Programmable Architecture

-Towards Human Interactive, Cybernetic Architecture-

Kensuke Hotta (B.Eng, M.Eng, Msc)
Architectural Association School of Architecture, 2013




2-3-2. Cybernetics

Cybernetics, which was advocated by American mathematician Norbert Wiener in the late 1940s, was a synthetic academic discipline that dealt with the matter of control and correspondence in a system like an organism or a machine. Wiener regarded the operation of the mind, life, society, language and many other things as a dynamic system of control. Our environment reflects the realities of the cybernetic realm as we deal with some things (variables) that cannot be controlled and with others that are adjustable. The aim of cybernetics is to create the most appropriate environment for us by properly setting the values of the controllable variables on the basis of the values from the past until the present.

2-3-2. サイバネティクス(Cybernetics)


The concept of cybernetics greatly influenced the disciplines of ‘Social Science’ as well as the disciplines of ‘Natural Science’, as it was relevant to a large number of academic disciplines. The concept of cybernetics had direct connections with such theories as automation, navigator, telecommunication, computer and automaton. However, as the theory of cybernetics aimed to study the nervous system as a kind of the correspondence system, it was applied to the fields of Physiology and Psychology. In addition to this, a discipline, which was called Bio-Cybernetics and aimed to investigate for instance the information of the living bodies, was invented. It was also applied to Economics, Sociology and the theory of financial planning and developed as operations research and the system theory. It can be argued that cybernetics provides the basic foundation of information science as we know it today.


The new system theories developed in the late twenty-century seek to explain various phenomena that cannot be captured within the framework of cybernetics, which considers systems from the perspective of control. Theories such as Humberto Maturana and Francisco Varela’s Autopoiesis, Magorou Maruyama’s second cybernetics, Hermann Haken’s Synergetics, basically aimed at superseding cybernetics.


These new system theories have a different orientation than cybernetics. Whereas cybernetics basically described a system as an entity that maintains itself toward the goal of control, new theories of system generally tended to illustrate system as the incessant process of deviation and pay attention to the dynamic order that is generated through these deviations. Ilya Prigogine’s 'dissipative structure' is a good example of such new system theory of deviation. It is a theory out of 'thermodynamic equilibrium', which sustains its stability by emitting energies and materials that are absorbed from the surroundings in different manners.


2-3-3. Control System and Control Theory

Control theories describe the methods in engineering and mathematics which aim to control dynamic behaviour. The usual objective of control theory is to control a system. It attempts to adjust the system behaviour through the use of feedback. Navigation, machine design, climate modelling and so on are examples of systems where control theory is applied. In control theory there are four basic functions: Measure, Compare, Compute, and Correct. These four functions are complemented by five elements: the Detector, the Transducer, the Transmitter, the Controller, and the Final Control Element. Block diagrams are often used to explain the flow of the system.

2-3-3. 制御系と制御理論


In the early control system, a relatively simple system called an ‘Open-loop Controller’ was used. An Open-loop Controller was also called a non-feedback system. As a result, the controller could not compensate for changes. For instance in a car using cruise control a change in the slope of the road could not be accounted for. With the development of the ‘Closed-loop controller sensors monitored the system output and fed back the data to maintain the desired system output. Feedback was able to dynamically compensate for the difference between actual data and desired data. It is from this feedback that the paradigm of the control loop arises: the control affects the system output, which in turn is measured and looped back to alter the control.


The system is often called the ‘plant’ and its output follows a control signal called the ‘reference’ (in this thesis it is called the ‘objective function’), which may be a fixed or changing value. A ‘Controller’ is another function which monitors the output and compares it with the reference. The ‘Error Signal’, which is the difference between actual (sensing data) and desired output (reference/objective function), is applied as feedback to the input of the system, to bring the actual output closer to the reference.


There are a number of key concepts referenced in control systems. These include ‘Stability’ which considers whether the output will converge to the reference value or oscillate (this will be explained later chapter). The ‘Transfer Function’, also known as the ‘system function’ or ‘network function,’ is a mathematical representation of the relation between the input and output based on the differential equations describing the system. This will be explained in a later chapter too.


Originally, control engineering was all about continuous systems. Development of computer control tools created a requirement for discrete control system engineering because the communications between the computer-based digital controller and the physical system were governed by a computer clock. The equivalent to the Laplace transform in the discrete domain was the z-transform. Today many control systems are computer controlled, consisting of both digital and analog components.


At the design stage either digital components are mapped into the continuous domain and the design is carried out in the continuous domain, or analog components are mapped into the discrete domain and design is carried out there. The first of these two methods is more commonly encountered in practice because many industrial systems have many continuous systems components, including mechanical, fluid, biological and analog electrical components, with few digital controllers.

 Therefore, all these developments have led to the development of a field called 'Control Engineering' which seeks stable behaviour in various related systems with a particular focus on the cybernetic aspect.



Shifting the conversation to recent architectural design theory, there are already examples of these concepts of control engineering, especially feedback, etc., being applied to architectural design. Alongside the development of digital control systems, the design process has progressed from paper-and-ruler based manual design to computer-aided design (CAD), and now to computer-automated design (CAutoD), which has been made possible by evolutionary computing. CAutoD can be applied not just to fine tuning a predefined control scheme, but also to control structure optimization, to system identification and to the invention of novel control systems based purely upon a performance requirement, independent of any specific control scheme.(Relevant statements are explained in the previous chapter and added to in later chapters.)


2-3-3-1. Feedback Control


Fig 2-3-3-1,1 Negative feedback(Redraw referring to Brews Ohare)
Feedback system, maintaining a desired system performance despite disturbance using negative feedback to reduce system error.
図2-3-3-1,1 負のフィードバック制御(Brews Ohare参考に著者作図)負のフィードバックにより計測値と目標値との差を減じ、外乱の中にあっても要求されるシステムパフォーマンスを維持する。

Feedback is a manipulation that turns an output (result) of a system back to being an input (cause). It is a basic principle which defines the behaviour of a system in the field of electronic engineering. Feedback systems aim to manipulate the behaviour of a dynamic system, which is a mathematical concept where a fixed rule describes the shift in certain conditions over time as inputs are applied. Control theories, such as cybernetics, explain how this behaviour is modified by feedback.


Feedback, generally speaking, is the phenomenon whereby the results of a system’s reactions influence the system itself. There are two kinds of feedback: one is negative feedback that functions in an inhibitory manner and the other is positive feedback that functions in a promotional way. Feedback works on the principle of self-control. It is an integral part of a living organisation that sustains homeostasis.


In contrast to feedback, the system that removes noise effects in advance by predicting them and taking appropriate steps to negate them is called a feed forward control system. Feed forward control systems can be argued to be more effective than feedback systems in that feedback systems cannot make modification operations before the noise effects appear. However, feed forward control generally must be used together with feedback systems. That is, the feed forward control system is used to remove the noise effects that can be predicted and the feedback system is used to take care of the rest of the noise effects.


2-3-3-2. Controller (P, PI, PID controller)

2-3-3-2. コントローラー(P, PI, PIDコントローラー)

Fig 2-3-3-2,1 PID Controller (P, PI, PID controller), drawn by Author referring to TravTigerEE
The PID Controller (Proportional-Integral-Derivative Controller), one of the most used feedback controllers in the classical control theory, controls by using: the proportional, the integral and the derivative values, denoted P, I, and D. The Ziegler-Nichols method is one of the most famous methods of adjusting parameters. Whereas feedback control systems require relatively high power through an actuator, feedback-measuring systems draw fairly low power devices as output devices are low power (for example, indicators and inverse transducers). Feedback in the measuring system improves accuracy in measurement, improves speed of measurement, allows remote indication and allows non contact measurement. However, it increases the complexity of design and operation, as well as size and cost.
図2-3-3-2,1 PIDコントローラー(P, PI, PIDコントローラー)Trav TigerEEを参考、筆者作成
PIDコントローラー(Proportional;比例、Integral;積分、Derivative;微分 Controller)、古典的な制御理論の中で、もっとも使用されるフィードバックコントローラ-のひとつである。P,I,Dの頭文字の順に、比例制御、積分制御、微分制御があり、それぞれの数式を使用して制御が行われる。ジーグラー・ニコルス法は最も有名なパラメータ調整法のひとつである。駆動装置は比較的高いパワーを必要とするが、比してフィードバックおよび計測システム(例えば、指示計や逆変換器)は比較的低いパワーで稼働する。測定データをシステムにフィードバックすることで、測定精度の向上、測定速度の向上、遠隔指示、非接触測定が可能になる。しかし、それにはシステムの設計や動作が複雑になり、サイズやコストも増加する。

A proportional-integral-derivative controller (PID controller) is a control loop feedback mechanism widely used in industrial control systems. A PID controller calculates an error value as the difference between a desired set point and a measured process variable. The controller attempts to minimise the error by regulating the process manipulating the variable. The PID controller algorithm contains three separate constant parameters–the proportional (P), the integral (I) and the derivative (D) values. Some applications may require using only one or two parameters (or control actions) to provide the appropriate system control. This is achieved by setting the other parameters to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. P depends on present errors, I on the accumulation of past errors, and D is a prediction of future errors, based on current change trends. The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve and a damper. However the use of the PID algorithm for control does not guarantee optimal control of the system or stabilisation of the system.


PID controllers originated in 1890s governor design and were subsequently developed for use in automatic ship steering. The theoretical analysis of a PID controller was first published by Russian American engineer Nicolas Minorsky, (Minorsky 1922). Minorsky was designing automatic steering systems for the US Navy, and from his analysis on observations of a helmsman, he noted the helmsman controlled the ship based not only on current error, but also on past error as well as the current rate of change. Minorsky reduced this to a series of equations. His goal was stability, not general control, which simplified the problem significantly. While proportional control provides stability against small disturbances, the integral term was added to deal with steady disturbances, in particular a stiff gale. The derivative term was added to improve control.

PIDコントローラーは1890年代の遠心式調速機の設計に端を発し、その後つづいて船舶の自動操舵用として開発された。PID コントローラーの理論的解析はロシア系アメリカ人技師 のニコラス・ミノルスキーによって初めて出版された(ミノルスキー 1922)。ミノルスキーはアメリカ海軍の自動操舵システムを設計していた。かれは、実際の操舵手の操作を観察し、操舵手は現在の誤差だけでなく、過去の誤差や、現在の変化率も考慮して操船していることに着目した。ミノルスキーは、これを一連の方程式に落とし込んだ。彼は目標を安定性とし、これは一般的な制御ではないので、問題は大幅に単純化された。比例制御は小さな外乱に対する安定性をもたらしたが、一方、定常的な外乱、特に強風に対処するために積分項が加えられた。また、微分項は制御を改善するために追加された。

Limitations of PID control

While PID controllers are useful to many control problems and often perform satisfactorily they do not provide optimal control in general. The fundamental difficulty with PID control is that it is a feedback system and thus overall performance is reactive and compromise-based. It lacks direct knowledge of the process. While PID control is the best controller where a model of the process doesn’t exist, better performance can be achieved by directly modelling the actor of the process without resorting to an observer.



PID controllers can fail to work properly when the PID loop gains are insufficient causing the control system to oscillate around the control set point value. The non-linearities of a process are also a difficulty. The system may not react to changing process behaviour as well as experiencing a lag in responding to large disturbances.

The most significant improvement to the difficulties described above is to incorporate a feed-forward control based on knowledge about the system, and use the PID only to deal with error. Alternatively, PIDs can be altered in some minor ways, such as cascading several PID controllers, changing the parameters (for example adaptively modifying them based on performance) and improving measurement (higher sampling frequency or precise, accurate and low-pass filtering).



2-3-3-3. Sensing / Mesurement and Noise

Overview: A sensor is a device that identifies events or changes in quantities and returns a corresponding output, generally in a format of an optical or electrical signal. For example, a thermocouple outputs voltage in response to temperature changes. A mercury thermometer is also a sensor which converts the measured temperature into the expansion and contraction of a liquid which can be read on a calibrated glass tube. Sensors are used in everyday items such as touch-sensitive lift buttons (tactile sensor) and desk lamps which can dim or brighten by touching the base, along with numerous other applications which most people are never fully aware of. With developments in precision machinery and easily-handled microcontroller platforms, new types of sensors are used extensively in various fields such as MARG sensors (Bennett, S. 1993). While analogue sensors such as potentiometers and force-sensitive resistor are still widely used. Applications for such sensors include manufacturing and machinery, airplanes and aerospace, cars, medicine and robotics. All living organisms have biological sensors with functions similar to those of the mechanical devices described.

2-3-3-3. センシング/計測とノイズ



A sensor's sensitivity relates to how much the sensor's output changes following the change of inputs. For example, if the mercury in a thermometer moves 1 cm when the temperature changes by 1 °C, the sensitivity is defined as 1 cm/°C (this means the slope Dy/Dx assumes a linear characteristic). Some sensors may have an impact on what they measure. For instance, a room temperature thermometer put into a cup of hot liquid cools down the liquid while the liquid heats up the thermometer. Sensors are designed to have a minimal effect on what is measured. Making the sensor smaller often improves this. Technological progress enables sensors to be manufactured on a smaller scale using MEMS technology. In most cases, micro sensors achieve significantly higher speed and sensitivity than macroscopic sensors.



In terms of measurement errors and noise, there are several kinds. One kind of error relates to the ‘Resolution’ of the sensor. The resolution of a sensor is the smallest change the sensor can detect in whatever it is measuring. The resolution is related to the precision with which the measurement is conducted. Another kind of error is ‘Noise’. In electronics, a random fluctuation in an electrical signal that varies in time is called noise and noise exists in any electronic circuits. Noise is a summation of undesirable or disturbing energy, regardless of whether it is natural or man-made. Although it is generally unwanted as it causes an error or undesired random disturbance in information signals, it could be utilised purposefully in some applications, such as in generating random numbers or dithering. To dither noise is intentionally applied to randomise quantization error.


The final kind of error is ‘Deviation’. Several types of deviation can be observed if the sensor is not appropriate.


・The sensitivity of the selected sensor may be different from the value expected. This is called a sensitivity error. The sensor may also be sensitive to properties other than the property intended to be measured. If the sensitivity is not constant over the range of the sensor, this is called non linearity. The amount the output differs from ideal behaviour over the full range of the sensor is often noted as a percentage of the full range.


・Property’s value exceeds the limits of the sensor's output range. The full scale range defines the maximum and minimum values of the measured property. If the sensor has a digital output, the output is only an approximation of the measured property. The output signal will eventually reach a minimum or maximum when measured.


・If the signal is monitored digitally, limitations of the examining frequency can cause an error. If the output signal is not zero when the measured property is zero, the sensor has an offset or bias.


・If the output signal slowly changes independent of the measured property, this indicates a slow deterioration of sensor properties over a long period of time.


These deviations can be classified as either systematic errors or random errors. Appropriate calibration strategies can compensate for systematic errors. Signal processing, such as filtering can reduce random error caused by noise.


2-3-3-4. Actuation

An actuator is a type of motor that plays a role in moving or controlling a mechanism within a system. It is powered by an energy source such as an electric current, hydraulic fluid pressure, or pneumatic pressure, and converts that energy into motion. The actuator can be controlled in a simple manner (a predetermined mechanical or electrical device), it can be software-based (e.g. a printer driver, robot control system) or it can have a human or any other input controlling it.

In terms of the application of actuators, in engineering, actuators are frequently used as mechanisms to introduce motion, or to clamp an object so as to prevent motion. In electronic engineering, actuators are a subdivision of transducers which are devices to transform an electrical signal into motion. In virtual instrumentation, actuators and sensors are the hardware complements of virtual instruments.




Motors are mostly used when circular motions are required while some actuators are intrinsically linear, such as piezoelectric actuators. However motors can also provide linear forces by transforming a circular motion to a linear one with a screw or a similar mechanism. Conversion between circular and linear motion is commonly made via a few simple types of mechanism such as a screw or a wheel and axle. Screw: The screw jack, the ball screw and the roller screw actuator all operate on the principle of the simple machine known as the screw. By rotating the actuator's nut, the screw shaft moves in a line. By moving the screw shaft, the nut rotates. Wheel and axle: the hoist, the winch, the rack and pinion, the chain drive, the belt drive, the rigid chain and the rigid belt actuator operate on the principle of the wheel and axle. By rotating a wheel/axle (e.g. drum, gear, pulley or shaft) a linear member (e.g. cable, rack, chain or belt) moves. By moving the linear member, the wheel/axle rotates.


Examples of other actuators include: the comb drive, the digital micromirror device, the electric motor, the electro active polymer, the hydraulic piston, the piezoelectric actuator, the pneumatic actuator, the relay, the servomechanism and the thermal bimorph. Here is a brief explanation of the mechanisms of various actuators.


・The ‘Hydraulic actuator’: A hydraulic actuator consists of a cylinder or fluid motor that uses hydraulic power to provide mechanical operation which gives an output as linear, rotary or oscillatory motion. As liquid is almost incompressible, a hydraulic actuator produces considerable force, but its acceleration and speed is limited. The hydraulic cylinder consists of a hollow cylindrical tube along which a piston that can slide. When pressure is applied on each side of the piston, it is called ‘double acting’. A difference in the pressure between the two sides of the piston results in the piston moving to one side or the other. The term ‘single acting’ is used when the fluid pressure is applied to just one side of the piston and the piston can move in only one direction. In this case a spring is frequently used to give the piston a return stroke.


・The ‘Pneumatic actuator’: A pneumatic actuator converts energy from vacuum or compressed air at high pressure into either linear or rotary motion. A pneumatic actuator is useful for main engine controls because of its quick response in starting and stopping as the power source doesn’t need to be stored in reserve to operate. Pneumatic actuators can produce large forces from relatively small pressure changes. These forces are often used with valves to move diaphragms and control the flow of liquid through the valve.

・「空気圧アクチュエータ」 は、真空または高圧の圧縮空気からのエネルギーを直線運動または回転運動に変換するものである。空気圧アクチュエータは、動力源を予備に蓄えておく必要がないことと、始動・停止時の応答が速いので、主機制御に効果的である。また、空気圧アクチュエータの特徴として、比較的小さな圧力変化から大きな力を発生させることができる。この力は、バルブでダイヤフラムを動かし液体の流れを制御するためによく使われる。

・The ‘Electric actuator’: It is one of the cleanest and most readily available kinds of actuators because it does not use oil. Electrical energy is used to actuate equipment such as multi-turn valves through an electric motor which converts electrical energy to mechanical torque.


・The ‘Thermal or magnetic actuator’ (shape memory alloys): These actuators use shape memory materials (SMMs), such as shape memory alloys (SMAs) or magnetic shape-memory alloys (MSMAs) which can be actuated by applying thermal or magnetic energy. The actuators tend to be compact, lightweight, economical and provide a high amount of power per unit volume.


・The ’Mechanical actuator’: A mechanical actuator functions by converting rotary motion into linear motion to execute movement. It involves gears, rails, pulleys, chains and other devices to operate such as rack and pinion.


2-3-3-5. Stability and Catastrophic Collapse

The field of ‘Stability Theory’ explores the stability of systems. Especially for the solutions of differential equations describing dynamic systems, various types of stability have been identified. ‘Nominal Stability’ is the stability of a closed loop system under the condition that a model is perfect. In contrast, ‘Robust Stability’ allows for uncertainty in a model. In the situation of plant instability, the amount of data is highly problematic. In order to resolve the issue, 'Calculation Stability' is an effective method. In this method, a sort of re-parameterization is frequently used.


「安定性理論」の分野はシステムの安定性を探求する学術分野である。特に力学系を記述する微分方程式の解については、様々な安定性のタイプが確認されている。「公称安定性(Nominal Stability)」とは、モデルが完全であるという条件のもとでの閉ループシステムの安定性のことである。これに対して、「ロバスト安定性(Robust Stability)」はモデルの不確実性を許容するものである。また、プラントが不安定な状況ではデータ量が重要な問題となるが、この問題を解決するためには「計算安定性」が有効な手法である。この方法では、ある種の「再パラメータ化」が頻繁に用いられる。

For stability in linear systems, ‘Exponential Stability’ is widely used. In linear systems, there are two types of stability. One is ’Internal Stability’, the other is ‘Bounded-input bounded-output Stability’ are present (BIBO Stability). The former deals with whether the system will output stable values when no inputs. The latter focuses on the system outputs within a certain range of values (called bounded) when there are bounded inputs.


In contrast, stability for nonlinear systems that have an input present is called 'Input-to-state Stability'. It amalgamates Lyapunov stability and a system similar to bounded-output stability. In terms of asymptotic stability in nonlinear systems, the most common type would be based on the theory of Lyapunov. (Lyapunov, 1992). ‘Lyapunov Stability’ concerns the stability of solutions near to a point of equilibrium. In simple terms, “if all solutions of the dynamical system that start out near an equilibrium point Xe stay near Xe forever, then x_e is Lyapunov stable”.

対照的に、入力が存在する場合の非線形系の安定性は、「入力‐状態安定性」と呼ばれる。これは、リアプノフ安定性と、有界出力安定性に似たシステムを融合させたものである。非線形システムにおける漸近安定性の観点からは、最も一般的なタイプはリアプノフの理論に基づくものであろう(Lyapunov, 1992)。 「リアプノフ安定性」は、平衡点に近い解の安定性に関係している。言い換えると、『平衡点Xe付近から出発した力学系の解がすべて恒常的にXe付近に留まるなら、x_eはリアプノフ安定である』ということである。

Below concrete descriptions, and explanations of the following system state aspects are given:‘Exponential Growth’,’ Generic Structure’, ‘Exponential Decay’, ‘Goal Seeking behaviour’, ‘Oscillation’, ‘S-shaped’, and ‘Catastrophic collapse’.


- Exponential Growth

In the paper, (Radzicki 1997) the author took ‘a herd of elephants’ as an example.

- 指数関数的成長

論文(ラドニチュキ;Radzicki 1997)では、「象の群れ」を例に説明されている。

Fig 2-3-3-5,1 The Diagrams of Exponential Growth
図2-3-3-5,1 指数関数的成長のダイアグラム

In the above model, which doesn’t have a feedback system, the number of the elephants simply increases. Additionally, the number of the elephants also increases even though the original number of the elephants starts at zero. The feedback regarding the number of the newborn children is added in the following diagram. 


Fig 2-3-3-5,2 The Diagrams of Exponential Growth Two
図2-3-3-5,2  指数関数的成長のダイアグラム2

The result is that if the number of the elephants begins with zero, the size of the herd of elephants remains zero. In this example, if the original number is set at ten, the result shows the exponential growth.


- Generic Structure

Over the years, system dynamicists have identified combinations of stocks, flows and feedback loops that seem to explain the dynamic behaviour of many systems. These frequently occurring stock-flow-feedback loop combinations are often referred to as ‘generic structures.’ The typical model of the generic system is as follows.



Fig 2-3-3-5,3 The Diagrams of Generic Structure
図2-3-3-5,3 ジェネリック構造のダイアグラム

The above diagram is an example of a loop system that the paper illustrated. The system can explain a large number of phenomena in the world. The following diagram, for example, shows how knowledge will be accumulated in a discipline of natural science.


Fig 2-3-3-5,4 The Diagrams of Generic Structure 2
図2-3-3-5,4 汎用的な構造のダイアグラム2

- Exponential Decay

The below diagram illustrates the exponential decay. If the target value (goal) is set to zero in a goal-seeking behaviour system, the result will be exponential decay. The following graph gives a typical example of this. Figures below is a system dynamics representation of a linear first order negative feedback loop system with an implicit goal of zero.


下図は指数関数的減衰(exponential decay)を説明している。目標探索システムで目標値(ゴール)をゼロにすると、値は指数関数的に減衰することになる。下図は、その典型的な例を示している。下図は、暗黙に目標値をゼロとした線形一次負帰還ループシステムのシステムダイナミクスを表している。

Fig 2-3-3-5,5 The Diagrams of Exponential Decay
図2-3-3-5,5  指数減衰のダイアグラム

- Goal-seeking Behaviour
In Chapter 3 Rdolzicki discusses two types of feedback loops : positive loops and negative loops. Positive loops generate exponential growth (or rapid increase) and negative loops produce goal-seeking behaviour. As the below diagram shows, the goal-seeking behaviour system always creates feedback which is the discrepancy between the goal and the stock.

- 目標達成のための行動


Fig 2-3-3-5,6 The Diagrams of Goal-seeking Behavior
図2-3-3,5,6 目標追求行動のダイアグラム

- Oscillation

Oscillation occurs due to the delay of the information in a feedback system. The ‘delay’ in the measuring part (sensing for example) causes a delay in transmitting the information. The following model, therefore, includes the ‘desired system level’, which controls the delay of the information. The blue line is the system. The system thus decreases the degree of instability in the oscillation system. There are four types of oscillation: ‘Sustained Oscillation’ ,‘Damped oscillation’ , ’Exploded oscillation’ and ’Chaos oscillation’.



Fig 2-3-3-5,7: The Diagrams of Oscillation
図2-3-3-5,7 振動のダイアグラム
Fig 2-3-3-5,8: The Diagrams of S-shaped Growth
図 2-3-3-5,8: S字成長のダイアグラム

- S-shaped Growth

S-shaped growth is the characteristic behavior of a system in which a positive and negative feedback structure fight for dominance but result in long-run equilibrium. In the paper, as an example of the s-shaped growth, Radzicki describes the relationship between elephants birth rate and their death rate.



- Catastrophic Failure

In relation to stability, ‘Catastrophic Failure’ means a sudden, general failure that recovery is impossible. It often leads to cascading systems failure. A cascading failure is a failure in a portion of a system made up of interconnected portions in which the failure of a portion can cause the failure of successive parts. Structural failure is the most common example of this. However, the term has often been extended to a lot of other disciplines where comprehensive and irrecoverable loss happens. These failures are explored by using the methods of forensic engineering, which tries to determine the cause or causes of failure.



2-3-4. Deterministic vs Stochastic in prediction and forecasting

Deterministic algorithms and stochastic algorithms are both versions of combinatorial optimization algorithms, a kind of heuristic algorithm which seeks an optimum solution without examining all possible solutions. Deterministic algorithms search for solutions by using a definitive selection. For example, searching in limited, specific areas is a deterministic algorithm. By contrast stochastic algorithms randomly make decisions while searching for a solution. Deterministic algorithms will, therefore, generate the same solution to a given issue repeatedly.By contrast, probabilistic or stochastic algorithms may not generate the same solution each time.

2-3-4. 予測・予想における決定論と確率論の比較


Heuristic algorithms are classified into repetitive algorithms and constructive algorithms. Typically constitutive heuristic algorithms start searching with a single element (although multiple elements are possible as a start). While searching for a complete solution other elements are continually selected and added creating a partial solution for an increasingly larger set of elements. Once a selected element is added, it is not removed from the partial solution at a later stage. Constitutive algorithms are successively augmenting themselves.


A repeatable heuristic method such as a search in limited areas requires two data inputs. The first is a description of the problem to be solved using examples and the second is an initial solution for the problem. Repeating heuristic methods change the solutions which are initially given in order to improve its evaluative function. When its evaluation level is not improved, the algorithm returns "No" and keeps the existing solution. If it is improved, the algorithm returns the improved solution, and repeats the evaluative steps using the new solution. Normally this process is repeatedly carried out until the evaluation level stops iproving. Frequently this algorithm is applied in conjunction with a constitutive heuristic method to improve the generated solution.

限られた領域での探索のような、繰り返し計算を使用するヒューリスティック手法では、2つのデータ入力が必要となる。1つ目は解決すべき問題の記述、2つ目は問題の初期解である。繰り返し計算を使用するヒューリスティック手法では、その評価(関数)を向上させるために、初期に与えられた解を変化させる。その評価が改善されない場合、アルゴリズムは 「No」を返し、既存の解を維持する。また評価が改善されていれば、改善された解を採用し、新しい解を用いて評価ステップを繰り返す。通常、この工程は評価の改善が止まるまで繰り返し行われる。このアルゴリズムは生成された解を改善するために、よく構成的ヒューリスティック手法と組み合わせて適用される。

In order to design a superior constitutive algorithm, a deep understanding and analysis of the problem to be solved is required along with the development of an appropriate constitutive heuristic method. In many cases, it is not easy to use heuristic techniques for real issues.