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Design and Testing This time, I plan to talk about the issues of design and testing. Design often includes experimental steps. Some people only treat the testing in design as a regular procedure. For example, they only want to know what kind of design usually includes which tests (for example, aircraft design generally requires wind tunnel testing, structural static testing, etc., and whether it must include free-fly model flight testing). However, what problems do these tests mainly solve, what role does testing play in the expansion of human knowledge, and whether special tests need to be specially developed in some special cases. They lack the necessary thinking ability. Testing is used in engineering design as a means of understanding, not as a routine procedure. Between human understanding and objective reality, human senses are the bridge that transmits information. People understand the world and adjust their actions through information sensed through their senses. Usually the "senses" just passively accept things from the outside world. "Experiment" is people's conscious observation and exploration activities, an initiative to expand information sources and broaden information channels. The information people perceive from the objective world is always partial and specific. However, due to the initiative of human cognition, people can summarize the understanding of the regularity of objects from this information. Similarly, although experiments are partial controlled actions, they can test whether people's understanding of the laws of the objective world is correct, or verify the objective effects of their own activities. Testing is to analyze certain parts of a product (local performance or local components) under controllable conditions, explore certain rules, confirm certain human understandings, or test the results of artificial measures, with the purpose of reducing technical risks in product development. Experiments can always have two outcomes: success and failure. Test failure is generally less costly than the failure of the product itself. Therefore, testing is a means of reducing product technical risks. Generally speaking, tests can be divided into two categories: developmental tests and confirmatory tests. Developmental experiments are an effective means of exploring designs (typically, Edison searched for materials suitable for making incandescent filaments from the carbides of 6,000 plants), and confirmatory experiments are to prove whether the artificially set products achieve their original purposes (such as testing the composition of each furnace of molten steel in steelmaking, delivery and flight test of finished products in aircraft production, etc.). The test specimen can be the product itself, some part of the product, or some model of the product. For example, the common method for aerodynamic testing in aircraft development is to use models in wind tunnels. ； The specimen used in testing the physical properties of materials can also be regarded as a model of the product. Models are increasingly used in engineering design. Some people in foreign science and technology circles believe that: “In science, the model approach is at the heart of what is called the 'scientific method'. ”The use of models in development can often save manpower, material resources, finance and time, and some phenomena that are otherwise difficult to observe can be investigated through experiments. Therefore, people are increasingly using models to conduct research. A model is an artificial system that simulates certain characteristics of an objective phenomenon. It is similar to the prototype only in specific characteristics. Generally speaking, the model simplifies the prototype and contains fewer factors, which makes it easier to build, test and observe. Therefore, the similarity between the model and the prototype is conditional. Models can generally be divided into two categories: material models and theoretical models. Material models can be divided into two types: geometric models and physical models. A geometric model refers to a model that is similar in appearance to the real thing, but has only been enlarged or reduced in size. In addition to using geometric models for exhibitions, teaching and other purposes, people can use factory models and city models to study the layout of factories and cities, and use terrain sand disks to study combat deployments, etc. They are often used as a means of transferring dimensions in production, such as wood molds and wax molds for sand molds in casting. In addition, templates, mold tires, frames, etc. used in forming and assembly are all geometric models. Although these geometric models do not necessarily simulate the entire geometric shape of the prototype, they must reflect the characteristics of the prototype in certain specific geometric properties. A physical model is a model that has similar physical phenomena to the prototype. For example, the light pattern on the photoelastic specimen is used to infer the internal stress distribution of the metal component. Use magnetic field distribution (which can be displayed through the distribution of iron powder) to infer the direction of invisible airflow streamlines, etc. Different physical phenomena can be represented by differential equations. Things with different properties can be used as physical models because these phenomena can be described by the same differential equations. Analog computers that use a network of different circuits connected to each other can solve differential equations. People use circuit characteristics to simulate the complex movement of aircraft in the air, so that the flight characteristics of a newly designed aircraft can be studied on a simulation computer before it is tested. An analog computer made of electrical circuits that looks nothing like an airplane, but can simulate the physical characteristics of an airplane. Therefore, physical models and prototypes are similar only in their physical properties. People have the ability to think abstractly. Humans can not only receive first signals from the outside world (such as sound, light, electricity, taste, etc.), but also receive and process second information, such as language, text, and symbols. From the perspective of the expanded model concept, language is also a model. Language and writing are the sounds or words that people make to express a certain object or concept. They are also a person's image of the object. The written characters are sometimes called information models or symbolic models, sometimes also called theoretical models. People often establish a certain theory about the objective world. As long as this theory is proven correct in practice, people can explain certain phenomena within the scope of application of the theory, make certain predictions about the future, or make certain decisions with the help of it. Recently, some theories that explain scientific phenomena are often called models. For example, the "Ita model", "straton model" and so on in the study of elementary particles. If the description of objective things is mathematically accurate, it can increase the accuracy of the model and enable people to obtain quantitative results when using this model. This theoretical model is called a "mathematical model". A mathematical model can be said to be a model made of mathematical materials. Although the name mathematical model has only been widely used in recent years, many physical discoveries since ancient times are essentially mathematical models. It should be noted that all models only represent specific aspects of the object to a certain extent, and they do not represent the object in other aspects. Models (including theories) may be perfect under certain conditions, but may be very poor under other conditions. For example, the commonly used relationship between pressure, volume and temperature of quantitative gases is a good model within a certain temperature range, but when the temperature is close to the liquefaction point of the gas, this relationship becomes completely invalid, and people have to find another new model. Models are always simplified. Therefore, there is no one all-encompassing, ultimate model. When using models (theories) to help understand and transform the world, you must pay attention to the scope of applicability of the model. On the one hand, we should make full use of the role of models in understanding, but not be blind to models with limitations. This should be fully noted. Law of Similarity When using a model to conduct tests, attention must be paid to the law of similarity between model conditions and real conditions, that is, the comparability of model tests and actual conditions. In terms of geometric size alone, after an object is enlarged or reduced in size, not all characteristics will be enlarged in the same proportion. The simplest example is: If you look at a 30-degree angle with a 2x magnifying glass, what will its angle become? The correct answer is: The angle is still 30 degrees, and the magnifying glass cannot magnify the angle. It can be seen that even geometric properties do not all change equally with size. By doubling the length of each side of a triangle, the area of the new triangle is four times larger than the original triangle, while the angles of the three angles remain unchanged. Some physical properties also do not change with size enlargement, or do not change with the proportion of size change. If a pendulum is doubled in size, its swing period is not doubled, but 1.414 times larger. Simply enlarging or reducing a clock cannot keep accurate time. In the history of the development of aviation technology, someone once imitated a successful small aircraft and enlarged it to create a large aircraft. As a result, the large aircraft created in this way lost the flying ability of the original small aircraft and could not even fly. There are already airplanes flying with a capacity of 600 passengers, but they are not designed to enlarge the size of small airplanes. There is a "square and cube law" at work when the size of a structure increases. This means that when the size is enlarged, the area of the structure will change according to the square of the size magnification, but the volume (and weight) will change according to the cube of the magnification. Therefore, the unit load-bearing capacity of the structure should be increased to support this structure. It can be seen that when the structure is slightly enlarged or reduced, there may not be a big problem, but if it exceeds a certain limit, the structural form must be changed or the structural materials must be changed. This is the principle that must be followed in the design of all large-scale designs, including large aircraft, large ships, large-structured buildings, and various large-scale equipment. In engineering design, it is common to use reduced models for testing. For example, in aircraft design, scaled-down aircraft models are often used to measure their aerodynamic performance in wind tunnels. However, since the model is reduced, the data obtained from the test cannot be directly used for design, but must be corrected according to the "law of similarity". “The law of similarity" is the "law of similarity", which is the condition that must be followed to make specific characteristics similar. Due to the size effect, people may notice a "small advantage", that is, a smaller structure will show some advantages. A children's toy car can still be driven if it is severely rusted, but a real car can no longer be used if it is rusted to such an extent. Small creatures can display many extraordinary abilities, such as the height of their jumps and the weight they can pull in multiples of their body weight. * * Surpassing humans is the beneficial effect of the "law of similarity" in the direction of shrinkage. Therefore, when using reduced-size structural specimens for strength tests, it is often necessary to increase the proportional load, or to conduct the entire test on a centrifuge, that is, in an artificially increased gravity field, in order to obtain test results that are comparable to reality. On the other hand, there is also a certain "scale effect", that is, characteristics that are not significant in a small scale will have obvious effects when the scale reaches a certain level. This is another reflection of the scale effect. Due to the scale effect, when designing experimental models and using experimental results, it is necessary to fully estimate the changes in things after changes in size or scale. When observing various objective systems, we should also pay attention to the differences that may occur between large systems and small systems. Developmental testing Developmental testing can be roughly divided into the following categories:: 1. Principle test: The test piece in this test may be different from the product, for example, a chemical reaction test in a glass container. 2. Universal test stand: This kind of test equipment can easily add or subtract components to simulate the required situation. For example, in electrical testing, using bus bars, you can connect the load at will ； Another example is the hydraulic test bench, which can test various hydraulic accessories. 3. Architecture test bed ； Replace the structure of the product with architecture. For example, a device called "Iron Bird" is commonly used in aircraft development. “"Iron Bird" cannot fly, it is just an experimental structure. The test of the aircraft control system is carried out on this steel frame of the same size. All control systems are installed on the steel frame to simulate the control performance of the aircraft in flight. 4. Model test: The model simulates a part of the product in a certain aspect, and the performance of this part of the product is understood through model testing. 5. Working prototype: The working prototype does not reach the level of the product in all aspects, but it is required to reflect the main functions of the product. In the early morning of April 17, 1945, the first nuclear bomb exploded at the New Mexico Test Site in the United States. * * device, it can be said that this is a working prototype. This device is not yet an actual nuclear weapon, but it can act like an actual nuclear weapon. * * A nuclear fission explosion also occurs. 6. Production prototype: This is a representative of a mature product, which not only reflects the various details of the design, but also reflects the characteristics of the production process. The purpose of the experiment may be to qualitatively prove certain theories or confirm the feasibility of a certain plan, or it may be to obtain quantitative data. Some experiments have both qualitative and quantitative purposes. A correct experiment should be reproducible and have precise results so that others can evaluate the experiment. Simplification of experiments Generally speaking, experiments always make some simplification of the actual situation to obtain as much information as possible from limited practice. If the test is more complicated and difficult to implement than the actual situation, people will not test it, but observe it in the actual operation of the product itself. Simplifying the test can reduce the scale of the test, but the simplification of the test should be "modeled" correctly, that is, the actual situation can be correctly inferred through the test results, and the correctness of the conclusion will not be affected by simplification. When planning an experiment to determine a problem qualitatively and quantitatively, you should usually pay attention to the following issues:: 1. Determine the scope of the test. The product is a complete whole. During the test, analytical thinking must be used to separate the parts that need to be understood from the objective whole. In 1903, when the Wright brothers in the United States were developing the first aircraft, they conducted many experiments on different aspects of the aircraft. They built a wind tunnel made of wooden boxes and tested the aerodynamic characteristics of a series of wing planes and sections in the wind tunnel. They also tested the strength of the components used to make the wing spars by placing them on the backs of two chairs. This shows: They have learned to separate the aerodynamic characteristics of the wing shape and the strength characteristics of the structural components from the entire aircraft and conduct tests separately. Without this kind of analysis ability, they can only use people to fly on airplanes and risk their lives like some explorers in ancient times. Some comprehensive tests can observe several phenomena at the same time, or measure several parameters at the same time. However, it is impossible to try to solve all the complex problems in one experiment. A trial that includes all relevant and irrelevant factors would make the trial unnecessarily large and complex and make it difficult to draw conclusions about the trial results. 2. Use the experimental conditions within your capabilities. Nobel Prize winner and geneticist Morgan once thought that the acidity of seawater might enhance the reproductive capacity of some deep-sea creatures. He hoped to verify his hypothesis through experiments, but when he couldn't find the acid, he went to the grocery store to buy a lemon and dripped the lemon juice into his goldfish tank, which confirmed his hypothesis. Similarly, when American aircraft designer Johnson designed a supersonic aircraft, the horizontal flight speed of the aircraft reached 2 times the speed of sound, but at that time the United States did not have a wind tunnel with 2 times the speed of sound. Johnson used rocket-mounted model wings to conduct free flight model tests, and used telemetry technology to find a reasonable wing method. After conducting 50 wing tests, he selected the wing form for this aircraft. On the contrary, a contrary example is: Once it was requested to compare the effectiveness of a new type of fire extinguishing agent on aircraft with traditional fire extinguishing agents, the person in charge of the test pointed out that a real engine nacelle should be built with an engine inside, and then the engine should be set on fire, and the new and old fire extinguishing agents should be sprayed out to compare the fire extinguishing effectiveness. ； In actual use, the aircraft flies at high speed, so this device should be tested in a supersonic wind tunnel. There was no such large supersonic wind tunnel at that time, so he concluded that "the performance of fire extinguishing agents is incomparable." This fully reflects the lack of ability to analyze things and the lack of working methods to expand understanding using the conditions within one's ability. In fact, when comparing fire extinguishing performance in engineering, the method used by British Airways is to extinguish a gasoline basin of the same area under open air conditions. Based on the time required for extinguishing, it is possible to obtain a preliminary comparison of the effectiveness of the two fire extinguishing agents. To conduct a new experiment, sometimes it is necessary to add some equipment and instruments, but smart experimenters are good at making use of the original conditions. When Galileo did the drop test of heavy objects, he did not build a special drop test stand. Instead, he used the Leaning Tower of Pisa. The test pieces used for falling were a lead ball and a hollow cannon ball of different weights. Of course, when a test method has been finalized and a large number of repeated tests are required, developing specialized and complex test equipment can improve test conditions and operations and increase the accuracy of test data. This is another aspect of the problem. For example, modern aviation departments have established many types of wind tunnel experimental equipment for aerodynamic research. However, pioneers should not only learn to use established conditions to conduct routine experiments, but also try to use all means within their capabilities to expand understanding, so that they can be at the forefront of understanding. People who lack creativity always complain that conditions are not enough ； And people with a pioneering spirit can move forward under all conditions. This was also reflected in the planning of the trial. 3. Use means to directly achieve the purpose of the test. During the test, do not confuse the relationship between the purpose and the means. Whether a trial is excellent cannot be judged by its large scale or the complexity of the technology used. The purpose of experiments is to expand people's knowledge. If the same purpose can be achieved, then small-scale, easy-to-implement, and quick-result experiments are better. In order to test his assistant's working ability, Edison asked him to determine the volume of a complex-shaped flask. This assistant had a good scientific education. He first divided the complex container into many small calculation units, and then calculated and superimposed each unit to obtain the calculation results. He went to see Edison with a large stack of calculation drafts. After listening to his report, Edison said nothing. He just filled the flask with water, then poured the water into the measuring cup, and the conclusion came out. In real life, it often happens that we pay too much attention to the test methods and ignore the test purpose. It is very important to always remember that "the most effective method to achieve the test purpose is the best method." 4. People who are good at using experimental results and live in the same environment will have different understandings due to different observation and thinking abilities. When traveling to the same place or experiencing the same event, some people gain a lot while others gain nothing. Similarly, the phenomena and data collected in an experiment also need to be carefully organized and summarized. As much information as possible should be extracted from these materials to further expand understanding. It is not only necessary to conduct the test correctly, but also to correctly judge the results of the test and draw correct conclusions from them. Design of Experiments In pioneering experiments, in order to reduce the number of experiments, "Design of Experiments" is a very effective method. “"Experimental design" is a branch of mathematical statistics in mathematics that specializes in how to select the number of test samples, reduce the number of tests, and find the optimal results. When there is only one changing parameter in the experiment, it is a single-factor experiment problem. For example, it is necessary to determine the proportion of a certain component in an alloy, or the value of a certain resistor in a circuit, so that the product can achieve optimal performance. Based on the understanding of the phenomenon, people can estimate in advance the possible range of the most estimated parameters. If the understanding of it is relatively clear, this estimate may be more precise and the estimate range may be narrower. ； On the contrary, the estimated range is wider. Now we need to deepen our understanding through a series of experiments. If you test one by one, it would take a hundred tests to narrow the estimate interval a hundred times. However, if you use the "golden section test technique" in the interval reduction method (also known as the 0.618 method), you only need to do 11 tests to reduce the interval to one percent. Doing 14 experiments can improve the accuracy of understanding the interval by 500 times. In multi-factor experiments, it is often necessary to isolate the effects of different factors. For example, we want to compare the yields of three seeds A, B, and C. If it is just a simple issue of seed yield, it seems that you only need to sow three kinds of seeds in three pieces of land of the same area, and then compare the yields. However, if the location of the experimental field is between mountains and rivers in the north-south direction, and between fertilizer fields and wasteland in the east-west direction, then three experimental fields of equal area are still randomly selected for experiments. The yield of the experimental field may be affected by the different fertility of the soil and the adequacy of irrigation, not just the result of the single factor of seeds. To estimate the impact of these factors, a reasonable method is to divide the experimental area into 9 experimental fields, as shown in the figure below. Each of the three different seeds is sown in three experimental fields with different locations. The yields of the three fields are averaged to obtain the contribution of this seed due to the variety (soil and irrigation factors are excluded). By comparing the average yield of the three fields adjacent to the fertilizer field with the average yield of the three fields adjacent to the wasteland, we can obtain the yield difference caused by the degree of soil fertility (while excluding factors such as seed variety and irrigation conditions). ； Differences due to irrigation conditions can be seen by comparing the average yields of the three plots on the mountain and the three plots near the water (excluding differences in seed varieties and soil conditions). Mountains¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤ Ａ ＢB Ｃ Wasteland C Ａ A Ｂ B Fertilizer fieldＢ C Ａ A River ~~~~~~~~~~~~~~ Latin square arrangement of seed experiments This experimental arrangement is called "Latin square", which means "square matrix composed of Latin letters", also known as "orthogonal design". Refers to the situation where each factor is regarded as acting alone and its cross-influence is ignored. "Orthogonal design tables" with different numbers of factors and different levels of each factor can be found in many "mathematical statistics" or "orthogonal design" books. In engineering design, tests involving many factors are often encountered. For example, in wind tunnel testing in aircraft design, even for the selection of wings, there are several wing plane parameters and section parameters. The front and rear edge devices of the wing (leading edge flaps, trailing edge flaps and ailerons) have several opening angle states. In multi-factor experiments, the use of "experimental design" technology has obvious effects. For example, when there are 8 parameters and each parameter has 7 numerical levels, if all possibilities of permutations and combinations are tested one by one, more than 5.76 million tests will be needed. However, using orthogonal design technology, only 49 tests are needed to select the optimal combination. The use of "experimental design" technology in developmental trials is very effective and has only been used in a few areas such as pharmaceutical formulations in the past. In the 1980s, a Chinese engineer went to a Japanese university as a visiting scholar. He applied this method to structural design experiments and received high praise from Japanese colleagues. Some people in our country have introduced the "orthogonal design" method into the selection of examples in parameter optimization, and have also achieved good results. These examples show that although "design by experiment" was a method proposed in the first half of the 20th century, it has great potential for promotion in engineering design. Design of experiments is an applied mathematics tool that is effective in engineering exploration. But I was surprised to find that many professionals engaged in engineering testing have not even heard of this method. This cannot but be said to be a defect in knowledge.