Analytic Models and R&D Simulations

Mathematical modeling and simulation are the tools of analysis-synthesis. We are outspoken proponents of Mathematica from Wolfram research, subscribe to the Wolfram's Premier Service, and use it extensively in modeling systems and subsystems, in examining extrema and engineering trade offs, for R&D, and even for financial functions.

Mathematica's extensive functions, excellent graphics, and recently added authoring tools make it our number one choice for analysis-synthesis.

Example applications include waves in a flexible medium, locus of roots in a plane, a simple analytical Laplace transform step function, solution of an unstable second order PDE, analysis of a helical closed form surface, vector velocity field for a circular shape in a motion detection algorithm, and an example cellular automaton from the NKS collection :

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Multi-Physics Numeric FEM Models and R&D Simulations

For extensively numeric multi-physics (electrostatics, electrodynamics, heat and fluid flow, stress and energy flow) problems in 1D, 2D, and 3D, we use FlexPDE Professional 3D 5.x.x. This highly flexible, scripted FEM (Finite Element) analysis tool allows broad exploration, discovery, and simulation of designs based on first principles. FlexPDE can analyze all of the preceding areas of physics, and can employ so-called moving meshes (motion of matter) while doing so.

An example of convective and conductive heat transfer analysis for a 19" rack application explores the effect of differing energy densities in a front panel heat sink block vs. various ambient air conditions :

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SPICE Circuit Models and R&D Simulations

SPICE and circuit modeling are one of AetherMachines' specialties. Models explore frequency and bandwidth effects, propagation and attenuation effects, device timing and interoperability, safety and loop stability, parametric temperature effects, Monte Carlo component value effects, and power dissipation and circuit loading effects.

Because of its good analytical capabilities, large libraries, and good interoperability with Eagle Professional circuit design software, we use B2SPICE Professional from Beige Bag. We also use Electronics Workbench.

Example applications are a fairly complex integrator/ramp circuit, a simple 2 amplifier IA analysis, and the accompanying 'scalar' thermal resistance model to the above 3D FEM heat flow analysis :

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3D Solid and 2D CAD Models

3D and 2D models enable property calculations (mass, weight, moments, centroids) that lend themselves to simulation of assemblies and assembly dynamics (as well as stresses). Using Alibre Design Expert (with 3D CAM, Motion, and other modules), we can make highly accurate 2D and 3D models that allow for pure analysis-synthesis (assemble, observe behavior, take apart, make optimizations, reassemble) for part assemblies. Presentation formats include all major CAD formats (including Solid Works import) and well as photo realistic rendering.

A rifle cartridge example and its photo realistic rendering with metallic specular effects, lighting, and coloration for brass, copper, and lead; an outdoor transmitting installation design, and a PC/ABS bracket created for injection molding, and von Mises stresses in an ABS part :

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Control and System Models and R&D Simulations

We have over 10 years experience in simulation of controls and systems ranging from torpedo interception behavior to turbines, diesel engines and torque converters, valves, servo valves, and generators. We are expert in the use of industrial strength state space simulation packages such as Easy5x, and also in Matlab and Simulink. In addition to s-domain, z-domain, and state space environments, we can supply simulations in mixed languages (combinations of C/C++, Fortran, and Visual Basic) for expanded or real time execution.

Simulation of control systems and plant responses are an absolute necessity for design, and are invaluable for exploring system operations and improvements during the lifecycle of the application. Our simulation experience includes HWIL (Hardware In The Loop) where actual controllers are run against highly accurate, real time models of the plant prior to startup - in one instance the simulation of entire combined cycle power plants (gas and steam turbines, generators, heat recovery steam generators) to verify control operation years ahead of startup and commissioning.

Because of it's good capabilities, very low TCO, and universal availability (as well as good interoperability with Matlab) we use SciLab from INRIA. The example below compares the step responses of continuous an sampled data PI control systems when connected to a lagging, Laplace domain plant model :

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Organizational and Process Models

For simulations of organizations and processes where s-domain and z-domain block diagrams and transfer functions might make it harder to capture, convey, and explore the relationships between rates and states (derivatives and integrals), we use Vensim PLE Plus. Vensim PLE Plus allows us to model business processes, sociological organizations, and even ecological processes in a concise, graphical manner and makes very easy to convey mathematical interrelationships to the customer.

Following is an example illustrating the effect of productivity and workforce improvements on business inventory :

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Six Sigma and Stochastic Models

Modeling of business processes is best done in conjunction with a Six Sigma type of analysis. We are Six Sigma Green Belt certified, and use SigmaXL for DOE, DMAIC, Monte Carlo, and SPC to analyze and implement quality and process improvements.

In addition to Six Sigma stochastic analysis, we are expert in the use of Hidden Markov Models (and have been awarded a patent for a generalization of the HMM mathematical structure) for analysis and pattern matching of speech and other complex waveforms and data.

A Six Sigma Process Capability analysis of the variation in the transfer function of an RTD circuit, caused by resistor tolerances, is followed by several examples of HMMs, including a graphical representation of a non-stationary transition matrix for the phoneme (states) in English :

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System Characterization and Debugging Through Analysis-Synthesis

One of the most interesting (and unfortunately often neglected) areas of modeling is the approach to debugging the operation of a system. How is the system currently operating, as opposed to how should it operate ? Is the proper operation of the system even completely understood ? Is the improper behavior repeatable ? What deviations from the rules, concepts, and mathematics of the proper operation could yield the improper ?

AetherMachines is expert in the analysis of systems in the time and frequency domains. We take great pride in being able to a) stimulate behaviors without further degradation or complication, b) mathematically identify and characterize these behaviors, and c) clearly convey the conceptual and first principle reasons for what was seen. Once these behaviors are thus understood, corrective measures (many times equally mathematical in nature) can be devised, and their relative merits and effectiveness often gauged through further modeling of the system in the true spirit of analysis-synthesis.

Our analysis equipment includes a four channel, 300 MHz Tek 2465; 2 channel 40 MHz DSO with spectrum analyzer, ARB AWG and unlimited duration 12 bit datalogger; 5 MHz signal generator with 150 MHz frequency counter, lin/log sweep, duty, AM/FM modulation, and VCO; 1 MHz, DDS synthesis, 32KB wave table ARB and sine/triangle/square wave function generator; 2 MHz, DDS synthesis, 8KB wave table ARB and sine/triangle/square wave function generator; in circuit LCR, ESR, D, and related component characteristics meter; 20 MHz analog sine/triangle/square wave generator; 1kHz - 450MHz RF signal generator; infrared thermometer, high voltage probe, a wide variety (2x 0-30V at 0-5A; 1-20V at 0-2A; 4x +/-12 at ~1A, 2x 5V at 5-10A, 24V at 4A, and 1-15V at 1A) of switch mode and linear bench top power supplies, as well as assorted single channel voltage, current, and temperature logging DVMs.

This range of capability allows us to quickly and accurately diagnose abnormal system behaviors, glitches, and frequency dependencies and share the results rapidly through e-mail, Microsoft Office, and other common electronic formats. Examples below are screen and video snapshots of various DSO and Tek waveforms, and the use of Mathematica to produce a complex test waveform for our 8KB AWG :

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