### Consulting

FCE consults its customers in the following areas

##### Mathematical Optimization

Linear, Non-Linear, Combinatorial

##### Pattern Recognition

Sensor based pattern recognition, Event based pattern recognition

##### Statistics

Univariate, Multivariate

##### Probability Calculus

Fault Tree analysis, Reliability Calculus, Decision Trees

Our mathematical expertise is implemented in the .NET framework and can result in a customer-specific software application

##### System development

Implementation and documentation in the Microsoft .NET environment

FCE, as a consequence of its long standing activity in the applied mathematics domain, has collected throughout the years, considerable expertise in modeling industrial processes. In many industrial applications, for instance in the power industry, in the rail and in the aviation sector or in the automotive manufacturing world, it has become standard to use mathematical models to find optimal operating conditions. FCE can help the customer to establish mathematical models mapping input to output parameters and use them to find optimal conditions. The Figure below illustrates the model identification task:

The formula symbolizes the second step, i.e. the optimization part once the model has been identified:

`$$y= f(x)$$`

$$x^* : f(x^*) = max_{x in R} f(x)$$

__Example 1__:

As an example consider a power transforming machine such as a gas turbine, which must operate under a wide set of ambient conditions, is controlled by a set of control variables and whose Key Performance Indicators are given by efficiency, emissions and vibrations. Under any set of ambient conditions it is mandatory to find an optimal set of operating variables such that a set of optimization criteria are satisfied whereby a certain efficiency level must be reached and emissions must not exceed a given threshold. FCE can help the customer to identify the above categories of variables, the KPI’s, ways to find a mathematical relationship between the two and use those relationships to find optimal operating conditions.

__Example 2__:

Assume the production manager in a discrete manufacturing process tries to optimize his KPI’s by computing optimal production sequences. The objects may be characterized by one or more attributes such as a 4-, 6- or 8-cylinder engine, body paint, automatic or manual transmission etc. The KPI’s may be represented by slack time in the production process, variance in the number of workers throughout the shift, timeliness, setup time and cost etc. FCE will then support the manager in establishing a mathematical model connecting the production sequence to the KPI’s and design an algorithm finding the optimal sequence which optimizes one or more KPI’s under a given set of constraints.