**). This is beyond doubt. But we must say

*Schematic image of electric motor experiment. A hand-dryer motor (in this study 100 and 200 V tested) is set on a base. A piezoelectric device monitors vibration. The sensor is connected to a logger (ADInstrument). It is* 

*the same analysis method as the EKG study, except for a higher sampling rate (20 or 40 kHz).*

**46**

**Figure 12.**

*A 200 V motor, overheating experiment. (A) mDFA results. (B) Example waves and peak-identifications. (C) Time zero, run motor. The time period P, heating up is insignificant. Q, Amplitude of signal decrease. Between U and V, a bang sound. Then smoking is started and gradually become worse, then the room was filled with smoke. Motor was stopped before igniting (see Off). It is perhaps fair to say that the time period lengths of R, S, T, and U are not identical. One thus can ignore R, S, T, and U, which do not interfere interpretation of data. The surge of large increase of SI occurs after Q.*

#### **7.4 Aluminum bar**

We test material's toughness or the fracture toughness by changing stress intensity. **Figure 15** shows a diagrammatic image of fracture testing. We set a cantilever. A bar was tightly set on the fixed base (see W, in **Figure 15**). Vibration was applied by a speaker (see S, in **Figure 15**). Vibratory wave was monitored by a piezo device. We apply downward pressure to one end of the bar (see caption of **Figure 15**).

**Figure 16** shows the summary of results. There is no load during the time period P. After P, an increase of a load is started. The bar distorts reversibly (Q, R, S in **Figure 16**). At time T, a catastrophic event, an irreversible fracture occurred (TU in **Figure 16**).

**Figure 16C** shows that, at normal state, SI is near 0.5 instead of near zero (**Figure 17**). This is not like motor (**Figure 13**).

Before the fracture event, **Figure 16C** shows unique results: SI attains a very high level, 1.2–1.4. This high value of SIs reminds us of ischemic heart disease's SI [1] (see Section 6.2). It is hidden threat. It is a high-risk state.

In summary, mDFA can monitor shear stress. Q-R-S periods are a period of reversible deflection. Among them, R-S periods are special. It is at a risky time: an elastic state shifts suddenly into an irreversible condition, which is catastrophe.

#### **Figure 14.**

*An example mDFA. Running motor. (A) An interval time series. (B) mDFA graph, log-log plotting and fitting lines. (C) mDFA results. Note that slopes are vertical, meaning a normal healthy motor has an SI around 0. (Supplement note: if the testing motor is set on unstable fixed base, such as the automobile engine in the car, giving rise to a resonance with the surroundings, then SI becomes approximately 0.5, like stochastic noise. Undescribed in this article).*

#### **Figure 15.**

*Schematic image of cantilever set-up. A bar (black bar) set on a base by a weight (W). One end receives downward force accelerating at a constant speed (an arrow). A speaker (S) generates vibration. Fluctuation signal passes through the material bar and reaches to a piezoelectric sensor (P), which is connected to PowerLab 4/20 (ADInstrument, Australia). The recording method is the same as that of EKG-study as aforementioned, except for a higher sampling rate (20 or 40 kHz). Inset: PowerLab's recorded wave profile, without load.*

For the safety, at the level where SI is about 0.6, inspectors are recommended to do their job for checking abnormality of materials, bridges, buildings, etc. However, it is just a biologist idea.

**49**

the idea.

**Figure 17.**

**Figure 16.**

*rate approximately 5 L per min.*

**7.5 Earthquake**

We consider that earthquake is fracture of rock structure underground, meaning fracture of materials. We expected that mDFA might help analyze these data. Ground vibration data are available from government institutions. We tested

*An example mDFA. Aluminum bar. No load. See* **Figure 14** *for comparison to motor tests.*

*mDFA results of cantilever experiment. (A) Vibration recording. (B) Diagrammatic representation of deflecting bar by a load. (C) SI value change over time. (D) Example waveforms. Material: aluminum L-shaped angle bar, cross section 3 mm thickness and 20 mm side. Load: tap water, flowing into a bucket at a* 

*mDFA Detects Abnormality: From Heartbeat to Material Vibration*

*DOI: http://dx.doi.org/10.5772/intechopen.85798*

*mDFA Detects Abnormality: From Heartbeat to Material Vibration DOI: http://dx.doi.org/10.5772/intechopen.85798*

**Figure 16.**

*Noise and Vibration Control - From Theory to Practice*

**48**

**Figure 15.**

**Figure 14.**

is just a biologist idea.

For the safety, at the level where SI is about 0.6, inspectors are recommended to do their job for checking abnormality of materials, bridges, buildings, etc. However, it

*Schematic image of cantilever set-up. A bar (black bar) set on a base by a weight (W). One end receives downward force accelerating at a constant speed (an arrow). A speaker (S) generates vibration. Fluctuation signal passes through the material bar and reaches to a piezoelectric sensor (P), which is connected to PowerLab 4/20 (ADInstrument, Australia). The recording method is the same as that of EKG-study as aforementioned, except for a higher sampling rate (20 or 40 kHz). Inset: PowerLab's recorded wave profile, without load.*

*An example mDFA. Running motor. (A) An interval time series. (B) mDFA graph, log-log plotting and fitting lines. (C) mDFA results. Note that slopes are vertical, meaning a normal healthy motor has an SI around 0. (Supplement note: if the testing motor is set on unstable fixed base, such as the automobile engine in the car, giving rise to a resonance with the surroundings, then SI becomes approximately 0.5, like stochastic noise. Undescribed in this article).*

*mDFA results of cantilever experiment. (A) Vibration recording. (B) Diagrammatic representation of deflecting bar by a load. (C) SI value change over time. (D) Example waveforms. Material: aluminum L-shaped angle bar, cross section 3 mm thickness and 20 mm side. Load: tap water, flowing into a bucket at a rate approximately 5 L per min.*

**Figure 17.**

*An example mDFA. Aluminum bar. No load. See* **Figure 14** *for comparison to motor tests.*

#### **7.5 Earthquake**

We consider that earthquake is fracture of rock structure underground, meaning fracture of materials. We expected that mDFA might help analyze these data. Ground vibration data are available from government institutions. We tested the idea.

**Figure 18** shows a gigantic earthquake vibration, recorded by a seismometer at Narita in Japan, approximately 500 km away from the seismic center. The date was 11 March, 2012, afternoon.

We obtained raw seismic data (**Figure 18**) from the High Sensitivity Seismograph Network Japan. Two arrows in **Figure 18** show the time of the big event. A flat line before the big event is NOT a true straight line (see A1 in **Figure 18**). We magnified y-axis scale. The conversion discloses hidden small vibrations (A2 and A3, **Figure 18**).

Linear y-axis is inconvenient for peak detection, because some are extremely large. We converted y-axis. We plotted it in a logarithmic scale. B2 shows the square of B1 (**Figure 18B2**). Then, we make it upside down (from **Figure 18B2, B3**).

After this pretreatment, we captured peaks by a lab made program (**Figure 18C**). We use the same program for R-R peak detection in the heartbeat study. The C1-trace shows a portion of C2-trace in enlarged time scale. The C3-trace shows an example of peak-to-peak interval time series.

**Figure 19** shows mDFA results. The observation period is from 3 to 29 March, 2012. The scaling exponent on 4 March was around 0.5 (SI = ~0.5) (**Figure 19B**). This means the vibration is stochastic movement. Then, SI grows up and attains a "risky" level about of 1.0. Since we are NOT specialists of seismology, we are afraid to say that it is hidden threat or high-risk state. However, in terms of chaos dynamic theory, 1.0 means the system's behavior is dynamic. It is like the heart system. It is never stable.

We know that it is too hasty to mention: this mDFA result is very similar to that of aluminum bar fracture experiment shown in **Figure 16**. In the aluminum bar fracture, SI grows up during the elasticity period, that is, reversible deflection.

#### **Figure 18.**

*Earthquake data and pretreatment for mDFA. A, Hidden vibration being exposed to view, a raw earthquake data (A1), an enlargement of Y-axis (A2), further enlargement of Y-axis (A3). B, An explanation of pretreatment procedures. A raw earthquake data (B1), logarithmic output of the square of B1, an inverse of B2 (B3). C, An example explanation of peak detection, with a faster chart speed (C1) and with a slower time (C2), accomplished peak-to-peak interval time series (C3).*

**51**

*mDFA Detects Abnormality: From Heartbeat to Material Vibration*

After the fracture event, aluminum's SI returns to a normal SI-value (around 0.5).

*mDFA results. A plotting (marked -o-) represents averaged SI-value of all box-size ranges.*

*mDFA results. Data: Narita seismometer. (A) Seismic intensities reported by Japan Meteorological Agency. The marks (X) indicate individual earthquakes. Five or six noticeable tremors before the big event are seen. (B)* 

This earthquake investigation using mDFA has just begun. We are not professionals, but **Figure 19B** results are remarkable. We hope that seismologists and

mDFA computation is simple. It is high school level mathematics: first, constructing peak-to-peak interval time series [x]; second, calculating an average value xave using 2000 data; third, computing Σ (x – xave); fourth, cutting the time series into box; fifth, drawing a fitting biquadratic line in each box; sixth, finding the first data (Ent) and the last data (Exit) in each box; seventh, calculating the difference

"variance" (statistics of root-mean-square); ninth, changing the size of box one by one, and repeating the statistics cyclically; tenth, making a log-log plotting graph that is box-size versus variance; eleventh, drawing a linear regression line; and

A 2000 "interval" data are fundamental. This length of data is not always rigid. A 2200-interval, for example, produces similar results to that of 2000-interval.

We hope that many people can make their own mDFA program. The basics are averaging, root-mean-square computation, and fitting. It has never been proposed before. In the present study, we extended mDFA to nonlife system. We then provide the comprehensive results by analyzing various real-world data, which include oscillation/vibration generated from materials. All our results are versatile; it could be applicable to the heart, a motor, materials, and possibly earthquake motion.

/2000 then obtaining

*DOI: http://dx.doi.org/10.5772/intechopen.85798*

**Figure 19B** shows similar trait in **Figure 16**.

**8. Conclusions**

**Figure 19.**

engineers might possibly have an interest in mDFA.

(Exit−Ent) in each box; eighth, calculatingΣ (Exit − Ent)<sup>2</sup>

twelfth, measuring slope of the line. At the end, the slop denotes SI.

*mDFA Detects Abnormality: From Heartbeat to Material Vibration DOI: http://dx.doi.org/10.5772/intechopen.85798*

**Figure 19.**

*Noise and Vibration Control - From Theory to Practice*

11 March, 2012, afternoon.

vibrations (A2 and A3, **Figure 18**).

peak-to-peak interval time series.

**Figure 18** shows a gigantic earthquake vibration, recorded by a seismometer at Narita in Japan, approximately 500 km away from the seismic center. The date was

Linear y-axis is inconvenient for peak detection, because some are extremely large. We converted y-axis. We plotted it in a logarithmic scale. B2 shows the square of B1 (**Figure 18B2**). Then, we make it upside down (from **Figure 18B2, B3**).

After this pretreatment, we captured peaks by a lab made program (**Figure 18C**). We use the same program for R-R peak detection in the heartbeat study. The C1-trace shows a portion of C2-trace in enlarged time scale. The C3-trace shows an example of

**Figure 19** shows mDFA results. The observation period is from 3 to 29 March, 2012. The scaling exponent on 4 March was around 0.5 (SI = ~0.5) (**Figure 19B**). This means the vibration is stochastic movement. Then, SI grows up and attains a "risky" level about of 1.0. Since we are NOT specialists of seismology, we are afraid to say that it is hidden threat or high-risk state. However, in terms of chaos dynamic theory, 1.0 means the system's behavior is dynamic. It is like the heart system. It is never stable. We know that it is too hasty to mention: this mDFA result is very similar to that of aluminum bar fracture experiment shown in **Figure 16**. In the aluminum bar fracture, SI grows up during the elasticity period, that is, reversible deflection.

*Earthquake data and pretreatment for mDFA. A, Hidden vibration being exposed to view, a raw earthquake data (A1), an enlargement of Y-axis (A2), further enlargement of Y-axis (A3). B, An explanation of pretreatment procedures. A raw earthquake data (B1), logarithmic output of the square of B1, an inverse of B2 (B3). C, An example explanation of peak detection, with a faster chart speed (C1) and with a slower time* 

We obtained raw seismic data (**Figure 18**) from the High Sensitivity Seismograph Network Japan. Two arrows in **Figure 18** show the time of the big event. A flat line before the big event is NOT a true straight line (see A1 in **Figure 18**). We magnified y-axis scale. The conversion discloses hidden small

**50**

**Figure 18.**

*(C2), accomplished peak-to-peak interval time series (C3).*

*mDFA results. Data: Narita seismometer. (A) Seismic intensities reported by Japan Meteorological Agency. The marks (X) indicate individual earthquakes. Five or six noticeable tremors before the big event are seen. (B) mDFA results. A plotting (marked -o-) represents averaged SI-value of all box-size ranges.*

After the fracture event, aluminum's SI returns to a normal SI-value (around 0.5). **Figure 19B** shows similar trait in **Figure 16**.

This earthquake investigation using mDFA has just begun. We are not professionals, but **Figure 19B** results are remarkable. We hope that seismologists and engineers might possibly have an interest in mDFA.

### **8. Conclusions**

mDFA computation is simple. It is high school level mathematics: first, constructing peak-to-peak interval time series [x]; second, calculating an average value xave using 2000 data; third, computing Σ (x – xave); fourth, cutting the time series into box; fifth, drawing a fitting biquadratic line in each box; sixth, finding the first data (Ent) and the last data (Exit) in each box; seventh, calculating the difference (Exit−Ent) in each box; eighth, calculatingΣ (Exit − Ent)<sup>2</sup> /2000 then obtaining "variance" (statistics of root-mean-square); ninth, changing the size of box one by one, and repeating the statistics cyclically; tenth, making a log-log plotting graph that is box-size versus variance; eleventh, drawing a linear regression line; and twelfth, measuring slope of the line. At the end, the slop denotes SI.

A 2000 "interval" data are fundamental. This length of data is not always rigid. A 2200-interval, for example, produces similar results to that of 2000-interval.

We hope that many people can make their own mDFA program. The basics are averaging, root-mean-square computation, and fitting. It has never been proposed before.

In the present study, we extended mDFA to nonlife system. We then provide the comprehensive results by analyzing various real-world data, which include oscillation/vibration generated from materials. All our results are versatile; it could be applicable to the heart, a motor, materials, and possibly earthquake motion.

The heartbeat data and/or material-vibration are not static and ever-changing phenomena. They fluctuate momentarily. We did not expect that a nonlinear-wayof-thinking method (mDFA) can distinguish the states between "intact heart" and "isolated heart" when we started investigation without questioning. It was more than what we thought. Invertebrate experiments, that is, isolated heart experiments and unpredictable death experiments were a never-to-be-forgotten experiment to discover the power of the mDFA technique.

Peng's DFA and mDFA each has different scope and concept. Peng's DFA considers criticality. In turn, mDFA deals with characteristics of fluctuation embedded in signal that fluctuates over time. In the future, not only a biologist but also engineers and seismology physicists hopefully study much more data in their discipline, by using mDFA.

If we need to find abnormality of a system, mDFA always requires comparison with a baseline SI value. There is a baseline value. That quantification method makes mDFA reliable and versatile.
