Introduction to Simulator (Part 1)
HITACHI Analog-Hybrid Computer
Technical Information Series No. 9
INTRODUCTION TO SIMULATOR
(Part 1)
do oe,
Hitachi, Ltd.
INTRODUCTION TO SIMULATOR
Hitachi Central Research Laboratory
Takeo Miura
Director
The field of application for simulators is extremely broad. Among the various
applications, there are some which do not attract public attention but have a very high utiliza-
tion rate in its specialized field, Furthermore, there are some which have been tried quite
recently and which seem to be quite promising.
In this article, the writer would like to discuss flood simulators which have been discussed
in relation with civil engineering from early times, simulators which analyse the response of
high structure constructions against earthquakes, and piping network simulators which calcu-
late the pressure and flow of huge piping networks like gas and water supply. After such
descriptions, the writer would like to explain about the biological simulators which have
attracted considerable attention quite recently, such as the human voice synthesizing appa-
tuses and simulators for biological organs.
1. FLOOD SIMULATOR
It is a very important matter to highly utilize water which is a natural resource.
For instance, it has long been debated in the field of civil engineering as to how river
flow should be adjusted and controlled for hydraulic power generator, irrigation, and pre-
vention of flood.
Recently, this has been advanced a step further, and the river flow mechanism has
been put into computers, and the detailed analysis of the river characteristics have been
made together with programmed flow control. There
is a tendency to control the river flow by a pre-
programmed system, automatically, in accordance
with the flow which changes momentarily.
Especially in recent years, the construction of
multi-purpose dam and river repairing work have
been advanced considerably, and the necessity of
automatic and man-made control of river flow has
demanded a clear grasping of the river character-
istics. On the other hand, the rapid progress and
development of the electronics have brought forth
the development of analog computers and digital com-
puter. The advent of these computers made possible
the formulation of a "live mathematical model", and
this made "simulators" possible,
Up to this time, "simulation'' was applied
chiefly to the control of man-made objects such as Fig.1 Flood Simulator
airplanes, missiles, and atomic reactors,
However, this has been advanced a step further, and how natural phenomena are being
taken up as the object.
1.1. Various Methods of Flood Prediction Calculations
1.1.1. Calculation of the Amount of Rainfall
From the amount of rainfall at the drainage basin aimed at, and the region adjoin-
ing such a drainage basin, the typical rainfall of the drainage basin aimed at can be
calculated from the following equations,
Ri = f;'Ra + fi" Ry +f,"
R, = f,"Rpy +f" Rp + f,™R,
Ra r, f,' Ry ti f,."Ru mid f,."Rw
ig 5
1.2.
Bit ae ae
Rorw Ras Typical rainfall of each drainage basin,
Ry ~ Rn * Amount of rainfall in the vicinity of the drainage basin
aimed at and which has influence on the drainage basin
area aimed at.
fe aes Typical rainfall coefficient
(A coefficient for calculating the typical amount of rain-
fall of a certain drainage basin aimed at from the amount
of rainfall in the drainage basin aimed at and the amount
of rainfall in the adjoining drainage basin regions. )
In case of calculating the typical amount of rainfall in a certain drainage basin aimed
at, the rainfall of the drainage basin aimed at is used.
Furthermore, the typical rainfall coefficient f ~f ™ is handled as a constant speci-
fied by the statistical data of the past.
Calculation of the Outflow Coefficient
The outflow coefficient for obtaining the amount of flow from the rainfall function
is generally given as a function of the total rainfall.
Calculate the total rainfall during the period in which the flood calculations are to be
made, then obtain the outflow coefficient f(t) of that drainage basin region. Subsequ-
ently, use this f(t) and calculate the am ount of flow from the amount of rainfall.
64
f(t) = F; ( ss Rj)
where
f(t) : Outflow coefficient of the drainage basin area i.
Rj + Amount of rainfall for the drainage basin area for each hour.
t : Elapsed time of rainfall.
Each of the abovementioned equations are composed of mathematical operations such
as addition, subtraction, multiplication and division. Therefore, it is easier to handle
this by a digital computer rather than an analog computer. As for the flood computing
machines which are in practical use at present, although the small scale ones are
calculated by hand, the large scale ones are calculated by the digital operation portion.
Calculation of the Amount of Flow
(Simulation of Drainage Basin)
For the simulation of drainage basin which had rainfall, there are various methods.
Each method has its own advantages and disadvantages. Therefore, at present, they are
selected and utilized adequately in accordance with the specific characteristics of the river.
In the following paragraphs, an explanation will be given for each method.
Storage Function Method
This is a method in which the calculation is made by the storage function based on
the concept that the amount of outflow at a certain drainage basin or outflow end of a
river can be expressed as a function of the storage amount of the drainage basin of the
river.
The following function relationship exists between the inflow amount (1) at point B of the
river shown in Fig. 2, and the outflow amount (O);
ds
ap 8 ee Ra eS eoy Woe Lae (ec aah Wasa Ve. anselaln tae a lose he Rag ane ae (a)
where
s Storage amount (m*) =S
I Inflow amount (m*/s)
O Outflow amount (m°/s)
Be
From equation (3), the following equation can be drived.
ds dO 57-0
: er et a Pe ONO aieslnrsvene Weems nme (a)
dO dt :
In case SS = 9(O) is substituted, equation (4) will become
do
g ao S SS = BS Ye =
ee fet =O eres Beets ee aia owe ts nabs Ss Felereceuins ae 2)
From equation (5)
siete el-
= 5 5 Ie a5) 22 seo. o Meth ipkatsretonereuers aalereeusltveseois's Sore vests (KO)
or
Py BE . -
o-f4 j (fl ROPER a sin ieis cls. 6/0016 see eierelnainne BINS CSO bre loelaVeral wise 6 AD)
where ¢(O) is called the storage function.
Generally speaking, part of the rainfall will not flow out on ee
interruption and ground moisture replenishment. In case rain falts-on dry ground,
it will wet the ground and part of the rainfall will be
absorbed by the ground. Consequently, it will not flow
to the river. Thus, it will become rainfall loss. //
Furthermore, part of it will penetrate into the ground, B
be stored, and gradually flow out and form the base
amount (i.e. The amount which flows out regardless of
whether it rains or not.) The amount of rainfall which
exceeds the penetration rate will become surface
storage (i.e. The amount of rain which is stored on the (0)
surface of the ground temporarily. This amount will Ph ri
flow into the river into the river in a very short period.),
and eventually become the surface outflow. Fig.2 Drainage basin
Besides the base outflow and surface outflow, there is
also the intermediate outflow. This outflow can be expressed as a function of storage
in the same way as the river. In case this relationship is illustrated by a model, it
will be as shown in Fig. 3.
In case the block diagrams of
equation (6) and equation (7) are made,
they will be as illustrated below:
Iifs lef2—li i
sieeve White
Qu | i I
| Ground Surface Storage f | Ff (0)d@ —o—()
| I
Qs Ground
| [Ss Penetration
Se |
round Storage |
Surface outflow’ Base outflow os Omni > 29
—Qs
"j
= fo(@)dé
Fig.4. Block Diagram based on
the Storage Function Method.
Q Amount of outflow
Fig.3 Model Diagram of Inflow and }
Outflow
In case of the above, if (O) = constant, the two circuits shown above will be sub-
stantially the same, and become the so called primary delay.
1.2.2. Unit Graph Method
1.2.3.
1.3.
eeiceg &
In case there is reinfall of a certain unit in the upper stream of the drainage
basin, the outflow from the lower stream is assumed by a certain pattern according
to this method. If the rainfall continues, the outflow is calculated by shifting the
unit time in accordance with the intensity of rain. In other words, the amount of
outflow versus the rainfall is assumed to be linear.
However, in the case of an actual river, this assumption is not necessarily correct,
and generally speaking, the relation between the two is non-linear. In spite of this,
since the computing machine will be Simplified, it is found to be quite useful as a
means for obtaining a rough idea of the outflow. As a case in which the storage
function method and unit graph method have been actually applied, the flood comput-
ing machine of The River Ishikari, Hokkaido can be given.
A unit graph which was utilized for this is shown in Fig. 6.
dQ
1
t
At dr t
Fig.5 Unit Graph Fig. 6
Outflow Function Method
If we assume that a unit amount of rain falls on the drainage basin having a
surface area of A in a short period of time d , the change dQ in outflow owing to
this rain will be as follows.
en mare Is pa). Ee Cane PAL ebay 6),
where’ a, a are constants.
If we represent the outflow coefficient by f, and take the units as A(km’), r(mm/h),
Q(m*/sec), the outflow for the rainfall time to will be
bo
Q= [seat = 0.2773frA x ( e'o(at+1)-e!( wt+1) }
t=t = ty
As for the abovementioned Q, if the rainfall r is obtained for each time zone, and
this is integrated, the outflow can be obtained from the rainfall, according to this
method. The r in equation (9) uses the rain amount function of 1.2.1.
River Tracing
Rain which has fallen in the mountains or on the plains will flow into the river with
the elapse of time. The analysis of flood waves in rivers is extremely difficult in
general. An explanation will be given on two methods which are used at present.
Method based on Equations of Motion and Continuity
The equation of motion for a non-constant flow in an open water channel can be
expressed in general as follows.
fF
oH Ve eed Oy, a, ay?
se eee eg ee =
0X CR ‘gat ax a5? 0 eeoeceee oe 6:00 66060 © 0.6 6.6.6 (10)
-4-
However, since the flood waves are chiefly taken up as the object, item 3 and item 4
are neglected. Therefore,
a
ax CR? gnaatapewanees Se ee ere
On the other hand, equation of continuity which puts into consideration the trans-
verse inflow can be expressed as follows.
Q and H can be obtained by making simulateneous equations from the above two and
obtaining the solution. However, by putting into consideration the solution by analog
computers, the equations shall be converted into
difference equations. The river is divided into
n parts, and at cross section n, the equation
using the middle step difference will be as shown pea = a
: below. | [ |
1
x Hn 1 = Hoes =v 2 / / |
Fn (pep aK) 7 (Qa eee eee (13) naif = en
dAn Qnt+i1 -Qn-1 4 4Xxn—1
ac siqiisvescis ittA)
where
4
F-LwRs A = £(H)
n2
n : Coefficient of roughness
The boundary condition at the upper stream of (13) and (14) will be as follows if they
are set from the amount of outflow Q' and its functional relation H .
Qo = Q' eoceece © 18 6 '6-6.)6 0 0 .0.0-D. 0 0.0.0 0 0 6 SO ONS SOE STE SUS TOT ET OTS 18, 6/d: Oke eoecee (15)
Ho = 6 (Q') SHO SC TRICO SE LOO BODO OC dhol eialelevels SOCORRO OT (16)
If a block diagram illustrating the above mentioned results are shown for one zone,
it will be as shown in Fig. 8 for equation (14), and as Fig.9 for equation (13).
Fig. 8 Fig. 9
Furthermore, an example of this system, there is the flood calculation of the Kitakami
River.
1.3.2. Method based on the Maskingham System
Generally speaking, the Maskingham equation can be expressed as follows.
Se FB (hel FD GY as ew cles tare wale A Al o> 1 a hfe (17)
K and X are constants which are determined by experiments.
In order to make this into a simultaneous equation with the equation of continuity, the
following conversion shall be made.
Equation (17) can be changed as follows.
1
. Ss
No 6 ee ae a Tas Sa 6)
On the other hand,
ds
at SMS CROE ot a ocal er) vce veins, vas eee (19)
and equation (18) can be re-written as follows.
In case we make the mathematical operation block diagram of equation (22) it will
be as illustrated in Fig. 10.
STE Beet OT aici sinh ig ARS SHS ne Mayoledniv-psejne v:000-0.0,8 02 (22)
EARTHQUAKE RESPONSE SIMULATOR
Japan which has many earthquakes is destined to construct its building earthquake
proof, For a long period of time earthquake proof buildings were designed to withstand
the earthquake force evaluated statistically and the skelton and materials were decided
accordingly. However, designs for super high structure buildings of 20 to 30 stories
and extremely important buildings such as atomic reactors were based on the fact that
earthquakes show a dynamic response which is the proper approach, and recently,
dynamic analysis or response analysis are made as a rule.
As for the content of the analysis response, for irregular waves such as earthquake vibra-
tions, the displacement and stress of the buildings wh‘ch are replaced by multi-mass
points are calculated from elasticity to plasticity. Thus, a considerably high calculating
technique will be required. The reason that calculation of high technique has become pos-
sible is due to the recent developments in electronic computers. Such calculations are
almost all done by digital computers in the United States, but in J apan, the analog type
and digital type are used together.
Especially, in the initial stage a few years ago, development and research work was done
by the analog computers.
As the first application of simulation in this field, there is an analog computer named
SERAC specializing in the response analysis of earthquakes.
SERAC is a slow speed type electronic tube analog computer, and it is the abbreviation of
STRONG EARTHQUAKE RESPONSE ANALOG COMPUTER.
In 1961, the Toyo Rayon Technological Research Assistance, "Strong Earthquake Response
Analysis Committee’ (Representative: Dr. Kiyoshi Muto, Tokyo University) planned this,
and the equipment was manufactured by the Hitachi, Ltd.
The vibration and damage conditions of buildings at the time of great earthquakes are
analyzed dynamically, and from the stand point of dynamics, it was utilized with the aim
of studying the earthquake proof designing methods for super high structure and modern
constructions,
At present, in order to make complex calculations of structures having extremely large
amounts of mass points accurately, the digital computers are used. However, in case of
studies for obtaining the tendency of the characteristics, or in the stage of trial designs,
since trial calculations are made a large number of times by changing the parameters,
the analog computers are put to use from the standpoint of convenience and speed, even
at the present time.
Furthermore, it is estimated that henceforth, for the calculation of the constants and
specific values of the vibrational system model, the digital computers will be utilized,
and for the parametric studies, analog computers will be utilized. For instance, if the
building cycle is changed and the acceleration added to the building is investigated (In
other words, the ration between the force added to the building and the weight of the
building), as the building cycle becomes longer, it was found that the acceleration becomes
very small.
As a result, a good example of analog computer utilization may be said to be the search
for possibilities of earthquake proof designs for super high structures. Furthermore, in
order to obtain the stress at each floor and to obtain the vibration quantitatively and accu-
rately, the digital computer is more suitable.
2.1, Simulation based on Analog Computers (Example of SERAC)
As almost all vibrational phenomena can be expressed by differential equations,
it is well known that not only the vibration of buildings caused by earthquakes but
also other vibrational phenomena are quite suitable for the analysis by analog com-
puters,
Especially, in the case where a phenomenon is precisely analysed. Since there are
non-linear factors such as backlash and plastic deformation, it is more practical to
utilize computers.
When we consider the simplicity of the program, the speed in obtaining solution and
the economics, it is not an exaggeration to say that it is one of the most suitable
fields of application for analog computers.
As the outstanding characteristics of SERAC, the following points can be given,
(1) A random wave like earthquake wave can be bed in as inputs. (In order that
recorded wave shapes of great earthquakes can be used directly. )
Se (2) Response calculations of vibrational systems which have bi-linear type non linear
type non linear characteristics, and which accompany hysteresis can be made.
(In order to simulate a condition in which the building undergoes a great deforma-
tion, and part of it is damaged and has entered the range of plastic deformation. )
Next, an explanation will be made in the following paragraphs on the method in
which earthquake response analysis is done by the SERAC,
2.1.1. Linear Response of One Mass Point System
The equation of motion in which one mass point system having a viscosity
damping property like the one shown in Fig.11, receives an earthquake vibration is
as follows:
déy dy, __dy
ae Ge cha et ek 0 ee ie ed
y
where x is
m : Mass
t : Time K /
y : Absolute displacement c /
of Mass Point | y
y, : Displacement of Fixed 4 G
Point i.e. earthquake y {}
c : Viscosity Damping yo
Coefficient (a) (b)
K =: Spring Constant
Fig.11 One Mass Point System
In case this relation is re-written
into an equation showing the relative displacement Y against the fixed point of the
a fe
mass point, it will be as follows:
sa hate Ng tN hs 66. ca nied oisinie aca: aarcys Maw stl bidldaa tae ape
c expresses the differential calculation of time t.
In order to solve this by the analog computer, this is changed to
Vassay = 2s 5 ete vs
y° na a mes
Ties Y —K/mY
and the block diagram shown in Fig. 12 is used. : ifn
hh I
c/m +2
yo is the record of the earthquake acceleration.
Records which were taken by a strong earth- —c/mY
quake meter designed especially for great
earthquakes was used,
This was enlarged and put through the equip- Fig.12 Block Diagram for One
ment via the photographic curve reader Mass Point System
(Photo-electric type function generator)
As for the time scale factor, 5, 10, or 20 is used. Since the continuing time
of the earthquake is from 10 seconds to 20 seconds, the time required for the
mathematical operation is about 3 to 4 minutes at the most.
.1.2. Non-Linear Response of One Mass Point System
The non-linear characteristics handled by SERAC are chiefly of a bi-linear
type having hysteresis as mentioned at the beginning, and are as shown in
Fig.13. Besides these characteristics, there is also a tri-linear type, but the
-block diagram would be extremely complicated.
The equation of vibration can be expressed as
follows.
mY + CY = Q(Y) = -my, ... (25)
The term Q(Y) on the above equation is the so-
called restoration force, and it is a function
of the relative displacement Y. Q Q
(In Fig. 13, this is expressed (P]}
by 3) Qr Qrt-
The mathematical operations -
performed by SERAC are done () Ae {Bl Olr7 5
in accordance with the block / e/ {E]
diagram shown in Fig. 14. (P)
(a) (b)
Comparator
Fig.13 Non-linear characteristics
Comparator & d=Y=y-Yo
Fig.14 Block Diagram of One Mass (E)
Point Non-Linear Vibration
®@ [P)
Fig.15 Division of Elasticity and Plasticity
in the Restoring Force
Lim
If we explain in detail the example shown in Fig. 13 (b), as shown in Fig. 15,
this is divided into the elastic portion E and the plastic portion P.
The E portion is represented by the loop shown in the top portion of Fig. 15,
and the P portion is calculated from the loop shown in the lower portion of
the same diagram.
For the changeover of the two, mechanical relays are used. If we start
from 0 point in Fig. 15, at first we will pass through the E loop (the same
as the elasticity block diagram shown in Fig. 12).
However, as the deformation increases and point (1) is reached, (E) will be
cut off and loop (P) is obtained.
If Q becomes a voltage equivalent to Q by the comparator (B), relay B will be
made to actuate. After advancing (P) for a while, E will appear again when
the relative speed is 0. (Point (2) in Fig. 15)
This is done by actuating the relay by comparator (A).
Henceforth, the same procedure is repeated.
The simulation of elasticity and plasticity by the mechanical relay system
operate quite accurately at a time lag which can be neglected. Thus, it is
utilized with great success. y
@ Integrater
WSs wal
@ Inverter
io—ov
5 Vo*=4
Y2 @ Potentiometer
=|) oz ojos
r] 1 . Ox Pex
a
=(Xe—¥e ® Absolute value
generator and
Integrator
Mi Vo
Vo~ f Wildl
© Voltage comparator
% oN
wv forr
Fig.16 Block Diagram of 5 Mass
Point Non-Linear Vibration
2.1.3.
2.1.4.
Response of Multi Mass Point
In case of a shearing force type multi-mass point, the number of circuits
shall be made to be the same as the number of mass points, and in the same
way as the one mass point system, they shall be combined.
For reference, if an equation for linear vibration of the i-th mass point is made,
it will be as follows:
m,¥; + ¢,(¥; - Yi_1)
+ Cian (Via = Neen)
+ Ki (Yi - Yier)
+ Kita (Yi - Yi+d
= 7 MNygemine snes Sicishaie resol Salo Magee oiaipleisisielsieiele.0 S650 wits oie a8)
In Fig. 16, a block diagram of 5 mass point/non-linear case is shown, Although
block diagrams of general mass points can/also be made, it would become ex-
tremely complex. Thus, it has not been given here.
Outline of the Equipment
In Fig. 17,the whole view of the SERAC is shown. It is composed of the
main body, photo electric cell function generator (photographic curve reader),
and recording machines.
The main body is almost the same
as an analog computer but in order
to simulate the plasticity deforma-
tion characteristics, it possesses
a non-linear element as shown in
Fig. 13 and Fig. 14.
The composing elements of the
main body are as shown in Table 1.
On the pre-patch board of the main
body, the above mentioned simula-
tion circuit is patched, and simulation
is made. Fig. 17
The photo-electric cell type function
generator is used for feeding earthquake waves into the simulation circuit. The
earthquake waves made on the recording paper are made to undergo pulse width
modulation by tracing with a light spot, and by restoring the output, it is then
taken out as an analog voltage reading.
Tablel. Composition of Elements
Elements Quantity
Integrator 17
Special Integrator 5
Adder 26
Inverter 16
Potentiometer 56
Voltage Comparator 12
Fig.18 Photoelectric
The external view is shown in Fig. 18. Curve Tracer
As for the recorded earthquake waves, strong earthquake records of the U.S.
which was prepared by Prof. Borg, and Japanese records prepared by the
= 40:=
Technical Research Division of Kashima Kensetsu Ltd. are used.
The devices for recording the solutions (simulation results for the displacement
and stress of structures) are done by the ordinary pen oscillographs.
Fig. 19 shows an 5 eae of a solution.
=
i =)
<=
Fig. 19
In this case, the beam direction of the building is replaced by the five mass
point system and the recorded earthquake waves of El Centro (California, USA,
1940) were put in and simulated. Furthermore a report of this was made.
The waves were as shown below.
No. 1 Channel Earthquake wave shape Yo
No. 2 Channel First Floor Relative Yi
Displacement
No. 3 Channel Second Floor Relative YY - Y;
Displacement
No. 4 Channel Third Floor Relative Y;, - Y2
Displacement
No. 5 Channel Fourth Floor Relative Y, - Y;
Displacement
No. 6 Channel Fifth Floor Relative Y - Y,
Displacement
2.2, Simulation based on Digital Computer
The only difference is the computer being used. As for the equations which
express the vibration of the structure, the same wave used for the analog com-
puter simulation were calculated by the digital computer. In case the analog
computer is used a simulation in which the vibration is about ten times as slow as
the actual earthquake is obtained.
re ig
Contrary to this, in case the digital computers are used, several hours of calcula-
tion will be required. However, in case of analog computers, in order to make
analysis of super high structures, if mass points are substituted for the number of
floors, a large scale computer will have to be set in proportion to the number of
pass points. On the other hand, in case of the digital computer, a similar calcula-
tion can be made so long as the time of calculation is changed.
Therefore, if precise data is required such as in the case of making confirmation
of the earthquake resistance obtained by calculations, simulations based on digital
computers are more suitable.
= 412)